Phase Behavior, Rheology, and Characterization of Lysozyme ? Single-Walled Carbon 
Nanotube Dispersions 
 
by 
 
Daniel Wallace Horn 
 
 
 
 
A dissertation submitted to the Graduate Faculty of 
Auburn University 
in partial fulfillment of the 
requirements for the Degree of  
Doctor of Philosophy 
 
Auburn, Alabama 
December 8, 2012 
 
 
 
 
Copyright 2012 by Daniel Wallace Horn 
 
 
Approved by 
 
Virginia A. Davis, Chair, Mary and John H. Sanders Associate Professor of Chemical 
Engineering 
Mark E. Byrne, Daniel F. and Josephine Breeden Associate Professor of Chemical Engineering 
Steve R. Duke, Alumni Associate Professor of Chemical Engineering 
Chris J. Easley, Assistant Professor of Chemistry and Biochemistry 
  
ii 
 
 
 
 
 
 
ABSTRACT 
 
 
Single-walled carbon nanotubes (SWNT) are one of the most promising materials in 
nanoscale science and technology with potential applications ranging from polymer 
nanocomposites to biocompatible smart materials. However, translating the extraordinary 
mechanical, thermal, optical and electrical properties of individual SWNT into macroscopic 
assemblies such as films and fibers is challenged by the aggregation of pristine SWNT. In order 
to achieve individual SWNT, their mutual attractive forces must be overcome. At that point, 
there must be a force of repulsion to stabilize the SWNT, thereby not allowing them to 
reaggregate. The research presented here concentrated on the application of lysozyme (LSZ) as a 
dispersing agent for SWNT. The structural nature of LSZ make it a well-suited dispersant for 
SWNT. Not only does LSZ enable the mechanical, electrical, thermal, and optical properties of 
SWNT to be exploited, but it also enhances the system by making it antibacterial. During this 
research, it was found that LSZ interacts with SWNT through ?-bonding of the aromatic SWNT 
sidewall with the tryptophan residue within the LSZ hydrophobic core allowing for SWNT to be 
soluble in aqueous solutions. Furthermore, this research showed that dispersions of LSZ-SWNT 
exhibit phase transitions from isotropic liquid to gel as the concentration of both LSZ and SWNT 
are increased via evaporation. It was then determined that the phase transitions were caused by 
depletion interactions between LSZ and SWNT due to the loss in free energy of mixing of the 
system at increased LSZ and SWNT concentrations. In order to increase the concentration of 
SWNT at which depletion aggregation occurred, the cationic surfactant 
iii 
 
tetradecyltrimethylammonium bromide (TTAB) was added to stabilize the system. Through 
stabilization of the LSZ-SWNT dispersions and the addition of synthetic or natural polymers, it 
was possible to assemble and process of concentrated dispersions into films and fibers which 
showed unique tailorability for use in novel applications. 
  
iv 
 
 
 
 
 
 
ACKNOWLDEGMENTS 
 
 
 I would like to thank my committee members for providing both their time and 
knowledge in the preparation and review of this manuscript. I would like to thank Dr. Virginia 
Davis for allowing me to formulate and tests my hypotheses while following my interest in this 
research. Thank you to Dr. Chris Easley for his hours of critical discussion and testing on the 
links between biology, chemistry, and engineering. Thank you to Dr. Mark Byrne and Dr. Steve 
Duke for providing inspirational advice, sometimes unrelated to research, and for showing that 
having a family in graduate school is not only possible but rewarding. Thank you to Brian 
Schwieker for the many hours of hard work in making all of my ideas of processing equipment 
become a reality and teaching me about everything outside of chemical engineering. Thank you 
to Georgetta Dennis and Karen Cochran for all the many miscellaneous things you did for me 
and my family during my stay here. Acknowledgement and thanks are also extended to Dr. 
Matthew Kayatin, Dr. Geyou Ao, Dr. Phillipe Poulin, Teng Xu, Joyanta Goswami, Zan 
Haywood, Phillip Higginbotham, Gloria Nyankima, Suzie Murdock, and Shannon McGee for 
teaching me numerous things and making research fun. Thank you to all my parents ? mom, 
Dick, and Mr. and Mrs. Ehrhart ? for your continued support throughout this process. Finally, no 
amount of thanks is enough to be given to my wife, Katie, and two sons, Caleb and Carter, for 
the time, effort, support, and love they have given to allow me to pursue my dreams, and always 
showing me that the troubles of this world are easily washed away with help and love from 
family.  
v 
 
 
 
 
 
 
Table of Contents 
 
 
Abstract ......................................................................................................................................... ii 
Acknowledgments ....................................................................................................................... iv 
List of Tables ............................................................................................................................... ix 
List of Figures ............................................................................................................................... x 
1. Introduction ............................................................................................................................... 1 
2. Background ............................................................................................................................... 4 
 2.1. Carbon Nanotubes ...................................................................................................... 4 
         2.1.1. Carbon Nanotube Molecular Structure ........................................................... 5 
         2.1.2. Carbon Nanotube Mechanical, Electrical, and Thermal Properties ................ 9 
 2.2. Lysozyme ................................................................................................................. 10 
         2.2.1. Lysozyme Protein Structure .......................................................................... 11 
         2.2.2. Lysozyme Enzymatic Activity ...................................................................... 14 
         2.2.3. Lysozyme Phase Behavior ............................................................................ 16 
 2.3. Lysozyme Dispersions of Carbon Nanotubes .......................................................... 17 
         2.3.1. Aqueous Lysozyme ? Carbon Nanotube Dispersions .................................. 18 
         2.3.2. Liquid Crystalline Lysozyme ? Carbon Nanotube Dispersions ................... 20 
         2.3.3. Gel Lysozyme ? Carbon Nanotube Dispersions ........................................... 24 
 2.4. Colloid Theory ......................................................................................................... 25 
         2.4.1. van der Waals Forces .................................................................................... 25 
vi 
 
         2.4.2. D.L.V.O. Theory ........................................................................................... 28 
         2.4.3. Binding Energy of Carbon Nanotubes .......................................................... 30 
 2.5. Thermodynamics of Carbon Nanotube Solutions .................................................... 32 
         2.5.1. Cylindrical Particle Theory ........................................................................... 33 
                 2.5.1.1. Cylindrical Particle Entropy of Mixing ............................................. 36 
                 2.5.1.2. Cylindrical Particle Enthalpy of Mixing ............................................ 37 
                 2.5.1.3. Cylindrical Particle Free Energy of Mixing....................................... 40 
         2.5.2. Cylindrical ? Sphere Particle Theory ............................................................ 42 
                 2.5.2.1. Cylindrical ? Sphere Excluded Volume Interaction .......................... 42 
                 2.5.2.2. Cylindrical ? Sphere Free Energy ...................................................... 45 
                 2.5.2.3. Cylindrical ?Sphere Phase Behavior ................................................. 48 
 2.6. Rheology Theory ..................................................................................................... 51 
         2.6.1. Cone and Plate Rheology .............................................................................. 52 
         2.6.2. Parallel Plate Rheology ................................................................................. 54 
         2.6.3. Linear Viscoelasticity ................................................................................... 57 
         2.6.4. Oscillatory Flow............................................................................................ 59 
         2.6.5. Shear Flow .................................................................................................... 64 
         2.6.6. Rheology of Particulate Suspensions ............................................................ 68 
         2.6.7. Rheology of Non-Spherical Particulate Suspensions ................................... 69 
3. Experimental Details ............................................................................................................... 74 
 3.1. Raw Materials .......................................................................................................... 74 
 3.2. Methods of Preparation ............................................................................................ 75 
         3.2.1. Sonication ..................................................................................................... 75 
vii 
 
         3.2.2. Centrifugation ............................................................................................... 75 
 3.3. Methods of Characterization .................................................................................... 76 
         3.3.1. Microscopy ................................................................................................... 76 
                 3.3.1.1. Atomic Force Microscopy ................................................................. 77 
                 3.3.1.2. Optical Microscopy ............................................................................ 78 
                 3.3.1.3. Scanning Electron Microscopy .......................................................... 79 
                 3.3.1.4. Transmission Electron Microscopy ................................................... 80 
         3.3.2. Rheology ....................................................................................................... 81 
                 3.3.2.1. Amplitude Sweep Test ....................................................................... 82 
                 3.3.2.2. Frequency Sweep Test ....................................................................... 83 
                 3.3.2.3. Transient Test..................................................................................... 84 
                 3.3.2.4. Flow Curve Test ................................................................................. 85 
         3.3.3. Spectroscopy ................................................................................................. 86 
                 3.3.3.1. Ultraviolet-Visible Spectroscopy ....................................................... 86 
                 3.3.3.2. Circular Dichroic Spectroscopy ......................................................... 87 
                 3.3.3.3. Fourier Transform Infrared Spectroscopy ......................................... 88 
                 3.3.3.4. Raman Spectroscopy .......................................................................... 89 
                 3.3.3.5. Fluorescence Spectroscopy ................................................................ 91 
                 3.3.3.6. Energy Dispersive X-Ray Spectroscopy ............................................ 93 
         3.3.4. Thermogravimetric Analysis ........................................................................ 94 
         3.3.5. Turbidimetric Analysis ................................................................................. 95 
         3.3.6. Ultimate Tensile Strength Analysis .............................................................. 96 
         3.3.7. Electrical Resistivity Analysis ...................................................................... 97 
viii 
 
 3.4. Methods of Macroscopic Assembly......................................................................... 98 
         3.4.1. Fiber Spinning ............................................................................................... 98 
         3.4.2. Film Drying ................................................................................................. 101 
 3.5. Mathematical Conversions..................................................................................... 102 
 3.6. Preparation of Carbon Nanotube ? Lysozyme Dispersions ................................... 104 
4. Results and Discussion ......................................................................................................... 110 
 4.1. Lysozyme Solution Characterization ..................................................................... 110 
         4.1.1. Ultraviolet-Visible Spectroscopy ................................................................ 110 
         4.1.2. Circular Dichroic Spectroscopy .................................................................. 114 
         4.1.3. Enzymatic Activity Analysis ...................................................................... 116 
         4.1.4. Thermogravimetric Analysis ...................................................................... 118 
         4.1.5. Rheological Behavior.................................................................................. 122 
 4.2. Lysozyme ? Carbon Nanotube Interaction ............................................................ 129 
 4.3. Lysozyme ? Carbon Nanotube Phase Behavior ..................................................... 147 
 4.4. Lysozyme ? Carbon Nanotube Phase Behavior Alteration ................................... 164 
 4.5. Lysozyme ? Carbon Nanotube Macroscopic Assemblies ..................................... 179 
         4.5.1. Fibers........................................................................................................... 179 
         4.5.2. Films ........................................................................................................... 192 
 4.6 Lysozyme ? Carbon Nanotube Antibacterial Activity............................................ 197 
5. Conclusions ........................................................................................................................... 203 
References   ............................................................................................................................... 206 
  
ix 
 
 
 
 
 
 
List of Tables 
 
 
Table 1. Raman spectroscopy data for LSZ, SWNT, and LSZ-SWNT dispersions ................. 136 
Table 2. UV-vis calibration curve data for SWNT ................................................................... 146 
Table 3. UV-vis calibration curve data for LSZ ....................................................................... 147 
Table 4. Phase transition data for LSZ-SWNT dispersions ...................................................... 153 
Table 5. Phase transition data for LSZ-SWNT and LSZ-TTAB-SWNT dispersions............... 167 
Table 6. Mechanical property data of LSZ-SWNT and LSZ-TTAB-SWNT fibers ................. 182 
Table 7. Raman spectroscopy data for LSZ-TTAB-SWNT fibers ........................................... 187 
Table 8. Electrical property data of LSZ-SWNT and LSZ-TTAB-SWNT fibers .................... 188 
Table 9. Raman spectroscopy data for LSZ-SWNT in PVA fibers .......................................... 191 
Table 10. Mechanical property data of LSZ-SWNT in PVA films .......................................... 196 
  
x 
 
 
 
 
 
 
List of Figures 
 
 
Figure 1. Geometrical construct of Ch on a graphene sheet ......................................................... 6 
Figure 2. Vectors specified by (n,m) for general CNT ................................................................. 7 
Figure 3. Schematic theoretical models for SWNT ...................................................................... 8 
Figure 4. Corey-Pauling-Koltun model of LSZ .......................................................................... 10 
Figure 5. Ribbon diagram of LSZ ............................................................................................... 11 
Figure 6. General structure of alpha helix .................................................................................. 12 
Figure 7. General structure of anti-parallel and parallel beta sheets ........................................... 12 
Figure 8. Ball-and-stick representation of LSZ structure ........................................................... 13 
Figure 9. Schematic mechanism of LSZ hydrolyses .................................................................. 15 
Figure 10. SEM of turbidity measurements for aqueous LSZ-SWNT dispersions .................... 20 
Figure 11. Schematic of a general liquid crystal showing order and orientation ....................... 21 
Figure 12. Images of LSZ crystals in a liquid crystalline phase ................................................. 21 
Figure 13. Schematic representation of D.L.V.O theory ............................................................ 28 
Figure 14. TEM of SWNT bundle .............................................................................................. 30 
Figure 15. Rigid rod in the Flory lattice ..................................................................................... 35 
Figure 16. Rigid rod divided into yi submolecules in the Flory lattice ....................................... 35 
Figure 17. Schematic illustration of excluded volume effects .................................................... 43 
Figure 18. Volume excluded to the center of mass of a rod and sphere ..................................... 44 
Figure 19. Phase behavior simulation results for addition of small spheres ............................... 49 
xi 
 
Figure 20. Diagrams of three phases of rod-sphere mixtures ..................................................... 50 
Figure 21. Coordinate system and geometric parameters for cone and plate geometry ............. 52 
Figure 22. Coordinate system and geometric parameters for parallel plate geometry ............... 55 
Figure 23. Illustration of the shear strain of a fluid between two parallel sliding plates ............ 57 
Figure 24. Illustration of a stress relaxation experiment ............................................................. 58 
Figure 25. Schematic of the imposed strain wave and resulting steady-state stress wave ......... 60 
Figure 26. Schematic of the trigonometric deconvolution of the steady-state stress wave ........ 61 
Figure 27. Prototypical linear viscoelastic responses of a solid and fluid .................................. 62 
Figure 28. Sliding plate model and relative coordinate system for simple shear ....................... 64 
Figure 29. Schematic diagram showing the notation for normal stresses in a shear field .......... 66 
Figure 30. Concentration regimes used to describe rod-like particles ........................................ 71 
Figure 31. Schematic mechanism by which sonication leads to dispersion of LSZ-SWNT .... 106 
Figure 32. Absorbance spectrum of LSZ solutions .................................................................. 111 
Figure 33. Absorbance spectrum of various concentrations of LSZ solutions ......................... 112 
Figure 34. Calibration curve for LSZ showing deviation from Beer-Lambert law .................. 113 
Figure 35. Calibration curve for LSZ ....................................................................................... 113 
Figure 36. Far-UV CD spectrum of LSZ solution .................................................................... 115 
Figure 37. Near-UV CD spectrum of LSZ solution .................................................................. 115 
Figure 38. Turbidimetric analysis of LSZ solutions ................................................................. 117 
Figure 39. Turbidimetric analysis of M. lysodeikticus .............................................................. 118 
Figure 40. Weight loss curve versus temperature for LSZ in argon and air ............................. 120 
Figure 41. Weight loss derivative curve versus temperature for LSZ in argon and air ............ 121 
Figure 42. Amplitude sweep data for LSZ solutions ................................................................ 123 
xii 
 
Figure 43. Frequency sweep data for LSZ solutions ................................................................ 124 
Figure 44. Frequency sweep data versus concentration for LSZ solutions .............................. 125 
Figure 45. Steady shear viscosity data for LSZ solutions ......................................................... 126 
Figure 46. Steady shear viscosity data versus concentration for LSZ solutions ....................... 128 
Figure 47. TEM image of LSZ-SWNT dispersion ................................................................... 131 
Figure 48. SEM image of LSZ-SWNT dispersion.................................................................... 132 
Figure 49. ATR-FTIR spectrum of SWNT, LSZ, and LSZ-SWNT dispersion ........................ 133 
Figure 50. Raman spectra of SWNT and LSZ-SWNT dispersions .......................................... 135 
Figure 51. UV-vis spectrum of LSZ-SWNT dispersion ........................................................... 138 
Figure 52. UV-vis difference spectra of LSZ solution and LSZ-SWNT dispersion ................ 140 
Figure 53. CD spectrum of LSZ solution and LSZ-SWNT dispersion .................................... 142 
Figure 54. Fluorescence spectra of LSZ solution and LSZ-SWNT dispersion ........................ 144 
Figure 55. Calibration curve for SWNT in LSZ-SWNT dispersions ....................................... 145 
Figure 56. Calibration curve for LSZ in LSZ-SWNT dispersions ............................................ 146 
Figure 57. Phase transition diagram for LSZ-SWNT ............................................................... 151 
Figure 58. Amplitude sweep data for LSZ-SWNT dispersions ................................................ 154 
Figure 59. Frequency sweep data for LSZ-SWNT dispersions ................................................ 155 
Figure 60. Frequency sweep data showing crossover for LSZ-SWNT dispersions ................. 156 
Figure 61. Graphical analysis of tan(?) versus angular frequency and concentration .............. 157 
Figure 62. Steady shear viscosity data for LSZ-SWNT dispersions ........................................ 158 
Figure 63. Graphical representation of the Cox-Merz rule for LSZ-SWNT dispersions ......... 160 
Figure 64. Inherent viscosity of LSZ-SWNT dispersions as a function of concentration ........ 163 
Figure 65. SEM image of LSZ-TTAB-SWNT dispersion ........................................................ 168 
xiii 
 
Figure 66. UV-vis spectra of LSZ and LSZ-TTAB-SWNT ..................................................... 169 
Figure 67. Amplitude sweep date for LSZ-TTAB-SWNT dispersions .................................... 171 
Figure 68. Frequency sweep data for LSZ-TTAB-SWNT dispersions .................................... 172 
Figure 69. Stead shear viscosity data for LSZ-TTAB-SWNT dispersions ............................... 173 
Figure 70. Amplitude sweep data for LSZ-SWNT and LSZ-TTAB-SWNT in PVA .............. 175 
Figure 71. Frequency sweep data for LSZ-SWNT and LSZ-TTAB-SWNT in PVA ............... 176 
Figure 72. Steady shear viscosity data for LSZ-SWNT and LSZ-TTAB SWNT in PVA ....... 177 
Figure 73. Inherent viscosity of all LSZ-SWNT dispersions as a function of concentration ... 178 
Figure 74. SEM image of LSZ-TTAB-SWNT in PVA fiber .................................................... 184 
Figure 75. Raman spectra of SWNT and LSZ-TTAB-SWNT in PVA fibers .......................... 186 
Figure 76. Optical micrographs of LSZ-TTAB-SWNT fibers before drawing ........................ 189 
Figure 77. Optical micrographs of LSZ-TTAB-SWNT fibers after drawing ........................... 190 
Figure 78. Raman spectra of LSZ-SWNT in PVA fibers before and after drawing ................. 191 
Figure 79. SEM images of LSZ-SWNT in PVA film ............................................................... 193 
Figure 80. Optical micrographs of post-process drawn LSZ-SWNT in PVA film ................... 194 
Figure 81. ATR-FTIR spectrum of LSZ-SWNT in PVA films ................................................ 195 
Figure 82. Far-UV CD spectrum of LSZ solution and LSZ-SWNT dispersion ....................... 198 
Figure 83. Turbidity of constituents in LSZ-SWNT dispersions or macroscopic assemblies .. 199 
Figure 84. Lytic activity of LSZ-SWNT dispersions and macroscopic assemblies ................. 201 
  
1 
 
1. INTRODUCTION 
Single-walled carbon nanotubes (SWNT) are strong, rolled layers of graphene having a 
diameter of approximately one nanometer, and a length ranging from a 100 nm to a few 
micrometers. Lysozyme (LSZ) is a small, globular polyampholytic enzyme with natural 
antibacterial activity. The intellectual contribution to science and engineering of this research 
was the understanding of phase behavior and rheology of LSZ-SWNT dispersion mixtures and 
supernatants, development of the initial methods of macroscopic assembly of LSZ-SWNT 
dispersions, and elucidation of the specific interaction between LSZ and SWNT. A key 
motivation for this research is the need for robust, antibacterial fibers, films, composites, or 
coatings for use in applications ranging from preventing bacterial growth to reducing the spread 
of communicable illnesses. In order to achieve these results, LSZ and SWNT were processed 
together. The goal of this research was to exploit the antibacterial properties of LSZ and the 
mechanical, electrical, thermal, and optical properties of SWNT to create dispersions, capable of 
macroscopic assembly for tailorable applications. In order to fully realize this goal to create solid 
macroscopic assemblies, the phase behavior and interaction between LSZ and SWNT had to first 
be understood. The following hypotheses were tested: dispersion mixtures of LSZ-SWNT 
transition from isotropic liquid to physically networked gels, supernatant dispersions of LSZ-
SWNT show no phase transition, and manipulation of the phase behavior for supernatants and 
mixtures enable processing into robust, solid macroscopic assemblies. 
Carbon nanotubes (CNT) have been recognized as very promising nanoscale materials 
with remarkable mechanical, electrical, optical and thermal properties. Their potential 
applications have been widely studied ever since the discovery of multi-walled carbon nanotubes 
(MWNT) by Iijima in 1989.1 The major obstacle in translating the unique properties of 
2 
 
individual CNT into macroscopic assemblies of films and fibers is dispersion of CNT as 
individuals or small bundles. Due to the smooth and highly polarizable side-walls, CNT exist as 
crystalline ropes or bundles with a characteristic van der Waals interaction energy of 
approximately 0.5 eV nm-1 of parallel contact.2 Considering the length of CNT is on the order of 
hundreds to thousands of nanometers, separation of individual CNT require significant energy. 
However, liquid dispersion processing techniques using solvents, polymers, and biopolymers 
have been shown to disperse CNT as individuals or small bundles at low volume fractions. More 
highly ordered liquid phases of CNT, such as gels or liquid crystalline phases, could be favorable 
starting materials for translating nanoscale properties into macroscopic assemblies composed of 
nanotubes.3-8 Non-covalent nanotube functionalization with natural biomolecules, such as LSZ or 
DNA, is an effective approach for obtaining novel materials with synergistic properties of both 
CNT and the biomolecule.3, 9 In addition, use of aqueous solutions of biomolecules, as opposed 
to solvents or polymers, has the capability to be more environmentally friendly and green. 
Previous work on LSZ-SWNT has shown the ability of LSZ to disperse SWNT as 
individuals or small bundles in the supernatant dispersion, determined the maintenance of LSZ 
activity in the presence of SWNT, and shown the capability of being processed into macroscopic 
assemblies through dilute layer-by-layer assembly.8, 10 To date, depending on the processing 
technique, either gel or isotropic phases have resulted from dispersions of purified SWNT in 
LSZ. In this research, the phase behavior of LSZ-SWNT dispersions were analyzed by 
rheological characterization coupled with cross-polarized optical microscopy. Evaporation of 
LSZ-SWNT dispersions without centrifugation resulted in a gel phase formation. However, 
evaporation of LSZ-SWNT supernatant after centrifugation resulted in maintenance of an 
isotropic liquid phase. The LSZ-SWNT supernatants contained more individually dispersed 
3 
 
SWNT compared to the non-centrifuged dispersion. In order to produce LSZ-SWNT dispersions 
with less aggregation at increased SWNT concentrations the synthetic surfactant 
trimethyltetradecylammonium bromide (TTAB) was added. After determination of phase 
behavior at large volume fractions of SWNT, various approaches of macroscopic assembly and 
post-assembly processing of LSZ-stabilized SWNT dispersions was explored. Rheology plays a 
central role in elucidating the structure-processing-property interrelationships for macroscopic 
assemblies produced from nanotube dispersions. Furthermore, understanding the molecular 
interaction between LSZ and SWNT allowed for understanding of changes when manipulation of 
the dispersion state occurred to alter the phase behavior. 
This dissertation outlines the phase behavior, rheology, characterization, and macroscopic 
assembly of LSZ-SWNT aqueous dispersions. Chapter 2 provides background information on 
materials used including LSZ and SWNT, general colloid theory, thermodynamics and phase 
behavior of rods and rod-sphere systems, and general theory of rheology. Chapter 3 provides 
information on the materials used in this research, instrumentation used for characterization, and 
experimental techniques. Chapter 4 presents the results and discussion on the characterization of 
LSZ solution, the LSZ-SWNT molecular interaction, phase behavior and alteration of LSZ-
SWNT dispersions, and the resulting macroscopic assemblies. Lastly, Chapter 5 provides the 
conclusions of this research and presents possible directions for future work in the field of LSZ-
SWNT dispersions. 
  
  
4 
 
2. BACKGROUND  
The observation of MWNT by Iijima in 1989 and the subsequent identification of SWNT 
along with Bethune et al. two years later launched the current explosion of interests in carbon 
nanotubes (CNT).1, 11-12 The extraordinary properties of CNT have resulted in their great 
potential in various applications including strong antimicrobial coatings, artificial muscles, 
chemical sensors and hydrogen storage.8, 13-16 After their discovery, the large scale production of 
carbon nanomaterials was the next step in stimulating the growth of research on small diameter 
nanoscale materials.  CNT production methods include laser vaporization, electric arc, chemical 
vapor deposition (CVD), and high-pressure carbon monoxide processing.2, 17-19 Synthesized 
nanotubes have polydisperse length and diameter distributions, and contain impurities such as 
metal catalyst particles, amorphous carbons, and fullerenes. These factors often complicate the 
translation of nanoscale properties into macroscopic objects. Thus, purification after synthesis is 
often performed, but this can lead to more defects in the nanotubes. By obtaining improved 
properties through optimized synthetic processing of CNT, the experimental and theoretical 
efforts in exploring the intrinsic characteristics of CNT during synthesis and their further 
application in novel materials have been made possible. 
2.1. CARBON NANOTUBES  
SWNT have been described as ladder polymers of pure carbon, where more than one 
bond needs to be broken in order to cleave the backbone.20 However, SWNT are much more 
robust than typical ladder polymers due to the highly ordered carbon-carbon bonds that must be 
cleaved in order for tube scission to occur. Since the sp2 hybridized carbon-carbon bond is 
among the strongest known, individualized, pristine SWNT are likely one of the most 
mechanically robust materials that will ever be discovered.21 However, the major obstacle for 
5 
 
current studies is difficulty in dispersing SWNT as individuals or small bundles. The barrier is 
due to the van der Waals forces between SWNT. To overcome this problem, chemical 
functionalization of SWNT by both covalent and non-covalent bonding has become a major 
focus. The end goal is to translate SWNT unique properties into macroscopic applications. In 
recent studies, covalent and non-covalent modification of SWNT with biological molecules has 
attracted significant attention to allow a pathway to translate SWNT properties into macroscopic 
assemblies. 
2.1.1. CARBON NANOTUBE MOLECULAR STRUCTURE 
SWNT are hollow cylinders of rolled graphene sheets having a diameter on the order of 
one nanometer and lengths of up to one micron or greater. Double-walled carbon nanotubes 
(DWNT) and MWNT are comprised of coaxially arranged, nested cylinders of graphene with 
diameters ranging from 2 to >50 nm with a concentric layer spacing of 0.34 nm.22-23 With 
variations in diameter and length even for each type, they have aspect ratios ranging from 
approximately 100 to 1000.23 However, the length, diameter, and, hence, aspect ratio, vary 
within and between samples, batches, laboratories, and manufacturers.22 In the absence of 
defects, the carbon atoms that make up the graphene sheet are covalently joined by an sp2 
hybridized bonds. However, the strain associated with bending of the graphene surface increases 
with decreasing tube radius and increases the sp3 hybrid character of the surface.24-26 Therefore, 
small diameter CNT are the most reactive. For this reason, MWNT and large diameter SWNT 
show weak sp3 hybridization unless the surface is chemically altered or functionalized.26  
All known SWNT synthesis methods give mixtures of diameters, lengths, and 
chiralities.21 The chirality of a CNT refers to the number of ways a graphene sheet can be rolled 
into a CNT. More specifically, tube chirality is identified with a pair of integers (n,m) which 
6 
 
define the circumferential chiral vector, Ch, which the graphene is rolled upon. Figure 1 displays 
the geometrical construct of Ch on a graphene sheet, and Equation 2.1 defines the chiral vector, 
Ch. The length of Ch is represented by the vector OA, the nanotube circumference. Orthogonal to 
Ch lays the translation vector T which defines the unit cell. The chiral indices (n,m) describe the 
number of steps along the hexagonal unit vectors a1 and a2 as shown in Figure 2. 
                                                                                       
 
Figure 1. Ch is defined on the graphene lattice by unit vectors a1 and a2 and the chiral angle ? 
with respect to the zigzag axis (? = 0o). The lattice vector of the one-dimensional unit cell is 
defined by T. The rotation angle ? and the translation ? constitute the basic symmetry operation 
R = (?|?) for the carbon nanotube. The diagram is constructed for (n,m) = (4,2). Reproduced 
from Dresselhaus et al.23 
 
The magnitude of the unit vector ai can be easily determined using geometry. The distance 
between adjacent vertices on a single hexagon is given by the carbon-carbon bond length, LC-C, 
7 
 
which is approximately 1.42 nm for graphene.23 From geometry, a hexagon is composed of six 
equilateral triangles, and each unit vector will bisect two equilateral triangles along a length of 
distance    LC-C, defining the lattice constant as 0.246 nm. Therefore, the length of vector Ch 
given by Equation 2.1 can be derived using the lattice constant. Equation 2.2 displays the 
relationship between tube diameter, tube intergers, and the magnitude of Ch. 
                  
 
 
  
     
                                                                                                  
 
Figure 2. Possible vectors specified by (n,m) for general CNT, including zigzag, armchair, and 
chiral tubes. Below each integer pair is listed the number of distinct caps that can be joined 
continuously to the CNT denoted by (n,m). Encircled dots denote metallic structure and small 
dots are for semiconducting tubes. Reproduced from Dresselhaus et al.23 
 
The division by ? is necessary to relate the tube circumeference to the diameter. As shown in 
Figure 2, the indicies (n,m) and therefore Ch determine the tubes electronic structure. Despite the 
structural similarity to a single sheet of graphite, which is a semiconductor with zero band gap, 
SWNT may be either metallic or semiconducting.27 More specfically, if the difference n ? m is 
8 
 
equal to zero the nanotube is a metallic, ballistic conductor with a band gap of zero. If the 
difference is nonzero and divisible by three, the nanotube is considered semimetallic with a band 
gap on the order of meV. In all other cases when the difference is nonzero and not divisible by 
three the nanotube is semiconducting with a band gap ranging from approximately 0.5 to 1.0 
eV.21 Structurally, the vectors (n,0) and (0,m) denote zigzag tubes, and the vectors having 
indicies of n = m denote armchair tubes; so named by examining a ring of carbon atoms around 
the circumference. Both armchair and zigzag tubes are achiral whereas all other vectors     
or zero are chiral as shown in Figure 3. 
 
Figure 3. Schematic theoretical model for a SWNT with the tube axis normal to: (a) the ? = 30o 
direction with (n,m) = (5,5) (an ?armchair? tube), (b) the ? = 0o direction with (n,m) = (9,0) (a 
?zigzag? tube), and (c) a general direction 0o < ? < 90o with (n,m) = (10,5) (a ?chiral? tube). 
Reproduced from Dresselhaus et al.23 
 
9 
 
2.1.2. CARBON NANOTUBE MECHANICAL, ELECTRICAL, AND THERMAL 
PROPERTIES 
The mechanical properties of CNT have been determined by both theory and experiment. 
The Young?s modulus, a mechanical measure of stiffness from the stress and strain exerted on a 
material, has been determined theoretically as 0.64 TPa for individual SWNT.28 In addition, the 
average experimental values as determined by atomic force microscopy for individual SWNT is 
1.25 TPa.29 This is consistent with experimental values for SWNT bundles ranging from 0.32 to 
1.47 TPa.30 Small diameter SWNT ropes have been experimentally extended elastically to 5.8%, 
therefore, the SWNT tensile strength can be calculated as approximately 37 GPa.31 For typical 
SWNT, the density normalized Young?s modulus is approximately 19 times that of steel and 2.4 
times that of silicon carbide nanorods. Similarly, the density normalized tensile strength is 
approximately 56 times that of steel wire and approximately 1.7 times greater than silicon 
carbide.27 It is because of these mechanical properties that assembly of macroscopic materials 
composed of CNT is of such importance. 
The electronic properties of MWNT and SWNT are quite similar in perfectly structured 
CNT.27 Due to their nearly one-dimensional structure, electronic transport occurs ballistically in 
the axial direction for metallic CNT.32 Therefore, high currents can be carried with resistivity on 
the order of 0.1 to 200 ??-cm.2, 33 The thermal conductivity of an individual MWNT has been 
reported in excess of 3,000 W m-1K-1.34 Correspondingly, the thermal conductivity for SWNT 
has been shown as 2,700 W m-1K-1 which exceeds that of diamond at 2,500 W m-1K-1, which is 
the current benchmark.35 In addition, superconductivity, an electrical resistance of approximately 
zero, has been experimentally observed in SWNT at extremely low temperatures.36-37 Thermal 
stability has been reported at temperatures as high as 2,800oC in inerts and 750oC in air.38  
10 
 
2.2. LYSOZYME 
LSZ was the second protein to have its crystal structure determined via X-ray diffraction, 
and has been studied extensively.39 LSZ is a polyampholyte, containing multiple hydrophobic 
and hydrophilic domains. This polyampholytic nature makes it a good dispersant for either 
hydrophobic or hydrophilic molecules. In the native, non-denatured conformation, the exposed 
LSZ surface is primarily hydrophilic. The surface hydrophilicity allows for stabilization and 
solubility in water. The stability and weak interactions are determined by colloid theory of the 
protein in solution, as discussed later. LSZ is a relatively small, globular protein, as shown in 
Figure 4. It has a diameter of approximately 3 nm and a molecular weight of approximately 
14,000 g mol-1 and is comprised of a single polypeptide chain of 129 amino acid residues.10, 40 Of 
the 129 residues, approximately 6 are lysine and 11 are arginine. These residues contain primary 
amines making the LSZ molecule strongly cationic with solubility in water of 10 mg mL-1.10 
 
Figure 4. Corey-Pauling-Koltun model of LSZ showing the globular nature of the tertiary 
structure. Carbon, nitrogen, oxygen and sulfur atoms are colored grey, blue, red and yellow, 
respectively. Adapted from Szymanska et al.41  
 
 
11 
 
2.2.1. LYSOZYME PROTEIN STRUCTURE 
LSZ contains two domains within its folded polypeptide chain, an ? and a ? domain as 
shown in Figure 5. The ?-domain contains four ?-helices and one 310 helix. The ?-domain has 
one three-stranded, anti-parallel ?-sheet, one 310 helix, and one amorphous loop.40 
 
Figure 5. Ribbon diagram of LSZ showing the two primary domains, ? and ?. The ?-domain 
consisting of the primary ?-helices, and the ?-domain consisting of the primary anti-parallel, 
pleated ?-sheet. Adapted from Knubovets et al.42 
 
The ?-helices are a common secondary structure of proteins that can vary in size from eight to 
hundreds of amino acid residues. The ?-helix is a right-handed coiled or spiral conformation, in 
which every backbone amino group hydrogen bonds to the backbone carbonyl group of the 
amino acid four residues earlier as shown in Figure 6. A 310 helix, comprised of only ten amino 
acid residues, is a right-handed coil in which every backbone amino group hydrogen bonds to the 
backbone carbonyl group of the amino acid three residues earlier. 310 helices are less common 
secondary structures of proteins. 
12 
 
 
Figure 6. Structure of alpha helix showing hydrogen bonding between amine and carbonyl 
groups of every fourth amino acid residue. Adapted from White.43 
 
?-sheets are regular secondary structures in proteins. ?-sheets consist of ?-strands connected 
laterally by at least two or three backbone hydrogen bonds, forming a generally pleated sheet. A 
? strand is a stretch of polypeptide chain, typically three to ten amino acids long, with the 
backbone in an a fully extended conformation. In an antiparallel arrangement, the adjacent ? 
strands alternate directions so that the amino terminus of one strand is adjacent to the carbonyl 
terminus of the next strand as shown in Figure 7. 
 
Figure 7. Structure of anti-parallel and parallel beta sheets showing hydrogen bonding between 
amine and carbonyl groups. Adapted from White.43 
13 
 
This arrangement, as compared to the parallel structure, produces the strongest inter-strand 
stability because it allows the inter-strand hydrogen bonds between carbonyls and amines of 
adjacent strands to be planar. An amorphous loop is simply a secondary structure which cannot 
be classified as any type of other known secondary structure.43 
In general, short amino acid chains do not exhibit much ?-helical or ?-sheet structure in 
solution since the entropic energy associated with folding the amino acid chain is not 
compensated for by a sufficient amount of stabilizing interactions. The backbone hydrogen bond 
interactions are considered weakened by the addition of hydrophilic molecules and are readily 
attacked by water molecules. However, in more hydrophobic environments, amino acid chains 
can adopt stable secondary structures. Furthermore, crosslinks or bridges can aid in 
conformationally stabilizing helices or sheets. Crosslinks stabilize the secondary structures 
through bonds which are stronger than the entropy related to unfolding. LSZ contains four 
disulfide bridges which stabilize the secondary structure as seen in Figure 8. 
 
Figure 8. Ball-and-stick representation of LSZ structure highlighting the disulfide bridges at the 
core. All protein atoms are shown as balls, and bonds between atoms are shown as a stick. 
Carbon, nitrogen, oxygen and sulfur atoms are colored grey, blue, red and yellow, respectively. 
Adapted from Szymanska et al.41 
14 
 
Because of these disulfide bridges, it is difficult for LSZ to completely lose its globular shape. 
Disulfide bridges are a covalent bond, derived by the coupling of two thiol groups. In the case of 
LSZ, the disulfide bridges are formed between the thiol groups of cysteine residues.43 The 
disulfide bond stabilizes the folded form of LSZ in several ways. First, it holds two portions of 
LSZ together, biasing the protein towards the folded morphology. More simply, the disulfide 
bond destabilizes the unfolded form of the protein by lowering its entropy. Second, the disulfide 
bond helps to form the nucleus of a hydrophobic core. Essentially, local hydrophobic residues 
condense around the disulfide bond and onto each other through hydrophobic interactions within 
the core of the LSZ. Third, the disulfide bond links two segments of the LSZ chain increasing the 
effective local concentration of protein residues and lowers the effective local concentration of 
water molecules in solution. Since water molecules attack hydrogen bonds and break up 
secondary structure, the disulfide bonds stabilize the secondary structure.44 Also, due to the 
disulfide bridges, LSZ is reasonably stable over a wide range of pH and temperature, with the 
isoelectric point of LSZ being 11 and the denaturation temperature being 76oC. Having such a 
high isoelectric point makes solutions of LSZ a very good electrostatic solvent having a charge 
of +8 at neutral pH.45 It should be noted that the other sulfur-containing amino acid, methionine, 
cannot form disulfide bonds. 
2.2.2. LYSOZYME ENZYMATIC ACTIVITY 
In addition to all the structural properties associated with LSZ that make it a good 
surfactant, the advantage of LSZ as a SWNT dispersant is the natural antibacterial activity LSZ 
possess. LSZ catalyzes the hydrolysis of 1,4-?-glycosidic linkages between N-acetylmuramic 
acid (NAM) and N-acetylglucosamine (NAG) which are components of the cell wall 
15 
 
peptidoglycan of bacteria, as shown in Figure 9.46 As such, LSZ is an enzyme which is an 
efficient antibacterial agent against Gram-positive bacteria. 
 
 
Figure 9. Schematic mechanism of LSZ hydrolyses. Glu35 is the active site of Glutamic Acid, 
however, it could also be represented by Asp52; N-acetylglucosamine is represented as NAG, 
and N-acetylmuramic acid is represented as NAM.  Adapted from White.43 
 
LSZ belongs to the hydrolases enzymatic class. Hydrolases catalyze the hydrolysis or 
hydrolytic cleavage of a chemical bond resulting in the formation of water. This class of 
enzymes is usually classified by the nature of the hydrolyzed bond, the chemical nature of the 
substrate, and finally by the enzyme. Within the class of hydrolases, LSZ belongs to the 
glycosylases family due to its reaction with the glycosidic bond between NAM and NAG. This 
reaction takes place in a long, deep cleft, which contains the active sites of LSZ. The active sites 
of LSZ are glutamic acid at residue 35 and aspartic acid at residue 52. The activity cleft is a very 
16 
 
specific active site, which can bind only six sugar rings from a polysaccharide chain and 
hydrolyze them into a disaccharide and a tetrasaccharide subunit.43 
LSZ can be inhibited from antibacterial activity by sodium dodecyl sulfate, alcohols, and 
oxidizers. However, LSZ activity can also be enhanced by the activator ethylene diamine 
tetraacetic acid due to its strong antioxidant properties. Unlike many antibacterials, LSZ has 
enzymatic activity in both its native and partially denatured states. Thus, making LSZ useful in 
processes which require some form of heat treatment.8 
2.2.3. LYSOZYME PHASE BEHAVIOR 
The strong bonding nature of LSZ allows for multiple phases to be created in an aqueous 
environment. Fully solvated LSZ in water is an isotropic liquid, showing very little difference 
from the solvent. As water is evaporated from the aqueous LSZ solution, the increasing 
concentration of LSZ causes the system to become a weakly linked gel, which is hypothesized to 
be held together via hydrophobic covalent bonding. Adding a co-solvent or using a solvent other 
than water can lead to the formation of other gels or liquid crystalline phases.40, 47 
In general terms, a gel transition of a polymeric system may be thought of as a nucleation 
process in which colloidal particles grow through condensation of macromolecular components 
into large clusters. Links between neighboring clusters then begin to occur until a network of 
clusters having developed with distinct interstices having developed between clusters. Distinct 
factors may induce these events, such as temperature, pH, or concentration conditions, or 
specific reactions leading to bond cleavage and cross-linking. In such cases, a new chemical or 
physical structure occurs. Solvent-induced LSZ gels are physically structured gels brought about 
by addition of the correct solvent to cause pH or ionic strength changes which can modify 
aspects of the three dimensional folding of the protein.40, 45, 48 This process usually takes place at 
17 
 
high LSZ concentrations and involves different kinds of interactions ? electrostatic and 
hydrophobic ? as well as intermolecular disulfide bridging formation. The specific behavior in 
each case is unique to the solvent and method of unfolding. However, the general behavior 
associated with most solvent-induced LSZ gels is that of translation of ?-helices into ?-sheets via 
hydrogen bond transfer.45 Common solvents and co-solvents used to create LSZ gels include 
flouroalcohols, tetramethylurea, and dimethyl sulfoxide.40, 49-50 
LSZ is known to form amyloid fibrils when incubated at low pH and elevated 
temperatures. Amyloid fibrils are polymeric ?-sheet aggregates of a protein consisting of 
relatively stiff, nonbranching fibrils that are approximately a few microns long and few 
nanometers wide. These fibrils can be considered to be long and rigid. In this respect, they are 
comparable to rod-like synthetic and biological polymers which are known to form liquid 
crystalline phases. The amyloid fibrils formed by LSZ do in fact form liquid crystal phases 
similar to that of DNA.47 The low pH needed for fibril formation is achieved through addition of 
a salt, generally sodium chloride. After addition of the salt, the LSZ solution is allowed to 
incubate which causes unfolding of the LSZ in such a way as to create stacked, order sheets of 
fibrils creating small domains of liquid crystals. Although liquid crystalline domains are evident 
due to the alignment of the amyloid fibrils, in literature, the distance over which the ordering 
occurs is debated.41, 47 
2.3. LYSOZYME DISPERSIONS OF CARBON NANOTUBES 
Throughout the literature there are various systems containing SWNT and LSZ. All the 
systems are aimed at combining SWNT properties with those of LSZ and other molecules. 
However, the solvent or solvents that are used to dissolve the LSZ into solution vary. The three 
most common systems are aqueous, gel, and liquid crystalline systems. Each of these solution 
18 
 
systems has their own unique reasons for research, properties, advantages, and disadvantages. 
Aqueous and liquid-crystalline systems will be covered in depth. Gelled systems will only be 
sparsely covered due to the amount of conflicting data in current literature. 
2.3.1. AQUEOUS LYSOZYME ? CARBON NANOTUBE DISPERSIONS 
Aqueous LSZ-SWNT dispersions are made with the initial LSZ solution solvent being 
water. The use of water as the primary solvent for the LSZ-SWNT dispersion is primarily three-
fold. First, water is a readily available solvent in which LSZ is extremely soluble. Second, there 
are little to no health and safety risks with handling or use of water. Third, since water is readily 
available, the cost impact of using water as a solvent is small in comparison with some more 
exotic solvents. 
Although, the use of water as the primary solvent seems practical, there are some unique 
properties of water and LSZ systems which give it advantages and disadvantages. LSZ is 
extremely soluble in water, however, over extended time periods (>1 week) at room temperature 
LSZ will aggregate to form macroscopic aggregates and fibrils. This aggregation makes the 
eventual dispersion of SWNT very difficult; a non-homogenous LSZ solution will not properly 
disperse individual tubes as will be discussed later. There is the possibility that LSZ is stable in 
water for longer periods at a lower temperature. However, this could reduce the ease with which 
processing can occur and could increase the economic capital for processing due to the need to 
refrigerate the solution below ambient conditions. Aggregation of LSZ in water has the 
possibility to occur, however, the use of water as the primary solvent does not reduce the 
antibacterial activity of the enzyme. Circular dichroism measurements in the far- and near-UV 
regions have been done to show that in water, LSZ does not change conformation of either the 
19 
 
secondary or tertiary structure.10, 51 The ability of water to maintain the antibacterial activity of 
LSZ is critical for the final desired properties. 
The advantages of using water as the primary solvent are akin to why it is used for 
research: it is economically viable, it has no health, safety, or environmental risks, it makes 
processing easier, and it maintains the antibacterial activity of LSZ. Water being used as the 
solvent helps for scale-up by reducing the initial capital expenditure and also by possibly 
reducing the operational expense of processing. The general inertness of water also creates 
favorable aspects of processing and handling. The use of materials that are a low risk for health 
and environmental issues reduces the capital expenditure of processing because less interlocks 
and safety precautions are needed. The wide use of water in commercially available and 
currently used processes makes design and acquisition of processing equipment much easier. 
Using other solvents that are volatile or flammable increases design and acquisition difficulty 
due to special precautions that must be taken. Finally, waters? ability to maintain the activity of 
LSZ makes it a great and practical solvent. If use of the water reduced or eliminated the 
enzymatic activity the justification for using LSZ as a dispersant would be questioned ? why use 
a relatively expensive biological molecule as a dispersant when many other organic surfactants 
could be used at lower cost. The ability for final products to be antibacterial is what justifies the 
use of LSZ as a dispersant. It is important to note, that the addition of SWNT to the LSZ solution 
does not eliminate the antibacterial activity of LSZ.8 Turbidimetric analysis was done for LSZ-
SWNT systems to show that the enzymatic activity of LSZ was maintained in the presence of 
SWNT, as seen in Figure 10. 
20 
 
 
Figure 10. Scanning electron micrographs of colony growth showing a control substrate still 
dense with Staphylococcus aureus on the left and a substrate coated with LSZ-SWNT that shows 
little evidence of S. aureus on the right. Adapted from Nepal et al.8 
 
In Figure 10, the difference in colony growth of the S. aureus shows that the LSZ-SWNT 
dispersion does in fact maintain antibacterial activity. The analysis shows that LSZ-SWNT 
maintains 92% of native LSZ activity.8 The disadvantage of using water is the short time frame 
of kinetic stability of LSZ in water. The short time scale before LSZ in water aggregates could 
make continuous, scaled-up processing and application difficult. 
2.3.2. LIQUID CRYSTALLINE LYSOZYME ? CARBON NANOTUBE DISPERSIONS 
Liquid crystalline LSZ-SWNT dispersions are made with the initial LSZ solution solvent 
being composed of a liquid crystalline mesophase, shown in Figure 11, and a secondary solvent. 
The secondary solvent can range from water to ethers. These solutions are made by first making, 
or purchasing, the liquid crystalline phase and then making a solution of LSZ with a solvent.52 
Although not discussed in the literature, in order to choose an adequate solvent for the LSZ it 
must be a good solvate for the LSZ and also be compatible with the liquid crystal. In general this 
requires that LSZ be soluble in the solvent and the solvent must be structurally similar to the 
liquid crystalline mesophase. After the liquid crystalline and LSZ solutions are made, they are 
21 
 
combined to form a ternary system in which the LSZ is held in between the mesophases in the 
solvent as shown in Figure 12. 
 
Figure 11. A schematic of a general liquid crystal showing order and orientation. The LSZ and 
SWNT integrate between the liquid crystalline structures adding greater stability. Adapted from 
Mishraki et al.53 
 
Figure 12. Photomicroscope images of LSZ crystals in hexagonal liquid crystalline mesophases. 
Adapted from Mishraki et al.53 
 
After formation of the ternary system, SWNT is added. The exact interaction between SWNT 
and the ternary system are not known, but are the areas of current research.41 The best possible 
22 
 
explanation for incorporation of SWNT is that the tubes disperse individually within the lattice 
spacing created by the ordered alignment of the liquid crystalline phase. By having a liquid 
crystalline phase, it would, in theory, be easy to individually disperse SWNT ? but not just 
disperse them individually, also have them align with little to no external force. Thinking 
geometrically, if the liquid crystalline phase is aligned rods facing parallel to a director with their 
mass centers randomly dispersed, such as a nematic liquid crystal, and SWNT were incorporated, 
it would be spatially impossible to incorporate the SWNT without having them be in alignment 
with the liquid crystal. For this reason, liquid crystals combined with other solvents for LSZ 
dispersions is a very desirable area of research. There are three major advantages to using liquid 
crystals for LSZ-SWNT dispersions: LSZ thermal stability, SWNT ordering, and ease of 
macroscopic assembly.52 The thermal stability of LSZ across a wide range of concentrations and 
pH was studied to determine if the liquid crystalline phase had any significant impact. It was 
found by Mishraki et. al. that not only does the denaturation temperature shift higher, but the pH 
dependent denaturation mechanism is virtually lost with only a 10% reduction in antibacterial 
activity. These findings prove that LSZ can be properly stabilized in such a way as to maintain 
proper activity while also being able to withstand higher temperatures; not only does this 
increase the range of applications but also decreases the difficulties in processing as described in 
the aqueous solutions section. Practical theory would lead to the idea that auto-alignment must 
occur if the tubes are indeed incorporated. Although there has been no documented research 
specifically on the auto-alignment of SWNT within the liquid crystalline-LSZ-solvent phase, 
there is research on the inclusion of SWNT and other nanorods in other liquid crystalline phases. 
The ease of macroscopic assembly is also an area that was not covered in literature, however, the 
order of alignment of liquid crystalline phases makes fluid phase processing of dispersions much 
23 
 
easier than isotropic solutions. The alignment also has the ability to increase the structural 
integrity of the final material. 
The disadvantages of using liquid crystalline phases in dispersing LSZ-SWNT are two-
fold: health, environmental, and process economics, and loss or drastic reduction of antibacterial 
activity. The health and environmental concerns of using liquid crystalline phases are mainly 
centered around the solvent used. If water were used as the secondary solvent, these concerns 
would not be viable. However, in the literature solvents such as glycerol monooleate, diethyl 
ether, and tetrahydrofuran are used.52-53 Each of these solvents introduces processing risks such 
as flammability, reactivity, and low level toxicity which increases the risk of processing and in 
turn the capital cost of processing as previously described. Another economic concern is the cost 
of the raw material used in operation. Use of exotic and expensive materials to produce the initial 
ternary system of liquid crystalline-LSZ-solvent could render the macroscale assembly 
processing not cost effective, and therefore not viable. Along with the economic concern, exotic 
solvents will reduce the overall applicability of using LSZ. Although the liquid crystalline phase 
has been shown to stabilize LSZ from temperature and pH, there are many other compounds that 
can cause the protein to denature such as alcohols and peroxides. If diethyl ether is used as a 
solvent, it can readily react to form peroxides which then denature the LSZ eliminating the 
antibacterial activity. Loss of the antibacterial activity renders the use of LSZ as a SWNT 
dispersant. The use of liquid crystalline phases with LSZ as a dispersant for SWNT has both 
advantages and disadvantages that would need to be weighed against what the final desired 
properties and applications are prior to choosing it as a method of dispersion. 
 
 
24 
 
2.3.3. GEL LYSOZYME ? CARBON NANOTUBE DISPERSIONS 
Gelled LSZ ? SWNT dispersions are made with the initial LSZ solution solvent being 
composed of a gelled polymer or a binary solvent-solvent system which induces gelling. The 
most commonly used polymer is glycerol.42 The combination of LSZ with glycerol shows many 
of the same affects as the combination of LSZ with liquid crystalline mesophases ? the structure 
of LSZ in the glycerol matrix is highly ordered and is therefore more thermally stable than in 
water.42 The combination of LSZ with a gelled solvent-solvent mixture, such as tetramethyl urea 
and water or dimethyl sulfoxide and water, shows similar attributes of thermal stability.48, 50 
Although there are some discernible differences between polymer gels and solvent-solvent gels, 
from this point forward the properties and aspects discussed will be common to both types of 
systems. The justification for using gelled systems is similar to that of using liquid crystalline 
systems: ordering and stability of the LSZ and SWNT. In theory, increased order will increase 
the stability, both kinetic and thermal, of the system. However, in the current literature, 
researchers are finding conflicting viewpoints as if stabilization occurs, why it occurs, and if the 
properties of LSZ are or are not affected. da Silva et al. have published that the stabilization of 
LSZ occurs due to the physical containment of the LSZ within the viscoelastic matrix of the 
gel.45 However, Knubovets et al. believe that the stability of LSZ is a localized effect and offers 
no macroscopic property enhancement.42 
Although the literature has conflicting view points, there are distinct advantages and 
disadvantages to working with a gelled system. The major advantage is order of the dispersion. If 
the LSZ ? SWNT is able to be ordered within a gel ? something that is inherent about the matrix 
of a gelled network ? then processing of the dispersion would be much easier as described 
previously. The primary disadvantage is the loss or suppression of antibacterial activity of the 
25 
 
LSZ. The confinement of LSZ within a gel matrix restricts the expression of the activity. By not 
allowing the LSZ to maintain or move into the native conformation, the matrix itself could 
prevent the active cleft from being exposed which prevents the activity of LSZ. On an 
elementary level, this could be thought of as putting a black coating on a light bulb; although the 
bulb may be capable of putting off light, it will not be able to do so because of the actions acted 
upon it with the paint. More research needs to be done in the area of gelled systems of LSZ ? 
SWNT in order to determine the actual affects of the gel on the system. Until such time, gel 
systems will remain intriguing because of their theoretical advantages. 
2.4. COLLOID THEORY 
CNT excellent material properties including low density and high aspect ratio make CNT 
desirable for many applications. However, in order to take advantage of their excellent 
properties, they must first be separated from themselves. It is CNT poor solubility characteristics 
that have hindered their manipulation and use in some applications.54 Colloidal forces at the 
interface of particles are important in determining, and in turn tailoring, characteristics of 
dispersions. Therefore, manipulation of the forces between CNT can lead to improved solubility, 
and the ability to optimize the attractive and repulsive forces within the dispersion. 
2.4.1. VAN DER WAALS FORCES 
The same forces that allow a gecko to scale horizontal walls are also responsible for the 
aggregation and binding of nanotubes to one another.55 Both are a result of van der Waals forces 
which have long been understood to cause negative deviations from Boyle?s law of ideal gases. 
For a closed system, this deviation is interpreted as an attractive force between particles or atoms 
reducing the force exerted on the container in a manner which is inversely proportional to the 
square of the system volume.56 This is intuitively explained by considering an air piston. As the 
26 
 
closed volume is compressed, the force needed to compress the fixed mass is reduced as particles 
become attracted to one another. These forces allow condensed phases to form and are stronger 
within solids and liquids than in gases. However, what is important to note is that the observance 
of what is deemed the van der Waals pressure indicates that even electrically neutral bodies 
attract.57 
The empty space between two atoms is actually a constant omni-directional sea of 
electromagnetic waves. This is a result of continuous interaction of charges in matter leading to 
spontaneous and transient electromagnetic fields. The additive effects of coordinated interactions 
of electromagnetic stimuli are what create van der Waals forces. Consider an atom surrounded 
by electromagnetic waves travelling in all directions. Now, allow the presence of a neighboring 
atom with omni-directional electromagnetic waves to interrupt fluctuations between the two 
bodies. The net interaction is that the atoms are pushed together by each atom?s uninterrupted 
electromagnetic waves.57 
In order to extend this idea to describe bodies larger than atoms or molecules, Hamaker 
introduced the concept of pairwise-summation for particles.58 The coefficient of interaction 
between objects is known as the Hamaker constant, A, and is a function of the materials 
involved. The Hamaker constant given by Equation 2.3 is typically on the order of 10-19 to 10-21 
J.58-59 
                                                                                      
In Equation 2.3, C is the coefficient in the atom-atom pair potential, ?1 is the number of atoms 
per unit volume in body 1, and ?2 is the number of atoms per unit volume in body 2.59 The atom-
atom pair potential is given by Equation 2.4. 
                                                                                         
27 
 
The potential, W, is the work required to bring the two atoms from infinite separation to a 
distance, D, apart and is negative due to the sign convention used for attraction.60 The idea of 
correlation to curved, nonlinear surfaces was termed the Derjaguin Approximation and took the 
attractive potential for planar surfaces and adapted it to describe curved surfaces at small 
separations. Interactions between cylindrical CNT are of interest in this research, therefore, only 
curved planar geometries are considered. For the non-retarded van der Waals interaction free 
energy between parallel cylinders of differing radii, the interaction potential is given by Equation 
2.5.59 
     
     
 
 
      
    
 
 
                                                                  
This expression for parallel cylinders gives the energy per unit length, L. The distance of 
separation between the two surfaces is given by D and the cylinder radii are given by R1 and R2. 
The attractive force between the two cylinders can then be derived by taking the derivative of the 
work with respect to separation distance. In general, for parallel cylinders the force is inversely 
proportional to D5/2 as shown by Equation 2.6. 
        
 
                                                                                 
If the cylinders are orthogonal instead of parallel, the expression for interaction potential yields 
the energy of separation with no dependence on length as given by Equation 2.7. 
                                                                                          
Correspondingly, for orthogonal cylinders the attractive force is inversely proportional to D2 as 
shown in Equation 2.8. 
                                                                                              
28 
 
In contrast to the determination of pairwise atom interactions, the Hamaker constants are 
typically determined from experimental data. Because of this, the properties of the bulk material 
are averaged instead of examining individual constituents. Regardless of methods of 
determination, the van der Waals potential functions are useful for determining the attractive 
potential as a function of radial dependence and separation distance. 
2.4.2. D.L.V.O. THEORY 
If the van der Waals forces acted alone in nature, it could be expected that all dispersed 
particles would fall out of solution immediately. However, this is not the case since particles 
suspended in media are often charged and stabilized electrostatically.59 Derjaguin, Landau, 
Verwey, and Overbeek (DLVO) considered particle and colloidal interactions as a function of 
two separable forces: van der Waals attractive forces and electrostatic repulsive forces. The total 
interaction potential for electrostatically stabilized particles is represented as the sum of the 
electrostatic repulsive forces and van der Waals attractive forces. Although the shape of the sum 
will vary with the magnitude of the contributions from each repulsive and attractive forces, 
Figure 13 displays a possible net energy curve as a function of interparticle separation. 
 
Figure 13. Schematic representation of the interaction potential for van der Waals attraction, 
electrostatic repulsion, and the total interaction potential showing metastable behavior. The 
primary (1o) and secondary (2o) minima are highlighted. Reproduced from Israelachivili.59 
29 
 
In this representation, the total interaction potential shows metastable behavior with a secondary 
energy minimum, 2o, at intermediate separation and a primary energy well, 1o, at close distances. 
The shape of the primary minimum is not highlighted well, but, in general, hard sphere behavior 
is shown at particle contact with the potential energy diverging to infinity which is consistent 
with the Pauli Exclusion Principle for atomic orbitals. The attractive behavior dominates at both 
small and large distances away from the 2o minimum. However, at small distances, the van der 
Waals attraction must always dominate due to the power law as given in Equation 2.3 which is 
not matched by any double-layer interaction.57, 59 If the 2o minimum is accompanied by a large 
enough potential energy barrier (the peak in the total energy curve) particles are kept from falling 
in the 1o well and forming irreversible aggregates. Typically, the energy at the 2o minimum, 
estimated at only a few kBT, is small enough that Brownian motion is enough to breakup particle 
flocculation.61 
The electrostatic force was introduced by the theory of an electric double layer which 
results from the charging of particle surfaces. This repulsive force explains why all particles in 
solution do not aggregate and precipitate out. In general, the charging of a surface results from 
the adsorption of ions from solution to a surface of oppositely charged ions or from the 
ionization or dissociation of surface groups.59 The result of an adsorbed surface charge is an 
oppositely charged region of counterions around the particle. In close proximity to the surface a 
narrow layer of bound ions develops and is known as the Stern layer. Surrounding the Stern layer 
is an atmosphere of loosely associated ions known as the diffuse double layer. To this end, like 
charged particles or surfaces will electrostatically repel each other in solution. 
Another important force that can contribute to suspension stability is that of steric forces. 
These are short range forces resulting from adsorbed surface groups on a particle or molecule 
30 
 
which physically prevent overlapping and mixing. If the interparticle separation approaches the 
dimensions of the adsorbed group then the space between the particles is depleted due to entropic 
effects causing flocculation. Essentially, the adsorbed group gains entropy by being free of 
constraint of the interparticle dimension causing the particles to be forced together by a depletion 
interaction.61  
2.4.3. BINDING ENERGY OF CARBON NANOTUBES 
It has been shown that in their natural, as produced state, SWNT self-organize into 
crystalline ropes 0.5 to 20 nm in diameter and tens to hundreds of microns in length.2 The van 
der Waals intertube bonding holds the individual tubes in a triangular lattice with a lattice 
separation constant of 1.7 nm as shown in Figure 14.2 
 
Figure 14. A single SWNT rope made up of approximately 100 SWNT as it bends through the 
image plane of the microscope, showing uniform diameter and hexagonal packing of the tubes 
within the rope. The diameter of the individual SWNT were determined to be approximately 1.38 
nm. Adapted from Thess et al.2 
 
The parallel alignment seen is a consequence of the highly polarizable and pristine nature of the 
sp2 hybridized carbon interface of SWNT.62 The pairwise interaction potential has been modeled 
31 
 
for parallel CNT revealing a deep potential energy well at equilibrium separation on the order of 
100 meV nm-1.63-64 Due to the high SWNT aspect ratio, the van der Waals attractive force 
becomes the obstacle for achieving stable dispersions as tubes tend to exist in ropes or 
arrangements of bundles. For tube-tube interactions, the binding energy of SWNT is 
approximately 0.5 eV nm-1, making them inherently difficult to process into individuals or small 
bundles.2, 62 It should be noted that this value is smaller but on the same order of magnitude as 
what is estimated by simulation.63 This discrepancy is likely due to the presence of defects on the 
sidewalls of tubes and solvent interactions. The lower value could also reflect the peeling of an 
outermost SWNT from the bundle rather than a SWNT centered in the rope. 
A continuum approach was taken in order to calculate the intertube interaction potential 
for CNT pairs.63 By this method, the interaction energy was determined over an effective area 
occupied by a carbon atom. The intertube potential for two structures was then calculated by 
integrating the Lennard-Jones potential over the surface of the tubes.65 From this model, the 
potential energy well depth was characterized at equilibrium spacing. Considering the symmetry 
of hexagons, the cohesive energy was calculated for a tube centered in a rope interacting with six 
nearest neighbors as three times the potential energy of the well depth.64 From these calculations, 
conclusions can be drawn as to how the van der Waals forces in roped or tube pairs scale with 
tube diameter. As tube diameter and separation distance are increased, the binding energy 
increases. The increase in binding energy with increasing diameter and separation distance may 
seem counterintuitive from the perspective of colloidal interactions modeled via Hamaker 
functions. However, it is important to note that the larger diameter tubes have more carbon atoms 
interacting per unit length than smaller diameter tubes. Thus, even through the separation 
between larger diameter tubes is larger, the models account for the presence of more carbon 
32 
 
atoms whose extra pull seems to outweigh the separation.63 In the same manner, one must also 
adjust the Hamaker constant to account for the presence of more C atoms. Because of this 
shortfall is should be noted that the van der Waals models based on Hamaker are of little utility 
in comparing interactions between CNT of different diameters and chiralities. In order to 
determine what manner CNT can be separated from one another, two modes of separation were 
compared: radial displacement and array peeling.65 Through theoretical arguments, results 
showed that array peeling of individual tubes from the outer diameter of a rope requires much 
smaller forces than dilation. Therefore, the likely mode of separation is array peeling as it can be 
accompanied by delivering much lower intensity energy density to the CNT as compared to 
dilation.65-66 
2.5. THERMODYNAMICS OF CARBON NANOTUBE SOLUTIONS 
Thorough thermodynamic analysis of SWNT dispersions and solutions are rare in 
literature. To date, only two exhaustive studies have been completed that try to describe the free 
energy of mixing, with each work taking a different approach. Sabba and Thomas published the 
first thermodynamic description of CNT solutions.67 Specifically, this approach was based on 
Onsager?s theory for anisotropic particles, and was used to describe the Helmholtz energy of 
mixing. The conclusion drawn from this work was that due to the large van der Waals attraction 
and poor solvents, a negative value for the free energy of mixing may only be obtained at low 
CNT concentration.67 However, further research has shown that stable solutions of CNT can be 
obtained at higher concentrations.5, 68-70 Bergin et al. published research to formulate a 
description of the Gibbs free energy of mixing, however it has since been strongly 
contradicted.70-71 It should therefore be noted that although a number of polymer models have 
been extended to CNT through theory, there have been a limited number of CNT systems for 
33 
 
which experimental data follows a CNT-specific model.71 From this it can be surmised that 
modeling of CNT systems is difficult, at this point in time. However, to present the information 
that is available this section will show the important thermodynamic properties of CNT 
dispersions. 
2.5.1. CYLINDRICAL PARTICLE THEORY 
Onsager and Isihara who theorized that the separation of an ordered phase of highly 
asymmetric particles will occur even in the absence of repulsive molecular forces.72-74 Similar 
conclusions were also made by Flory who considered the role of polymer chain inflexibility in 
polymer crystallization.75 It was argued that if one were to imagine placing long, stiff molecules 
one at a time into the volume, after a certain fraction was added it would be impossible to find 
space for additional molecules without relaxing the chain stiffness. It was then hypothesized that 
only through the development of order could additional molecules be added.75 Flory later extend 
these theories to semi-flexible and rod-like polymers.76 However, it has been argued that Flory?s 
lattice approach does not adequately describe liquid crystalline ordering due to restrictions 
placed on chain flexibility. Therefore, initially, Onsager?s theory was deemed more appropriate 
for studying liquid crystalline phases while Flory?s theory was deemed more useful for 
describing concentrated solutions.77 However, since the discovery of CNT, Onsager theory has 
been shown to be equally applicable for liquid crystalline and concentrated solution phases.68, 78 
Flory?s semi-flexible model considered polymer chains having many segments arranged 
on a two dimensional lattice. As a result of the constraint of chain stiffness, chain segments had 
to be placed co-linearly with adjacent segments of the molecule; with the assumption that the 
chains exist in a configurational arrangement that is energetically favorable as compared to 
others but still defined by the lattice. This assumption and treatment restricts the placement of 
34 
 
subsequent chain segments. With the geometrical constructs in place and considering the 
molecules already on the lattice, the next step was to estimate the possible number of vacant sites 
accessible as the next chain segment was added. This type of exercise was independently 
developed by Flory and Huggins for a two component liquid mixture of polymers in solvent 
assuming no change in the volume of mixing.75-76, 79-80 Flory then extended this treatment for 
semi-flexible polymers by including the degree of chain bending. The result of that exercise was 
an expression for the total number of possible lattice configurations and subsequently the 
partition function. To address the situation where the solute behaves as a rigid rod, where chain 
bending is zero, with no preferred chain orientation, the model for semi-flexible molecules was 
modified by pushing the flexibility and interaction parameters to zero giving two extreme cases. 
The partition function for athermal systems of rigid rods was then extracted.80 At one extreme, 
the system existed in complete disorder, whereas at the other extreme the rods existed in parallel 
alignment. However, neither extreme was able to adequately describe the intermediate 
arrangement of rods in concentrated solutions. 
In development of theory for the intermediate orientations, the lattice model was 
modified to overcome the inability to accommodate a rod in a continuously varying range of 
orientations.76 Figure 15 displays a molecule inclined at an angle ? with respect to the principal 
axis of the lattice.76 Instead of treatment as a continuous rod, Flory divided each molecule into a 
series of smaller molecules having parallel arranged segments as seen in Figure 16.81-82 
 
 
35 
 
 
Figure 15. A rigid rod in the Flory lattice tilted at angle ? to the director. The rod length is taken 
to be xd so that x plays the role of the aspect ratio where d is the characteristic dimension of the 
cubic lattice cell. Reproduced from Beris and Edwards, Cifferi, and Wang and Zhou.77, 81-82 
 
Figure 16. A rod divided into yi submolecules having x/yi segments per submolecule and tilted 
at angle ? to the director. The term yid represents the height with respect to the director with 
units of lattice cell number. Reproduced from Beris and Edwards, Cifferi, and Wang and Zhou.77, 
81-82 
 
Introduction of the parameter yi, known as the disorder index defined by Equation 2.9, requires 
that x be the rod aspect ratio with a diameter equivalent to the lattice size. Therefore, a total of yi 
submolecules are taken to have x/yi segments per submolecule aligned along the principle axis 
with each submolecule occupying one lattice site.81 
                                                                                      
The omission of the index on the rod length x indicates that all solute molecules are taken to be 
of uniform length. In this case, with j molecules already in place, the number of sites accessible 
to an additional molecule inserted into the lattice must be considered along with the molecule 
orientation. This was achieved by estimating the probability of finding a vacant site while 
36 
 
inserting each of the subsequent submolecules one at a time, row by row.77 A conditional 
probability allowing for the necessary lattice sites in adjacent rows must also be upheld. What 
results is the partition function for disordered rods in an athermal solution with a solvent. Both of 
Flory?s extreme cases for semi-flexible rods can be recovered from this treatment. In perfect 
alignment, the angle of inclination would disappear and there would be only one submolecule 
per rod. More simply, for perfect order the disorder index is unity and approaches the molecule 
aspect ratio for complete disorder. The partition function, Z, for rods of random disorder is 
displayed by Equation 2.10 where Stirling?s approximation has been used to treat the logarithm 
of combinatory factorials.77 
                                                                     
In Equation 2.10, ns and nx represent the number of solvent and solute molecules, respectively, 
with vs and vx representing the volume fraction of solvent and solute molecules, respectively. The 
rod aspect ratio is taken to be x and ? manifests itself as the rotational degeneracy factor which is 
an arbitrary constant. 
2.5.1.1. CYLINDRICAL PARTICLE ENTROPY OF MIXING 
The partition function can be related to the nanotube-solvent system by using more 
convenient factors suitable for experiment. The nanotube loading is an independent variable 
defined by the volume fraction, ?, and the aspect ratio, ?. With these conventions, and 
combining terms, the partition function can be written in a more useful form shown in Equation 
2.11.83 
                                                                         
This expression in itself contains the statistical configuration information for the isotropic array 
of nanotubes approximated as rigid rods in an athermal solution. The change in entropy upon 
37 
 
mixing ?Smix can then be obtained by using the Boltzman relation as shown in Equation 2.12 
where kB represents Boltzman?s constant.83 
                                                                 
2.5.1.2. CYLINDRICAL PARTICLE ENTHALPY OF MIXING 
When describing the enthalpy of mixing, it is first necessary to consider the existence of 
CNT at their natural state. Evidence of crystalline ropes on CNT was shown with hexagonal 
close packing.2 Consider CNT having density of ?CNT existing in bundles of radius R1 and length 
L1, then the number of bundles N1 in a fixed mass of CNT can be defined by Equation 2.13. 
        
         
                                                                       
Bergin et al. considered this system and determined the enthalpy of mixing for a solvent-CNT 
dispersion by calculating the energy required to separate all molecules to infinity less the energy 
required to bring them back arranged in a dispersed phase.84 Here a dispersed phase is considered 
one in which the final solute bundle size has been reduced with respect to the bulk starting 
material. This was treated by dividing the contributions into five energetic components.84 The 
first component being the energy required to create the surfaces associated with the individual 
nanotubes,      . This is a direct function of the intertube attractive potential. A second 
component was derived considering the energy required to remove all solvent molecules to 
infinity,      . This was taken as the difference between the solvent energy of cohesion less the 
solvent interfacial energy, and is by definition a function of the pure solvent only. In order to 
arrange the CNT in a dispersed state, a third term      was used in the exact same way as 
     but differing in the bundle size, R2, when the CNT are redispersed. In theory, R2 will be 
smaller than the original bundle size. The fourth component,      , takes the solvent molecules 
38 
 
from infinite separation to a molecular packing appropriate for the liquid specific volume while 
leaving voids for the newly dispersed CNT bundles. The term       is identical to       less the 
solvent interfacial surface energy interacting with the surface of the dispersed bundles. The final 
component is the interfacial energy associated with the placement of CNT in the voids, 
         . The value of this energy is estimated as twice the solvent-CNT binding energy, 
             . Combining all the above terms yields an equation for the enthalpy of mixing shown in 
Equation 2.14.84 
                                                                               
In this analysis, the magnitude of attraction was taken to be positive by convention. Bergin et al. 
then assumed the solvent external surface area was the same before and after mixing and that the 
bundle size was much reduced compared to the original state leading to an approximate solution 
as shown in Equation 2.15.84 
            
     
                                                                      
Next, the solute-solvent binding energy can be approximated by Equation 2.16 using the identity 
in Equation 2.17.84 
                              
 
                                                            
          
 
                                                                           
In relation to traditional polymer science,       can be thought of as cohesive energy density, and 
?i can be considered as a solubility parameter. By relating the CNT loading to the total solution 
volume, Vmix, the enthalpy of mixing can be a function of more experimental variables as shown 
in Equations 2.18 and 2.19.84 
39 
 
       
       
                                                                         
       
   
    
 
                                                                  
Inspection of these equations shows that in order to minimize the enthalpy of mixing, the surface 
solvent parameters for the CNT and solvent should be nearly equal. The origin of R2 in the 
denominator is a result of estimating the tube or bundle number density, N2, in the final state 
from the SWNT tube density and bundle size. It is important to note that these parameters are 
similar to, but not identical to the regular solubility parameters used in Scratchard-Hildebrand 
solution theory. In Equation 2.19, the solute and solvent parameters are a function of the surface 
energy whereas Scratchard-Hildebrand uses the cohesive energy density.56 Hence, from here on 
the parameters defined by Equation 2.17 are referred to as surface-solubility parameters. It is 
important to point out that approximation introduced in Equation 2.16 allows the surface 
solubility parameters to be estimated from the pure component interaction energy using Equation 
2.17. From these equations, it can be seen that to minimize enthalpy of mixing, the surface 
tension must be minimized.84  
Alternatively, the enthalpy of mixing can be defined by using the Flory-Huggins 
parameter, ?. The Flory interaction parameter is dimensionless and describes the interaction 
energy between solute-solute, solute-solvent, and solvent-solvent.56 For ideal solutions, ? is zero 
and can take positive or negative values for real solutions. For chemically similar mixtures, ? is 
small compared to unity.56 Additionally, ? is inversely related to the temperature but independent 
of solute concentration.83, 85 Equation 2.20 expresses the enthalpy of mixing as a function of ?.83 
                                                                                 
40 
 
This expression was originally adapted from the van Laar heat of mixing by Flory.85 In the case 
for the CNT-solvent system it is more useful to write ns in terms of the solvent volume fraction. 
Equation 2.21 introduces the solvent molar volume in order to link these terms. 
             
  
                                                                    
Inserting the expression for ns into the equation for the enthalpy of mixing yields Equation 2.22. 
     
      
  
                                                                       
By taking advantage of Equation 2.22, the enthalpy of mixing can be measured more accurately 
than by Equation 2.19, and this was used by Bergin et al. to validate the estimation for the 
enthalpy of mixing.84 In order to minimize the enthalpy of mixing, ? should be small or 
negative.56 In addition, ? can be directly related to the solubility parameters and the solvent 
molar volume by Equation 2.23.56 
                                                                                 
Inspection of Equation 2.22 again supports the minimization of ?, and therefore ?Hmix, by 
matching ?i for the solute and solvent. However, the form of Equations 2.19, 2.23, and any 
solubility parameter based expression contains a shortcoming for estimating the enthalpy of 
mixing in a real solution. The square of the difference in these equations cannot yield an 
enthalpy of mixing less than zero.83 Thus, exothermic mixing cannot be effectively predicted or 
described. 
2.5.1.3. CYLINDRICAL PARTICLE FREE ENERGY OF MIXING 
The driving force behind dissolution of a solute into a solvent can be defined by the 
Gibbs free energy. Equation 2.28 gives the free energy of mixing at constant temperature and 
pressure.83, 86 
41 
 
                                                                             
In the absence of metastabilities, dissolution into a single phase occurs only if the change in free 
energy upon mixing can be decreased. Criteria for dissolution can be displayed as shown in 
Equation 2.25 
                                                                        
From this, dissolution can be viewed as competition between the enthalpy and entropy of mixing 
as shown by Equation 2.26.84 
                                                                              
From Equation 2.26 it can be deduced that at constant temperature and pressure, minimizing 
?Hmix and maximizing ?Smix will help drive solubility. For typical small molecule solutions then 
enthalpy of mixing is small and positive whereas the entropy of mixing is of a large magnitude 
resulting in an overall negative free energy of mixing which drives dissolution in the solvent. As 
a result of their inherent properties and structure, CNT behave differently than such an ideal 
small molecule system. It has been generalized that in most CNT dispersions, the large intertube 
van der Waals attractive potential is expected to result in a positive enthalpy of mixing.84 This is 
manifested in a contribution to ?Hmix via the E2CNT term of Equation 2.14. Furthermore, the CNT 
stiffness and high molecular weight generally result in small, positive entropy of mixing.84 By 
comparison, Flory-Huggins theory for a system of low molecular weight solute and solvent to 
that of a low molecular weight solvent and a high molecular weight solute, one finds the entropy 
of mixing becomes smaller as the aspect ratio increases. This is a result of the loss in 
conformational entropy.83 Therefore, a positive free energy of mixing results in CNT-solvent 
systems which prevents spontaneous dissolution. Whereas a negative free energy of mixing can 
42 
 
result in the spontaneous exfoliation of CNT in solution leading to a dynamic equilibrium 
between individual tubes and small bundles.84 
2.5.2. CYLINDER-SPHERE PARTICLE THEORY 
Numerous studies have investigated the phase behavior, thermodynamics, and structure 
of suspensions of rod-like colloids and spherical colloids, independently. However, far fewer 
studies have been conducted on colloidal suspensions of rod-like particle with spherical particles. 
The theory of hard rod fluids are better understood and developed than hard sphere systems. This 
was recognized by Onsager who realized that the isotropic to nematic transition in rod-like 
colloids occurs at such a low concentration that only two-body interactions were necessary to 
quantitatively explain the phase transition.87 This is in contrast to theory of phase transitions of 
hard spheres, for which no experimentally validated theory exists.88 Rigorous combination of 
hard rod theory with hard sphere theory for binary mixtures has been limited. However, the 
limited research has shown that manipulation of rod theory to account for spheres is capable of 
producing simulated results which mimic experimental data of ideal systems of monodisperse 
hard spheres and hard rods with no interactions. It should therefore be noted that the modeling of 
cylinder-sphere systems at this time is mostly theoretical with little application toward 
interacting, polydisperse systems such as LSZ-SWNT. The overall generalizations of the ideal, 
theoretical systems are good indications though of what could happen in complex systems. Of 
particular interest in rod-sphere systems are the free energy of mixing and excluded volume 
interactions which determine the equilibrium phase behavior for rod-sphere suspensions.87, 89 
2.5.2.1. CYLINDER-SPHERE EXCLUDED VOLUME INTERACTION 
The free volume of a suspension composed of a binary mixture of macromolecules is 
maximized when the two components phase separate. Increasing the free volume, or reducing the 
43 
 
excluded volume, raises the translational entropy of the macromolecules, but does so at the 
expense of lowering the entropy of mixing. At low concentrations, the mixing entropy dominates 
and the solution is miscible, but with increasing concentration, if the gain in free volume is 
sufficient, phase separation will occur, as shown in Figure 17. This effect is known as depletion. 
The depletion effect may cause like particles to flocculate, known as depletion attraction, or it 
may cause like particles to separate, known as depletion repulsion.90 
 
Figure 17. a.) A schematic illustration of excluded volume effects in a miscible, nematic phase 
of rods and spheres, b.) A schematic illustration of transition to a layered phase, the large 
excluded rod-sphere volume vanishes, c.) Illustration of the immiscible phase where the system 
bulk phase separates into a rod-rich phase and sphere-rich phase. Adapted from Dogic et al.89 
 
Theoretical and experimental studies of depletion interactions between two charged spherical 
colloids have been presented by Walz and are expected to be qualitatively similar to the case of 
charged rods.91 The total potential of mean force between rods suspended in spheres is the sum 
of an attractive potential caused by the depletion force, and a repulsive potential arising from the 
electrostatic repulsion.  The range of the depletion attraction is the effective sphere diameter, and 
44 
 
the depth of the attractive interaction is proportional to the number density of the depletant. If the 
rods are sufficiently charged and strongly repel each other, then the rods will never come close 
enough to each other to exclude the spheres from the region between the rods, and thus will 
never feel the depletion force. Altering the electrostatic repulsion and allowing the rods to come 
within the sphere diameter of one another, and the depletion force will be felt. 
In order to properly determine the phase dependence of depletion interactions, the 
physical volume of space mutually excluded between pairs, ?i-j, was determined as shown in 
Equations 2.27, 2.28, and 2.29.92 
                                                                         
                   
 
  
      
                                             
                                                                                 
In the above equations for excluded volume, L and d stand for the length and diameter of the 
rods, respectively, D is the diameter of the sphere, and ? is the angle between the axes of the 
interacting rods. The physical excluded volume is shown in Figure 18. 
 
Figure 18. (a) Volume excluded to the center of mass of a rod (spherocylinder ? sc) due to the 
presence of a sphere (sp) is indicated by light shading. (b) Volume excluded to the center of mass 
of a second rod due to the presence of a first rod. Adapted from Dogic et al.89 
 
45 
 
2.5.2.2. CYLINDER-SPHERE FREE ENERGY 
In hard particle fluids all allowed configurations have the same energy, and therefore it is 
the number of states, or equivalently the entropy of a system that determines the equilibrium 
phase. The concept that entropy alone is sufficient to drive a transition from a disordered to 
ordered phase is an old idea in colloid sciences.90 The physical origin of the entropically driven 
phase transition in colloidal mixtures is both extremely simple and general. Most colloidal 
suspensions consist of particles whose interactions are dominated by steric repulsion, and so it is 
natural to consider the simplified case of hard particles as a model system. The phase behavior of 
a colloidal suspension of hard particles is found by minimizing the free energy, where the 
interaction enthalpy is zero for sterically repelled particles. Thus, the phase behavior of hard 
particles is determined by maximizing the entropy. Examples of entropically driven ordering are 
the liquid crystalline phases exhibited by hard rods or the fluid-crystal transition of hard spheres. 
These phase transitions have been studied extensively with theory and computer simulations, but 
experimental data of rod-sphere colloidal suspensions is scarce. Another class of entropically 
driven ordering arises in rod-sphere mixtures where a demixing transition occur. The usual 
scenario is that if the shape of the two components is different enough, bulk phase separation 
will occur for an appropriate composition of components.89 For entropically determined 
ordering, phase transitions or demixing are driven by differences in physical properties, such as 
shape, which can create bulk or microphase separation.90 For rod-sphere systems, the physical 
and thermodynamic origin of this separation can be explained in terms of the depletion 
interaction between molecules which is entropically driven by the sum of electrostatic and steric 
repulsive forces, and van der Waals attractive forces as previously described.93-95 Bulk phase 
separation, which is common to rod-sphere systems, occurs when the rods and spheres 
46 
 
completely separate (in the absence of any interaction) forming a rod-rich and sphere-rich 
phase.89 Another less common type of separation seen in rod-sphere systems is that of 
microphase separation. In microphase separation the system starts demixing into regions which 
are either rod- or sphere-rich. However, unlike bulk separation, the liquid-like regions grow to a 
critical size at which point they can form kinetically stable three-dimensional equilibrium 
structures.89-90 
Onsager theory, despite its? inherent limitations with a second virial approximation, 
provides a natural framework for the understanding of the physical rod-sphere problem in terms 
of the steric effects associated to the particular molecular geometries considered. For finite size 
molecules, Onsager theory tends to become inaccurate at high concentrations typical in phase 
transitions, and the scaled particle theory of Parsons and Lee can be adapted.92 Application of 
Onsager and Parsons-Lee theories to the case of rod-sphere systems have received considerable 
attention within the context of the stability of colloidal suspensions. Although the properties of 
these binary mixtures have been determined theoretically, experimental data of rod-sphere 
systems is not extensively available. What little experimental data is available of phase behavior 
and thermodynamics of rod-sphere systems is to a large extent unexplained by theory, although 
some relevant effects have been reproduced in theoretical and computer simulations.92 However, 
the Onsager and Parsons-Lee theories show capability for predicting, both quantitatively and 
qualitatively, the phase behavior and thermodynamics of rod-sphere systems. Onsager theory 
uses the probability distribution for the orientation of rod-like particles with respect to a fixed 
reference frame is determined by a single-particle distribution function, and Parsons-Lee theory 
uses the scaling approximation which takes into account higher virial coefficients. Combination 
47 
 
of the Onsager and Parsons-Lee theories leads to Equations 2.30, 2.31, and 2.32 for the free 
energy of a rod-sphere mixture.92 
                              ?             
 ?                                                                    
             ?    ?  ?                                                      
                ?  ?                                                         
Here,        is the concentration-independent portion of the free energy per particle, ? is the 
particle density, xc and xs are the molar fractions of rod and sphere particles, respectively, a is the 
aspect ratio of the rods, ? is the angle between rod axes, ?i-j is the pairwise excluded volume as 
discussed previously, and   ?  is the particle distribution function. In the isotropic phase, all 
orientations for the particle distribution function are equally probable, mathematically shown in 
Equation 2.33a. However, in the liquid crystalline phase the orientation is dependent of the axial 
symmetry and the director angle, ?, which is the angle between the molecule and the nematic 
director vector, mathematically shown in Equation 2.33b.92 
  ?   
 
      
 
      
                                                                                          
From the Equations 2.30 through 2.33 it can be seen that the equilibrium phase behavior in a rod-
sphere mixture is determined by four parameters: the aspect ratio of the rod, the ratio of the 
diameter of the rod to the diameter of the sphere, the total volume fraction of spheres and rods, 
and the partial volume fraction of spheres. 
 
 
48 
 
2.5.2.3. CYLINDER-SPHERE PHASE BEHAVIOR   
The physical origin of the phase behavior of spheres and rods can be explained in terms 
of the depletion interaction which is entropically driven by steric repulsive interactions between 
the rod and sphere particles. A dilute particle solution can be treated as an ideal gas of hard 
spheres, whose mean size is given by the radius of gyration, Rg, of the spherical particle.96 In the 
rod-sphere mixture, the center of the rod cannot penetrate into the shell with thickness Rg 
surrounding each spherical particle, called the depletion zone. When two colloidal particles 
approach each other, these depletion zones will overlap. The translational entropy of the particle 
then increases. Due to these interactions, mixtures of rods and spheres can form miscible 
isotropic, immiscible isotropic, miscible nematic, and immiscible nematic phases. Miscible 
phases are those which the rod and sphere are homogenous within the mixture. Immiscible 
phases are those which contain rod-rich and sphere-rich regions. In recent years, mixtures of 
colloidal rods and nonadsorbed polymers have been investigated from experimental, theoretical, 
and computer simulation points of view. Mixtures of rod-like colloidal particles, such as 
bacteriophage fd virus or tobacco mosaic virus, and flexible polymers, such as polyethylene 
oxide, exhibit various phase behaviors as a function of the concentration of constituents.96 These 
phase behaviors can be explained by the concept of the depletion interaction as well as the 
concentration and size of the spherical and rod colloidal particles. 
The effect of rod concentration and size on mixtures of rods and spheres has been 
theoretically determined. At low concentrations of rods, the mixing entropy dominates and the 
spherical particles are miscible with the rods particles. With increasing rod concentration, the 
increase of the translational entropy compensates for the decrease of mixing entropy and phase 
separation occurs, although the interaction between constituents is purely repulsive.96 At smaller 
49 
 
rod length, the miscible, isotropic phase persists to much higher concentrations until an eventual 
transition is made to a miscible, nematic phase, as predicted by Onsager and Flory theories. As 
the rod length is increased, the transition from miscible, isotropic to miscible, nematic occurs at a 
much lower rod concentration. With increasing rod length, the excluded volume due to the rod-
sphere interaction grows proportionally to the rod length and consequently the rod-sphere and 
rod-rod excluded volume increases which allows formation of a miscible, nematic phase at lower 
concentrations.89 
The effect of sphere concentration and size on mixtures of rods and spheres is rather 
counterintuitive. While holding the concentration of the rods constant, increasing the 
concentration of small spheres will transform the system from miscible, isotropic to miscible, 
nematic as shown in Figure 19. 
 
Figure 19. Simulation results for addition of small spheres. Phase behavior changes from 
isotropic (left) to nematic (right) by increasing concentration of small spheres. Adapted from 
Dogic et al.89 
50 
 
If the sphere radius is halved while keeping the volume fraction of spheres constant, then the 
number of spheres is increased by a factor of eight. At the same time, the result of reducing the 
sphere size is a decrease in the excluded volume of the rod-sphere system. However, the 
eightfold increase in the number of rod-sphere interactions more than compensates for the 
decrease in the excluded volume between the rods and spheres. This leads to the increased 
stability of the nematic phase with decreasing sphere size. 
While holding the concentration of rods constant, increasing the concentration of large 
spheres will transform the system from a miscible, isotropic to an immiscible isotropic phase. 
Further increasing the sphere concentration will cause the rod rich phase to transform from 
isotropic to nematic, as shown in Figure 20. 
 
Figure 20. Diagrams of three phases of rod-large sphere mixtures with increasing large sphere 
concentration from left to right ? miscible, isotropic (left), immiscible, isotropic (middle), 
immiscible, nematic (right). Adapted from Urakami et al.96 
 
At low volume fractions of large spheres where the mixture directly bulk phase separates, the 
ratio of rod-sphere excluded volume to rod-rod excluded volume is much greater than unity. This 
indicates that demixing very effectively reduces the unfavorable rod-sphere interactions. These 
results gives a physical picture of the excluded volume effect. Unlike small spheres, large 
51 
 
spheres cannot fit into the gap between rod layers. Consequently there is no way to gain free 
volume by transitioning to an ordered phase. Thus, to gain free volume, the system bulk phase 
separates at the lowest volume fraction of spheres possible.78, 89 
When the sphere size is small, the overlap volume of the depletion zones is small because 
the depletion zone surrounding a rod is thin. In this case, the gain of translational entropy cannot 
compensate for the decrease of mixing entropy, resulting in the miscible state even when the 
isotropic-nematic transition of rods takes place. On the other hand, when the sphere size is large, 
the overlap volume of the depletion zones exceeds a threshold value. Then the increase of the 
translational entropy of spheres compensates for the decrease of the mixing entropy, and the 
system transforms to the phase separated state.89-90, 92, 96 
2.6. RHEOLOGY THEORY 
Rheology is the field of science that studies the flow and deformation of matter.97 Of 
particular interest to this research is the study of complex fluids. Complex fluids show behavior 
that is intermediate between classical solids and liquids. Classical materials show either viscous, 
liquid-like behavior or elastic, solid-like behavior, which will be discussed in later sections. For 
reference, a classical solid will maintain its shape indefinitely whereas a classical liquid will take 
the shape of its container.98 In general, many complex fluids will show intermediate behavior in 
that they will maintain their shape for a certain time, but eventually flow. A fluid of this type is 
termed viscoelastic, as it behaves like an elastic solid over short timescales and a viscous liquid 
over long time scales. Interestingly, a material does not have to be out of the ordinary to be 
considered complex. Mayonnaise, paints, ice cream, and even blood are common examples of 
complex fluids. Many common complex fluids are engineered to have a complex rheological 
response such as the yield stress of toothpaste or ketchup.98 
52 
 
A variety of instruments are available to measure rheological properties of fluids. Simple 
flow indexers and capillary viscometers are commonplace in industrial settings. However, 
research grade rotational rheometers are available and are capable of measuring both steady state 
and transient flow properties of materials under controlled stresses and strains. In addition, 
temperature and pressure controlling capabilities are available with many research grade 
rheometers.97 
2.6.1. CONE AND PLATE RHEOLOGY 
The features of a cone and plate rheometer are displayed in Figure 21 utilizing a spherical 
coordinate system of (r, ?, ?). A flat, circular plate of radius R is opposed by a linearly 
concentric upper cone. The tip of the cone is flattened so that no physical contact is made with 
the lower plate. The cone angle, ?, is typically only a few degrees, and the rotation of the cone 
occurs at an angular speed of ?. Derivation of the velocity profile, shear stress, first normal 
stress, and torque can be found in Macosko which start from the equations of motion in spherical 
coordinates.61, 99  
 
Figure 21. Coordinate system and geometric parameters describing the cone and plate measuring 
geometry. Adapted from Macosko.61 
 
53 
 
Assuming that the velocity is a function of r and ? only, and the only non-diminishing 
component is in the ? direction, the shear stress can be measured from the raw torque as shown 
in Equation 2.34. 
                                                                                   
During an experiment, the rheometer measures the raw torque from the torque transducer, 
required to maintain the set test variable which is commonly the shear rate of the angular 
frequency at a set strain amplitude. It is important to note that there is no ? angular dependence 
on the shear stress due to the small magnitude of ?. Thus, the shear stress imposed on the fluid is 
essentially constant and uniform, and therefore the shear strain and shear rate are uniform.61 The 
shear strain in cone and plate geometry is measured by introducing the angular displacement, ?d. 
Equation 2.35 represents the angular displacement under steady shear. 
   ?                                                                           
The definition of shear strain can then be rewritten as shown in Equation 2.36. 
                                                                                
Likewise, the expression for shear rate in a cone and plate geometry can be rewritten as shown in 
Equation 2.37. 
  ?   ?   ?  ??                                                           
Here the angular speed of the cone is given by ? and the cone angle is represented by ?. The first 
normal stress difference is measured directly in cone and plate geometry by the total thrust on the 
plate. The value of N1 as well as its interpretation can be derived from Equation 2.38. 
                                                                         
54 
 
Here N1 is taken to be the difference between the normal stress in the direction of flow and the 
direction orthogonal to the lower plate. The quantity Fz is the normal force measured by the 
rheometer force transducer taken to be the force required to hold the apex of the cone at the 
center of the lower plate.97-98 As displayed in Figure 21, the rheometer used in this study 
measures the normal force in the upward direction. Thus, the magnitude of Equation 2.38 must 
be adjusted for the coordinate system as displayed in Equation 2.39. 
                                                                               
2.6.2. PARALLEL PLATE RHEOLOGY 
Since the cone and plate geometry provides a uniform stress it is the preferred geometry 
for many rheologists. However, if suspensions of particles have dimensions comparable to the 
small gap between the cone and plate, a parallel plate geometry must be used. In many ways, the 
two geometries are similar, with the largest difference being that the flow between the parallel 
plates is non-homogenous and a function of the radial distance r. Figure 22 displays the 
geometrical constructs of the parallel plate geometry. A cylindrical coordinate system is used to 
describe the plates in (r, ?, z). Two identical and coaxial flat parallel disks are rotated to impose 
flow. Typically, the upper plate is rotated with an angular speed ? in the direction of ?. The gap 
between the plates, h, is held constant and can be adjusted throughout testing. An adjustable gap 
is advantageous for correcting sample edge defects or checking for sample slip, whereas with the 
cone and plate geometry the gap is fixed and requires reloading upon edge failure. Derivation for 
the velocity profile, shear stress, first normal stress, and torque can be found in Macosko which 
starts from the equations of motion in cylindrical coordinates.61, 99  
55 
 
 
Figure 22. Coordinate system and geometric parameters used to describe the parallel plate 
measuring geometry. Adapted from Macosko.61 
Assuming that the velocity is a function of r and z only and the only non-diminishing component 
is in the ? direction, then the shear stress can be measured from the raw torque as shown in 
Equation 2.40. 
                      
 
                                                      
Through examination of Equation 2.40 it shows that the derivative of the natural log of the 
torque with respect to the natural log of the plate edge shear rate,    , cannot be determined 
accurately without sufficient data to correlate the two variables.61 However, if the fluid is 
Newtonian, the derivative equals unity and the shear stress is defined as the apparent shear stress, 
?a. Equation 2.41 shows the expression for the apparent shear stress. 
                                                                                
Often, the apparent shear stress is simply used to calculate an apparent viscosity since only the 
raw torque measurement is required. Inaccuracies may be contained within measurements but 
this is often not addressed in the literature. However, in the case of sinusoidal varying 
measurements within the linear viscoelastic regime, the derivative in Equation 2.40 also 
56 
 
diminishes to unity, and the apparent shear stress given by Equation 2.41 is exact.61 In both 
cases, Equation 2.40 and Equation 2.41 are functions of the radius of observation. This is a result 
of the shear rate being a function of the angular speed which varies with radial distance from the 
center of the plate, which can be mathematically corrected. Equation 2.42 displays the shear rate 
for the parallel plate geometry. 
      ?                                                                        
Equation 2.43 gives the shear rate for the parallel plate geometry at the plate edge. 
     ?                                                                         
As with the shear rate, the shear strain also varies with radial position and can be calculated from 
Equation 2.44. 
                                                                              
To evaluate the viscoelastic modulii, the strain must also be measured at the plate edge as given 
by Equation 2.45. 
                                                                            
In contrast to the cone and plate geometry, the first normal stress difference cannot be measured 
alone for a parallel plate geometry. Instead what is obtained is the difference between the first 
and second normal stress differences as shown by Equation 2.46. 
                             
 
                                             
The normal force is represented by Fz and is taken to be positive, consistent with Figure 22. 
Again, as with the cone and plate geometry, consideration must be taken for the coordinate 
system of the instrument being used and properly accounted for in determination of magnitude. 
57 
 
In order to completely decompose the difference between N1 and N2, measurements must be 
made in both parallel and cone and plate geometries and then compared. 
2.6.3. LINEAR VISCOELASTICITY 
A classic example which illustrates how the behavior of complex and ideal fluids differ in 
response under applied strain is stress relaxation. The shear strain is a measure of the sample 
deformation due to an applied force, F. Figure 23 illustrate a sliding plate model where the 
sample is placed in the gap of height h.100 
 
Figure 23. Illustration of important terms used in describing the shear strain of a fluid between 
two parallel sliding plates. Reproduced from Mezger.100  
 
In Figure 23, the lower plate is stationary and the deflection of the upper plate is shown by the 
distance s. Equation 2.47 defines the strain as the ratio of deflection distance to gap height. 
                                                                                       
The shear strain, by definition, is a dimensionless number, and is equivalent to the tangent of the 
deflection angle ?. For a point of reference, a deflection angle of 45o corresponds to a strain of 1 
or 100%. Often, the strain set points are quite small ? less than 5% - and therefore the deflection 
is small enough to consider the microstructure of the material to be undisturbed. While operating 
58 
 
the rheometer in strain-controlled mode, the user sets the strain and therefore the deflection 
angle. The deflection angle is then fixed by the instrument throughout the test. 
Figure 24 illustrates various response types when a step increase in strain is imposed on a 
fluid and the dissipation of relaxation of the stress is measured. 
 
Figure 24. Illustration of a stress relaxation experiment. (a) The step increase in strain, and (b) 
the stress vs. time response of various fluid types. Reproduced from Macosko.61 
 
Figure 24(a) shows the step strain imposed on the fluids. Figure 24(b) shows the typical 
relaxation response for various types of fluid. The Newtonian fluid relaxes as soon as the strain 
reaches a constant value characteristic of a prototypical viscous liquid. Conversely, the Hookean 
solid shows prototypical elastic behavior with no stress relaxation. Intermediate behavior is seen 
for both the viscoelastic liquid and viscoelastic solid where the stress relaxes over some given 
time. The difference being that the viscoelastic liquid will eventually relax to zero stress whereas 
the viscoelastic solid approaches an equilibrium value.61  
The stress relaxation data can be easily converted into a modulus by taking the stress to 
strain ratio. This modulus, the stress relaxation modulus, is defined in Equation 2.48. 
59 
 
                                                                                 
Typically, for imposed step strains larger than unity, the stress is both a function of time and the 
imposed strain. The behavior is known as nonlinear viscoelasticity. On the other hand, for small 
strains, typically less than unity, log-log plots of the stress relaxation modulus superimpose. This 
region of strain showing independent stress modulus is known as the linear viscoelastic regime. 
Equation 2.49 defines the linear relaxation modulus. 
                                                                             
Both G and ? are only functions of time in the linear viscoelastic regime. This is a fundamental 
observation and can be exploited to further characterize the material. 
2.6.4. OSCILLATORY FLOW 
In the linear viscoelastic regime, all measurements made at small strains less than the 
critical strain, ?c, of that material are related to one another. To this end, small-amplitude 
oscillatory shear measurements provide important structural information without significantly 
deforming the fluid?s microstructure. Furthermore, by changing the frequency of strain, one can 
vary the timescale of observation. Typically a sinusoidal wave in stress or strain is imposed on 
the fluid with the frequency measured in cycles per second or more commonly as angular 
frequency, ?, in units of radians per second. The strain relationship can be represented by 
Equation 2.50 where ?0 represents the strain amplitude. 
?                                                                          
In addition, the strain rate is found by taking the time-derivative of the strain as shown in 
Equation 2.51. 
  
                                                                     
60 
 
At steady state, the stress will also oscillate sinusoidally with the same frequency but shifted by 
the phase angle, ?, in regards to the strain wave as shown in Equation 2.52.61 
                                                                     
The graphical representation of the applied strain wave and the resultant strain wave are shown 
in Figure 25. The stress will be out of phase with the strain rate unless the fluid is Newtonian. In 
that case, ? will shift the stress by 45o and the trigonometric functions will be of equal value. 
 
Figure 25. The imposed strain wave and resulting steady-state stress wave under simple shear 
flow. The stress wave is in frequency with the strain but shifted in phase by angle ?. Reproduced 
from Ferry.101 
 
The stress wave can be decomposed further by applying the sum-difference identity which leads 
to Equation 2.53. The first term of the equation represents the stress component in phase with the 
strain wave and the second represents the stress component out of phase with the strain. Both 
components oscillate on the same frequency but do not necessarily have to be of the same 
magnitude. 
                  ?                                            
Equation 2.53 to holds true regardless of the deformation mode, provided that the strain 
amplitude does not exceed the limit of linear viscoelasticity.97 The components of Equation 2.53 
are graphically shown in Figure 26. 
61 
 
 
Figure 26. Trigonometric deconvolution of the steady-state stress wave in to its in-phase and 
out-of-phase components. Reproduced from Ferry.101 
 
Taking the ratio of Equation 2.53 to the strain amplitude, two independent modulii can be 
defined by Equation 2.54 and Equation 2.55.101 
       
 
                                                                        
        
 
                                                                        
Equation 2.54 displays the in-phase modulus, more commonly referred to as the storage or 
elastic modulus, which represents the storage of elastic energy in the material. Equation 2.55 
displays the out-of-phase modulus, more commonly referred to as the loss or viscous modulus, 
which represents the loss of viscous energy through the material.98 For a perfectly elastic solid, 
the phase angle is close to zero and all energy is stored in the material as indicated by G? having 
no value. For a perfectly viscous liquid, the phase angle is approximately 45o and all energy is 
dissipated through the sample with G? having a magnitude of zero. Figure 27 displays typical 
linear viscoelastic responses of storage and loss modulii.98 
62 
 
 
Figure 27. The prototypical linear viscoelastic response in terms of frequency dependent storage 
modulus, G?, and loss modulus, G?, for (a) a ?solid-like? fluid and (b) a ?liquid like? fluid. 
Reproduced from Larson.98 
 
For ?solid-like? response shown in Figure 27(a), G? is much greater than G? in magnitude, and 
G? is also nearly or completely frequency independent. G? does not necessarily have to be 
frequency independent and may show some upturn at low frequency as a result of aging.102 For 
the ?liquid-like? response in Figure 27(b), G? dominates in magnitude and both modulii scale 
with frequency in a power-law fashion. As previously discussed, real complex fluids are 
expected to show some behavior intermediate to the two ideal responses. 
Taking advantage of Equations 2.54 and 2.55 the expression for the stress wave can be 
written in a more convenient form as shown in Equation 2.56. 
                                                                            
Another useful parameter is defined by taking the ration of the loss modulus to the storage 
modulus as shown in Equation 2.57. 
      
  
                                                                              
63 
 
Equation 2.57 is also known as the loss tangent or damping factor. The magnitude of this 
equation is greater than unity for materials behaving more as liquids, and less than unity for 
materials behaving more as solids. More simply, the behavior of a material as solid or liquid can 
be inferred from the dominant modulus at a given frequency. The loss tangent is simply another 
means to measure energy dissipation in viscoelastic materials.97 
The complex modulus, G*, is defined by considering the amplitude of the stress 
waveform as a whole and taking its ratio to the strain amplitude.98 Its magnitude is defined by 
Equation 2.58. 
               
 
    
                                                           
The magnitude of G* can be interpreted as a measure of the overall resistance to deformation. 
This measurement takes no consideration in to how the energy is dissipated via G? and G? 
individually. Finally, dividing the complex modulus by the angular frequency gives the 
magnitude of the complex viscosity, ?*, as shown in Equation 2.59. The complex viscosity is a 
measure of a materials resistance to flow under oscillatory shear. 
       
  
    
  
  
 
   
  
  
 
 
 
 
                                            
In many cases, the complex viscosity can be related to the shear or apparent viscosity by means 
of the Cox-Merz rule. The Cox-Merz rule does not hold for liquid crystals and many non-ideal, 
multicomponent, or interacting systems. This relationship is strictly empirical and states that 
shear viscosity of a fluid at steady state is equivalent to the complex viscosity of that fluid in the 
linear viscoelastic regime provided that they are measured at equivalent magnitudes of rotational 
shear rate and angular frequency.61 Mathematically this can be expressed by Equation 2.60 with 
the condition of Equation 2.61. 
64 
 
                                                                          
                                                                           
Again, the Cox-Merz rule only holds true if the conditions of matching shear rate and angular 
frequency are met. It is important to note the    used in Equation 2.61 is intended to represent the 
shear rate, but its? meaning still holds true as the rate of deformation. The difference is that under 
steady rotational shear the shear strain and therefore shear rate is held constant whereas under 
oscillatory flow it remains a function of time. 
2.6.5. SHEAR FLOW 
All the geometries of various measuring systems may vary, however, all are similar in 
that they impose a drag flow by a controlled motion along the system boundary. Figure 28 shows 
a simple sliding plate geometry where the bottom boundary is stationary and the top plate moves 
at a set velocity of rotation. All motion is along one coordinate direction, x1, with velocity 
varying in a second coordinate direction, x2, orthogonal to the shear.97  
 
Figure 28. The sliding plate model, and relative coordinate system for simple shear. Adapted 
from Gupta and Mezger.97, 100 
 
65 
 
The upper plate in Figure 28 moves along the positive x1 direction with velocity v while the 
sample remains between the gap of height h. Mathematically, viscometric flow translates to there 
being only one non-zero velocity component, v1, and therefore one zero component to the 
velocity gradient tensor.61 This non-diminishing component is known as the shear rate,   , and 
can be represented by Equation 2.62. 
        
 
                                                                            
It should be noted that the shear rate is simply the velocity gradient, and is often referred to as 
the rate of deformation or strain rate. For sliding plate geometries, the magnitude of the shear 
rate is the velocity divided by the gap as shown by Equation 2.63. 
                                                                                  
The force that the flowing fluid is exerting on the surface in the direction parallel to flow is 
known as the shear stress, ?. After imposing a steady shear to a fluid from a state of rest, the 
shear stress does not reach steady state immediately.98 Rather, the stress goes through a transient 
period where it varies with time. The ratio of the instantaneous stress to the imposed steady shear 
rate gives the transient start-up viscosity as shown by Equation 2.64. 
                                                                                  
After a certain period of time in which the steady shear has been applied, the shear stress will 
then come to a steady state. Thus, the shear stress is no longer a function of time, and the shear 
viscosity can be defined as shown by Equation 2.65. 
                                                                              
66 
 
The behavior of the shear stress as a function of various shear rates is one way to define the type 
of material or fluid. The simplest response is that of a Newtonian fluid in which the shear stress 
is directly proportional to the shear rate and the viscosity is therefore constant. Deviation from 
this behavior indicates a shear rate dependence on viscosity and materials exhibiting this type of 
response are classified as non-Newtonian. 
A common phenomenon with complex fluids is that of a yield stress. Fluids with some 
solid-like character will not flow initially upon the initiation of shear. Instead, the stress grows 
linearly with the shear rate up to a critical value, above which the material yields or flows at a 
constant shear stress. It is noteworthy to point out that the yield stress describes the point at 
which flow begins.98 
In general, a fluid is a material that cannot support a shear stress without flowing.61 
Consider a fluid element as displayed in Figure 29. If at rest all surface stresses on the element 
act orthogonal to the surface ? normal stresses ? and are not only equal in magnitude but 
independent of orientation of the element. This type of normal stress is known as the hydrostatic 
pressure and is compressive in nature. The absence of motion within the element also implies the 
absence of shear stresses. Thus, for a fluid in motion it follows that there must be either shear 
stresses present or normal stresses that are unequal. These shear stresses are known as viscous or 
extra stresses because they act on a fluid in addition to the fluid pressure. 
 
Figure 29. Schematic diagram showing the notation for normal stresses in a shear field. Adapted 
from Gupta.97 
67 
 
The tensor Tii contains the contributions of the pressure and the extra stress as shown by 
Equation 2.66. 
                                                                             
As a consequence of most liquids being considered incompressible, the application of equal 
normal stresses along the three coordinate directions shown in Figure 29 does not lead to 
deformation or change in volume. Therefore, it is only unequal normal stress that may cause 
motion or strain in liquids.97 This means that one cannot determine the absolute value of the 
normal stresses from controlled strain experiments, but only normal stress differences because 
the value of p is indeterminate. Equation 2.67 gives the expression for the first normal stress 
difference, N1, and Equation 2.68 gives the expression for the second normal stress difference, 
N2. 
                                                                     
                                                                     
Subtraction of normal stresses eliminates the pressure term leaving only the difference between 
the extra stresses. A negative first normal stress difference tends to force the plates together and 
the positive first normal stress difference tends to push them apart. A negative second normal 
stress difference tends to bulge the fluid at the edges of the plate.86 The most common instance of 
a positive first normal stress difference is the die swell experienced by a melt extruded polymer 
emerging into the atmosphere. In general, if the fluid being sheared is polymeric in nature, the 
normal stresses become unequal in magnitude, and if the fluid is Newtonian their magnitudes 
remain equal.97 
 
 
68 
 
2.6.6. RHEOLOGY OF PARTICULATE SUSPENSIONS 
Suspensions consist of discrete particles dispersed in a liquid medium.61 The 
hydrodynamic disturbance resulting from the presence of particles was first determined by 
Einstein in 1906. The presence of particulates can not only drastically change the measured 
viscosity, but can also introduce non-Newtonian behavior to the fluid under study. The particle 
will modify the velocity distribution in the flowing liquid. Extra energy dissipation will arise 
because of this and will be reflected in a proportional increase in viscosity. The stability of these 
types of fluids are of primary concern if one is to measure the rheological responses of a 
dispersion. A rigorous examination of important assumptions and criteria that need to be met for 
accurate rheological measurements can be found in Macosko.61 In general, for reproducible 
results, the fluid structure or dispersion state should not change over the time-scale of the 
experiment. 
Particle settling is the primary cause for concern as particles larger than approximately 
one micron tend to settle under the influence of gravity alone.98 This can be circumvented by 
either matching the density of the suspending medium to that of the particle or by using a 
medium that is viscous enough to prevent sedimentation. By matching the density of the particle 
and fluid, the buoyant force can be exploited to support the particles in suspension. Similarly, if 
the particles are Brownian, the ratio of gravitational to Brownian forces should be less than unity 
indicating stability from thermal motion. Brownian motion is the name given to the irregular 
movement of pollen in water as observed by Robert Brown.103 If the particle dimensions are 
small enough then the random thermal motion of solvent molecules can transfer momentum to 
the particle. By this analysis, a density difference of greater than 1 g mL-1 leads to the 
sedimentation of particles greater than two microns in diameter.98 On the other hand, if the 
69 
 
medium is viscous enough, the rate of particle settling can be slowed considerably. Depending 
on the viscosity of the solvent, this may be enough to allow for stable measurements to be taken 
over the duration of the testing. An approximate criterion for neglecting the effect of settling in 
spherical particles can be obtained from Stoke?s law.61 
2.6.7. RHEOLOGY OF NON-SPHERICAL PARTICULATE SUSPENSIONS 
The rheology of non-spherical suspensions depends on the particle loading, aspect ratio, 
distribution, and rheology of the suspending medium.97 To begin to understand how elongated 
particles flow, single, non-interacting particles in dilute suspensions were considered. At these 
conditions, the suspension can be essentially thought of under the constraints of an ideal gas. 
Jeffery considered non-interacting particles dispersed in a Newtonian fluid in the absence of 
Brownian motion. Solving the appropriate equations of motion he concluded that non-spherical, 
non-Brownian particles not only translate but rotate indefinitely under the influence of a shearing 
flow.97-98 The rotation was discovered to be periodic with time, known as the Jeffery orbit. 
Particles with large aspect ratios were predicted to rotate rapidly when their longest dimension is 
orthogonal to flow and slowly when it is parallel to flow. The consequence of this type of 
behavior is that the viscosity is also periodic and cycles with time.97 
If Brownian motion cannot be neglected, deviations from the Jeffery orbit for particles 
are observed and must be accounted for probabilistically. In absence of flow, an important 
Brownian phenomena known as the dilute-solution rotary diffusivity, Dr0, can be calculated. The 
rotary diffusivity is a measure of the rate at which a particle reorients by Brownian motion. For 
rods of length L and diameter d, the rotary diffusivity can be estimated from the theory of Doi 
and Edwards and that of Kirkwood and Auer, as shown in Equation 2.69.98, 104-105  
    
                
                                                          
70 
 
From Equation 2.69, it can be seen that there is a logarithmic dependence on the aspect ratio. The 
viscosity of the suspending fluid or solvent is represented ?s, the temperature T, and the 
Boltzmann constant kB. If the solvent is non-Newtonian then the viscosity should be taken in the 
limit of zero-shear as ?0. 
Under the application of shear, the crossover from Brownian to non-Brownian behavior 
for a flowing suspension can be calculated by the magnitude of the rotational Peclet number.98 
Equation 2.70 displays the dimensionless Peclet number, Pe. 
      
 
                                                                       
The shear rate in the numerator should be taken as the lowest value imposed in experiment in 
order to characterize the lower transition limit. Similarly, the rotary diffusivity in the 
denominator can be taken as the dilute solution rotary diffusivity. A value of Pe greater than 
unity indicates a dominating contribution by the imposed shear rate and thus a non-Brownian 
behavior. On the other hand, a value of Pe less than unity indicates that the rotary diffusivity 
dominates and thus Brownian motion is relevant in the imposed shear field. Identifying 
Brownian and non-Brownian behavior is important for interpretation of particle dispersions as 
the stress tensor contains an elastic contribution from Brownian motion.98 In the absence of 
Brownian motion, this contribution is simply neglected. 
Relaxing the criterion for dilute dispersions brings in some additional considerations in 
describing particulate suspensions. To this end, the rheology of rod-like particles is defined by 
unique concentration regimes as shown in Figure 30. 
71 
 
 
Figure 30.  Concentration regimes used to describe rod-like particles. Adapted from Larson, and 
Doi and Edwards.98, 104 
 
The major assumption is that the rods are rigid and inflexible with the absence of attractive 
interactions.104 In the dilute regime the rods are able to rotate freely without interacting with 
neighboring rods. Considering a rod of length L rotating about its center of mass there is a 
volume of approximately L3 that must be free of nearest neighbors. Equation 2.71 shows the 
relationship between the number concentration, ?, and volume fraction of rods, ?. 
    
   
                                                                         
From this equation, one can define transitions between each regime.  Rod-rod interactions can be 
assumed to occur when the number density approaches L-3 but experiment has shown 
disagreement with this prediction. The volume fraction which delineates semi-dilute behavior 
can be seen in Equation 2.72. 
         
 
                                                                   
As shown by Figure 30, the semi-dilute regime is characterized by having neighboring rods 
impeding the rotation of one another, but still allowing translation through the suspending fluid. 
72 
 
Therefore at rod concentrations somewhat above ?0 a rod may be inserted with negligible 
probability of intersecting another and therefore excluded volume is not a factor.98 The effect of 
the rod volume is indicated in Figure 30 by the size of the lines used to represent each rod. While 
increasing concentration in the semi-dilute regime, there lays a point in which the rods have 
trouble isotropically arranging themselves due to excluded volume interactions. This condition 
delineates the semi-dilute from the concentrated isotropic regime as calculated by Equation 2.73. 
                                                                                
In practice, for both rigid and flexible rod-like particles and polymers, these naming conventions 
for various concentration regimes are used. The logic being that in the case of flexibility, the 
swept area would be smaller. Therefore, the transitions predicted for rigid rods would be 
conservative estimates on the higher end of each concentration regime. For non-Brownian rods 
the interpretation of when the crossover from the dilute to semi-dilute occurs is physically taken 
to be the point when the rods begin to influence each other hydrodynamically. It is important to 
note that the crossover is not necessarily at the same concentration that Brownian motion of one 
rod would be affected by its nearest neighbors.98 
Other deviations between Brownian and non-Brownian behavior can be seen in the shear 
viscosity of suspensions. At low shear rates, the theory of Doi and Edwards predicts a large 
increase and domination of the stress contribution from Brownian motion as the concentration is 
taken from dilute to semi-dilute.98 However, in non-Brownian solutions this is not the case and 
the same dramatic viscosity increase is not expected. The modest particle contribution to the 
viscosity was experimentally and theoretically confirmed for fibers with large aspect ratios by 
Yamane et al. and Bibbo.106-107 This occurs because in the absence of Brownian motion the fibers 
readily rotate to align, with the shear flow contributing little to the shear viscosity which is 
73 
 
especially true at large Pe. Therefore, the shear history must be considered when measuring the 
rheological properties on non-Brownian suspensions and is of the utmost importance for 
reproducible results. For repeatability, it is necessary to allow sheared suspensions to relax back 
to isotropic ordering before characterization. 
As the concentration of the particles is increased through the semi-dilute regime there is a 
critical point where three-dimensional network formation occurs known as percolation. This 
onset of network formation is interpreted differently depending on the mode of percolation. 
Rheological percolation occurs when the particle network is sufficient to impede the motion of 
the solvent. If the solvent is a high molecular weight polymer, then percolation occurs when the 
size of the polymer chain is large compared to the separation between the rods or particles.108 
Depending on the length of the polymer, percolation may be a result of entanglement instead of 
molecular contact. This is initially characterized by a solid-like, viscoelastic response over short 
timescales. A second mode of percolation exists in which electrical conductivity can be 
recognized. However, the formation of conductive networks occurs on a different length scale. It 
has been shown that physical contact does not need to occur in CNT systems since the intertube 
distances only need to be close enough for electrons to jump from one tube to another. This 
distance has been estimated to be less than five nanometers.108-109 Being that CNT are 
compromised of some non-metallic tubes, not all particles contribute to network conductivity. 
Thus, in CNT systems electrical percolation can be assumed to occur at higher concentration of 
CNT than rheological percolation. Furthermore, CNT with sidewall defects contribute little to 
the electrical conductivity of the network.108 In general, the larger the aspect ratio, the less 
packing density of the particles and the lower one would expect to find the critical volume 
concentration.110 
74 
 
3. EXPERIMENTAL DETAILS 
3.1. RAW MATERIALS 
 Two types of SWNT were used in the current research: Unidym (Sunnyvale, CA) 187.1, 
187.2, and 187.3 and Southwest Nanotechnologies (SWeNT) (Norman, OK) CG200-L100 and 
L014. Unidym, are high pressure carbon monoxide process (HiPco) SWNT and have a purity of 
99% as determined by thermogravimetric analysis, non-SWNT carbon content of 3%, average 
length and diameter of 1042 nm and 1.24 nm, respectively, as determined by AFM, and D/G 
ratio of 0.1 on both 514 nm and 785 nm lasers. SWeNT CG200 are cobalt-molybdenum catalyst 
process (CoMoCat) SWNT and have a purity of 93% as determined by thermogravimetric 
analysis, non-SWNT carbon content of 14%, average length and diameter of 860 nm and 1.36 
nm, respectively, as determined by AFM, and average D/G ratio of 0.06 and 0.09 on 514 nm and 
785 nm lasers, respectively. The HiPco SWNT will have impurities such as amorphous carbon 
and iron from catalysts, and the CoMoCat SWNT will have impurities such as amorphous 
carbon, cobalt and molybdenum from catalysts, and other non-SWNT carbonaceous material. 
 Dialyzed, lyophilized LSZ from chicken egg white was purchased from Sigma Aldrich 
(St. Louis, MO) and used as delivered. All the following data is given from the manufacturer. 
The molecular mass was calculated as 14,307 Da as determined by the specific amino acid 
sequence. The isoelectric point was given as 11.35, and the extinction coefficient at 280 nm was 
given as 36. The LSZ was determined to be 90% pure via spectroscopy with the impurities being 
buffer salts of sodium acetate and sodium chloride. Powdered TTAB was purchased from Sigma 
Aldrich and used as delivered. The molecular mass was calculated as 336.4 Da as determined by 
the molecular structure. Powdered hydroxypropyl methylcellulose (HPMC) was purchased from 
Sigma Aldrich with approximately 28 to 30 % methoxy groups and 7 to 12 % hydroxypropoxy 
groups and used as delivered. Hydrolized poly(vinyl alcohol) (PVA) with an average molecular 
75 
 
mass of 195 kDa and 99.3% purity was purchased from Sigma Aldrich and used as delivered. It 
should be noted that all solutions and dispersions were made using deionized (DI) water. 
3.2. METHODS OF PREPARATION 
 Preparation of LSZ-SWNT dispersions requires two primary techniques. First, sonication 
is used to disperse SWNT within the LSZ solution. Second, if needed, the bulk mixture will be 
centrifuged to remove any excess material. Other initial steps of preparation were attempted. 
However, due to the large van der Waals force of attraction between SWNT, tip sonication was 
necessary to disperse them with no visible aggregates seen via optical microscopy at 50x 
magnification. 
3.2.1. SONICATION 
Sonication is the technique of applying sound energy to disturb particles within a sample. 
Sonication energy is applied using either an ultrasonic bath or an ultrasonic probe. It can be used 
to disperse or dissolve materials by breaking intermolecular interactions. In this research, 
sonication was used specifically for preparing the initial dispersions of LSZ-SWNT. More 
specifically, it was used to break apart large bundles of CNT being held together via van der 
Waals forces to allow LSZ to intercalate and disperse the SWNT. The sonicator used in this 
research was a Sonics and Materials Inc. (Newtown, CT) Vibra Cell VC 750 operated at 60% 
amplitude with a sonication sequence of 5 s on and 2 s off for 30 minutes. 
3.2.2. CENTRIFUGATION 
Centrifugation is a technique that uses centrifugal force for the separation of mixtures. 
More dense components of the mixture migrate away from the axis of rotation, and less dense 
components of the mixture migrate towards the axis of rotation. The material which collects at 
the bottom of the test tube is known as the precipitate, while the remaining material is called the 
76 
 
supernatant. The precipitate falls to the bottom due to higher density and a larger sedimentation 
coefficient, which is a function of sedimentation velocity and centrifugal acceleration. 
The rate of centrifugation is specified by the acceleration which needs to be applied to the 
sample. This is measured in revolutions per minute or gravitational equivalence. The acceleration 
at which particles precipitate is a function of their size and shape, the size, shape, and interaction 
of the solvent molecule, the density difference between the particles and the liquid, and the 
solvent viscosity. The acceleration of centrifugation can range from 1 to 100,000 times gravity. 
In this research, centrifugation was used to remove excess LSZ and bundles or aggregates 
of SWNT from the bulk dispersions. The centrifuge used in this research was a Fisher Scientific 
(Pittsburgh, PA) accuSpin Micro 17 with capabilities of holding 24 microcentrifuge tubes with 2 
mL volumes and reaching accelerations from 300 to 17,000 x g. For this research the centrifuge 
was operated at 17,000 x g for 3 hours. 
3.3. METHODS OF CHARACTERIZATION 
 Characterization of LSZ-SWNT dispersions was carried out via four primary 
characterization methods: microscopy, spectroscopy, rheology, and thermal analysis. Each 
method was used to determine or probe an aspect of the dispersion state. Many of the methods 
overlap and were used as validation to support other methods results. 
3.3.1. MICROSCOPY 
Microscopy is the scientific field of using microscopes to view samples that cannot be 
seen within the resolution range of the human eye. The three branches of microscopy used in this 
research are optical, electron, and probe microscopy. Optical and electron microscopy involve 
the diffraction, reflection, or refraction of light or electron beams interacting with the specimen 
and the subsequent collection of this scattered light or electron signal in order to create an image. 
77 
 
Probe microscopy can involve the physical contacting or close contacting of a sample where the 
topography is mapped. 
3.3.1.1. ATOMIC FORCE MICROSCOPY 
Atomic force microscopy (AFM) is a form of high-resolution scanning probe 
microscopy. The demonstrated resolution is on the order of fractions of a nanometer. Binnig, 
Quate, and Gerber invented the first AFM in 1986.111 The AFM is used primarily for imaging 
and measuring materials at the nanoscale. 
The AFM consists of a cantilever with a probe tip at its end that is used to scan the 
material surface. When the probe tip is lowered toward the material surface, forces between the 
tip and the sample lead to a deflection of the cantilever. Depending on the material being 
scanned and the scanning mode, forces that are measured in AFM include mechanical contact 
force, van der Waals forces, capillary forces, chemical bonding, electrostatic forces, or magnetic 
forces. The deflection of the cantilever is measured by a laser reflected from the probe tip surface 
to an array of detectors which measures the changes in cantilever position to develop an 
image.111 If the tip scanned at a constant height above the sample, there would be a risk that the 
tip would collide with the surface and not capture relevant data. Therefore, dynamic feedback 
mechanisms are employed to adjust the probe tip-to-sample distance. This feedback is 
accomplished by maintaining a constant force between the tip and the material being scanned.112 
In the current research, the AFM was operated in a static, non-contact mode. In static 
mode, the probe tip is rastered across the surface of the sample, and the contours of the surface 
are measured directly using the deflection of the cantilever. In non-contact mode, the tip of the 
cantilever does not contact the sample surface. The cantilever is instead oscillated at a frequency 
slightly above its resonant frequency where the amplitude of oscillation is typically a few 
78 
 
nanometers. van der Waals and electrostatic forces, which are strongest directly above the 
surface, act to decrease the resonance frequency of the cantilever. This decrease in resonant 
frequency combined with the feedback loop system maintains a constant oscillation amplitude or 
frequency by adjusting the average tip-to-sample distance. Measuring the tip-to-sample distance 
at each raster point allows the AFM to develop a topographic image of the material surface.112 
AFM was specifically used in this research to determine whether SWNT are dispersed as 
individuals or small bundles, and to determine the average aspect ratio of the SWNT while in 
dispersion. The AFM used in this research was a Pacific Nanotechnology (Berkley, CA) Nano-R 
SPM. 
3.3.1.2. OPTICAL MICROSCOPY 
The optical microscope, also known as a light microscope, uses visible light and a system 
of lenses to magnify images. Optical microscopes are popular because the use of visible light 
allows the sample to be viewed directly by the human eye rather than needing detectors and 
signal transducers. Anton van Leeuwenhoek is credited with bringing the microscope to broad 
use in scientific fields around the middle of the 16th century. 
All optical microscopes designed for viewing samples by transmitted light share the same 
basic components of the light path: light source, diaphragm, condenser lens, objective, and 
ocular lens. In addition, the microscope used in the current research contains variable angle 
polarizers, dark and bright field capabilities, and multiple condenser lenses for different viewing 
modes. 
Optical microscopy was specifically used in this research to study the phase behavior and 
transitions of LSZ-SWNT dispersions. The optical microscope used in this research was a Nikon 
(Melville, NY) Eclipse 80i with transmitted light. 
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3.3.1.3. SCANNING ELECTRON MICROSCOPY 
The scanning electron microscope (SEM) is a type of electron microscope that images the 
sample surface by scanning it with a high-energy beam of electrons in a raster scan pattern. The 
electrons interact with the atoms that make up the specimen producing scattering signals that 
contain information about the sample's surface topography. The signals result from interactions 
of the electron beam with atoms at or near the surface of the sample. The SEM was developed 
over several decades by various researchers including Max Knoll, Manfred von Adrenne, 
Charles Oatley, and Gary Stewart.113 
A field emission SEM uses a field emission cathode in the electron gun to provide a 
narrower probing beam. This results in both improved spatial resolution and higher 
magnification capabilities.113 In the field emission SEM used for this research, an electron beam 
is thermionically emitted from an electron gun fitted with a tungsten filament cathode. The 
electron beam is focused by two condenser lenses then passes through a pair of deflector plates 
in the electron column, which deflect the beam allowing it to raster over the sample surface. 
When the electron beam interacts with the sample, the electrons lose energy by repeated 
random scattering and absorption within the specimen, which can extend from 0.1 ?m to 5 ?m 
into the surface. The energy exchange between the electron beam and the sample results in the 
reflection of high-energy electrons by elastic scattering, emission of secondary electrons by 
inelastic scattering and the emission of electromagnetic radiation, each of which are picked up by 
detectors. Electronic amplifiers are then used to amplify the detector signal which is displayed as 
variations in brightness. Therefore, the resulting signal from the detectors is a distribution map of 
the intensity of the electrons being emitted from the scanned area of the specimen.114  
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Magnification in an SEM is unlike optical or transmission electron microscopes. 
Magnification in the SEM is not a function of the power of the objective lens. Rather, 
magnification results from the ratio of the dimensions of the raster on the specimen. Therefore, 
higher magnification results from reducing the size and speed of the raster on the specimen.114 
SEM was specifically used in this research to determine qualitatively if there was a 
molecular interaction between LSZ and SWNT, and to aid in determining quantitatively whether 
SWNT are dispersed aggregates or small bundles. The SEM used in this research was a JEOL 
(Tokyo, Japan) 7000F FE-SEM with energy dispersive X-ray spectroscopy capabilities. 
3.3.1.4. TRANSMISSION ELECTRON MICROSCOPY 
Transmission electron microscopy (TEM) is an electron microscopy technique where a 
beam of electrons is transmitted through a specimen. The beam of electrons interacts with the 
specimen as it passes through, and an image is formed from the interaction of the electrons 
transmitted through the specimen. The image is then magnified and focused onto an imaging 
detector. The first TEM was built by Max Knoll and Ernst Ruska in 1931.115 
The TEM is capable of imaging at a significantly higher resolution than light 
microscopes, owing to the small frequency wavelength of electrons. At lower magnifications 
TEM image contrast is determined by the absorption of electrons in the sample. This is due to the 
thickness and composition of the sample material. At higher magnifications, complex wave 
interactions will modulate the intensity of the image.116 TEM can be used to identify or observe 
modulations in chemical identity, crystal orientation, and electronic structure, as well as 
transmission imaging. 
The TEM used for this research consists of a tungsten emission source connected to an 
electron gun. By connecting this emission source to a high voltage source the electron gun emits 
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electrons by thermionic electron emission. Electromagnetic lenses are then used to bend the 
electrons allowing for variable focusing power. Also, electrostatic fields can be used to cause the 
electrons to be deflected at a constant angle. After the electron beam has been properly 
transmitted through the sample, an electron imaging detector signal is focused and magnified for 
the image. 
TEM was used specifically in this research to aid in characterizing LSZ-SWNT 
dispersions as well as qualitatively imaging the interaction between LSZ and SWNT. The TEM 
used in this research was Zeiss (Thornwood, NY) EM 10 TEM. 
3.3.2. RHEOLOGY 
Rheology is the scientific field that studies the deformation and flow of materials. It is a 
branch of physics due to the fact that many of the variables used are from the field of mechanics. 
Rheology studies both the flow behavior of fluids and the deformation behavior of solids. The 
connection between the two is that at after long relaxation times, even solid-like materials will 
flow or deform, such as the creeping of stained glass windows. The behavior of real materials is 
based on the combination of the ideal behavior of fluids and solids. When a material such as 
rubber is loaded in shear or extension an instantaneous deformation is followed by a continuous 
deformation or ?creep?. When the load is removed, part of the deformation recovers instantly 
while some deformation recovers with time and still other deformation is permanent. The time 
dependant response is known as viscoelasticity. When defined by stress relaxation, the stress of a 
purely viscous liquid will instantly relax to zero after the subjected strain, while a purely elastic 
solid will show no relaxation.61 In this research, rheology was used to determine the molecular 
structure by probing the dispersion state using four different tests: amplitude sweep, frequency 
sweep, transient or start-up flow test, and flow curve or steady shear test. The rheometer used in 
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this research was an Anton Paar (Ashland, VA) Physica MCR 301 with attachments for 
temperature control. Rheology for this research was run at 10oC over three separate loads with 
three runs of each test for each load. To prevent evaporation a water-cooled Peltier hood was 
used, and all data was collected above the torque transducer limit of 0.1 ?Nm. 
3.3.2.1. AMPLITUDE SWEEP TEST 
 An amplitude sweep test is an oscillatory test with variable wave amplitude and constant 
wave frequency. An amplitude sweep is used to determine the linear viscoelastic range and limit 
of linear viscoelasticity of a material. The linear viscoelastic range is determined by range of 
amplitudes of strain for which the storage and loss modulii show a constant plateau value. 
Linear-elastic behavior is found whenever Hooke?s law applies as shown in Equation 3.1, and 
linear-viscous behavior is found whenever Newton?s law applies as shown in Equation 3.2.100 
  
                                                                                     
  
                                                                                      
In these equations, ?A is the variable stress amplitude, ?A is the variable strain amplitude, and     
is the variable shear amplitude. The limit of the linear viscoelastic range is the point at which the 
storage modulus deviates significantly from the plateau of the linear viscoelastic range. The 
significance of the limit of linear viscoelasticity is that at strain amplitudes lower than the limit, 
the structure of the material is stable or undisturbed. However, at strains above the limit, the 
structure of the sample could be deemed to have been irreversibly changed or disrupted. 
 The microstructural behavior of a material can also be elucidated from the linear 
viscoelastic range. If the storage modulus is larger than the loss modulus, then elastic behavior 
dominates over viscous behavior and the material is a viscous solid; indicating the microstructure 
83 
 
has a certain amount of rigidity. Even materials with low viscosity will show this type of 
response if they have a stable chemical network which gives it rigidity. If the loss modulus is 
larger than the storage modulus, then viscous behavior dominates elastic behavior and the 
material shows liquid or sol character. Materials which are highly viscous will even show this 
behavior if they are lacking the chemical or physical network of forces which would stabilize the 
material.100 For this research, the amplitude test was run at an angular frequency of 10 s-1 from 
0.01% to 100% strain. 
3.3.2.2. FREQUENCY SWEEP TEST 
 A frequency sweep test is a measure of the viscoelastic oscillatory response with variable 
wave frequency and constant wave amplitude. The importance of the frequency sweep is that it 
probes the time-dependant shear behavior of materials. Short-term behavior is probed at high 
frequency by rapid movements, and long-term behavior is probed at low frequency by slow 
movements. Prior to running a frequency sweep, an amplitude sweep must be run in order to 
determine what constant wave amplitude (strain) to run that is not greater than the strain limit of 
linear viscoelasticity. 
 Interpretation of frequency sweep data can be counterintuitive unless the mathematics 
behind each variable is understood. In general, the storage and loss modulii will increase as 
frequency increases indicating the material becomes more rigid. The dominance of either the 
storage or loss modulii at each frequency will indicate the character of the material; whether or 
not it is more solid or more fluid. At the same time as the storage and loss modulii increase, the 
complex viscosity decreases indicating the resistance to flow of the material decreases with 
increasing frequency. Mathematically, the complex viscosity is the quotient of the complex 
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modulus divided by the frequency. Therefore, as the frequency is increased, the complex 
viscosity will decrease. 
With increasing frequency, the internal structure of the physical network becomes more 
inflexible and rigid. In this rigid structure, more deformation energy is stored than lost so the 
elastic behavior becomes increasingly dominant, thus the storage modulus will become more 
dominant. At the same time, the portion of the lost deformation energy decreases, therefore 
reducing the importance of the viscous behavior and causing the loss modulus to become less 
important. Due to the intermolecular interaction in dispersions, such as those in this research, the 
elastic behavior dominates over the viscous and the sample shows elastic character. For a stable 
dispersion, the loss modulus and storage modulus will be relatively parallel straight lines with 
shallow slopes.100 For this research, frequency sweep tests were run at 2% strain from an angular 
frequency of 0.01s-1 to 100 s-1. 
3.3.2.3. TRANSIENT TEST 
 A transient test is a flow test with constant shear rate. This test is used to find the time 
necessary to overcome transient effects and reach a steady state viscosity at the given shear rate. 
For a transient test, the time of the test must be sufficiently long enough. Otherwise, start effects 
or time-dependent transition effects will result in the transient viscosity rather than the steady-
state viscosity, which is needed to develop flow curves. 
 Transient tests can also be used to identify phenomena such as low shear aggregation or 
low shear flocculation. Aggregation and flocculation both result in molecules ?sticking? to one 
another. However, aggregates require a large amount of energy to be broken apart and are seen 
as a primary energy well in DLVO theory, whereas flocs can be broken easily and are seen as a 
secondary energy minimum in DLVO theory; in the remainder of this section, aggregates will be 
85 
 
described. For some dispersions or suspensions, the amount of energy needed to move the 
molecular constituents close enough to one another to have them aggregate, or stick to one 
another, is very low. Low shear aggregation occurs when the shear energy causes constituents 
within the dispersion or suspension to overcome solvation or repulsive forces and attract to one 
another. As molecules begin to attract to one another, a snow ball effect occurs where small 
aggregates continuously join to eventually form macroscopic aggregates. This is rheologically 
seen by increasing viscosity with time at a constant, low shear rate. The viscosity will slowly 
increase then begin to exponentially increase as larger and larger aggregates are formed. For this 
research, the transient test was run at a shear rate of 0.1 s-1 for 1,000 s. 
3.3.2.4. FLOW CURVE TEST 
 A flow curve test is a flow test with specific variable shear rates taken over a specific 
varying time frame. As discussed in the previous section, transient effects can invalidate the 
steady-shear viscosity measurements. Therefore, transient test are run at the lowest applicable 
shear rate to determine the longest time needed for the shear rates tested. After determination of 
this testing period, the time frame can be reduced as the shear rate is increased. As a general rule 
of thumb, the time to sample the viscosity at a specific shear rate is equal to the reciprocal of the 
shear rate. 
 From the data collected of viscosity at certain shear rates, viscosity or flow curves are 
developed which show the dependence of viscosity for a material on shear rate. There are four 
common responses of viscosity versus shear rate: Bingham plastic, shear thinning or 
pseudoplastic, shear thickening or dilatants, and Newtonian. A Bingham plastic initially responds 
to an applied shear stress by deforming but not flowing. However, when the shear stress exceeds 
a critical value, known as the yield stress, the material will flow in the same way as a Newtonian 
86 
 
fluid. Pseudoplastic fluids are those where viscosity is a decreasing function of shear rate, or 
more simply offer less resistance to flow at higher shear rates. Dilatant fluids are those where the 
viscosity is an increasing function of shear rate, or more simply, the fluids resistance to shearing 
becomes larger the faster it is sheared. Finally, a Newtonian fluid viscosity is independent of 
shear rate. It should be noted that for all testing methods temperature is a variable which can alter 
the microstructure of the material. For this research, flow curves were run with a time sampling 
interval dependent upon the results from the transient tests from shear rates of 0.01 s-1 to 100 s-1. 
3.3.3. SPECTROSCOPY 
Spectroscopy is the study of the interaction between materials and radiated energy. 
Spectroscopy originated through the study of visible light dispersed according to its wavelength 
by a prism. However, the concept has expanded to comprise any interaction with radiative 
energy. Spectroscopy types are distinguished by the type of radiative energy involved in the 
interaction, such as, electromagnetic radiation, particle radiation, and acoustic radiated pressure 
waves. Types of spectroscopy can also be distinguished by the nature of the interaction between 
the energy and the material, such as, absorption, emission, elastic scattering, inelastic scattering, 
and impedance. 
3.3.3.1. ULTRAVIOLET ? VISIBLE SPECTROSCOPY 
Ultraviolet-visible spectroscopy (UV-vis) refers to absorption spectroscopy in the 
ultraviolet-visible spectral region. This means it uses light in the visible and adjacent near-UV 
range. The absorption or reflectance in the visible range directly affects the perceived color of 
the chemicals involved. In this region of the electromagnetic spectrum, molecules undergo 
electronic transitions meaning absorption measures transitions from the ground state to the 
excited state of the sample. 
87 
 
UV-vis is routinely used in the quantitative determination of solutions of biological 
macromolecules. The quantitative determination of solutions is done via the Beer-Lambert Law. 
The Beer-Lambert law states that the absorbance of a solution is directly proportional to the 
concentration of the absorbing species in the solution and the path length, as shown in Equation 
3.3.  
                                                                                     
In Equation 3.3, A is the measured absorbance, I0 is the reference intensity of the incident light, I 
is the transmitted intensity, L the pathlength through the sample, and c the concentration of the 
absorbing species. For each species, ? is a constant known as the molar absorptivity or extinction 
coefficient and is a fundamental molecular property. Thus, for a fixed path length and known 
concentration, UV-vis can be used to determine the extinction coefficient of the absorbent 
molecule in the solution. This allows for development of calibration curves showing absorbance 
versus concentration.117 
 UV-vis was used specifically in this research to characterize the LSZ solutions used, 
develop calibration curves, determine the enzymatic activity of LSZ solutions and LSZ-SWNT 
dispersions, and determine interactions changes in dispersions. The UV-vis used for this research 
is a Cary (Santa Clara, CA) 3E UV-Vis Spectrophotometer. 
3.3.3.2. CIRCULAR DICHROIC SPECTROSCOPY 
Circular dichroism (CD) refers to the differential absorption of left and right circularly 
polarized light. This phenomenon is exhibited in the absorption bands of optically active chiral 
molecules. CD spectroscopy has a wide range of applications in many different fields. Most 
notably, ultraviolet CD is used to investigate the secondary structure of proteins. Ultraviolet-
visible CD is used to investigate charge-transfer transitions. Near-infrared CD is used to 
88 
 
investigate geometric and electronic structure. Infrared circular dichroism is used for structural 
and vibrational studies.118 
CD is exhibited by biological molecules, because of their dextrorotary (right-handed) and 
levorotary (left-handed) constituents. More importantly, secondary and tertiary structure will 
impart a distinct CD spectrum to its respective molecule. Therefore, the alpha helix of proteins 
and the double helix of nucleic acids have CD spectral signatures unique to their structures, 
much like a human finger print.118 
CD spectra can be readily used to estimate the fraction of a molecule that is in the alpha-
helix conformation or the beta-sheet conformation. It can also be used to study how the 
secondary structure of a molecule changes as a function of temperature; in this way it can reveal 
important thermodynamic information about the molecule, such as the enthalpy or Gibbs free 
energy of denaturation.118 
CD was specifically used in this research to determine the effect that the molecular 
interaction between LSZ and SWNT has on the secondary and tertiary structure, and thereby the 
activity, of LSZ. The CD used in this research was a JASCO (Easton, MD) J-810 
Spectropolarimeter. 
3.3.3.3. FOURIER-TRANSFORM INFRARED SPECTROSCOPY 
Fourier transform infrared spectroscopy (FT-IR) is a spectroscopic technique which is 
used to obtain an infrared spectrum of absorption or emission of a solid, liquid, or gas. An FT-IR 
spectrometer simultaneously collects raw spectral data in a wide spectral range. The Fourier-
Transform algorithm is required to convert the raw data collected into the actual spectrum. 
Rather than shining a monochromatic beam of light at the sample, FT-IR shines a beam 
containing many different frequencies of light at once, and measures how much of that beam is 
89 
 
absorbed by the sample. Then, the beam is modified to contain a different combination of 
frequencies, giving a second data point. This process is repeated many times. Afterwards, a 
computer takes all the data and works backwards using the Fourier-Transform to infer what the 
absorption is at each wavelength.119 
The FT-IR beam is generated by starting with a broadband light source containing the full 
spectrum of wavelengths to be measured. The light shines into a certain configuration of mirrors 
that allows some wavelengths to pass through but blocks others. The beam is then modified for 
each new data point by moving one of the mirrors thereby changing the set of wavelengths that 
pass through. Computer processing then turns the raw data into the desired result of light 
absorption for each wavelength.120 
FT-IR was specifically used in this research to study the chemical bonding structure 
found in the LSZ-SWNT dispersions. The material used for FT-IR was loaded in two separate 
methods; either as effluent from the thermogravimetric analysis oven, or as an undisturbed solid 
or liquid sample for transmission or ATR. The FT-IR used in this research is a Thermo Scientific 
(Waltham, MA) Nicolet iS10 FT-IR with SMART iTR and ATR. 
3.3.3.4. RAMAN SPECTROSCOPY 
 Raman spectroscopy, named after Sir Chandrasekhara Venkata Raman, is a 
spectroscopic technique used to study vibrational, rotational, and other low-frequency modes in a 
system. It relies on inelastic, or Raman scattering, of monochromatic light. The monochromatic 
light is usually from a laser in the spectral range needed during experimentation. The laser light 
interacts with molecular vibrations, phonons, or other excitations in the system, resulting in the 
energy of the laser photons being shifted up or down. The shift in energy gives information about 
the vibrational modes in the system.121 
90 
 
Spontaneous Raman scattering is typically very weak, and as a result the main difficulty 
of Raman spectroscopy is separating the inelastically scattered light from the elastically, 
Rayleigh, scattered light. Modern instrumentation typically uses filters for laser rejection and 
spectrographs ? axial transmissive, Czerny-Turner, or Fourier-Transform detectors. There are 
also a number of advanced types of Raman spectroscopy to enhance the weak inelastic scattering 
signal, including surface-enhanced Raman, resonance Raman, tip-enhanced Raman, polarized 
Raman, stimulated emission Raman, transmission Raman, spatially offset Raman, and hyper-
Raman.121-122 
The Raman effect occurs when light impinges upon a molecule and interacts with the 
electron cloud and the bonds of that molecule. For the spontaneous Raman effect, a photon 
excites the molecule from the ground state to a virtual energy state. When the molecule relaxes it 
emits a photon and it returns to a different rotational or vibrational state. The difference in 
energy between the original state and this new state leads to a shift in the emitted photon 
frequency away from the excitation wavelength. If the final vibrational state of the molecule is 
more energetic than the initial state, then the emitted photon will be shifted to a lower frequency 
in order for the total energy of the system to remain balanced. This shift in frequency is 
designated as a Stokes shift. If the final vibrational state is less energetic than the initial state, 
then the emitted photon will be shifted to a higher frequency, and this is designated as an Anti-
Stokes shift. Raman scattering is an example of inelastic scattering because of the energy transfer 
between the photons and the molecules during their interaction. It should be noted that the 
Raman effect is a light scattering phenomenon which should not be confused with absorption 
where the molecule is excited to a discrete, real energy level.121 
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Raman spectroscopy was specifically used in this research to study the changes which 
occur to the SWNT through addition of LSZ elucidating interactions, charge transfer, and 
possible processing fractionation. A Renishaw (Gloucesterchire, UK) in Via microRaman was 
used for Raman spectroscopy. Samples were prepared by drying in a vacuum over for 24 hours. 
The samples were then placed on a glass slide by suspending on double-sided tape. Prior to 
running test on all samples, each laser was calibrated using a silicon reference. Each sample was 
scanned by a 514 nm and 785 nm laser to probe both the semi-conducting and metallic CNT 
present. Each run by each laser consisted of 10 scans over a Raman shift from 100 cm-1 to 3200 
cm-1. 
3.3.3.5. FLUORESCENCE SPECTROSCOPY 
Fluorescence spectroscopy is a type of electromagnetic spectroscopy which analyzes the 
fluorescence from a sample. It involves using a beam of light that excites the electrons in 
molecules of certain compounds and causes them to emit light, or fluoresce. Fluorescence 
spectroscopy is primarily concerned with electronic and vibrational energy levels within a 
molecule or compound. Generally, the species being examined has a ground electronic state and 
an excited electronic state of higher energy. Within each of these electronic states are various 
vibrational states.123 
In fluorescence spectroscopy, the species is first excited from its ground electronic state 
to one of the various vibrational states of a higher energy level. Collisions with other molecules 
cause the excited molecule to lose vibrational energy until it reaches the lowest vibrational state 
of the excited energy level. The molecule then drops down to one of the various vibrational 
levels of the ground electronic state which emits a photon in the process. As molecules may drop 
down into any of several vibrational levels in the ground state, the emitted photons will have 
92 
 
different energies, and thus frequencies. Therefore, by analyzing the different frequencies of 
light emitted in fluorescent spectroscopy, along with their relative intensities, the structure of the 
different vibrational levels can be determined.123-124 
Fluorophores are more likely to be excited by photons if the transition moment of the 
fluorophore is parallel to the electric vector of the photon. For fluorophores in solution this 
means that the intensity and polarization of the emitted light is dependent on rotational diffusion. 
Therefore, anisotropy measurements can be used to investigate how freely a fluorescent 
molecule moves in a particular environment, and is of particular use in determining binding 
events of biological molecules.123-124 
In a typical experiment, the different wavelengths of fluorescent light emitted by a 
sample are measured using a monochromator, holding the excitation light at a constant 
wavelength. This is called an emission spectrum. An excitation spectrum is the opposite, where 
the emission light is held at a constant wavelength, and the excitation light is scanned through 
many different wavelengths. Both types of experiments use the same setup. The light from an 
excitation source passes through a filter and strikes the sample. A portion of the incident light is 
absorbed by the sample and results in the fluorescence of any molecules at the excitation 
wavelength. The fluorescent light is emitted in all directions. Some of this fluorescent light 
passes through a second filter and reaches a detector, which is usually placed at 90? to the 
incident light beam to minimize the risk of transmitted or reflected incident light reaching the 
detector. Various light sources may be used as excitation sources, including lasers, photodiodes, 
and lamps.123 
 Fluorescence spectroscopy and anisotropy were used in the current research to determine 
the specific interaction between LSZ and SWNT as well as their direct binding interaction. A 
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Perkin Elmer (Waltham, MA) LS 55 Luminescence Spectrometer was used for fluorescence 
measurements. Emission spectra were taken at room temperature scanning from 300 nm to 500 
nm with a 0.5 nm resolution and a scan rate of 500 nm/min with an incident angle of 90o. The 
excitation wavelength was set to 280 nm to probe the quenching of the tryptophan within LSZ 
when coupled with SWNT. Anisotropic fluorescence data was collected at an excitation 
wavelength of 295 nm with an emission wavelength of 345 nm. The excitation and emission slits 
were each set at 15 nm where a G-factor was calculated at 1.581. 
3.3.3.6. ENERGY DISPERSIVE X-RAY SPECTROSCOPY 
Energy-dispersive X-ray spectroscopy (EDS) is an analytical technique used for the 
elemental analysis or chemical characterization of a sample. It relies on the investigation of an 
interaction of some source of X-ray excitation and a sample. Its characterization capabilities are 
due in large part to the fundamental principle that each element has a unique atomic structure 
allowing unique set of peaks on its X-ray spectrum. To stimulate the emission of characteristic 
X-rays from a specimen, a high-energy beam of charged particles such as electrons, protons, or a 
beam of X-rays, is focused into the sample being studied. At rest, an atom within the sample 
contains ground, unexcited state electrons in discrete energy levels.114 The incident beam excites 
an electron in an inner shell, ejecting it from the shell while creating a void where the electron 
was. An electron from an outer, higher-energy shell then fills the hole, and the difference in 
energy between the higher-energy shell and the lower energy shell may be released in the form 
of an X-ray.114 The number and energy of the X-rays emitted from a specimen can be measured 
by an energy-dispersive spectrometer. The energy of the X-rays are characteristic of the 
difference in energy between the two shells, and of the atomic structure of the element from 
which they were emitted, this allows the elemental composition of the specimen to be measured. 
94 
 
The four primary components of the EDS setup are the excitation source, the X-ray detector, the 
pulse processor, and the analyzer.114 
Accuracy of EDS spectrum can be affected by various factors. Many elements will have 
overlapping peaks so the accuracy of the spectrum can also be affected by the nature of the 
sample. X-rays can be generated by any atom in the sample that is sufficiently excited by the 
incoming beam. These X-rays are emitted in any direction, and so they may not all escape the 
sample. The likelihood of an X-ray escaping the specimen, and thus being available to detect and 
measure, depends on the energy of the X-ray and the amount and density of material it has to 
pass through. This can result in reduced accuracy in inhomogeneous and rough samples.114 
The EDS in this research was used to determine molecular constituents of complex 
mixtures of LSZ-SWNT, LSZ-TTAB-SWNT, and other compounds. A JEOL (Tokyo, Japan) 
7000F FE-SEM with energy dispersive X-ray spectroscopy was used for performing EDS 
analysis. 
3.3.4. THERMOGRAVIMETRIC ANALYSIS 
Thermogravimetric analysis (TGA) is a testing method performed on materials which 
determine changes in weight with relation to changes in temperature. TGA is most commonly 
used for determination of characteristics of materials or mixtures such as degradation 
temperatures, concentration of mixture components, and determination of crystallization of 
components with a mixture among others. 
The analyzer consists of a high-precision balance with a pan for loading the sample. The 
sample is placed in a small electrically heated oven with a thermocouple to accurately measure 
the temperature. The atmosphere within the oven may be an inert gas, to prevent oxidation or 
other undesired reactions, or air to allow for complete combustion of all components. A 
95 
 
computer is used to control the instrument. Analysis is carried out by raising the temperature of 
the sample gradually and plotting mass, or weight percent, against temperature. 
The TGA used in this research was used to characterize the SWNT and determine 
concentrations of LSZ and SWNT in evaporated samples prior to fiber spinning or film coating. 
The effluent vapor could then be sent to an FT-IR for further analysis. The TGA used in this 
research was a TA Instruments (New Castle, DE) TGA Q50. 
3.3.5. TURBIDIMETRIC ANALYSIS 
Turbidimetry or turbidimetric analysis is the process of measuring the loss of intensity of 
transmitted light due to the scattering effect of particles suspended in it. Turbidimetry can be 
used in biology to find the number of cells in a solution and is usually carried out in a UV-vis 
spectrophotometer. For processing, light is passed through a filter creating a light of known 
wavelength which is then passed through a cuvette containing a solution of interest. A detector 
then collects the light which passes through the cuvette. A measurement is then given for the 
amount of absorbed or transmitted light.125 
The turbidimetric analysis was used to determine the lytic activity of all dispersions and 
macroscopic assemblies. A Cary (Santa Clara, CA) 3E UV-vis Spectrophotometer was used for 
the turbidimetric analysis of this research. First, a 66mM solution of potassium phosphate buffer 
was adjusted to a pH of 6.24 with potassium hydroxide at room temperature. Next, a bacterial 
cell suspension in the potassium phosphate buffer containing 0.015 wt. % Micrococcus 
lysodeikticus (Sigma Aldrich) was prepared. Next, 1 cm path length quartz cuvettes were filled 
with 2.5 mL of bacterial suspension, at which point 0.1 mL of buffer solution or liquid 
dispersions are added. Finally UV-vis is performed on the buffered bacterial suspension followed 
96 
 
by UV-vis of a buffered bacterial suspension containing the liquid dispersions where kinetic 
scans are at 450 nm for 5 min. 
3.3.6. ULTIMATE TENSILE STRENGTH ANALYSIS 
Ultimate strength tensile testing is a fundamental materials science test in which a sample 
is subjected to uniaxial tension until failure. Properties that are directly measured via a tensile 
test are the load and the elongation. From these measurements the following properties can also 
be determined: Young's modulus, Poisson's ratio, yield strength, tensile strength, maximum 
elongation, toughness, and strain-hardening characteristics, among others. 
The most common testing machine used in tensile testing is the universal testing 
machine. This type of machine has two crossheads. One is adjusted for the length of the 
specimen and the other is driven to apply tension to the test specimen. The machine must have 
the proper capabilities for the test specimen being tested. There are three main parameters: force 
capacity, speed, and precision and accuracy.126 Force capacity is important for ultimate strength 
testing because the machine must be capable of generating enough force to fracture the 
specimen. The crosshead speed is also important as it must be able to be set fast or slow enough 
to properly mimic the actual application. Finally, the machine must be able to accurately and 
precisely measure the gauge length and forces applied; for instance, a large machine that is 
designed to measure long elongations may not work with a brittle material that experiences short 
elongations prior to fracturing. Alignment of the test specimen in the testing machine is critical, 
because if the specimen is misaligned the testing machine will exert a non-linear force on the 
specimen creating data capable of being misinterpreted.126 
The test process involves placing the test specimen in the testing machine and applying 
tension to it until it fractures. During the application of tension, the elongation of the gauge 
97 
 
section is recorded against the applied force. The data is manipulated so that it is not specific to 
the geometry of the test sample. The elongation measurement is used to calculate the engineering 
strain, ?. The force measurement is used to calculate the engineering stress, ?. The machine does 
these calculations as the force increases, so that the data points can be graphed into a stress-strain 
curve. 
Tensile testing was used in this research to determine the mechanical properties of the 
macroscopic assemblies produced in this research. An Instron (Norwood, MA) 5565 Calibration 
Lab was used as the testing machine. After the fibers were spun, samples were glued into a 
testing frame with a gauge length of 26 mm. The load cell used for this testing was 100 cN with 
a cross-head separation speed of 1.0 mm/min. The load and gauge length were balanced and 
zeroed before each run. Test data collected for each sample were load, extension, time, and 
strain. Analysis to determine specific mechanical properties was done using Excel. 
3.3.7. ELECTRICAL RESISTIVITY ANALYSIS 
Electrical resistivity is an electrical property of a material that quantifies how strongly the 
material opposes the flow of electric current. A low resistivity indicates a material that readily 
allows the movement of electric charge whereas a high resistivity indicates a material that will 
not allow the movement of an electric charge. 
Quantum mechanics states that electrons in an atom cannot take on any arbitrary energy 
value. Rather, there are fixed energy levels which the electrons can occupy, and values in 
between these levels are impossible.127 When a large number of such allowed energy levels are 
spaced close enough together then it can be said that the energy levels together form an "energy 
band". There can be many such energy bands in a material, depending on the atomic number and 
their distribution.128 Two such bands important in the discussion of resistivity or conductivity of 
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materials are the valence band and the conduction band. Electrons in the conduction band may 
move freely throughout the material in the presence of an electrical field. In insulators and 
semiconductors, the atoms influence each other in such a way that between the valence band and 
the conduction band there exist a band-gap of energy levels, which the electrons cannot occupy. 
In order for a current to flow across this band-gap, a relatively large amount of energy must be 
furnished to an electron for it to leap across into the conduction band. Thus, large voltages can 
yield relatively small currents. Therefore, the measure of electrical resistivity of a material is 
influenced by the molecular make-up of the material, the surroundings of the material, and the 
power of the electrical charge.127-128 
 The electrical resistivity of the macroscopic assemblies in this research were measured by 
the 2-wire Ohms test method using an HP 34401A Multimeter (Palo Alto, CA). The fibers were 
placed on slides and Pelco? colloidal silver paste from Ted Pella, Inc. (Reading, PA) was used 
to create the lead contacts which were separated about ~ 1mm apart. 
3.4. METHODS OF MACROSCOPIC ASSEMBLY 
 Macroscopic assembly of nanomaterials can be carried out in a myriad of methods: fiber 
spinning, film drying, charge layering, spray coating, chemical layering, etc. In each method, it is 
desired to maintain the nanostructured properties of each system through processing. Therefore, 
it is necessary to understand how each processing method affects and changes the dispersion 
state. In the current research, wet and dry fiber spinning and film drying have been completed. 
3.4.1. FIBER SPINNING 
 Traditional fiber spinning techniques include melt and solution spinning which can be dry  
or wet spun. In addition, techniques such as solid state drawing, solid state extrusion, gel 
spinning, and a combination of solid state drawing and tensile drawing have been used 
99 
 
successfully to obtain mechanically stable fibers. In order to process these fibers, solvents are 
used to cause solidification of the fiber solution, and after solidification the solvent must be dried 
off. However, most solvents used for these solutions are not sufficiently volatile to be easily 
removed. To prevent this problem, wet solution spinning uses a non-solvent (coagulant) to 
extract the solution solvent in a process known as coagulation. After coagulation of the fiber, it 
can be washed and/or heat treated in order to achieve desired properties.129 
 By adequately understanding the physical process of fiber formation, the physical 
properties of the fiber will be able to be determined by the chemical nature of the solution rather 
than by the coagulation process. Wet solution spinning involves the investigation of two 
problems: the structure formation in various processing conditions, and the relationship between 
structure and macroscopic properties.129 Understanding these problems is very difficult since 
heat and mass transfer accompany phase transition in the coagulation, drying, and heat treatment 
processes. 
 Fiber solidification occurs through the coagulation process. The spinning solution 
undergoes a change in composition depending on the outward flux of the solvent and the inward 
flux of the coagulant. Thus, the coagulation process and the resulting morphology and 
mechanical properties are controlled by thermodynamic and transport effects, such as phase 
boundary shifts and flux ratios. These complex issues are both difficult to model and difficult to 
predict. Therefore, rather than study these directly, research has been done on variables which 
influence each to determine final fiber properties.129 Temperature and coagulant concentration 
are the two most common variables. Increasing temperature of the spinning bath will increase the 
solubility of the system and also increase the diffusion coefficients and fluxes. It was found that 
with increasing temperature fibers possessed better mechanical properties despite surface 
100 
 
defects.129 This indicates the internal structure of the fiber was quickly coagulated not allowing 
for void formation. Increasing concentration of the coagulant will speed the mass transfer by 
increasing the inward coagulant flux and outward solvent flux. It has been shown that with 
increasing coagulant concentration fibers were more homogenous at the surface and had 
mechanical properties that were dependant on the temperature of the coagulant.129 This indicates 
that the increased concentration of the coagulant creates a skin at the outer most layer which 
prevents voids and pits from forming. It was also proposed by Hancock et al. that the mechanism 
of surface void formation was a function of interfacial instability due to capillary forces between 
the solvent and coagulant. Fiber post-treatments have also been studied to determine changes in 
morphology or mechanical stability. However, it has been thoroughly documented that when 
using a volatile coagulant, post-treatment does not result in morphological or mechanical 
changes to the fiber.129-130 Therefore selection of coagulants is important and should be 
determined through experimentation. 
 In the current research fibers were spun by wet and dry spinning. For each, dispersions 
were extruded through a 21-gauge, stainless steel needle using a Harvard apparatus syringe pump 
with a stainless steel, 10 mL syringe at a volumetric rate of 0.5 mL per minute. Wet spinning of 
fibers was carried out by extrusion of dispersions into a PVA solution at room temperature. The 
coagulant solution speed varied from 50 to 150 revolutions per minutes. After coagulation, the 
fibers were removed from the PVA bath and washed in DI water. The fibers were then hung to 
be dried at room temperature. Dry spinning of fibers was carried out by extrusion of dispersions 
onto a Teflon mold. The dispersions were then allowed to dry at room temperature prior to 
removal from the mold. Post-processing of dry spun fibers was carried out by submersion of the 
fiber in methanol at room temperature for 24 hours. After submersion, the fibers were removed 
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and drawn at a ratio of 6:1. Drawing was carried out by taping the ends of a 3 cm section of fiber 
to posts on a measured rail system. The posts were then separated to a distance of 18 cm. 
3.4.2. FILM DRYING 
 Film drying of dispersions is a key processing technique for macroscopic assembly of 
nanomaterials. Film drying can consists of single drop-dried layers of solution or multiple layers 
of solution created via multiple drying steps or through layer interactions holding each layer 
separately. Regardless of the type of film, the structure and properties of the final product are 
influenced by the dynamics which take place when being processed. 
 Similar to the process of fiber spinning, film drying is theoretically governed by the 
thermodynamics and transport phenomena of the multicomponent system. The removal of 
solvents from a film is a complex heat and mass transfer process. Temperature and 
concentration, therefore, are of critical importance in creating robust films. Temperature will 
directly affect the thermodynamics and kinetics of transport. Increasing the temperature of a 
drying system will increase the diffusion rate thereby reducing the drying time of the film. 
However, increases in diffusion rate will cause internal forces between the evaporating solvent 
and non-evaporating mixture to be strained which could adversely affect the final structure of the 
film.131 Increasing diffusion rate will also cause the vapor-liquid phase boundary to move at a 
more rapid pace causing non-homogeneity in the finalized film. Altering the concentration of the 
system is an even more complex problem. The concentration of the solvent, film mixture, or 
ambient air could be altered which will change the way in which the film dries. Increasing the 
concentration of the solvent at a fixed dispersion concentration will lead to less mechanically 
stable films which are more homogenous. This is due to the reduced mass of film mixture which 
eventually becomes the film, and it is for this reason the film is more homogenous; there is not a 
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sufficient film material to impede evaporation which creates homogenous layering effects.132 
Increasing the concentration of the film mixture will be not as homogenous as the 
aforementioned increased solvent film but will be more structurally sound films up to a critical 
concentration of diminishing returns. At this critical concentration, the amount of film mixture 
will be great enough that entrapment of the solvent occurs creating a complex gelled network 
rather than a dry film.131 Therefore, the concentration of the film should be increased to the 
critical concentration which depends upon the solvent molecule size and volatility. Although it is 
possible to alter the atmosphere in which the film is drying, most research has steered away from 
this opting for completely dry conditions due to the complexity involved in maintaining a steady-
state transport condition. 
 In the current research, films were created by drying of single layers on a glass or Teflon 
substrate. The concentrated mixtures were extruded on to the substrate via a syringe. After being 
placed on the substrate the films are dried on an orbital mixer in a fume hood. 
3.5. MATHEMATICAL CONVERSIONS 
 Preparation of LSZ-SWNT dispersions was carried out on a weight basis. This is the 
most practical and most convenient from an experimental stand point. However, understanding 
of phase behavior and dispersion kinetics is based on volume, or more importantly position 
which is a basis of volume. Therefore, mathematical analysis was carried out to determine 
various important properties of constituents of LSZ-SWNT dispersions. 
 The density of LSZ is needed in order to determine the volume fraction present in a LSZ 
solution. Since LSZ is a globular protein, it was modeled as a sphere with a diameter of 3 nm in 
order to obtain the volume of a single LSZ molecule, VLSZ, as shown in Equation 3.4. 
                    
 
             
 
                                     
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After determination of VLSZ, the specific volume of LSZ,      , was determined using Avogadro?s 
number, NA, as shown in Equation 3.5. 
                         
 
                       
                  
          
        
 
                                                                                                               
After determination of the specific volume of LSZ, the density of LSZ, ?LSZ, can be determined 
by using the molecular weight of LSZ, MWLSZ, as shown in Equation 3.6. 
            
   
 
                        
                  
                                          
 Determination of volume fraction of rods, SWNT, or spheres, LSZ, in a solution was 
carried out by knowing the mass fraction of each in solution or dispersion. The formula for 
determining the volume fraction of LSZ, ?LSZ, from the mass fraction of LSZ is shown in 
Equation 3.7. 
                            
                
 
    
    
    
     
    
    
 
    
         
        
   
       
        
In the above equation, mLSZ is the mass of LSZ, mH2O is the mass of water, ?H2O is the density of 
water, and ?LSZ is the mass fraction of LSZ. Equation 3.7 can be further simplified since the 
density of water and LSZ are constants. The resulting equation, shown in Equation 3.8 gives the 
volume fraction of LSZ as only a function of the mass fraction of LSZ. 
     
    
         
        
   
       
 
 
         
               
                    
   
                   
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After determination of the volume fraction of LSZ in solution, the volume fraction of SWNT, 
?SWNT, can be determined as shown in Equation 3.9. 
                                                          
     
     
        
         
     
     
 
        
           
            
    
        
                                                                                        
In the above equation, ?LSZ-H2O is the density of the LSZ solution, mSWNT is the mass of SWNT, 
?SWNT is the density of SWNT, and ?SWNT is the mass fraction of SWNT. By examination of 
Equation 3.9, it can be seen that in order to determine the volume fraction of SWNT the LSZ 
solution density, SWNT density, and SWNT mass fraction must be known. The density is 
estimated for the SWNT being used, and the LSZ solution density is known through 
experimentation. Therefore, Equation 3.9 can be simplified to show the volume fraction of 
SWNT as only a function the mass fraction of SWNT as shown in Equation 3.10. 
      
        
           
            
    
        
 
    
          
                   
                   
    
         
Any further mathematical analysis which was performed was done on a singular basis 
and did not encompass the entire scope of research. It will, therefore, be discussed on an 
individual basis as it arises. 
3.6. PREPARATION OF LYSOZYME ? CARBON NANOTUBE DISPERSIONS 
Preparation of LSZ-SWNT dispersions is straight forward and many papers present 
preparation methods which are very similar.3, 8, 10, 51, 133-134 Each preparation method contains 
four basic steps: preparation of a solution of LSZ and a solvent or solvents, after the solution has 
105 
 
stabilized, introduction of SWNT into the LSZ solution, sonication of the LSZ-SWNT 
dispersion, and when needed, centrifugation of the sonicated solution of LSZ-SWNT. 
Preparation of the LSZ-solvent solution is required prior to the addition of SWNT to 
ensure the LSZ has had adequate time to homogenize within the solution. If the LSZ solution is 
not homogenous then there will be areas of high, and consequently low, concentrations which 
will reduce the effectiveness of the LSZ in dispersing the SWNT. The timing and method of 
homogenization is also critical in achieving a dispersion with no visible aggregation via optical 
microscopy. If stirring rods are used, too little time will lead to a non-homogenous solution. 
Addition of SWNT to the LSZ solution has similar caveats as the LSZ-solvent solution. The 
SWNT must be added to the solution and allowed to homogenize, to the greatest possible extent 
by magnetic or physical stirring methods, allowing the most intimate contact between SWNT 
and LSZ. If proper mixing of the SWNT in the LSZ is not allowed there will be areas of high 
SWNT concentration with LSZ concentration possibly below that need to individually disperse 
the SWNT, which will adversely affect the dispersion. Therefore, the time of mixing and type of 
mechanical agitation used to mix must be taken into account as variables affecting the final 
dispersion state. Sonication of the LSZ-SWNT dispersion is done either using a bath or tip 
sonicator. Sonication is the application of high energy sound waves to a dispersion in order to 
break apart particles; if the amplitude and frequency of the waves can be controlled they should 
be optimized so as to minimize the damage to the SWNT and LSZ, but still allow enough energy 
to overcome the van der Waals forces of attraction between SWNT allowing the LSZ to 
intercalate between the individual tubes. Sonication is done specifically to overcome the van der 
Waals forces between SWNT allowing them to separate, at which time the LSZ is able to move 
between the tubes, interact, and stabilize them as individuals. Along with the frequency and 
106 
 
amplitude of the sonicating waves, time is also an important variable of sonication. Since the 
waves are high energy, the portion of the wave energy that is remaining after use for mechanical 
separation is dissipated as heat and sound energy. If the sonication is allowed to carry on for too 
long, the heat energy can cause damage to the LSZ and also cause evaporation of the solvent, 
which in turn changes the dynamics of the system and affects the final dispersion state. Therefore 
the duration of sonication and the wave characteristics must be accounted for in variables 
affecting the final dispersion state. Centrifugation of the sonicated dispersion is done in order to 
separate the kinetically unstable SWNT and LSZ from the supernatant which is typically the 
desired phase of individually dispersed SWNT. Figure 31 shows a schematic representation of 
the process which occurs during sonication. 
 
Figure 31. Possible mechanism where sonication leads to dispersion. SWNT bundles are 
?frayed? and LSZ partially unfolds. The unfolded LSZ then adsorbs onto the ?frayed? SWNT. 
Any remaining LSZ returns to native conformation and any non-LSZ-adsorbed SWNT rebundle 
to form aggregates.51 
 
107 
 
Centrifugation rate and duration are both variables which affects what SWNT and LSZ which are 
deemed to be kinetically unstable. Depending on the stabilization of the individually dispersed 
SWNT, centrifugation rates can range from 300 x g to 100,000 x g with time ranging from 30 
minutes to 72 hours. If the centrifugation rate is very high, then SWNT which may not be 
perfectly kinetically stable may precipitate out of the dispersion because the centrifugal force 
overcomes the stabilizing and van der Waals forces. Although long durations and high speeds 
seem to be bad, low times and low speeds will not do the proper job of removing the unstable 
constituents. If the rate is too low then the centrifugal force is not great enough to pull 
aggregated SWNT to the bottom of the centrifuge tube. In parallel, if the duration is not long 
enough then the time for the SWNT and LSZ to navigate the tortuous path to the bottom of the 
centrifugation will not be met and the final dispersion will be left with unstable SWNT and LSZ 
? mainly aggregates of each. The major difference between papers is the concentrations of LSZ 
and SWNT that are used to achieve stable dispersions. Although, many research groups use 
various initial concentrations of both SWNT and LSZ, they all use greater amounts of LSZ than 
is theoretically needed. This is because if a mixture is mixed so that the exact amount of LSZ is 
added to individually disperse a set amount of SWNT, there are possibilities that LSZ will not 
properly intercalate to give individual SWNT. Therefore, by adding additional LSZ (or any 
dispersant), there are statistically greater chances of having LSZ intercalate since the 
concentration is so high that if some LSZ does not intercalate there is excess in order to fill that 
void. However, as will be discussed, the excess LSZ has a role in the phase behavior of LSZ-
SWNT dispersions through depletion interactions. Regardless of all the variables that must be 
accounted for in preparation of the dispersion and the differing initial concentrations that can be 
used, the end goal is to achieve a stable dispersion of individually dispersed SWNT. 
108 
 
In the current research, LSZ-SWNT dispersions are prepared following a similar method 
as the one described above. The desired amount of LSZ is weighed and poured into a beaker. 
The appropriate amount of deionized water is then added to the beaker along with a magnetic 
stirring rod; the beaker is then covered with Para-Film to prevent evaporation. For this research, 
all dispersions were made with 100 mL total volumes. The LSZ solution is stirred at 
approximately 100 repetitions per minute for thirty minutes to allow for solvation and complete 
mixing. The correct amount of SWNT are weighed and poured into the LSZ solution. The 
solution is then stirred with a spatula to incorporate all of the SWNT. The LSZ-SWNT 
dispersion is then magnetically stirred for one hour at approximately 100 repetitions per minute 
to allow for complete mixing of SWNT within the LSZ solution. The LSZ-SWNT dispersion is 
then tip sonicated for thirty minutes at 60% amplitude, which equates to approximately 55 J. 
After sonication, the LSZ-SWNT is termed to be a mixture or bulk dispersion. If desired, the 
LSZ-SWNT uncentrifuged dispersion is then centrifuged for three hours at 17,000 times gravity. 
Depending on the size of the initial dispersion, multiple batches of centrifugation must occur to 
process all of the material. After centrifugation, the liquid supernatant is removed via pipette and 
stored. It should be noted that LSZ-SWNT dispersions, both centrifuged and uncentrifuged, are 
stored at approximately 5oC in order to help maintain the activity of LSZ and prevent any 
thermal energy from causing unwanted enzyme interactions. Dispersions of LSZ-SWNT 
stabilized with TTAB were prepared analogous to LSZ-SWNT. TTAB and LSZ were added to 
DI water and magnetically stirred for 10 minutes at which point SWNT was added and tip 
sonicated. Again, two sample preparation methods were used to create mixture and supernatant 
dispersions. After sonication, the mixture was processed by centrifugation at 1,000 x g for 30 
minutes and removing the supernatant, whereas the supernatant was centrifuged for 3 hours at 
109 
 
17,000 x g. Evaporation of the LSZ-TTAB-SWNT dispersions was used to create concentrated 
samples for analysis and fiber spinning. Solutions of LSZ-SWNT or LSZ-TTAB-SWNT in PVA 
were created by combining dilute mixture or supernatant dispersions with solutions of 185 kDa 
PVA. The PVA solution was 4.10 vol.% in DI water mixed via magnetic stir bar at 50oC for 3 
days. After combination of the dispersions with the polymer solution, the resultant solutions 
were mixed via magnetic stir bar for 20 minutes then concentrated via evaporation on an orbital 
mixer for fiber spinning.  
110 
 
4. RESULTS AND DISCUSSION 
4.1. LYSOZYME SOLUTION CHARACTERIZATION 
Prior to using LSZ as a dispersant for SWNT, the aqueous LSZ solution was 
characterized independently. This was done in order to determine changes due to the inclusion of 
SWNT. Understanding the original LSZ state along with any changes will allow for the 
determination of the concentration in dispersed SWNT, and also allowing for the elucidation of 
changes in secondary and tertiary structure, LSZ-SWNT binding sites, and changes in enzymatic 
activity. 
4.1.1. ULTRAVIOLET ? VISIBLE SPECTROSCOPY 
UV-vis was used to develop calibration curves for LSZ in order to determine 
concentrations of unknown LSZ samples. UV-vis was also used to indicate a molecular 
interaction between SWNT and LSZ. LSZ has a characteristic absorption peak at a wavelength 
of 280 nm. This characteristic peak, shown in Figure 32, is due to the hydrophobic tryptophan 
residue located within the core of LSZ. As shown in Figure 32, processing of LSZ analogous to 
that used in processing the LSZ-SWNT dispersions does not significantly alter the absorption 
spectra. The slight difference between the unprocessed solution, and the sonicated and sonicated, 
centrifuged solutions is due to the partial unfolding and refolding of LSZ before and after 
sonication. Changes in the absorbance of a solution, especially protein solutions, are primarily 
due to the change in the environment surrounding the primary absorbing chromophore. 
111 
 
 
Figure 32. Absorbance spectrum of 0.30 vol. % LSZ solutions at various stages of processing. 
 
After determination that processing of LSZ does not alter the absorption spectrum, a calibration 
curve was constructed. In order to construct the calibration curve, serial dilution was used to 
cover a range of 1.20 vol. % LSZ to 0.01 vol. % LSZ. The absorption spectrum of LSZ solution 
at various concentrations is shown in Figure 33. 
112 
 
 
Figure 33. Absorbance spectrum of LSZ solutions with the water baseline removed at 
concentrations ranging from 1.20 vol. % to 0.01 vol. %. Subtraction of the water baseline is 
essential in determining the actual absorbance of LSZ corresponding to the known concentration. 
 
At LSZ concentrations above 0.48 vol.%, absorption flattening occurs. At sufficiently high 
concentrations, the absorption bands will saturate and show absorption flattening. The absorption 
peak appears to flatten because close to 100% of the light is being absorbed. The concentration at 
which this occurs depends on the particular compound being measured. Solutions that are not 
homogeneous can show deviations from the Beer-Lambert law because of absorption 
flattening.117 This can happen, for instance, where the absorbing chromophore is located within 
suspended particles, as is the case with LSZ solutions. For clarity, Figure 34 shows the deviation 
of from the Beer-Lambert law for LSZ solutions at concentrations above 0.48 vol.%. Figure 35 
113 
 
shows the calibration curve of LSZ given in volume percent with the extinction coefficient of 
4.31 mm-1 vol.%-1 or 36,669 cm-1 M-1. 
 
Figure 34. Calibration curve for LSZ showing deviation from the Beer-Lambert law at a 
concentration above 0.48 vol. % LSZ. 
 
Figure 35. Calibration curve for LSZ showing only usable concentrations and calibration 
equation from linear data fit with statistical R2 of >0.99. 
 
114 
 
4.1.2. CIRCULAR DICHROIC SPECTROSCOPY 
 CD was used to determine the initial secondary and tertiary structure of LSZ in order to 
compare it to LSZ-SWNT dispersions to determine any alterations that occur during the binding 
of LSZ to SWNT. Secondary structure can be determined by CD spectroscopy in the far-UV 
spectral region from 190 nm to 250 nm. At these wavelengths, the chromophore is the peptide 
bond, and the signal arises when it is located in a regular, folded environment. Alpha-helix, beta-
sheet, and random coil structures each give rise to a characteristic shape and magnitude of CD 
spectrum. Alpha helices show characteristic peaks between 200 nm and 230 nm. Beta 
sheets show a characteristic peak centered at 215 nm. Random coils show a characteristic peak 
centered at approximately 200 nm.118 Figure 36 shows the secondary structure of LSZ at various 
processing conditions to be dominated by the alpha helix with an unsmoothed bimodal response 
between 200 nm and 230 nm. The alpha helix rich secondary structure of LSZ is important for 
the enzymatic activity of the protein. The CD spectrum of a protein in the near-UV spectral 
region from 250 nm to 350 nm can be sensitive to certain aspects of tertiary structure. At these 
wavelengths, the chromophores are the aromatic amino acids and disulfide bonds, and the CD 
signals they produce are sensitive to the overall tertiary structure of the protein and the 
environment surrounding them.118 Signals in the region from 280 nm to 300 nm are attributable 
to tryptophan and those from 310 nm to 330 nm are attributable to disulfide bonds. Figure 37 
shows the near-UV spectrum for LSZ solution after various processing steps. 
115 
 
 
Figure 36. Far-UV CD spectrum of 0.30 vol. % LSZ solution both before and after processing. 
The lack of deviation of the sonicated and sonicated, centrifuged solutions shows that processing 
does not fully disrupt the secondary structure of LSZ. 
 
Figure 37. Near-UV CD spectrum of 0.30 vol. % LSZ solution both before and after processing. 
The lack of deviation of the sonicated and sonicated, centrifuged solutions shows that processing 
does not disrupt the tertiary structure of LSZ. 
116 
 
4.1.3. ENZYMATIC ACTIVITY ANALYSIS 
The enzymatic activity of LSZ is derived from its? secondary structure of alpha helices 
and is predominantly active against Gram-positive bacteria. In order to quantify the activity of 
LSZ, turbidimetric analysis was done. Turbidity is the haziness or cloudiness of a suspension 
resulting from light scattering around colloidal entities. The turbidity of the bacterial suspension 
predominantly occurs at the cell surface because of the high refractive gradient between the fluid 
and the cell surface. Turbidimetric analysis is the application of measuring antibacterial activity 
of reacting agent in the presence of a known bacterial agent. A bacterial culture during the log 
phase of growth is relatively homogeneous and each cell is actively metabolizing and dividing at 
about the same rate. Consequently if a chemical agent is added to a culture in the log phase then 
any change in growth rate may be attributed to the action of the reacting agent. The turbidimetric 
analysis used in this research uses a UV-vis spectrophotometer to measure the increase of light 
transmitted at 450 nm through a sample containing Micrococcus lysodeikticus and LSZ, which is 
the standard method of activity analysis for LSZ.117 Figure 38 shows the turbidimetric analysis of 
several solutions of LSZ. Reduction in the absorbance of transmitted light at 450 nm shows that 
LSZ lyses the M. lysodeikticus making the solution clearer (less turbid). As shown in Figure 38, 
the different processing methods ? none, sonicated, and sonicated,centrifuged ? do not show 
significant differences. This indicates that the processing methods for creating the LSZ-SWNT 
dispersions do not affect the inherent activity of LSZ. The trendlines shown for each processing 
method are fitted to the linear cell death region of the bacterial solution as described by 
Michaelis-Menten kinetics. The slope from each trendline can be used to determine the specific 
activity of LSZ using Equation 4.1.   
          
          
   
       
  
                                                                
117 
 
The activity from equation 4.1 is given in active units per volume of LSZ where the  AbsEnzyme 
is the linear cell death region trendline slope,  AbsRef is the trendline slope from the water 
reference as given in Figure 39, V is the volume of LSZ present in the injected solution, and 
0.001 is the definition of LSZ activity in units of Abs active unit-1 min-1. 
 
Figure 38. Turbidimetric analysis of 0.3 vol.% LSZ solutions at various processing conditions. 
Linear fit of cell death region shown for each processing method with the slope of the line 
equation used to calculate activity. 
 
The specific activity of LSZ can be calculated from Equation 4.1 and the data given in Figure 38, 
it is possible to calculate the specific activity of LSZ at each processing methods. The LSZ 
solutions maintained 5630 ? 140 active units per mL LSZ through processing. For reference, 
Figure 39 shows the turbidimetric analysis of M. lysodeikticus with the addition of water. 
118 
 
 
Figure 39. Turbidimetric analysis of M. lysodeikticus and water as a reference. 
 
4.1.4. THERMOGRAVIMETRIC ANALYSIS 
 TGA was done in both air and argon for LSZ and SWNT dispersions and solid 
assemblies to determine the thermal decomposition behavior. The thermal decomposition 
temperature, Td, should not be confused with the denaturation temperature. Td is the temperature 
at which a molecule chemically decomposes into its? constituent components and is primarily 
exothermic. Thermal denaturation is the act of a protein or enzyme losing its? structure and 
unfolding due to the application of heat. There are three stages of protein thermal denaturation 
prior to thermal decomposition. Quaternary structure denaturation is the dissociation or spatial 
movement of protein subunits; tertiary structure denaturation involves the disruption of covalent 
interaction between amino acids, such as disulfide linkage breaks and dipole-dipole interaction 
119 
 
disruption; and secondary structure denaturation is responsible for the loss of all regular 
repeating patterns of alpha helices and beta sheets adopting a random coiled structure.135 It 
should be noted that the primary structure denaturation cannot occur because denaturation is the 
unfolding of the protein, and after losing all secondary structure it is completely unfolded. 
Rather, the primary structure is disrupted by the act of thermal decomposition when the thermal 
energy input is large enough to disrupt the covalent peptide bonds which hold together the 
protein. 
 LSZ has a characteristic Td at approximately 270oC in argon and 255oC in air as 
determined by the onset point of decomposition. It has a Td at approximately 323oC in argon and 
approximately 305oC in air as determined by the derivative weight loss curve. The onset point Td 
was determined to be the intersection of the tangent line from the initial LSZ dry weight and the 
inflection point of the loss curve, which is the peak maximum of the weight loss derivative 
curve. The weight loss derivative curve is calculated by determining the slope between points 
using the least-squares method; the peak maximum of the weight loss derivative curve shows an 
alternative method of determining Td. The TGA weight loss curve and weight loss derivative 
curve for LSZ in air and argon can be seen in Figure 40 and Figure 41, respectively. 
120 
 
 
Figure 40. TGA weight loss curve versus temperature for LSZ in argon (red) and air (blue). 
Curves are averages of three runs of each air and argon; error for LSZ in argon is 0.61% and 
error for LSZ in air is 1.01%. Diamond markers indicate the decomposition onset temperature 
and the square markers indicate the residual weight fraction. 
 
Figure 40 shows that LSZ has a characteristic weight loss curve from approximately 220oC to 
350oC in both air and argon. The difference of 15oC in onset point Td is due to the mechanism by 
which decomposition takes place in each atmosphere. In air, combustion takes place to thermally 
decompose the molecules, whereas in argon, thermal cracking takes place to thermally 
decompose the molecules. Figure 40 also shows that in air LSZ has a second and third loss from 
approximately 400oC to 550oC and 620oC to 670oC, respectively, which are not seen in argon. 
These losses are attributed to the buffering materials in the raw LSZ, sodium acetate and sodium 
121 
 
chloride. The buffering salts are also the difference for the residual difference between air and 
argon. In air, the buffer salts break down leaving a residue of 0.3 wt.%, whereas in argon, the 
buffer salts do not break down leaving a residue of 25.4 wt.%. 
 
Figure 41. TGA weight loss derivative curve versus temperature for LSZ in argon (red) and air 
(blue). Curves are averages of three runs of each air and argon; error for LSZ in argon is 0.61% 
and error for LSZ in air is 1.01%. Diamond markers indicate the decomposition temperature. 
 
Figure 41 shows that for the derivative curve method LSZ has a Td of 323oC in argon and 305oC 
in air. The difference of 18oC is analogous to that of the differences in the onset point Td. The 
shape of the air and argon curves after the decomposition temperatures are different due to the 
second and third losses which occur in air but not in argon. The difference in onset point Td and 
derivative Td show that each method can consistently measure change in Td with both giving 
122 
 
consistent differences between air and argon for LSZ. It should be noted that the heating rate can 
alter Td, therefore, to compare data between runs the same heating rate must be used. 
4.1.5. RHEOLOGICAL BEHAVIOR 
  Rheology of aqueous LSZ solutions was done in order to determine the microstructural 
response and viscosity to increasing LSZ concentrations. The importance of determining the 
solution rheological characteristics is in order to mathematically remove the effects of LSZ and 
water in the LSZ-SWNT dispersions. As previously discussed, concentrating LSZ solutions at 
ambient conditions leads to aggregate and fibril formation. Therefore, the various concentrations 
of LSZ were individually made by combining the desired amount of LSZ with DI water and 
mixing to create homogenous solutions. The concentration range tested was from 0.30 vol.% to 
9.50 vol.% with a total of eight concentrations being tested. The elastic effect of LSZ was not 
seen in aqueous solutions until approximately 2.5 to 3.0 vol.% LSZ. Therefore, data below these 
concentrations is sparse due to the torque detection limits of the rheometer used. It should also be 
noted that each data set was collected over three separate loadings with three runs per loading for 
a total of nine runs per test. 
 The solutions were first subjected to an amplitude sweep in order to determine the limit 
of linear viscoelasticity. The limit of linear viscoelasticity was determined by graphical analysis 
where the correlation in the direction of the tangent line of the low-strain plateau was lost. The 
critical strain was determined via graphical analysis to be approximately 1.6%. Another 
interesting note is to see that increase in LSZ concentration of approximately three-fold only 
leads to an approximate one order of magnitude increase in the solid-like response of the 
solution. Figure 42 shows the storage modulus of LSZ solutions as a function of amplitude 
strain.  
123 
 
 
Figure 42. Amplitude sweep test data showing storage modulus as a function of amplitude strain 
for concentrations of 3.04 vol.% LSZ, 6.20 vol.% LSZ, and 9.50 vol.% LSZ. The critical strain 
was determined to be 1.6% by graphical analysis where the correlation in the direction of the 
tangent line of the low-strain plateau was lost. Error for each concentration is less than +/- 3%. 
 
 After determination of the critical strain, the linear viscoelastic oscillatory response of the 
dispersions was tested to probe the time-dependent behavior of increasing concentrations of 
LSZ. Figure 43 shows the storage modulus for increasing concentrations of LSZ as a function of 
angular frequency. As expected, the elastic behavior increases for increasing concentration of 
LSZ. However, the slope of the storage modulus versus angular frequency does not drastically 
change with increasing concentration. This indicates that the elasticity of the gel network created 
by LSZ does not increase in strength with increasing concentration of LSZ. The linear slope for 
124 
 
each concentration can be found by taking the exponential function of the slope from the 
logarithmic fit of each data set ? 1.00 for 3.04 vol.% LSZ and 1.01 for 6.20 vol.% LSZ and 9.50 
vol.% LSZ.  
 
Figure 43. Linear viscoelastic oscillatory response showing the storage modulus as a function of 
angular frequency for concentrations of 3.04 vol.% LSZ, 6.20 vol.% LSZ, and 9.50 vol.% LSZ. 
Error for each concentration is less than +/- 3%. 
 
After determination of the elastic response as a function of frequency, storage modulus was 
plotted versus LSZ concentration to determine the effect of LSZ concentration on the elasticity 
of the solution. Figure 44 shows the storage modulus scales with LSZ concentration by a power 
law function. 
125 
 
 
Figure 44. Linear viscoelastic oscillatory response showing the storage modulus as a function of 
LSZ concentration for angular frequencies of 0.1 s-1, 1.0 s-1, 2.5 s-1, and 10.0 s-1. Error for each 
concentration is less than +/- 3%. 
 
 After the microstructure was probed by oscillatory testing, the viscosity of the solutions 
was determined via steady shear flow curve testing. The flow characteristics of each dispersion 
varied for each concentration as seen in Figure 45. At concentrations below 0.60 vol.% LSZ, the 
solutions acted as Newtonian fluids. This indicates that there was not yet any interaction between 
LSZ molecules to induce any kind of shear response. At concentrations above 0.60 vol.% LSZ, 
the solutions show differing slopes of shear thinning behavior. This shows that above this 
concentration, there was a physical interaction between LSZ molecules creating a system which 
126 
 
shows a shear response. As the shear rate is increased, however, the network attractive force is 
over come by shear force causing the viscosity to decrease. 
 
Figure 45. Flow curve showing viscosity versus shear rate for concentrations of 0.30 vol.% LSZ 
to 9.50 vol.% LSZ, and a power law model fit. The power law model shown has K = 0.025 Pa-s2 
and n = 0.220. Error for each concentration is less than +/- 4%. 
 
The viscosity continues to decrease with shear rate with a power law nature until approximately 
10 s-1 when the shear thinning behavior begins to level off into an infinite shear viscosity plateau. 
The power law nature of the shear thinning behavior is shown by the power law model in Figure 
45, as described by Equation 4.2. 
   ?                                                                                       
127 
 
For the entire concentration range studied K varies from 0.0013 Pa-s2 to 0.0250 Pa-s2 and n 
varies from 0.22 to 1.00. After determining the shear nature of the LSZ solutions, the viscosity 
was plotted as a function of LSZ concentration as shown in Figure 46a. The LSZ solution 
viscosity is integral to determine the specific and inherent viscosity of LSZ-SWNT dispersions 
as will be discussed in detail later. Third-order polynomial fits were chosen to determine the 
function of LSZ solution viscosity versus LSZ concentration. The fit was controlled by dictating 
that at zero LSZ concentration the viscosity would be 1.308 mPa-s which is the viscosity of 
water at 10oC to ensure the generated equation had a true physical meaning for the system they 
were describing. 
The rheological behavior of particulate suspensions of hard spheres is well documented 
by Russel et al., Hiemenz and Rajoagopalan, Kim and Karrila, Mackosko, Brady, Mellema, and 
Larson.61, 136-140 At concentrations below 3 vol.%, the shear viscosity of a hard sphere suspension 
can be predicted by Equation 4.3 which Einstein calculated from the viscous dissipation 
produced by the flow around a single sphere.98 
                                                                                 
As shown in Figure 45, concentrations below 3 vol.% follow a power law function as described 
in Equation 4.2 and would therefore deviate significantly from the linear function of Equation 
4.3. Taking the effect of multibody interactions into account, Batchelor, was able to adapt 
Equation 4.3 for hard spheres with rigid repulsion interactions to generate Equation 4.4 which 
has been shown to be valid for concentrations below 10 vol.%.98 
                                                                              
128 
 
 
Figure 46. a.) LSZ solution viscosity as a function of LSZ concentration for shear rates of 0.1 s-
1, 1.0 s-1, 10.0 s-1, and 100.0 s-1. Third-order polynomial fits are used to create the equations for 
LSZ viscosity contribution and are shown with the corresponding statistical R2 values, b.) 
reduced viscosity as a function of LSZ concentration (red) with a linear fit showing deviation 
from the Batchelor expansion of the Einstein equation (blue), and c.) relative viscosity versus 1-
?/?m (red) with a power law fit showing deviation from the Krieger-Dougherty equation (blue). 
129 
 
By manipulating Equation 4.4 to show reduced viscosity ? subtracting one and dividing by ? ? it 
is possible to see that the slope of the reduced viscosity versus concentration curve should be 6.2, 
however, this slope for LSZ solutions is 40.5, as shown in Figure 46b. The higher slope for the 
reduced viscosity versus concentration curve is an indication of the non-spherical nature of LSZ, 
which is validated by x-ray diffraction data showing a globular structure with two main axes 
with slightly different lengths: 3.08 nm and 2.95 nm.39 Furthermore, hard-sphere rheology theory 
would dictate that for high-shear relative viscosity versus concentration the curve would follow 
the Krieger-Dougherty equation shown in Equation 4.5 and Figure 46c with an intrinsic viscosity 
of approximately 2.5 where ?m is the maximum packing volume of hard spheres, which is 
approximately 0.63.98 
         
 
 
      
                                                      
For LSZ solutions to fit Equation 4.5, ?m must be set to 0.37 which is significantly lower than 
the 0.63 for hard spheres. The lower packing volume is also an indication of the ellipsoidal or 
globular nature of LSZ. Furthermore, after fitting of the Krieger-Dougherty equation, the 
intrinsic viscosity is determined to be 6.56 for LSZ which is approximately 2.6 times greater than 
that of hard spheres; another indication that LSZ is not purely spherical but elongated on one 
axis. LSZ solutions clearly do not follow hard-sphere rheology in which the only interactions 
between particles were rigid repulsions that would occur only when particles come into contact. 
Therefore it should be noted that for LSZ-SWNT rheology, the cylinder-sphere phase behavior 
theory was used as a starting point for the determination of what could happen in the system. 
4.2. LYSOZYME ? CARBON NANOTUBE INTERACTION 
Aqueous dispersions of LSZ and SWNT are only possible because the LSZ and SWNT 
interact with one another on a molecular level to produce a kinetically stable dispersion. The 
130 
 
interaction between LSZ and SWNT was probed using a combination of methods including 
TEM, SEM, UV-vis, Raman spectroscopy, CD, and fluorescence spectroscopy and anisotropy. 
There are two common approaches to immobilizing proteins on SWNT: covalent and 
non-covalent. Several researchers have used EDC/NHS chemistry to covalently attach enzymes 
such as  LSZ,141-142 horseradish peroxidase,44 and  organophosphate hydrolase7 to SWNT. 
However, covalent attachment of proteins to CNT has the disadvantages of increasing processing 
time and cost. In addition, covalent functionalization disrupts the intrinsic sp2 bond structure that 
is responsible for the unique properties of SWNT. Therefore, understanding the non-covalent 
interactions between proteins and pristine SWNT is important for producing materials that 
combine protein function with the intrinsic properties of pristine SWNT. However, while there 
have been several studies on LSZ-SWNT dispersions, the details of the interaction are not well 
understood. It has been hypothesized that the size of SWNT facilitated SWNT fitting into LSZ?s 
hydrophobic pocket and that the primary interaction was therefore ?-? stacking between 
hydrophobic residues.143 Other research has echoed this hypothesis and further suggested that 
partial unfolding during sonication facilitated dispersion.51, 144 In this section evidence is 
provided of the importance of hydrophobic interactions and ?-? stacking, and that the binding 
mechanism is between tryptophan (aromatic amino acid residue) and the aromatic SWNT 
sidewall.9 LSZ contains three hydrophobic residues within its core: methionine, phenylalanine, 
and tryptophan. Of these three amino acids, it is less likely that methionine interacts with the 
SWNT sidewall since it does not possess any aromatic rings to enable ?- ? stacking with SWNT. 
Phenylalanine and tryptophan both possess aromatic rings, but phenylalanine?s benzene group is 
less likely to interact than tryptophan?s aromatic indole group due to its larger size and higher 
electrostatic potential.145 
131 
 
The close association between LSZ and SWNT was visualized using TEM and SEM. 
TEM imaging of LSZ SWNT dispersions show a thin polymer boundary surrounding SWNT 
bundles, as show in Figure 47. The disparity in transparency between the outer boundary and the 
encapsulated material clarify that the outer material is much more susceptible to electron 
transmission, as is the case with biological polymers such as LSZ.  
 
Figure 47. TEM micrograph at 160,000x of 0.30 vol.% LSZ ? 0.07 vol.% SWNT dispersion 
showing an interaction between LSZ and SWNT with SWNT bundle sizes of approximately 25 
nm to 50 nm. 
 
Although SEM is primarily intended for scanning the surface of molecules, a certain amount of 
transmission occurs. The ability of electrons to scan a surface versus transmit through the surface 
is dependent upon the electronic conductivity of the molecules being imaged. If the material is 
highly conductive, then the electrons will scan the surface giving a high resolution, opaque 
image. If the material is not conductive the electrons can transmit through the material giving a 
low resolution, partially translucent image. Since the SWNT are significantly more electrically 
conductive than LSZ, SWNT appear opaque under SEM while LSZ appears translucent. As 
shown in Figure 48, small SWNT bundles are intimately surrounded by LSZ; no other materials 
132 
 
were present in the sample. In addition, as the electrical energy from the electrons was 
transferred to the LSZ in the form of thermal energy, the LSZ began to swell. This is a common 
effect in SEM of proteins and biological polymers. Figure 48(a) was taken last sequentially, and 
it can be seen by comparison with Figure 48(b) and 48(c) that the empty spaces between the 
coated SWNT have been filled in by the swelling of the bound LSZ. Further evidence of this 
effect is shown by the size ratio of LSZ to SWNT increasing by approximately three-fold from 
Figure 48(b) to 48(d). The exact bundle size cannot be determined from this image due to the 
limits of resolution, but previous studies have shown that dispersions prepared by the same 
method dispersed SWNT as individuals and small bundles.8  Since drying can affect both 
morphology and the specificity of interaction, additional methods were used to confirm the 
nature of the SWNT-LSZ interaction. 
 
Figure 48. Scanning electron micrograph of a dried 0.30 vol.% LSZ ? 0.07 vol.% SWNT 
aqueous supernatant illustrating the direct interaction between SWNT (opaque) and LSZ 
(translucent) along with swelling of biopolymer LSZ layer; (a) 50,000x, (b) 200,000x, (c) 
300,000x, and (d) 400,000x. 
133 
 
Immobilization of LSZ on SWNT was also evidenced by attenuated total reflectance 
Fourier transform Infrared Spectroscopy (ATR-FTIR) and Raman spectroscopy. Figure 49 shows 
the ATR-FTIR spectra of dried samples of SWNT, LSZ, the aqueous LSZ-SWNT mixture prior 
to centrifugation, and the resulting LSZ-SWNT supernatant. The LSZ, LSZ-SWNT mixture and 
resulting supernatant show the characteristic amide I (~1650 cm-1) and amide II (~1535 cm-1) 
peaks characteristic of proteins and enzymes. In addition, the LSZ-SWNT mixture and 
supernatant overlay the LSZ peak at ~3300 cm-1 which is the overtone to the amide I peak and is 
characteristic of amino radicals present in each sample.  
 
Figure 49. ATR-FTIR spectrum of SWNT, LSZ, 0.5 wt.% LSZ ? 0.1 wt.% SWNT mixture and 
the resulting supernatant. The LSZ and LSZ-SWNT dispersions show the amide I and II peaks as 
well as the characteristic amino radical peak characteristic of LSZ confirming adsorption of LSZ 
to SWNT. 
134 
 
Furthermore, the LSZ-SWNT mixture and supernatant show increasing absorbance from 
~1500cm-1 to ~700cm-1 similar to that seen in pristine SWNT. This result clearly indicates that 
SWNT were stabilized in solution by the presence of LSZ, and thus carried over into the dry 
sample, in agreement with previous work.8, 51, 134, 146 The data also shows that a portion of SWNT 
was lost during centrifugation, but the relative increase between 1200cm-1 and 700 cm-1 in the 
supernatant (compared to the pure LSZ) shows that LSZ-stabilized SWNT are still present in the 
supernatant. Interestingly, the peak (1000 to 900 cm-1) in the SWNT IR absorption band is red-
shifted in the dispersed SWNT, where there is a constant increase through 700 cm-1. This is an 
effect of the aqueous dispersion of LSZ since the dispersed SWNT spectrum is distinctly 
different from the spectra of non-interacting, dry mixed LSZ and SWNT (see supporting 
information). This ATR-FTIR data thus supports that there is an interaction between LSZ and 
SWNT, and this interaction is further interrogated below using other spectroscopic methods.  
Figure 50 shows the Raman spectra (514 & 785 nm excitation), of the LSZ-SWNT 
mixture and supernatant as well as the initial SWNT material. Several facets of these spectra 
support the existence of noncovalent functionalization of individual SWNT with LSZ. The 
spectra show characteristic radial breathing modes (RBM) from 100 cm-1 to 400 cm-1, the D peak 
due to sp3 hybridized carbons at ~1335cm-1, the G peak due to tangential sp2 hybridized carbons 
at ~1589 cm-1, and the G? peak at ~2645 cm-1 which is the second overtone of the D peak. It has 
been previously reported that LSZ preferentially adsorbs to larger diameter nanotubes.144, 147 The 
inset of Figure 50(a) & (b) shows the RBM peaks. All obvious RBM peaks present for SWNT 
used in the dispersions are present in both the mixture and supernatant with similar relative 
intensities. This suggests that in this work there was no significant fractionation based on 
diameter. The D/G ratios vary only slightly between SWNT (0.13), LSZ-SWNT mixture (0.14), 
135 
 
and LSZ-SWNT supernatant (0.16). This indicates that the immobilization is through a 
noncovalent interaction; covalent functionalization would significantly increase the D:G ratios. 
The noncovalent interaction is further evidenced by the linearity of the data of ID/IRBM vs. ID/IG 
of each excitation laser (see supplementary information).148 As shown in Figure 50(b), the LSZ-
SWNT supernatant Raman spectra shows significant luminescence interference from 600 cm-1 to 
3200 cm-1. The observation of luminescence is associated with individual, non-covalently 
functionalized SWNT. As the concentration of individual SWNT increases within a dispersion, 
the luminescence intensity increases dramatically and the Raman scattering signal will 
essentially be buried under the luminescence.149-151 Therefore, the Raman spectra of LSZ-SWNT 
supernatant at 785 nm excitation further validates the non-covalent functionalization of SWNT 
dispersed as individuals by LSZ.  
 
Figure 50. Raman spectra with a) 514 nm and b) 785 nm excitation of SWNT, the LSZ-SWNT 
mixture, and the resulting supernatant. The full spectra show the RBM, D-, G-, and G?-peaks 
characteristic of stretching modes within SWNT; the inset highlights the RBM peaks. 
 
Several features of the Raman spectra are indicative of charge transfer between the LSZ and 
SWNT via non-covalent bonding.23, 152-154  Another interesting facet of the Raman spectra is the 
136 
 
suggestion of charge transfer between the LSZ and SWNT in both the mixture and supernatant. 
Both the G153-154 and G?23, 152 peaks have been used to elucidate doping effects. While 
luminescence prevents accurate determination of differences in peak location and intensity using 
785 nm excitation, the spectra using 514 nm supports charge transfer (see Table 1). Compared to 
the pristine SWNT, the mixture and supernatant show an upshift in the G?-peak, from 2636 cm-1 
to 2654 and 2645 cm-1 respectively. In contrast, the G/G? ratio for the pristine SWNT was 1.9 but 
only 1.4 for the mixture and 1.0 for the supernatant which indicates doping.152  No G-band shift 
was observed between the SWNT LSZ-SWNT mixture, but there was a 5 cm-1 shift between the 
pristine SWNT and LSZ-SWNT supernatant. These results are in contrast to those of Xie et al. 
who found that the frequency of G? did not shift and who stated that no charge transfer is 
expected due to the lack of a metallic center in LSZ.144 The difference in these charge transfer 
results are likely due to the different starting materials and processing methods used to produce 
the respective dispersions 
514 nm Laser 
Sample Raman Shift (cm
-1) Intensity Ratios 
RBM D G G? D/G G/G? D/RBM 
SWNT 263 1338 1589 2636 0.126 1.899 0.861 
LSZ-SWNT Mixture 263 1335 1589 2654 0.136 1.374 0.657 
LSZ-SWNT Supernatant 263 1333 1594 2645 0.157 1.008 0.449 
Table 1. Peak positions of RBM, D, G, and G? for each dispersion tested along with the D/G, 
G/G?, and D/RBM ratios from the Raman spectra of 514 nm excitation laser. The shifts in G and 
G?, and the decrease of G/G? are indicative of charge transfer between the LSZ and SWNT. 
 
In an attempt to increase the adsorption of LSZ to SWNT through hydrogen bond 
interactions between hydroxyl and amine or carboxyl groups, SWNT were functionalized via 
acid oxidation to introduce carboxyl and hydroxyl groups and increase SWNT hydrophilicity. It 
137 
 
is well established that the introduction of carboxyl, hydroxyl and other hydrophilic groups as a 
result of oxidation significantly increases SWNT dispersibility in water.155-157 Counterintuitively, 
the dispersibilty of SWNT-Ox with LSZ was much poorer than for pristine SWNT. In fact, the 
SWNT-Ox supernatant was virtually clear whereas the pristine SWNT supernatant was 
characteristically black. Comparing the relative changes in absorbance for the initial mixtures 
and supernatants elucidated the marked difference between SWNT-Ox and pristine SWNT 
dispersed with LSZ. The ratio of [SWNT-Ox]supernatant:[SWNT-Ox]mixture was 23% and the ratio 
[SWNT]supernatant:[SWNT]mixture was 34% at 506 nm. Assuming no significant change in the 
extinction coefficients for SWNT-Ox and SWNT in aqueous LSZ, the supernatant concentration 
of SWNT-Ox was 27.0 mg/L compared to 108.0 mg/L for pristine SWNT. The possibility that 
the reduced dispersibilty of the SWNT-Ox  was due to isoelectric effects was explored based on 
Nepal and Geckler?s finding that the dispersion limit of individual SWNT in aqueous LSZ was  
pH-dependent.143  For the SWNT used in their work, the dispersion limit was nearly constant at 
89 mg/L for 1.4 < pH < 8.2 using similar centrifugation conditions of 3 hours at 18,000 g. Near 
the isoelectric point, pH = 10.2, virtually no SWNTs could be dispersed. However, SWNT 
dispersibilty increased again above the isoelectric point. The SWNT mixtures and supernatants 
in the present work had very similar pH values of 5.3 and 5.6 respectively. For SWNT-Ox, the 
mixtures and supernatants had pH values of 7.4 and 7.2 respectively. Buffering the SWNT-Ox 
mixture with 66mM KH2PO4 to obtain a pH of 5.2, similar to the pristine SWNT, resulted in a 
supernatant with pH of 5.3 but an even lower SWNT-Ox concentration of 19.0 mg/L, which is 
contrary to the expectations. Therefore, electrostatic effects are not the primary reason for 
SWNT-Ox having a lower supernatant concentration than pristine SWNT. Most likely, the 
reduced dispersibility was due to SWNT-Ox?s reduced potential for hydrophobic interaction with 
138 
 
LSZ. This indicates that the hydrophobic interaction between LSZ and SWNT is more important 
to dispersion stabilization than favorable hydrophilic interactions with water. 
UV-vis of the supernatants of LSZ-SWNT dispersions show the characteristic, sharp van 
Hove singularities which are indicative of the presence of individual or small bundle SWNT, as 
shown in Figure 51. van Hove singularities are discontinuities in the one-dimensional electronic 
structure of SWNT. The discontinuities arise from overlapping electronic transitions in the 
repeating structure of SWNT. Since UV-vis probes the electronic structure of materials, the van 
Hove singularities are easily seen as peaks in the absorbance between wavelengths of 
approximately 450 nm and 800 nm. The van Hove singularities can also be used to qualitatively 
describe the dispersion state of SWNT. Large, jagged peaks occur when SWNT are dispersed as 
individuals or small bundles, whereas small, broad peaks occur due to absorbance quenching 
when SWNT are dispersed as large, aggregated bundles. Previous investigations further 
confirmed individual dispersion using AFM and ellipsometry.158  
 
Figure 51. UV-vis absorbance spectrum of 0.30 vol.% LSZ ? 0.07 vol.% SWNT supernatant 
showing van Hove singularity peaks characteristic of individually dispersed SWNT. 
139 
 
Comparing aqueous LSZ solutions and LSZ-SWNT dispersions of equal LSZ concentrations 
show changes in the LSZ spectral profile in the presence of SWNT. As apparent from the black 
color of the dispersions, SWNT-dependent increases in absorbance at all wavelengths were 
significant and could overshadow changes in the LSZ spectrum. Therefore, difference spectra, 
shown in Figure 52, were obtained by subtracting the absorbance spectrum of the 0.30 vol.%  
LSZ solution without SWNT. This enabled changes in the LSZ spectrum resulting from the LSZ-
SWNT interaction to be extracted. At 280 nm, the wavelength where tryptophan absorbs,159 the 
data show an increased absorbance of approximately 0.09 for the LSZ-SWNT supernatant and 
approximately 0.31 for the LSZ-SWNT mixture. In addition, a hyperchromic shift was observed 
which was likely due to two phenomena. First, the partial unfolding of LSZ during sonication 
could cause the shift.51 When LSZ intercalates between and partially envelops SWNT, the 
environment surrounding the hydrophobic core of the protein is altered. More specifically, the 
tryptophan chromophore in the hydrophobic core is no longer buried within the LSZ core. The 
emergence of the chromophore from the hydrophobic core could increase the absorbance of light 
at 280 nm. Second, ?- ? stacking of an aromatic ring with the sidewall of SWNT can change the 
electronic structure of the chromophore. Consequently, an increase in absorbance intensity of the 
chromophore at a given wavelength could also be due to the overlap of p-orbitals excited by UV-
light.160  
140 
 
 
Figure 52. UV-vis absorbance difference spectra of 0.30 vol.% LSZ ? 0.07 vol.% SWNT 
mixture and 0.30 vol.% LSZ ? 0.07 vol.% SWNT supernatant. The absorbance difference 
intensities have been down shifted to the LSZ solution (zero) beginning at 348 nm to highlight 
the hyperchromic shift due to the adsorption of LSZ to SWNT. 
 
Of the three amino acids showing Cotton effects between 250 nm and 350 nm in CD 
spectra (tryptophan, tyrosine, and phenylalanine), tryptophan is twice as abundant in LSZ and 
absorbs about four-fold more light at 280 nm compared to tyrosine; phenylalanine is also less 
abundant and has negligible absorbance at 280 nm.161 This allows CD to be used for relatively 
selective examination of the interaction between tryptophan and the sidewall of SWNT. 
Specifically, CD was used to show that the addition of SWNT causes a definitive change in the 
optical polarity of LSZ. The supernatant of LSZ-SWNT dispersion was used to compare the CD 
141 
 
spectra to enhance the spectral changes due to binding which could be masked by excess LSZ 
present in the mixtures. Due to its electronic structure and chirality, the tryptophan within LSZ 
will naturally absorb more left polarized light than right leading to a slight increase between 280 
nm and 300 nm wavelengths.161  As shown in Figure 53, even after sonication and centrifugation, 
the aqueous LSZ solutions show a tryptophan peak between wavelengths of 280 nm and 300 nm; 
this is consistent with literature values for LSZ.162   However, the addition of SWNT quenches 
the optical polarity at these wavelengths by approximately 23% in the supernatant. The change in 
structure observed in the CD spectrum upon interaction with SWNT is believed to be due to the 
electronic structure and hydrophobic core environment of LSZ, specifically tryptophan, being 
altered as a result of the a hydrophobic, ?-? stacking interaction between the LSZ and SWNT. 
The final methods used to elucidate the specific interaction between LSZ and SWNT 
were fluorescence spectroscopy and anisotropy. The dominant fluorophore within LSZ is 
tryptophan which has an excitation of 280 nm. Tryptophan?s maximum emission wavelength is 
highly sensitive to the polarity of the surrounding environment, but is generally around 335 nm. 
In addition to effects of solvent polarity on the fluorescence of tryptophan, binding can cause two 
changes: shifts in the emission maximum wavelength and in fluorescence intensity.163-164 Horsely 
et al.30b were able to determine the quenching constant for bound LSZ by probing the tryptophan 
excitation and showed that it increased when bound to variously charged silica surfaces. 
Therefore, it would be expected that the tryptophan emission fluorescence intensity would 
decrease, or quench, in LSZ-SWNT dispersions if the tryptophan residue was bound to SWNT. 
142 
 
 
Figure 53. Circular dichroism spectrum of 0.5 wt.% LSZ solution and 0.5 wt.% LSZ ? 0.1 wt.% 
SWNT supernatant which shows the loss of the tryptophan peak between wavelengths of 280 nm 
and 300 nm due to the interaction between the LSZ tryptophan and the sidewall of SWNT. The 
molar ellipsticity of the LSZ solution has been upshifted to that of the LSZ-SWNT supernatant 
for clarity. 
 
The LSZ and LSZ-SWNT supernatant were excited at 280 nm to specifically probe the 
tryptophan fluorescence within LSZ for proof of LSZ interaction with SWNT and specific 
interaction of tryptophan with SWNT. Since the absorption of excitation light at 280 nm by 
SWNT could result in false interpretation of fluorescence quenching, the extinction coefficients 
of both LSZ and SWNT were determined through differential absorbance at varying dilution 
factors (see supporting information) and used to obtain a corrected LSZ-SWNT supernatant 
143 
 
emission spectrum. Figure 54 shows the fluorescence emission spectrum of the LSZ solution and 
the corrected spectrum of the LSZ-SWNT supernatant dispersion. Even after sonication, the fact 
that the tryptophan fluorescence within the LSZ-SWNT dispersion is still quenched by 
approximately 13% relative to the processed LSZ solution provides further evidence of 
tryptophan-SWNT interaction. It is hypothesized that the quenching of the tryptophan 
fluorescence results from ?-? stacking interaction which occurs between the tryptophan residue 
and the sidewall of SWNT.165 To further illuminate the interaction between LSZ and SWNT, 
anisotropic fluorescence measurements were performed. Fluorescence anisotropy is 
concentration independent and ideally suited for measuring binding events, especially the 
association of proteins with other molecules.123 Due to changes in rotational freedom, binding of 
proteins to other molecules increases the dependence of their fluorescence on the polarity of the 
excitation light. Based on the concentration of LSZ and SWNT present in the sample used for 
anisotropy measurements, for every individual SWNT present there were approximately 1800 
LSZ molecules present. Even if full coverage of each SWNT is assumed,  only  400 LSZ 
molecules bind to SWNT, leaving an excess of 1400 LSZ molecules in solution. Therefore, the 
change in anisotropy of LSZ bound to SWNT was not very pronounced due to the presence of 
unbound LSZ. Tracking the fluorescence emission at 345 nm, the anisotropy of LSZ solutions 
was observed to be 0.160 and that of the LSZ-SWNT supernatant solutions was 0.166, as shown 
in the inset of Figure 54. Although this difference of 0.006 seems small, the result was consistent 
over all tests and statistically significant. A t-test of the data collected for each solution revealed 
p < 0.0001 indicating that the means were distinctly different. In conjunction with the 
fluorescence quenching, the anisotropy increase shows a direct, binding interaction between LSZ 
144 
 
and SWNT that was shown through emission quenching to be tryptophan interacting with the 
SWNT sidewall. 
 
Figure 54. UV-vis fluorescence spectra of 0.5 wt.% LSZ solution and 0.5 wt.% LSZ ? 0.1 wt.% 
SWNT supernatant excited at 280 nm showing the quenching of the fluorescence intensity of the 
LSZ-SWNT supernatant due to the binding of excitation-probed tryptophan within LSZ with 
SWNT. The inset shows the results of the anisotropy measurements with error. 
 
 For this research it was imperative to be able to determine the dilute and concentrated 
concentrations. For concentrated samples, TGA can be used to directly determine the 
concentrations. In order to determine the concentration of LSZ and SWNT in the dilute phase, 
UV-vis was used. First, bulk mixtures of LSZ-SWNT were analyzed to determine absolute LSZ 
and SWNT absorbance, at 280 nm and 506 nm respectively, as a function of concentration and a 
145 
 
calibration curve was formed for both SWNT absorbance versus concentration and LSZ 
absorbance versus concentration as shown in Figure 55 and Figure 56. Second, supernatants of 
LSZ-SWNT were analyzed to determine the absorption of both LSZ and SWNT. Finally, the 
supernatant LSZ-SWNT absorption at both 280 nm and 506 nm was super imposed on the bulk 
mixture calibration curves to give the actual concentration of LSZ and SWNT in the supernatant. 
It should be noted that the initial volume for each dispersion was 100 mL. From this analysis it 
was determined that after centrifugation approximately 92% of the SWNT is centrifuged out, and 
approximately 49% of the excess LSZ is centrifuged out. Table 2 and Table 3 show the data used 
in this analysis. 
 
Figure 55. SWNT calibration curve for mixture and supernatant showing absorbance at 506 nm 
versus volumetric concentration of SWNT. As can be seen the supernatant curve super imposed 
perfectly onto mixture curve. Data for this figure can be seen in Table 2. 
146 
 
 
Initial SWNT Concentration 
(vol. %) 
Actual SWNT Concentration 
(vol. %) 
Absorbance 
(? = 506 nm) 
M
ixture
 0.0697 0.06967 0.9495 0.0557 0.05573 0.7578 
0.0418 0.04179 0.5770 
0.0279 0.02786 0.3780 
0.0139 0.01393 0.2015 
Su
pe
rn
atan
t 0.0697 0.00545 0.0741 
0.0557 0.00436 0.0602 
0.0418 0.00327 0.0442 
0.0279 0.00218 0.0304 
0.0139 0.00109 0.0143 
Mixture Trendline Slope 13.66 
Supernatant Trendline Slope 1.07 
Relative Coefficient 0.08 
Table 2. UV-Vis SWNT calibration curve data. Supernatant SWNT concentration determined 
via superposition of absorption data onto SWNT mixture calibration curve. 
 
Figure 56. LSZ calibration curve for mixture and supernatant showing absorbance at 280 nm 
versus volumetric concentration of LSZ. The supernatant curve super imposed directly onto 
mixture curve. Data for this figure can be seen in Table 3. 
147 
 
 
Initial LSZ Concentration 
(vol. %) 
Actual LSZ Concentration 
(vol. %) 
Absorbance 
(? = 280 nm) 
M
ixture
 0.2981 0.29813 3.0315 0.2384 0.23841 2.4607 
0.1787 0.17874 1.8621 
0.1191 0.11911 1.2584 
0.0595 0.05953 0.7121 
Su
pe
rn
atan
t 0.2981 0.15279 1.5465 
0.2384 0.12218 1.2482 
0.1787 0.09160 0.9606 
0.1191 0.06104 0.6728 
0.0595 0.03051 0.3767 
Mixture Trendline Slope 10.32 
Supernatant Trendline Slope 5.29 
Relative Coefficient 0.51 
Table 3. UV-Vis LSZ calibration curve data. Supernatant LSZ concentration determined via 
superposition of absorption data onto LSZ mixture calibration curve. 
 
This section has provided additional evidence of the close interaction between LSZ and 
SWNT and not only supported but refined previously reported hypotheses that the interaction is a 
hydrophobic one involving ?-? stacking. The results of this work verify that there is a direct 
molecular interaction between LSZ and SWNT through the indole moiety of tryptophan and the 
aromatic sidewall of SWNT. These results shed light on the interactions between LSZ and 
nanotubes and reveal important information for the molecular design and manipulation of 
nanomaterials and biopolymers. Furthermore, these results provide a foundation for additional 
work on elucidating the interactions between pristine carbon materials and other proteins. 
4.3. LYSOZYME ? CARBON NANOTUBE PHASE BEHAVIOR 
Aqueous solutions of LSZ have been shown to be an effective dispersant of low 
concentrations of individual SWNT, however, there were no previous studies on the rheological 
characterization or phase behavior of higher concentration dispersions. This section, describes 
148 
 
the application of optical microscopy and rotational rheology to dilute to concentrated LSZ-
SWNT dispersion rheology and phase behavior. It should also be noted that each data set was 
collected over three separate loadings with three runs per loading for a total of nine runs per test. 
The LSZ-SWNT dispersions were shown to have a defined phase transition where an increase in 
the number and size of SWNT aggregates was seen and the elasticity of the dispersions was 
increased due to the formation of physical LSZ networks. The depletion effect and network 
formation were further validated by the increase of viscosity with concentration after aggregation 
of SWNT. Finally, various ratios of LSZ:SWNT supernatant and mixture dispersions were 
shown to collapse onto a master viscosity curve after accounting for the presence of LSZ. The 
ability to produce and tailor the unique properties of biomolecule-SWNT dispersions through 
changes in processing method represents a significant advancement in the future development of 
functional materials with synergistic properties of biomolecules and SWNT. This was achieved 
by first understanding, the microstructure and aqueous phase behavior of LSZ-SWNT 
dispersions. LSZ-dispersed SWNT show unique interactions,9 and the LSZ activity is maintained 
throughout fiber and film processing methods; this will be discussed further in later sections. To 
fully understand the structure-property-processing relationship between initial dispersions of 
LSZ-SWNT and the final macroscopic assembly properties, rheological characterization of each 
constituent of the system was completed in addition to the combined dispersion. Previous 
rheological characterization of LSZ solutions to this point have consisted primarily of interfacial 
rheology166-168, rheology of LSZ within gel40, 42, 45, 48, 50 or liquid crystalline52-53 systems, or 
computational simulation of aqueous LSZ solutions.169 Rheological characterization of SWNT 
dispersions has been ever evolving since their discovery to include the understanding of phase 
behavior for SWNT in superacids,68, 149, 170 SWNT-polymer systems,6, 109, 171-173 and even SWNT-
149 
 
biomolecule dispersions.3-4, 174-175 Although characterization of SWNT-biomolecule dispersions 
is available, they primarily consist of SWNT dispersed with other rod-like molecules such as 
hyaluronic acids or deoxyribonucleic acids which form liquid crystalline systems. Until now, no 
extensive experimental phase behavior or rheological characterization has been done on 
spherical biomolecule-dispersed SWNT solutions such as LSZ-SWNT. 
 In order to fully understand the phase behavior of LSZ-SWNT dispersions, it is first 
advantageous to understand the phase behavior theory of hard rods with hard spheres, as 
discussed previously. The phase behavior of any mixed colloidal system is found by minimizing 
the free energy of mixing. The particles present in LSZ-SWNT dispersions cannot interpenetrate 
and the interaction energy is constant as long as the particles maintain interaction.90, 176 
Therefore, the phase behavior is determined by maximizing the mixing entropy. For entropically 
determined ordering, phase transitions or demixing are driven by differences in physical 
properties, such as shape, which can create bulk or microphase separation.90 For rod-sphere 
systems, the physical and thermodynamic origin of this separation can be explained in terms of 
the depletion interaction between molecules which is entropically driven by the sum of 
electrostatic and steric repulsive forces, and van der Waals attractive forces.93-95 When a rod and 
sphere approach each other, their individual depletion zones will overlap increasing the 
translational entropy of the system at the expense of the mixing entropy.177 At low sphere 
concentration, the mixing entropy dominates and the mixture is miscible. However, with 
increasing sphere concentration the mixing entropy decreases (due to the rise in translational 
entropy) and phase separation will occur.87, 92, 96, 177 Bulk phase separation, which is common to 
rod-sphere systems, occurs when the rods and spheres completely separate (in the absence of any 
interaction) forming a rod-rich and sphere-rich phase.89 Another less common type of separation 
150 
 
seen in rod-sphere systems is that of microphase separation. In microphase separation the system 
starts demixing into regions which are either rod- or sphere-rich. However, unlike bulk 
separation, the liquid-like regions grow to a critical size at which point they can form kinetically 
stable three-dimensional equilibrium structures.89-90 Although demixing will occur for LSZ-
SWNT systems, it is important to note that through variation of parameters such as sphere or rod 
diameter or concentration it is possible to create other types of phases and phase separation.87, 89-
90 LSZ-SWNT systems will inherently show some deviation from current theory for three 
primary reasons: 1. the aspect ratio of SWNT is significantly greater than rods typically used in 
the theoretical simulations,178 2. LSZ is not perfectly spherical nor considered a hard sphere,135, 
161, 169 and 3. LSZ and SWNT interact with one another.9 
The phase behavior of LSZ-SWNT dispersions is complex and highly dependent upon 
constituent concentrations. LSZ-SWNT dispersions begin as an isotropic liquid and transition to 
a gel as the concentrations of LSZ and SWNT are increased. The increase in LSZ concentration 
is what causes the transition to a gel. Depletion of LSZ from between SWNT at a critical 
concentration creates an increased LSZ concentration surrounding the SWNT bundles or 
aggregates in a given volume. The increased concentration of LSZ leads to the formation of a 
physically networked gel structure, which increases elastic behavior.179 
 The aggregation state of the dispersions was first characterized by cross-polarized optical 
microscopy. The optical phase behavior transitions of LSZ-SWNT, shown in Figure 57, can be 
seen as the concentration where the number and size of SWNT aggregates increases. It should be 
noted that the clusters seen should also be flocs which have formed at the secondary energy 
minimum predicted by DLVO theory, however, the exact thermodynamic nature of the clusters 
is unknown and will henceforth be referred to as aggregates. 
151 
 
 
Figure 57. Phase transition diagram for LSZ-SWNT showing the LSZ and SWNT concentration 
at transition. In addition, the rheological parameter tan(?) shows the increase in elasticity at each 
ratio across the transition indicating the formation of a physically gelled network. 
 
The increase in aggregation is due to a depletion interaction between the spherical LSZ and 
cylindrical SWNT, which is similar to the depletion interactions of colloids and polymers. The 
depletion physically occurs as the concentration of LSZ and SWNT increase in a given volume 
causing the overlap of independent depletion zones. The LSZ acts as a depletant which causes 
attractive interactions between the SWNT. Depletion is effective at any concentration of SWNT, 
however this attractive interaction induces a phase separation of the SWNT only when the LSZ 
concentration is sufficiently large. The system phase separates between a SWNT rich phase and 
SWNT dilute phase. The loss of mixing entropy of the SWNT is compensated by the reduction 
of excluded volume of the LSZ as the SWNT are packed together. This leads to an increase of 
the translational entropy of LSZ. Here the SWNT rich phase does not reach true thermodynamic 
equilibrium. Instead this phase is in the form of amorphous aggregates. The system can be 
viewed as a kinetically arrested microphase separation. On the other hand, at significantly low 
152 
 
concentrations of LSZ, the electrostatic and steric stabilization of SWNT is reduced and the 
SWNT naturally reaggregate due to the strong van der Waals forces of attraction. As a 
consequence, there exist an optimum concentration range of LSZ to achieve homogenous 
dispersions of stabilized SWNT. This phase behavior is quantitatively seen through the 
rheological parameter tan(?) as shown in Table 4; tan(?) is the ratio of the viscous modulus to the 
elastic modulus and is therefore a measurement of the elasticity of a material. The decrease in 
tan(?) across the transition at each volume ratio indicates an increase in the elasticity of the 
dispersion microstructure. This reflects the presence of a physical network created by the 
depletion induced aggregates of SWNT. As can be seen from Table 4, the concentration of 
SWNT at transition was approximately 0.1 vol.% for all ratios. This indicated a possible critical 
SWNT concentration at 0.1 vol.% SWNT at which the overlapping depletion zones of LSZ and 
SWNT create an interaction potential great enough to remove the intercalated LSZ and force 
SWNT reaggregation. Another interesting note from Table 4 is the increase in viscosity from the 
monophasic to the demixed phase. For dispersions of rigid rods, increasing the concentration up 
to or past the point of aggregation should cause a decrease in the elasticity and viscosity of the 
dispersion.61, 98, 104 The decrease is due to the loss of rigid rod-solvent interactions and 
homogeneity within the dispersion which would decrease the elasticity and viscosity of the 
dispersion due to the loss in interfacial surface area of the rigid rods at aggregation leading to 
more fluid-like character of the dispersions.61, 98 Therefore, the aggregated state of SWNT in the 
demixed phase would create a decrease in elasticity and viscosity. However, the creation of the 
physically networked LSZ after depletion aggregation causes the elasticity and viscosity of the 
dispersion to increase. 
 
153 
 
Dispersion                      
(Volumetric Ratio) 
Monophasic Demixed 
tan(?) Viscosity (Pa-s) [SWNT] (vol.%) [LSZ] (vol.%) tan(?) Viscosity (Pa-s) [SWNT] (vol.%) [LSZ] (vol.%) 
8.5:1.0 LSZ:SWNT 
Mixture 0.464 0.464 0.079 0.673 0.193 5.700 0.092 0.782 
6.4:1.0 LSZ:SWNT 
Mixture 0.424 0.424 0.098 0.627 0.226 4.371 0.114 0.730 
4.3:1.0 LSZ:SWNT 
Mixture 0.659 0.659 0.073 0.312 0.298 1.213 0.080 0.342 
2.1:1.0 LSZ:SWNT 
Mixture 0.650 0.650 0.152 0.326 0.184 6.716 0.166 0.355 
Table 4. Phase behavior transitions showing the increase in elasticity by the change in tan(?), the 
increase in viscosity, and the LSZ and SWNT concentrations for the monophasic and demixed 
regimes. 
 
It should be noted that the supernatant, which is in equilibrium with the precipitate of SWNT 
aggregates, contains a low volume fraction of SWNT. Subsequently, evaporation of the 
supernatant did not result in any depletion. However, the supernatant should not be viewed as a 
separately processed dispersion of LSZ-SWNT but rather a LSZ-SWNT dispersion with a lower 
volume fraction of LSZ and SWNT present, which represents the dilute regime of the LSZ-
SWNT phase behavior. 
In order to probe the microstructure of LSZ-SWNT amplitude and frequency sweep 
oscillatory rheology tests were run. Figure 58 shows the storage modulus from an amplitude 
sweep for increasing concentrations of LSZ-SWNT. As would be expected for a system that 
transitions from isotropic liquid to gel, the elastic behavior increases as the concentration of 
SWNT and LSZ are increased. The important information gained from the amplitude sweep is 
that the critical strain and linear viscoelastic region are consistent among all concentrations 
tested. The critical strain was determined via graphical analysis to be approximately 2.5% to 
3.9%. Another interesting note is that increases in SWNT concentration of approximately 0.5 
154 
 
vol.% can lead to increases in the solid-like response of a liquid of approximately four orders of 
magnitude. 
 
Figure 58. Amplitude sweep test data showing storage modulus as a function of amplitude strain 
for concentrations of 0.0494 vol.% SWNT, 0.0644 vol.% SWNT, 0.1174 vol.% SWNT, 0.1463 
vol.% SWNT, 0.2052 vol.% SWNT, 0.2828 vol.% SWNT and 0.4195 vol.% SWNT. Error for 
each concentration was less than +/- 5%. Open symbols indicate supernatant dispersions. 
 
 After determination of the critical strain, the linear viscoelastic oscillatory response of the 
dispersions was tested to probe the time-dependent behavior of increasing concentrations of LSZ 
and SWNT. Figure 59 shows the loss and storage modulii for increasing concentrations of LSZ 
and SWNT. As expected, the elastic behavior increases with increasing concentration showing 
an important trend that the slope of the storage modulus decreases with increasing concentration. 
155 
 
The slope for 0.0494 vol.% SWNT was approximately 0.5, the slope for 0.2052 vol.% SWNT 
was approximately 0.1, and the slope for 0.4195 vol.% SWNT was approximately zero. This is 
an indication that with increasing concentration the elasticity of the dispersion becomes more 
frequency-independent and in addition the decreasing slope indicates that there was the 
formation of a percolated network. More specifically in the case of LSZ-SWNT the network was 
a physically gelled network created by LSZ in addition to the physical percolation of SWNT 
bundles and aggregates at high concentrations as shown in Figure 57. 
 
Figure 59. Linear viscoelastic oscillatory response showing a.) loss and b.) storage modulus as a 
function of angular frequency for concentrations of 0.0494 vol.% SWNT, 0.0644 vol.% SWNT, 
0.1174 vol.% SWNT, 0.1463 vol.% SWNT, 0.2052 vol.% SWNT, 0.2828 vol.% SWNT and 
0.4195 vol.% SWNT. Error for each concentration is less than +/- 5%. Open symbols indicate 
supernatant dispersions. 
 
Figure 60 shows the storage and loss modulus of 0.0494 vol.% SWNT and 0.1174 vol.% SWNT 
versus angular frequency to show the crossover point from elastically dominated dispersion to 
viscous dominated dispersion. The crossover for 0.1174 vol.% SWNT was approximately 0.015 
156 
 
s-1 indicating that at frequencies below that the dispersion will have more fluid-like character. 
However, the crossover for 0.0494 vol.% SWNT was approximately 0.15 s-1. 
 
Figure 60. Linear viscoelastic response for the storage and loss modulus of 0.0494 vol.% SWNT 
and 0.1137 vol.% SWNT dispersions as a function of angular frequency showing the crossover 
point and how that point increases frequency with decreasing SWNT concentration until the fluid 
character of the dispersion completely dominates the elastic character over all frequencies. Error 
for each concentration is less than +/- 5%. Open symbols indicate supernatant dispersions. 
 
The increase of crossover frequency is indicative that the viscous character of the dispersion will 
increase until it completely dominates at lower LSZ and SWNT concentrations.  To further 
elucidate the elastic response of each dispersion with increasing concentrations of LSZ and 
SWNT, tan(?) was plotted versus angular frequency as shown in Figure 61a. This shows that for 
157 
 
all bulk LSZ-SWNT dispersions, the elastic nature of the dispersion dominated of the viscous 
nature. Furthermore, tan(?) trended with SWNT concentration in a power law fashion as seen in 
Figure 61b. 
 
Figure 61. Graphical analysis of tan(?) versus a.) angular frequency and b.) SWNT 
concentration showing that for LSZ-SWNT dispersions the elastic behavior typically dominates 
the viscous behavior, and that tan(?) scales with concentration by a power law with a statistical 
R2 of 0.97. Error for each concentration is less than +/- 5%. Open symbols indicate supernatant 
dispersions. 
  
After the microstructure was probed by oscillatory testing, the viscosity of the dispersions 
was determined via steady shear flow curve testing. For all concentrations of LSZ-SWNT 
dispersions the flow characteristics were the same. Each concentration showed shear thinning 
behavior over the entire range of shear rates tested as shown in Figure 62. 
158 
 
 
Figure 62. Flow curve showing viscosity versus shear rate for concentrations of 0.0494 vol.% 
SWNT, 0.0644 vol.% SWNT, 0.1174 vol.% SWNT, 0.1463 vol.% SWNT, 0.2052 vol.% SWNT, 
0.2828 vol.% SWNT and 0.4195 vol.% SWNT, and a power law model fit. The power law 
model, as shown by Equation 4.2, has K = 1.88 Pa-s2 and n = 0.048. Error for each concentration 
is less than +/- 5%. Open symbols indicate supernatant dispersions. 
 
The shear thinning behavior of LSZ-SWNT indicates the tumbling and flow alignment of 
SWNT. With regard to actual nature of the dispersion, the gel nature of the concentrated LSZ-
SWNT dispersion and the isotropic liquid nature of the initial dispersion follows a power law 
fluid as described by Equation 4.2. For the entire concentration range studied, from 0.0050 vol.% 
SWNT to  0.4195 vol.% SWNT, K varies from 0.25 Pa-s2 to 10 Pa-s2 and n varies from 0.01 to 
0.25. From the flow curve data, it is important to note that there is no initial or final plateau over 
159 
 
the shear rates tested. When shear measurements are being taken, it is important to understand if 
any other forces are acting on the particles in the dispersion, as discussed in Section 2.6.7. 
Equations 2.69 and 2.70 were used to determine if the Brownian motion of the SWNT had any 
effect on the rheological shear data obtained. The calculations were done on the most dilute 
dispersions, 0.295 vol.% LSZ ? 0.005 vol.% SWNT, at the lowest possible shear rate that was in 
torque, as required by Equations 2.69 and 2.70. The rotary diffusivity was calculated to be 17.16 
s-1 which generated a Peclet number of 0.0005 indicating that Brownian motion is in fact relevant 
in the dispersions under shear. This result was predicted by Larson who found that for particles 
whose longest dimension is less than 10 ?m the Peclet number will be much less than unity, and 
therefore Brownian motion must be considered.98 Considering the length of the SWNT used was 
on the order of 1 ?m it holds that Brownian motion could create effects in the rheological data of 
the system.180 To further show how dispersions, such as LSZ-SWNT, can deviate from classical 
systems the application of the Cox-Merz rule was determined for LSZ-SWNT dispersions. 
Deviations from the Cox-Merz rule can elucidate interactions among constituents in dispersions 
and show how systems deviate from idealized systems. The Cox-Merz rule, given in Equation 
4.6, states that for corresponding values of shear rate,   , and angular frequency, ?, the steady 
shear viscosity, ?, and complex viscosity,   , will have the same values.100 
                                                                                       
Figure 63 shows the steady shear viscosity and complex viscosity versus shear rate and angular 
frequency, respectively, for various concentrations of LSZ-SWNT dispersions. 
160 
 
 
Figure 63. Deviation from the Cox-Merz rule for 0.0494 vol.% SWNT, 0.1463 vol.% SWNT, 
and 0.2052 vol.% SWNT dispersions. Deviation occurs due to the physical gel network formed 
after the depletion interaction present in LSZ-SWNT dispersions. Error for each concentration is 
less than +/- 4%. Open symbols indicate supernatant dispersions. 
 
From Figure 63, it is obvious that LSZ-SWNT dispersions deviate from the Cox-Merz rule. This 
is due to the physical interactions that take place between LSZ and SWNT, and also due to the 
gel network that is forming as the concentration of LSZ and SWNT is increased. Of note in 
Figure 63 is that as the concentration of SWNT and LSZ increase, the deviation of the Cox-Merz 
rule increases. For 0.0494 vol.% SWNT the deviation is approximately 70%, for 0.1463 vol.% 
SWNT the deviation is approximately 76%, and for 0.2052 vol.% SWNT the deviation is 
approximately 83%, indicating that the elasticity of the gel network is increasing which is 
161 
 
causing the deviation to increase. Mezger affirms that the Cox-Merz rule holds for many 
polymer solutions, however, fails for most dispersions.100 This is primarily due to the chemical 
and physical attractive and repulsive nature of the constituents of the dispersions which were not 
accounted for in the development of the Cox-Merz rule. The upturn at high frequencies is likely 
due to the inertia of the measuring system. 
 The interaction of LSZ with SWNT has been shown spectroscopically9, 181 and now 
through rheological analysis. However, from Figure 62 it can be surmised that the viscosity of 
LSZ-SWNT dispersions does not scale linearly. In fact, after analysis of LSZ-SWNT viscosity 
versus LSZ and SWNT concentration independently, there is no definitive trend across all 
concentrations tested. This is likely due to the fact that the viscosity of the LSZ-SWNT 
dispersion is a function of not just LSZ or SWNT concentration but rather both. In order to 
account for the various concentrations of both LSZ and SWNT present at each data point, the 
reduced and inherent viscosity at each data point was determined. The reduced and inherent 
viscosities, shown in Equations 4.7 and 4.8, were used to compare the deviation of LSZ-SWNT 
dispersion rheology from that of typical rod rheology (reduced viscosity), and to show the trend 
of LSZ-SWNT viscosity data (inherent viscosity).  
              
       
                                                                            
               
    
                                                                                   
The relative viscosity, ?r, was calculated as the LSZ-SWNT dispersion viscosity,?, divided by 
the LSZ viscosity,?s, for the specific concentration of LSZ present in the dispersion, where 
?SWNT is the volume fraction of SWNT in the respective dispersion. By accounting for both the 
LSZ and SWNT present in each dispersion, it can be shown that the inherent viscosity of the full 
range of concentrations of LSZ-SWNT dispersions can be modeled as a power law versus 
162 
 
SWNT concentration, as shown in Figure 64a. Figure 64b show the reduced viscosity of dilute 
dispersions of LSZ-SWNT as a function of shear rate to show the deviation of LSZ-SWNT from 
typical rod rheology. The reduced viscosity versus shear rate for dilute dispersions of SWNT 
should follow the theory of Kirkwood and Plock at Weissenberg numbers above 1, which states 
that the log-log plot of reduced viscosity versus shear rate will have a slope of -0.5. This has 
been validated in experiment by Davis et al. who found that for SWNT in superacid, in the dilute 
phase, the reduced viscosity versus shear rate curve had a slope of -0.5.5 The dashed line in 
Figure 64b is a slope of -0.50, but the data much more closely follows the solid line which has a 
slope of -0.74. This is a definitive indication that LSZ-SWNT dispersion rheology does not 
follow that of typical SWNT or rigid-rod rheology. 
The dilute solution data ? SWNT concentrations less than 0.01 vol.% as determined from 
the maximum of the dilute to semi-dilute transition for the SWNT used from Doi & Edwards104 ? 
for both reduced and inherent viscosity can be used to find the intrinsic viscosity of SWNT based 
on models developed for polymer solutions.182 Although LSZ-SWNT does not follow the rigid 
rod rheology theory of Kirkwood and Plock, the dilute phase data was used to compare the 
intrinsic viscosity of LSZ-SWNT dispersions with the intrinsic viscosity of SWNT dispersions 
which follow rigid rod rheology. The reduced viscosity as a function of concentration, as shown 
in Equation 4.9, was used by Huggins to correlate the intrinsic viscosity where k? has been 
termed the Huggins constant.79-80 For this equation, the viscosities should be taken at the lowest 
possible shear rate for extrapolation to zero concentration. Therefore each viscosity is from a 
shear rate of 0.1 s-1. 
    
              
                                                                       
163 
 
Figure 64c shows the dilute phase reduced viscosity as a function of concentration to determine 
the intrinsic viscosity. 
 
Figure 64. a.) Inherent viscosity versus SWNT concentration at a shear rate of 0.1 s-1 showing 
power law fit with a statistical R2 of 0.99, b.) reduced viscosity versus shear rate showing lines 
with slopes of -0.50 (dashed) and -0.76 (solid) (note all concentrations are supernatant 
dispersions), c.) the reduced viscosity linear fit of dilute, supernatant concentration data with a 
statistical R2 of 0.78. Error for each concentration is less than +/- 4%. 
 
By fitting a linear trendline through the dilute reduced viscosity solution data and extrapolating 
to zero concentration, it is possible to determine the intrinsic viscosity. The reduced viscosity 
gives an inherent viscosity of 7290. It is of distinct importance to note that the dilute solution 
164 
 
reduced viscosity data gives an intrinsic viscosity that is within 1% of the values in literature for 
SWNT intrinsic viscosity.149 
The complex nature of LSZ-SWNT dispersions has been shown through oscillatory and 
steady-shear rheological analysis in addition to optical microscopy. Analysis of the viscoelastic 
oscillatory response indicates the physical networking of LSZ after the development of depletion 
induced aggregates with increasing LSZ and SWNT concentration.  Furthermore, it shows that 
the elasticity of LSZ-SWNT dispersions scales by a power law with respect to SWNT 
concentration. Analysis of the steady shear viscosity shows shear thinning, power law nature of 
LSZ-SWNT dispersions versus shear rate, the complex interaction of LSZ-SWNT through the 
deviation from Cox-Merz, and the collapse of all LSZ-SWNT dispersions on to a master curve 
by accounting for the presence of both LSZ and SWNT through use of inherent viscosity. 
Understanding the rheological nature and phase behavior of LSZ-SWNT dispersions aids in their 
processing and macroscopic development. 
4.4. LYSOZYME - CARBON NANOTUBE PHASE BEHAVIOR ALTERATION 
Several groups have demonstrated that aqueous solutions of LSZ are an effective 
dispersant of low concentrations of individual SWNT. In this research, concentrated dispersions 
of LSZ-SWNT were shown to have a defined phase transition where an increase in the number 
and size of SWNT aggregates occurred. Increased aggregation in LSZ-SWNT dispersions 
decreases the opportunity to translate the unique properties of SWNT to practical applications by 
reducing the surface-to-volume ratio and by limiting processability. To decrease the size and 
number of aggregates, as well as shift the concentration at which aggregation occurs to a higher 
value, TTAB, a cationic surfactant, was added to the LSZ-SWNT dispersions. This section 
165 
 
describes how the addition of TTAB increased dispersion stabilization and increased the SWNT 
concentration at which aggregation occurred by an order of magnitude. 
The cationic surfactant 0.34 vol.% TTAB was added to the initial mixtures of LSZ-
SWNT. Surfactants have played a major role in the study and assembly of SWNT since their 
discovery.54, 183-185 The likely mechanism of SWNT dispersion with surfactants for this system is 
based on the surface charging of SWNT.186 Surfactants adsorb on SWNT by their hydrophobic 
tails. The hydrophilic heads of the surfactant create an effective charge on the SWNT surface. 
The surface charge then creates an electric double-layer. This double-layer induces an 
electrostatic repulsion and stabilizes the SWNT against aggregation from van der Waals forces 
as predicted by Derjaguin-Landau-Verwey-Overbeek (DLVO) theory.59 However, zeta-potential 
studies of surfactants with SWNT have given insight into the possible interaction with 
SWNT.187-188 Initial thoughts on surfactant interactions with SWNT were that of surfactant 
wrapping of the SWNT invoked the formation of cylindrical micelles around the SWNT with the 
hydrocarbon chains arranged along the SWNT sidewall. However, more recent studies using 
small-angle neutron scattering and density functional theory calculations suggest that the 
interaction is a random and disordered adsorption of surfactant molecule tails onto the SWNT 
surface. Regardless of exact interaction with SWNT, the stabilization mechanism remains that of 
electrostatic repulsion between surfactant molecules leading to colloidal stability as described by 
DLVO theory. TTAB is a cationic surfactant with a positively charged ammonium bromide head 
group and a 14-carbon tail, and was used because it showed a non-inhibitory effect toward the 
lytic activity when conjugated with LSZ. In theory, the TTAB will create a complex with both 
LSZ and SWNT to increase the stabilization of the dispersions. 
166 
 
The interaction of cationic surfactants with LSZ has been well studied.189-192 It is 
generally accepted that the binding of TTAB to LSZ occurs by a combination of electrostatic and 
hydrophobic interactions. More specifically, Hayashi et al.190-191 and Subramanian et al.192 have 
shown through optical spectroscopy that the saturated TTAB tail binds with surface bound indole 
moieties of tryptophan and phenolic moieties of tyrosine amino acid residues along with exposed 
carboxyl groups which have been ionized by the aqueous environment. In addition to the 
interaction of TTAB with LSZ, there will also inherently be an interaction between TTAB and 
SWNT. However, there was no literature found on the interaction of cationic surfactants with 
biomolecule-SWNT complexes. Although the multiple interactions ? LSZ-SWNT, LSZ-TTAB, 
TTAB-SWNT, and LSZ-TTAB-SWNT ? are inherently complex and would be difficult to 
deconvolute, it is likely that the interactions are hydrophobic in nature and exist between the 
sidewall of SWNT, hydrophobic core of LSZ, and hydrophobic alkyl-tail of TTAB. 
The addition of TTAB to the LSZ-SWNT dispersions increases the colloidal stability and 
alters the phase behavior transitions of the mixture and supernatant dispersions. Table 5 shows 
the phase behavior transitions of LSZ-TTAB-SWNT mixture and supernatant dispersions. The 
phase transition of LSZ-TTAB-SWNT is shown by the SWNT concentration at which the 
number and size of SWNT aggregates increases. The reason for this aggregation is believed to be 
analogous to that of LSZ-SWNT dispersions. Even in the presence of TTAB, depletion 
interactions can take place.183 
 
 
 
167 
 
Dispersion                                             
(Volume Ratio) 
Demixed 
[SWNT] (vol.%) 
Demixed 
[LSZ] 
(vol.%) 
2.1:1.0 LSZ:SWNT Mixture 0.166 0.355 
2.1:1.0 LSZ:SWNT Supernatant 0.075 1.057 
0.9:1.2:1.0 LSZ:TTAB:SWNT Mixture 1.877 1.596 
0.9:1.2:1.0 LSZ:TTAB:SWNT Supernatant 0.687 1.151 
Table 5. The phase transition concentrations for volumetric each ratio showing the demixed 
concentration of SWNT and LSZ for LSZ-SWNT and LSZ-TTAB-SWNT dispersions. 
 
Table 5 shows the demixed concentration for LSZ and SWNT for the LSZ-SWNT mixture 
containing the largest quantity of SWNT, and the LSZ-TTAB-SWNT mixture and their 
supernatant dispersions. For quantitative comparison, it should be noted that the concentration 
ratios of LSZ:SWNT for TTAB dispersions were significantly lower than original LSZ-SWNT 
dispersions. The LSZ-SWNT phase behavior, indicates that decreasing the LSZ:SWNT ratio 
would decrease the concentration at which aggregation occurs. However, for LSZ-TTAB-SWNT 
the concentration at which the transition occurs is an order of magnitude higher for the mixtures. 
Moreover, the use of TTAB as a stabilizing agent allowed the LSZ-TTAB-SWNT supernatant to 
maintain enough SWNT after centrifugation to show the depletion phase transition. This 
transition occurred approximately two orders of magnitude higher for the LSZ-TTAB-SWNT 
supernatant than the most concentrated LSZ-SWNT supernatant dispersion, which did not go 
through a phase transition. It should be noted that the original LSZ-SWNT supernatant 
dispersion had such a low SWNT concentration that analytical measurement of the exact 
concentration was not possible, therefore it was estimated from a dispersion mass balance. It is 
speculated that the increased size and total charge of the LSZ-TTAB complex compared with 
168 
 
LSZ contributes to the stabilization. This was supported by an increase in the zeta-potential of 
LSZ-TTAB-SWNT from LSZ-SWNT of +24 mV to +31 mV. 
SEM on a dried LSZ-TTAB-SWNT supernatant dispersion qualitatively confirmed the 
presence of a continued interaction between LSZ and SWNT with the addition of TTAB. Figure 
65 shows an opaque SWNT bundle surrounded by a semi-translucent layer of LSZ and TTAB. 
This layer appears similar to the LSZ layer previously reported in the absence of TTAB.9 
 
Figure 65. Scanning electron micrograph of an 0.24 vol.%  LSZ ? 0.34 vol.% TTAB ? 0.28 
vol.% SWNT supernatant dispersion illustrating the interaction between SWNT (opaque) and 
LSZ-TTAB (translucent); magnification is 190,000x. 
 
The presence of TTAB in the translucent shell surrounding the SWNT was confirmed by EDS. 
Six scans of random locations within Figure 65 had an average elemental percentage of 11.8 % 
bromine. This supports the interaction between LSZ, TTAB, and SWNT. It is this cooperative 
interaction which allows for increased stabilization of SWNT. 
169 
 
UV-vis spectroscopy of LSZ-TTAB-SWNT was carried out in order to confirm the 
presence of individual or small bundle SWNT within the dispersion and reveal the difference in 
LSZ-SWNT and LSZ-TTAB-SWNT dispersions. Figure 66 shows UV-vis spectroscopy of the 
supernatant of a 0.24 vol.% LSZ ? 0.28 vol.% SWNT and 0.24 vol.%  LSZ ? 0.34 vol.% TTAB 
? 0.28 vol.% SWNT dispersions. 
 
Figure 66. a.) UV-vis spectroscopy of the supernatant of a 0.24 vol.% LSZ ? 0.28 vol.% SWNT 
and 0.24 vol.%  LSZ ? 0.24 vol.% TTAB ? 0.28 vol.% SWNT dispersions showing sharp van 
Hove singularity peaks between 1.6 and 2.4 eV, elucidating the ability of LSZ-TTAB solutions 
to disperse SWNT as individuals or small bundles; LSZ-TTAB-SWNT down shifted by 0.065 to 
elucidate similarities, b.) UV-vis difference spectra of the supernatant of 0.24 vol.% LSZ ? 0.28 
vol.% SWNT and 0.24 vol.%  LSZ ? 0.24 vol.% TTAB ? 0.28 vol.% SWNT dispersions 
showing a change in the surroundings of the LSZ tryptophan chromophore. 
 
Figure 66a shows sharp van Hove singularity peaks between 1.6 and 2.4 eV for both dispersions, 
making clear the ability of LSZ-TTAB solutions to disperse SWNT as individuals or small 
bundles. The absorbance values of the LSZ-TTAB-SWNT dispersion at ~1.6 eV have been down 
shifted by 0.065 to coincide with the same wave energy absorbance values of the LSZ-SWNT 
170 
 
dispersions. Shifting of the absorbance by an offset value was chosen over normalization, 
because normalization of the data would lead to smoothing and quenching of the peaks. 
Alteration of the peak structure would then not illuminate the dispersibility of SWNT with LSZ-
TTAB solutions. The offset was necessary due to the increased concentration of SWNT 
maintained in the LSZ-TTAB-SWNT supernatant, as described above. In addition to showing 
dispersibility, UV-vis also confirms that the solvent environment surrounding the LSZ is much 
different between the LSZ-SWNT and LSZ-TTAB-SWNT dispersion. Figure 66b shows the 
absorbance difference spectra of the supernatant of a 0.30 vol.% LSZ ? 0.28 vol.% SWNT and 
0.24 vol.%  LSZ ? 0.28 vol.% SWNT ? 0.34 vol.% TTAB dispersions, where 0.30 vol.% LSZ 
solution absorbance values have been subtracted to clarify the difference in the solvent 
environment of the LSZ chromophore tryptophan. As can be seen from the figure, the LSZ-
SWNT dispersions shows a hyperchromic shift whereas the LSZ-TTAB-SWNT dispersion 
shows a hypochromic shift. Shifting in the absorbance intensity of a chromophore is due to 
changes in the solvent surroundings.159-160 Hyperchromic shifts of LSZ are due to the solvent 
surrounding of the LSZ chromophore tryptophan becoming more exposed to aqueous 
environments. This is the case for LSZ-SWNT dispersions when the LSZ hydrophobic core 
opens to bind with the hydrophobic sidewall of SWNT in the aqueous dispersion.9 Hypochromic 
shifts also occur due to changes in the solvent surrounding of the chromophore. For LSZ-TTAB-
SWNT, the hypochromic shift likely occurs due to encapsulation of LSZ or LSZ-SWNT within 
the hydrophobic core of a TTAB micelle. Although the interaction between LSZ, TTAB, and 
SWNT would be difficult to deconvolute, it still disperses SWNT as individuals or small bundles 
as evidence by Figure 65 and 66a. 
171 
 
 For a comparative analysis, rheology of LSZ-TTAB-SWNT dispersions was carried out 
in a manner analogous to that of LSZ-SWNT dispersions. It should first be noted that although 
eight different concentrations of LSZ-TTAB-SWNT dispersions were run, the torque data for 
oscillatory test on six of them was too low to be considered valid data, therefore only the data for 
the two concentrations is shown for oscillatory tests. First, an amplitude sweep was run to 
determine the limit of linear viscoelasticity, as shown in Figure 67. The critical strain was 
determined to be approximately 4.0% as determined by graphical analysis where the correlation 
in the direction of the tangent line of the low-strain plateau was lost. In comparison to LSZ-
SWNT dispersions, the critical strain is higher for dispersions with TTAB. The exact reason for 
this is unknown, however, it is hypothesized that the interactions between the constituents 
structurally stabilizes the dispersion better allowing for absorbance of higher amounts of energy 
prior to deformation. 
 
Figure 67. Amplitude sweep test data for LSZ-TTAB-SWNT dispersions showing storage 
modulus as a function of amplitude strain for concentrations of 0.556 vol.% SWNT and 0.742 
vol.% SWNT. The critical strain was determined to be 4.0%. Error for each concentration is less 
than +/- 2.6%. 
172 
 
After determination of the limit of linear viscoelasticity, the linear viscoelastic oscillatory 
response was probed by a frequency sweep, as shown in Figure 68. Of interesting note for the 
frequency sweep data is that although there is a large jump in the magnitude of the storage 
modulus with the increase in concentration, the slope of the two lines remains similar ? 0.25 for 
0.556 vol.% SWNT and 0.23 for 0.742 vol.% SWNT. This indicates that there is no change in 
the elastic structure of the material, such as the physical networking seen with LSZ-SWNT 
dispersions. 
 
Figure 68. Linear viscoelastic oscillatory response for LSZ-TTAB-SWNT dispersions showing 
storage modulus as a function of angular frequency for concentrations of 0.556 vol.% SWNT and 
0.742 vol.% SWNT. Error for each concentration is less than +/- 3.1%. 
 
173 
 
Finally the viscosity response of the dispersions was probed by steady-shear flow curve testing, 
as shown in Figure 69. Not all concentrations follow a shear-thinning pattern. For concentrations 
lower than 0.199 vol.% SWNT, the dispersions were nearly Newtonian as opposed to the shear-
thinning response of the higher concentration dispersions. Moreover, the most dilute dispersions 
less than 0.1 vol.% SWNT have viscosities that are approximately 0.0014 Pa-s, only slightly 
higher than the viscosity of pure water at 10oC, 0.0013 Pa-s, and significantly lower that the 
LSZ-SWNT dispersion viscosity at the same concentration. Although the exact understanding for 
the difference in shear-thinning versus Newtonian behavior compared to LSZ-SWNT dispersions 
is not known it is likely due to the surface tension effects of adding TTAB to the dispersion. 
TTAB is a surfactant, and surfactants are compounds which decrease the surface tension, or 
interfacial tension, for liquid-liquid, solid-liquid, or liquid-gas systems. 
 
Figure 69. Viscosity response for LSZ-TTAB-SWNT dispersions showing viscosity as a 
function of shear rate for concentrations of 0.079 vol.% SWNT, 0.099 vol.% SWNT, 0.146 
vol.% SWNT, 0.199 vol.% SWNT, 0.375 vol.% SWNT, 0.556 vol.% SWNT, and 0.742 vol.% 
SWNT. Error for each concentration is less than +/- 4.2%. 
174 
 
Surface tension is a contractive force of the surface of a liquid that allows it to resist external 
forces.193 This property is caused by cohesion forces of similar molecules and is a measure of 
energy per unit area. The cohesive forces among liquid molecules are responsible for the 
phenomenon of surface tension. In the bulk of the liquid, each molecule is pulled equally in 
every direction by neighboring liquid molecules, resulting in a net force of zero. The molecules 
at the surface do not have other molecules on all sides of them and therefore are pulled inward 
creating an internal pressure forcing liquid surfaces to experience surface tension.193 Another 
way to view surface tension is in terms of energy. A molecule in contact with a neighbor is in a 
lower energy state than if it were not in contact. More simply, interior molecules having more 
contacts have a lower energy, but the boundary (surface) molecules are missing neighbors and 
have a higher energy.193 Therefore, reducing the surface tension of the dispersion will reduce the 
contractive force holding particles together which could account for the Newtonian-like behavior 
of the dispersions until the concentrations of LSZ and SWNT become significant enough to 
overcome the reduced surface tension. 
 The addition of TTAB was able to stabilize the aggregation of the dispersion to a higher 
concentration. However, the extensional properties of the concentrated LSZ-TTAB-SWNT 
dispersion were still not good enough to produce robust fibers. In order to improve the poor 
extensional properties of the LSZ-SWNT and LSZ-TTAB-SWNT dispersions, various synthetic 
and natural polymers, were combined with the dispersions to assist in fiber spinning. To fully 
understand the effect on the phase behavior of each dispersion with the addition of an elastic 
polymer, rheology of LSZ-SWNT in PVA and LSZ-TTAB-SWNT in PVA dispersions was 
completed. 
175 
 
 An amplitude sweep was run to determine the limit of linear viscoelasticity, as shown in 
Figure 70. The critical strain was determined to be approximately 6.3% for LSZ-SWNT in PVA 
and 10% for LSZ-TTAB-SWNT in PVA as determined by graphical analysis where the 
correlation in the direction of the tangent line of the low-strain plateau was lost. In comparison to 
the LSZ-SWNT or LSZ-TTAB-SWNT dispersions, the critical strain is higher for dispersions 
containing PVA. This is due to the presence of the elastically robust polymer which structurally 
stabilizes the dispersions allowing for absorbance of higher amounts of energy prior to 
deformation. 
 
Figure 70. Amplitude sweep test data for a.) LSZ-SWNT in PVA and b.) LSZ-TTAB-SWNT 
dispersions showing storage modulus as a function of amplitude strain for various 
concentrations. The critical strain was determined to be a.) 6.3% and b.) 10%. Error for each 
concentration is less than +/- 2.4%. 
 
After determination of the limit of linear viscoelasticity, the linear viscoelastic oscillatory 
response was probed by a frequency sweep, as shown in Figure 71. At concentrations below 0.18 
vol.% SWNT, the slopes of the storage modulus lines (~0.5) remains similar for both LSZ-
SWNT and LSZ-TTAB-SWNT. The lack of a change in slope between PVA containing 
176 
 
dispersions with different constituents (TTAB versus no TTAB) compared to the drastic 
differences in the absence of PVA indicates that PVA dominates the elastic response. 
 
 
Figure 71. Linear viscoelastic oscillatory response for a.)LSZ-SWNT in PVA and b.) LSZ-
TTAB-SWNT in PVA dispersions showing storage modulus as a function of angular frequency 
for various concentrations. Error for each concentration is less than +/- 2.6%. 
 
The shear-thinning viscosity response of the dispersions is shown in Figure 72. As with the LSZ-
SWNT and LSZ-TTAB-SWNT dispersions, the shear-thinning behavior of each concentration 
follows different power law parameters. It should be noted that the comparison of magnitudes of 
each dispersion modulus or viscosity will tell which dispersion may be more elastic or flow 
easier, however, the interactions involved in a five component system would need to be 
deconvoluted in order to tell exactly how or why the dispersions responded the particular way 
that they did. 
 
177 
 
 
Figure 72. Viscosity response for a.) LSZ-SWNT in PVA and b.) LSZ-TTAB-SWNT in PVA 
dispersions showing viscosity as a function of shear rate for various concentrations. Error for 
each concentration is less than +/- 5.0%. 
 
 Finally, for a complete comparative analysis of all dispersions ? LSZ-SWNT, LSZ-
TTAB-SWNT, LSZ-SWNT in PVA, and LSZ-TTAB-SWNT in PVA ? the inherent viscosity of 
each dispersion was determined by determining the relative viscosity of each dispersion. The 
relative viscosity equations for each dispersion are shown in Equations 4.10 through 4.13. For 
dispersions containing PVA, the relative viscosity included a correction factor which was the 
viscosity of PVA at the given concentration, ?PVA, to account for the viscosity of PVA in each 
dispersion. 
                     
   
                                                             
                          
   
                                                             
                            
        
                                                             
                                 
        
                                                             
178 
 
The relative viscosity was then plugged in to Equation 4.8 to determine the dispersion inherent 
viscosity. From the relative viscosity it is also possible to determine the intrinsic viscosity of the 
dispersion as shown in Equation 4.9. However, for each dispersion except LSZ-SWNT, the 
dilute regime did not have enough concentrations (data points) to properly determine the intrinsic 
viscosity. The inherent viscosity for each dispersion was then plotted versus SWNT 
concentration; all the data collapsed onto a master inherent viscosity curve for SWNT dispersed 
with LSZ, as shown in Figure 73. To further show the trend, a power law trendline was fit to the 
data and it should be noted that the power law trend has a very similar equation for all 
dispersions to what was initially shown for LSZ-SWNT dispersions. 
 
Figure 73. Inherent viscosity of LSZ-SWNT dispersions versus SWNT concentration at a shear 
rate of 1.0 s-1 showing the collapse of all dispersions on to a master curve with a power law fit 
having a statistical R2 of 0.97. 
179 
 
 The addition of TTAB to LSZ-SWNT dispersions electrostatically stabilized the 
dispersion allowing for higher SWNT concentrations with reduced aggregation. The addition of 
natural or synthetic polymers then altered the phase of LSZ-SWNT or LSZ-TTAB-SWNT 
dispersions from an isotropic liquid to an elastic gel. Through stabilization and alteration of the 
LSZ-SWNT phase behavior, it was then possible to create robust and tailorable macroscopic 
assemblies. 
4.5. LYSOZYME CARBON NANOTUBE MACROSCOPIC ASSEMBLIES 
 Processing of nanomaterial dispersions into macroscopic, solid materials is a challenging 
and active area of research. The two most commonly explored techniques are fiber spinning and 
film casting. In this work, wet and dry fiber spinning as well as film casting were investigated. 
Post-processing of fibers and films was attempted through drawing to attempt to increase the 
mechanical robustness and tailorability of the assemblies. Finally, each film and fiber was 
characterized for important properties including mechanical, electrical, optical, and antibacterial 
analysis. 
4.5.1. FIBERS 
Creating fibers from LSZ-SWNT dispersions was initially attempted by wet spinning. 
Wet solution spinning involves the injection of a concentrated dispersion into a rotating 
coagulation bath. It should be noted that coagulation does not require a rotating bath, however, 
with coagulation being a competitive diffusion event, the rotation allows for keeping constituents 
separated while promoting elongation. The rotation of the coagulation bath creates a drawing 
effect that when coupled with the injection of the dispersion creates a force balanced system 
between the shear force of extrusion and the rotational force of the coagulation bath. To ensure 
the most uniform fiber and the most consistent coagulation, the push and pull forces must be 
180 
 
nearly equal; in order for drawing to occur through coagulation the rotation rate should be 
slightly faster than the injection rate. Therefore the velocity of the injection rate must be nearly 
equal the tangential point velocity were the needle injects the dispersion. If the velocities do not 
closely match two differing discontinuities can occur. First, if the injection rate is too fast, 
coagulation cannot occur uniformly and the fiber will breakdown into small sections rather than 
a continuous fiber. Second, if the injection rate is to slow, then inhomogeneous sections of fiber 
will be formed creating fracture points in the structure due to the lack of adequate injection rate 
to create a homogenous fiber. To determine the correct injection rate, the tangential velocity can 
be calculated from Equation 4.14 where v is the tangential velocity, r is the radius from the 
center of the beaker, and n is the rotational speed at the center. 
                                                                                   
In order to match that velocity, the volumetric injection rate must have an equivalent velocity. 
The volumetric flow rate can be calculated from Equation 4.15 where    is the volumetric flow 
rate, v is the tangential velocity from Equation 4.3, and d is the diameter of the needle. 
      
 
                                                                            
Attempts to wet solution spin LSZ-SWNT dispersions failed due to the presence of aggregates. 
While some small sections of fiber could be obtained by wet spinning into a stagnant 1-butanol 
coagulation bath, the mechanical properties were too poor to enable testing. The increased 
concentration at which aggregation occurs in LSZ-TTAB-SWNT dispersions enabled solution 
spinning. Initial wet spinning of a dilute LSZ-TTAB-SWNT dispersions into a PVA coagulation 
bath was performed in order to capitalize on the previous advances made for conventional PVA-
SWNT fibers.183-184, 194 Wet spinning of a dilute 0.24 vol.%  LSZ ? 0.28 vol.% SWNT ? 0.34 
vol.% TTAB dispersion into a rotating PVA coagulation bath resulted in fibers with smooth 
181 
 
surfaces and cylindrical geometries, and were mechanically robust enough to be tested for tensile 
properties as shown in Table 6. However, coagulation had the unintended consequence of 
eliminating the fiber?s antibacterial activity. Since PVA does not inhibit LSZ activity, as will be 
shown later, it was surmised that the external layer of PVA masked the antibacterial activity of 
LSZ by physically covering the LSZ present on the surface of the SWNT. Dry spinning of a 
concentrated 3.17 vol.% LSZ - 4.63 vol.% TTAB - 3.71 vol.% SWNT dispersion resulted in 
fibers with antibacterial activity, as will be discussed later, but an order or magnitude lower 
Young?s modulus and tensile strength. The dry solution spinning was carried out by injection of 
concentrated dispersions through 0.51 mm diameter needles into molds precut on a Teflon sheet 
at a volumetric rate of 0.5 mL/min. Each fiber was allowed to air dry. Following drying, the 
fibers were removed from the molds for characterization. The order of magnitude difference 
between the dilute LSZ-TTAB-SWNT wet spun (line 1) and concentrated LSZ-TTAB-SWNT 
dry spun (line 2) Young?s modulus and tensile strength are due to the inclusion of PVA in the 
wet spun fibers. In order to gain the elastic and elongational benefits of PVA without completely 
overcoating the LSZ, PVA was incorporated directly into the dispersion. However, exploration 
of numerous solvents failed to coagulate the resultant dispersion; salts were not used since they 
could crystallize into the fiber matrix. Therefore, the resulting fibers were dry spun. Dry spinning 
of free-standing fibers from SWNT dispersions has typically failed due to either solvent 
volatility or a lack of extensional viscosity. In this case, however, dry spinning of continuous 
fibers onto Teflon surfaces was possible. In order to understand the influence of the dispersion 
state on fiber properties, four different dispersions were dry spun at the same conditions. Table 6 
shows the tensile properties of the LSZ-SWNT and LSZ-TTAB-SWNT mixture and supernatant 
dispersions in PVA. 
182 
 
Sample 
Young's 
Modulus     
(GPa) 
Tensile 
Strength (MPa) 
Strain at 
Failure           
(%) 
Toughness 
(J/g) 
LSZ-TTAB-SWNT Mixture                                                   
0.24 vol.% - 0.34 vol.% - 0.28 vol.%                                                              
Wet Spun into 4.10 vol.% PVA      
3.5 ? 0.5 49.1 ? 6.0 3.0 ? 0.7 - 
LSZ-TTAB-SWNT Mixture                                       
3.17 vol.%  - 4.63 vol.%  - 3.71 vol.%                                                                 
Dry Spun 
0.4 ? 0.0 4.5 ? 0.6 1.9 ? 0.3 - 
LSZ-SWNT Mixture in PVA                                            
0.71 vol.% - 0.16 vol.% in 10.21 vol.%                                                        
Dry Spun 
22.3 ? 1.7 723.4 ? 47.5 3.7 ? 0.4 15.6 
LSZ-SWNT Supernatant in PVA                                                                
0.36 vol.% - 0.03 vol.% in 9.99 vol.%  Dry Spun 26.3 ? 1.6 774.5 ? 53.0 37.6 ? 0.8 268.4 
LSZ-TTAB-SWNT Mixture in PVA                                         
1.00 vol.% - 1.44 vol.% - 1.17 vol.% in 9.68 vol.%                                                   
Dry Spun 
32.0 ? 0.3 891.6 ? 30.5 61.2 ? 2.8 385.7 
LSZ-TTAB-SWNT Supernatant in PVA                                       
0.51 vol.% - 0.73 vol.% - 0.24 vol.% in 10.93 vol.%                                                        
Dry Spun 
47.0 ? 1.4 1718.6 ? 93.7 86.9 ? 13.2 660.9 
Table 6. Mechanical test data for LSZ-SWNT and LSZ-TTAB-SWNT fibers from both wet and 
dry spun assembly methods illustrating the effect of dispersion state and processing method on 
the final mechanical properties. 
 
The differences in strength, elasticity, and toughness is a function of the dispersion state from 
which each fiber was made. The respective supernatant fibers have greater strength and tensile 
properties than the respective mixture fibers. This is due to the larger number and size of 
aggregates present within the mixture fibers, which create non-homogenous sections easily torn 
by the stress during mechanical testing. The individual or small bundle SWNT present in the 
supernatant are more easily aligned through flow alignment during syringe-pump injection to the 
molds. This alignment, in addition to reduced aggregation, leads to the increased mechanical 
properties.195 The removal of SWNT aggregates by centrifugation in the supernatant eliminates 
183 
 
discontinuities in the homogeneity of the fiber. It is these discontinuities (SWNT aggregates) 
within the mixture fibers which induce failure during the tensile testing of these fibers thereby 
reducing their overall strength.196 Comparison of the 3.17 vol.% LSZ - 4.63 vol.% TTAB - 3.71 
vol.% SWNT mixture dispersion dry spun not containing PVA shows that there is over a two 
order of magnitude difference in the tensile properties when compared to the 0.71 vol.% LSZ - 
0.16 vol.% SWNT mixture in 10.21 vol.% PVA and 1.00 vol.% LSZ - 1.44 vol.% TTAB - 1.17 
vol.% SWNT mixture  in 9.68 vol.% PVA. It is the inclusion of PVA which creates a synergistic 
effect in increasing the mechanical properties of the fibers, as the contribution of pure PVA to 
the system is estimated at less than 1% of the mechanical strength.197-198 The increased 
mechanical robustness of LSZ-TTAB-SWNT is due to the increased concentration of phase 
transition as seen in Table 5. The decrease in number and size of SWNT aggregates in the LSZ-
TTAB-SWNT allows for better mechanical translation of SWNT properties. 
In addition to ultimate strength and stiffness, particular attention should be given to 
toughness. It is probably one of the most critical parameters in many applications, including 
ballistic and aviation materials, as it is the total energy needed to rupture a fiber. It should first be 
noted that methods of improving toughness in CNT nanocomposite systems are not well-
understood and have been achieved in the past mostly by rather accidental discoveries.199 LSZ-
TTAB-SWNT in PVA mixture and supernatant dry-spun fibers have a toughness of, 386 J/g and 
661 J/g, which is approximately 2.7% and 38.7%, respectively, greater than any previously 
reported toughness values of SWNT composites.199 For comparison, spider silk has a Young?s 
modulus of 4 GPa and a toughness of 217 J/g. Overall, it is hypothesized that the strengthening 
and toughening mechanisms are likely to be a synergistic multiscale action of intermolecular 
interactions, improved load transfer, surface roughening, and energy dissipation. Of particular 
184 
 
interest to this research are previous studies on SWNT composite fibers have shown that PVA 
forms a coating on the nanotubes providing an important interphase region where the toughness 
arises from chain extension in amorphous regions between relatively rigid SWNT and 
amorphous PVA. In addition, slippage between individual nanotubes within bundles might also 
contribute to toughness.199-203 The differences in mechanical properties, dispersion state, and 
processing methods demonstrates the ability for the complex LSZ-SWNT system to be adapted 
to overcome a myriad of obstacles. 
Concentrated dispersions of LSZ-TTAB-SWNT in PVA were further characterized. SEM 
images of 1.00 vol.% LSZ - 1.44 vol.% TTAB - 1.17 vol.% SWNT in 9.68 vol.% PVA and 0.51 
vol.% LSZ - 0.73 vol.% TTAB - 0.24 vol.% SWNT in 10.93 vol.% PVA dry spun fibers show 
varying surface morphology and mechanical robustness through the knot tied in each, as shown 
in Figure 74.183-184 The maintenance of the relatively smooth surface with PVA may be due to 
the hydrogen bond interactions between PVA and the hydrophilic surfaces of LSZ and TTAB. It 
is this interaction which also play critical roles in the mechanical properties of the fibers. 
 
Figure 74. Scanning electron micrographs showing the mechanical robustness (knot) and smooth 
surface morphology of a.) 1.00 vol.% LSZ - 1.44 vol.% TTAB - 1.17 vol.% SWNT mixture in 
9.68 vol.% PVA fiber extruded from a 0.84 mm diameter needle and b.) 0.51 vol.% LSZ - 0.73 
vol.% TTAB - 0.24 vol.% SWNT supernatant in 10.93 vol.% PVA fiber extruded from a 0.26 
mm diameter needle. The scale bar shown in each image is 500 nm. 
185 
 
The variations in the fiber surfaces shown in Figure 74 are likely due to differences in pressure 
drop associated with needle diameters used as well as the differences in the initial dispersion 
state. Pottick showed with poly(p-phenylene benzobisthiazole) that increasing the pressure drop 
during extrusion modifies the surface morphology of fibers.129 In the case of these fibers, the 
increased pressure drop leads to smoother surfaces. However, the ribbon-like structure of these 
fibers is due to the drying process. As the water evaporated, the weight of the fiber caused it to 
collapse from a cylindrical fiber into a ribbon-like structure. 
Figure 75 shows the Raman spectra (514 nm excitation), of the LSZ-TTAB-SWNT 
mixture and supernatant in PVA as well as the initial SWNT material.  Raman spectroscopy was 
performed using both 514 nm and 785 nm excitation lasers. The 514 nm laser data is of 
particular interest as it probes the LSZ-SWNT system as well as the PVA polymer backbone. 
The spectra show characteristic radial breathing modes (RBM) from 100 cm-1 to 400 cm-1, the D 
peak due to sp3 hybridized carbons at ~1335cm-1, the G peak due to tangential sp2 hybridized 
carbons at ~1589 cm-1, and the G? peak at ~2645 cm-1 which is the second overtone of the D 
peak.  Several facets of these spectra support the existence of noncovalent functionalization of 
individual SWNT with LSZ-TTAB complex. The D:G ratios vary only slightly between SWNT 
(0.13), LSZ-TTAB-SWNT mixture (0.15), and LSZ-TTAB-SWNT supernatant (0.12) indicating 
a noncovalent interaction. An interesting facet of the Raman spectra shown in Figure 4b is the 
evidence of charge transfer by the G?-peak. Both the G153-154 and G?23, 152 peaks have been used 
to indicate doping effects. However, for the data collected here, charge transfer is best elucidated 
by the G?-peak position shift as well as a decrease in G:G? as shown in Table 7 due to the G?-
peak being independent of tensile load transfer.152, 204 Charge transfer for the present system is 
expected due to the presence of the quaternary ammonium ion present in the cationic surfactant 
186 
 
TTAB. The lack of a shift in the G-peak could be explained by a combinatorial effect of charge 
transfer causing an upshift in frequency and tensile load transfer causing a downshift in 
frequency.205 The presence of tensile load transfer is supported by the increase in mechanical 
data from LSZ-TTAB-SWNT to LSZ-TTAB-SWNT in PVA. Another interesting aspect of the 
Raman spectra is the shifting of the RBM peak positions as shown in the inset of Figure 75a. As 
previously described, the addition of TTAB to the LSZ-SWNT results in significant debundling 
of the SWNT as evidenced by the van Hove singularities shown in Figure 66a. This debundling 
of SWNT has been reported to result in shifting of RBM peaks.206 In addition, it has been shown 
that changes in aggregation state result in different chirality SWNT being in resonance with a 
fixed-wavelength laser.207 Furthermore, charge transfer has been linked to shifts in the RBM 
peaks.208 It is not fully understood for this system the reason for the shifting, but is likely due to 
one of the aforementioned. Finally, Raman shows the polymer backbone of the PVA present in 
each fiber as shown by the peak for the supernatant and mixture at ~2910 seen in Figure 75a and 
b.209-210 
 
Figure 75. a.) Raman spectra of SWNT and LSZ-TTAB-SWNT mixture and supernatant fibers 
using a 514 nm excitation laser showing the characteristic RBM, D-, G-, and G?-peaks, as well as 
the CH2 stretch associated PVA for those dispersions containing PVA. b.) Magnified Raman 
spectra showing the shifts in the G?-peak and characteristic CH2 stretch associated with the 
polymer backbone stretching of PVA. 
187 
 
514 nm Laser 
Sample D-Peak G-Peak G'Peak D/G G/G' Shift Intensity Shift Intensity Shift Intensity 
SWNT 1338 4339 1589 34316 2636 18070 0.126 1.90 
LSZ-TTAB-SWNT 
Supernatant in PVA 1338 2289 1589 18928 2650 12278 0.121 1.54 
LSZ-TTAB-SWNT 
Mixture in PVA 1332 5668 1586 38497 2646 25287 0.147 1.52 
Table 7. Raman spectroscopy data for 514 nm excitation laser. The changes in G?-peak position 
coupled with the decrease in G:G? indicate charge transfer between SWNT and LSZ-TTAB 
complex present in each fiber. 
 
The electrical conductivity of the fibers was tested as shown in Table 8. As would be 
expected, the fibers which contain no natural or synthetic polymer have significantly higher 
conductivities than those which contain PVA or were spun into PVA. This is due to the fact that 
PVA is an insulator. It should also be noted that although some biopolymers have been shown to 
help electrical conductivity, LSZ has been shown to have insulating properties which will 
naturally inhibit the electrical conductivity of the fibers.211 For reference, pure SWNT fibers 
have been shown to have electrical resistivity as low as 0.1 ??-cm.2, 33 Therefore, by 
comparison, all the fibers created in this research can be classified as insulators although they are 
capable of carrying small amounts of electrical current. It could be possible to increase the 
conductivity of these fibers through introduction of additional electrically conductive materials, 
such as polypyrrole.109, 212 However, consideration should be taken into how the introduction of 
other materials is going to affect the mechanical, antibacterial, or optical properties of the 
dispersion. 
 
188 
 
Sample 
Electrical 
Resistivity             
(??cm) 
Electrical 
Conductivity         
(S?m-1) 
LSZ-TTAB-SWNT Mixture                                                   
0.24 vol.% - 0.34 vol.% - 0.28 vol.%                                                              
Wet Spun into 4.10 vol.% PVA      
1.17E+07 8.74
LSZ-TTAB-SWNT Mixture                                       
3.17 vol.%  - 4.63 vol.%  - 3.71 vol.%                                                                 
Dry Spun 
4.65E+05 230.32
LSZ-SWNT Mixture in PVA                                            
0.71 vol.% - 0.16 vol.% in 10.21 vol.%                                                        
Dry Spun 
3.38E+09 0.04 
LSZ-SWNT Supernatant in PVA                                                                
0.36 vol.% - 0.03 vol.% in 9.99 vol.%               
Dry Spun 
2.23E+09 0.05 
LSZ-TTAB-SWNT Mixture in PVA                                         
1.00 vol.% - 1.44 vol.% - 1.17 vol.% in 9.68 
vol.%                                                          
Dry Spun 
2.94E+08 0.41 
LSZ-TTAB-SWNT Supernatant in PVA                                       
0.51 vol.% - 0.73 vol.% - 0.24 vol.% in 10.93 
vol.%                                                        
Dry Spun 
2.98E+08 0.41 
Table 8. Electrical resistivity and conductivity of various fibers from both wet spun and dry spun 
assembly methods, illustrating the effect of dispersion state and processing methods on the 
electrical conductivity of macroscopically assembled fibers. 
 
Optical microscopy of fibers of LSZ-TTAB-SWNT mixtures and supernatants in PVA 
reveal the reduced aggregation state of the dispersion compared to the LSZ-SWNT dispersion 
microscopy, as well as the anisotropic effects of drawing. Microscopy was done on both the 
mixture and supernatant fibers. Figure 76 shows the non-polarized and cross-polarized optical 
micrographs of 0.51 vol.% LSZ - 0.73 vol.% TTAB - 0.24 vol.% SWNT supernatant in 10.93 
vol.% PVA fiber extruded from a 0.26 mm diameter needle. As can be seen, both images show 
homogenous fibers with no visible aggregation. The lines seen in each image are not SWNT 
aggregates but rather drying defects associated with the PVA present in each fiber.129 These 
189 
 
defects, which can be folds, tears, wrinkles, etc., can cause increased absorption, reflection, or 
refraction of transmitted light leading to the lines seen in Figures 76 and 77.130 In addition to not 
showing any visible aggregation, the images also do not show optical anisotropy under cross 
polarized light. This is due to the lack of alignment of either SWNT or PVA. Figure 77 shows 
optical micrographs of 0.51 vol.% LSZ - 0.73 vol.% TTAB - 0.24 vol.% SWNT supernatant in 
10.93 vol.% PVA fiber extruded from a 0.26 mm diameter needle which has been drawn after 
drying. The non-polarized, partially polarized, and cross-polarized micrographs show the change 
in color associated with alignment anisotropy. This anisotropy is likely the alignment of the PVA 
polymer backbone. The differences in Figures 76 and 77 are important as it shows the 
tailorability of the dispersions, and how different methods in processing can create macroscopic 
assemblies with unique properties for a wide range of applications. 
 
Figure 76. a.) Non-polarized (0o) and b.)cross-polarized (89o) optical micrographs of 0.51 vol.% 
LSZ - 0.73 vol.% TTAB - 0.24 vol.% SWNT supernatant in 10.93 vol.% PVA fiber extruded 
from a 0.26 mm diameter needle. The scale bar shown in each image is 100 ?m. 
190 
 
 
Figure 77. a.) Non-polarized (0o), b.) partially cross-polarized (79o), and c.) cross-polarized 
(138o) optical micrographs of 0.51 vol.% LSZ - 0.73 vol.% TTAB - 0.24 vol.% SWNT 
supernatant in 10.93 vol.% PVA fiber extruded from a 0.26 mm diameter needle which has been 
drawn showing alignment anisotropy. The scale bar shown in each image is 100 ?m. 
 
To further elucidate the alignment of SWNT and the PVA polymer backbone, polarized Raman 
spectroscopy was done as shown in Figure 78. Because of the anisotropic polarization of SWNT, 
the ratio of SWNT Raman G-band intensity, parallel versus perpendicular, provides a useful 
probe of the relative degree of alignment. The alignment of SWNT fibers has been well 
documented, and various SWNT materials have been shown to have different alignment ratios: 
pristine, extruded SWNT fibers ? 20:1,5, 69 magnetically aligned SWNT fibers ? 4:1,213 gel-spun 
polymer-SWNT composites ? 106:1.214 For the 514 nm and 785 nm excitation laser the 
alignment is 3.3:1 and 9.1:1, respectively, indicating that post-process drawing of the fibers 
aligns the SWNT and polymer backbone present in the fibers leading to the anisotropy as seen in 
Figure 77. However, of interesting note in Figure 78 is that the intensity of the PVA specific 
stretching at ~2900 for 514 nm indicates that the alignment of the polymer backbone is not likely 
the primary cause of optical anisotropy. 
191 
 
 
Figure 78. Raman analysis of LSZ-SWNT in PVA fibers with excitation laser of a.)514 nm and 
b.) 785 nm showing alignment through the ratio of G?:G?. Also of note is that the intensity of the 
PVA specific stretching at ~2900 cm-1 for 514 nm indicates that the alignment of the polymer 
backbone is not likely the primary cause of optical anisotropy. 
514 nm Laser 
Sample D/G G/G' SWNT Alignment PVA Alignment 
LSZ-SWNT in PVA - 0o 0.200 0.840 3.260 1.014 
LSZ-SWNT in PVA - 90o 0.372 0.743 
785 nm Laser 
Sample D/G G/G' SWNT Alignment PVA Alignment 
LSZ-SWNT in PVA - 0o 0.153 4.694 9.147 - 
LSZ-SWNT in PVA - 90o 0.398 3.492 
Table 9. Raman spectroscopy data for 514 and 785 nm excitation laser showing the D/G and 
G/G? ratio along with the alignment ratio ? G(0o):G(90o) ? for LSZ-SWNT in PVA fibers 
indicating an increase in alignment of polymer backbone and SWNT through post-process 
drawing. 
 
 
 
192 
 
4.5.2. FILMS 
Previous research on the layer-by-layer assembly of aqueous dispersions of 0.30 vol.% 
LSZ ? 0.07 vol.% SWNT with 0.81 vol.% dsDNA ? 0.12 vol.% SWNT resulted in a unique 
coating possessing antibacterial activity and high Young?s Modulus.19 However, depletion 
attraction limited the robustness of free standing films from higher concentration dispersions. 
PVA is known for its flexibility and tensile strength, and has been incorporated into LSZ-SWNT 
dispersions to add elasticity and fill voids between SWNT resulting from microstructural 
defects.15 The PVA forms a structural matrix surrounding the LSZ-SWNT bundles to achieve 
greater durability and elasticity. Film casting was carried out by extrusion of concentrated LSZ-
SWNT in PVA dispersions into either a 6 in diameter glass Petrie dish or onto a 4 in diameter 
circular Teflon mold. The dispersions were manually leveled through rotation of the substrate to 
allow for homogeneity of the film thickness. After the dispersion was leveled it was allowed to 
dry in a fume hood. Regardless of LSZ, SWNT, or PVA content in the final, dry film the average 
moisture content was approximately 6%. 
SEM was used to characterize the surface morphology of the film as well as show the 
presence and size of SWNT. To prepare the film for SEM, a small section of the film was cut and 
a scalpel was used to create a tear through the middle to allow for visualization of SWNT as 
shown in Figure 79. The surface of the film was smooth as evidenced in Figure 79a which is 
expected due to the presence of the PVA. The smoothness of the surface along with no definitive 
voids or fractures in the macroscopic structure aids in the mechanical robustness of the film, 
which will be discussed later. The presence of small bundle SWNT of approximately 10 nm 
diameter, as shown in Figure 79b, indicates the starting dispersion was well dispersed and 
stabilized. The presence of small bundle SWNT also increases the mechanical robustness of the 
193 
 
film through increased interfacial interactions, as compared to that of large bundle SWNT. It 
should be noted that electron microscopy of drawn films was completed but showed no 
difference in surface morphology. 
 
Figure 79. SEM images of LSZ-SWNT in PVA film at a) 25,000x and b.) 150,000x showing the 
smooth surface morphology as well as the presence of SWNT bundles approximately 10 nm in 
diameter. 
 
Optical microscopy was used to identify anisotropic changes in the film after post-process 
drawing of the film. As with the fibers, LSZ-SWNT in PVA films show optical anisotropy under 
cross-polarized light, as shown in Figure 80. The reason for anisotropy is analogous to that seen 
in the fibers ? the alignment of SWNT and PVA polymer backbone. The ability to change the 
optical properties of both the fibers and films only increases the potential applications and allows 
for tailorability of the film through processing. 
194 
 
 
Figure 80. Optical micrographs of post-process drawn 40 vol.% LSZ ? 5.1 vol.% SWNT in 54 
vol.% PVA film at cross polarizations of a.) 4o, b.) 48o, and c.) 93o showing the optical 
anisotropy induced through alignment of the SWNT and polymer backbone. The scale bar shown 
in each image is 100 ?m  
 
FTIR analysis was conducted to ascertain interaction between LSZ, SWNT, and PVA 
within the solid films. Figure 81 shows the ATR-FTIR spectra of the two LSZ-SWNT in PVA 
film types: mixture films and a supernatant film. The two film spectra were compared to 
individual ATR-FTIR spectra of dried SWNT, LSZ, and PVA samples. The characteristic amide I 
(~1650 cm-1) and amide II (~1535 cm-1) peaks of LSZ were present in the mixture and 
supernatant films of LSZ-SWNT in PVA. The films also reflected several characteristic peaks of 
PVA, evident in all three spectra: the C-H stretch in alkyl chains produces a peak at ~2940 cm-1, 
the stretching C=O in alcohols present a peak at ~1740 cm-1, the C-O stretching in alcohols 
shows a peak at ~1140 cm-1, and at ~2950 cm-1 a peak is caused by the terminating methyl group 
in PVA interacting with a terminating amine group in LSZ producing methylamine vibrations.29 
Indications of SWNT can also be ascertained. The LSZ-SWNT mixture and supernatant films 
show increasing absorbance from ~1500 cm-1 to ~700 cm-1 which is also seen in pristine SWNT. 
These results clearly indicate that LSZ, SWNT, and PVA interacted and carried over from the 
liquid dispersion into the film, in agreement with previous work.8, 51, 134, 146 A primary indication 
195 
 
of the presence of interaction rather than separate individual components is the red or blue 
shifting of peaks relative to their pure components attributed to the change in molecular 
orientation due to the effect of being dispersed in aqueous media by the changing polarity of the 
environment.9 This ATR-FTIR data thus supports that there is an interaction between LSZ, 
SWNT, and PVA within the films. 
 
Figure 81. ATR-FTIR spectra a.) covering the entire frequency range scanned and b.) an 
enlarged section showing the amide I (1650 cm-1) and II (1535 cm-1) peaks of all LSZ 
containing samples, as well as, the methylamine peak (1430 cm-1) present in all LSZ-PVA 
containing samples. 
 
Mechanical characterization was conducted to determine the tensile properties of each 
type of film. Significant property differences were seen between the two film types. As shown in 
Table 10, films cast from the supernatant films were stronger than those from the bulk mixture.  
The Young?s modulus and tensile strengths were 63% and 34% higher respectively.  These 
results can be attributed to the supernatant films being comprised primarily of individual SWNT; 
individuals have greater specific surface area, and therefore more interfacial interactions with the 
matrix and greater reinforcement potential. 205, 215 Another way to view the strength results is to 
196 
 
note that the number and size of aggregates present in the mixture is considerably greater and 
aggregated SWNT do not translate their outstanding mechanical properties to the macroscale. In 
addition, the aggregates can develop fault lines within the films, where the film will be weaker 
and more susceptible to stress during tensile testing. Counterintuitively, the film from the bulk 
mixture had more than twice the elongation at break. At this point it is not clearly understood as 
to why this phenomena occurred, however, it is likely a function of colloidal interactions in the 
dispersion state, surface area of accessible SWNT, and/or the concentrations and interactions 
among the constituents. 
Sample 
Young's 
Modulus 
(MPa) 
Tensile 
Strength 
(MPa) 
Tensile 
Strain             
(%) 
Control Film: 47 wt.% LSZ - 53 wt.% PVA 490 ? 51 69 ? 4.8 27 ? 0.28 
Mixture Film: 45 wt.% LSZ - 9 wt.% SWNT - 45 wt.% PVA 3100 ? 34 86 ? 1.9 6.7 ? 0.77 
Supernatant Film: 34 wt.% LSZ - 4.5 wt.% SWNT - 61 wt.% PVA 4100 ? 270 120 ? 4.3 12 ? 0.90 
Table 10. Mechanical property data collected from the ultimate tensile strain test conducted on 
both mixture and supernatant LSZ-SWNT in PVA films. 
 
Finally, as expected due to the high PVA concentration, characterization of electrical 
properties showed no evidence of conductivity for either type of film. The experiments were 
performed on several film pieces, with varying distances from the edge. Various regions of the 
film showed negligible differences in results. Only by positioning the electrical leads 
unrealistically close did any electrical current pass. This suggests that PVA and LSZ are so 
resistive and in such high loadings that their presence negated the intrinsic conductivity of the 
SWNT. 
 
 
197 
 
4.6. LYSOZYME ? CARBON NANOTUBE ANTIBACTERIAL ACTIVITY 
 LSZ is already commercially used in food packaging and mouthwash,216 and there is 
interest in using it for antibacterial surfaces.8, 217  The combination of the antibacterial activity of 
LSZ with the mechanical and electrical properties of SWNT has potential for robust 
multifunctional materials. A key goal of this work was to maintain the antibacterial property of 
LSZ during processing with SWNT. Although LSZ can be used purely as a dispersant for 
SWNT, the uniqueness of this system is that LSZ provides enzymatic activity to the dispersion. 
In order to prove the maintenance of the antibacterial properties of LSZ while dispersed with 
SWNT, CD was performed to show no significant changes in the secondary structure of LSZ and 
turbidimetric analysis was done to show the actual antibacterial activity of the LSZ-SWNT 
dispersions. 
 CD measurements were taken of 0.30 vol.% LSZ ? 0.07 vol.% SWNT dispersions to 
elucidate that no negative change in secondary structure occurred due to the addition of SWNT 
as shown in Figure 82. A negative change could have three separate consequences: loss of alpha 
helical structure, addition of beta sheet structure, or addition of random coil structures. As 
previously mentioned, alpha helices show characteristic peaks between 200 nm and 230 nm, beta 
sheets show a characteristic peak centered at 215 nm, and random coils show a characteristic 
peak centered at approximately 200 nm.118 As shown in Figure 82, the characteristic alpha helix 
peaks are present in both the LSZ-SWNT dispersion and processed LSZ solution. The noticeable 
difference between the LSZ solution and the LSZ-SWNT dispersion is the peak between the 
wavelengths of 200 nm and 210 nm. This difference in peak magnitude has been described as an 
alpha helical well, and is possibly caused by the increased ordering of the alpha helices upon 
binding to SWNT. 
198 
 
 
Figure 82. Far-UV CD spectrum of 0.30 vol.% LSZ ? 0.07 vol.% SWNT and 0.30 vol.% LSZ 
solution which has been processed showing characteristic alpha helical peaks. 
 
CD measurements are able to determine the secondary structure of proteins and enzymes present 
in a solution. The material becoming more ordered or more disordered, will lead to changes in 
the magnitude of a representative peak. The more disordered a molecule becomes, the lower the 
magnitude of the peak and vice versa. Therefore, the binding of LSZ to SWNT shows increases 
in the secondary structure ordering of LSZ alpha helices. Although it is not known at this time 
how the increased ordering affects the LSZ, it is hypothesized that the increased ordering could 
produce a synergistic enzymatic affect. 
 Turbidimetric analysis was performed on all dispersions and macroscopic assemblies of 
LSZ-SWNT to show that the LSZ has maintained its antibacterial properties within the LSZ-
199 
 
SWNT complex. In order to determine the contribution of each constituent and the contribution 
of the interactions, all individual constituents were tested for activity. Figure 83 shows the 
activity analysis for water, LSZ, TTAB, PVA, LSZ-TTAB, and LSZ-PVA solutions. The 
decrease in absorbance for all solutions containing LSZ shows that they possess lytic activity, 
whereas the lack of a decrease in all the solutions which do not contain LSZ show no activity. 
The lack of lytic activity in TTAB and PVA verifies that the only active constituent in all 
prepared dispersions is LSZ.  
 
Figure 83. Turbidimetric analysis of all individual constituents present within LSZ-SWNT or 
LSZ-TTAB-SWNT dispersions or macroscopic assemblies showing non-inhibitory effect of 
TTAB and PVA on native LSZ activity. Activity was tested against M. lysodeikticus. It should be 
noted that the calculated error for each sample was less than that of the UV-vis, therefore, the 
error shown is that inherent of the UV-vis used in characterization. 
200 
 
Furthermore, the similar rates of cell death during lysis by the LSZ-TTAB and LSZ-PVA 
confirm the non-inhibitory nature of TTAB and PVA toward the native activity of LSZ. After 
processing of LSZ-SWNT dispersions, fibers, and films, turbidimetric analysis was done to 
determine the effect of dispersion state and processing on the LSZ activity in each dispersion and 
fiber. Figure 84 shows the activity of each dispersion and processed fiber as a percentage of 
native LSZ activity maintained where each sample has been normalized for the amount of LSZ 
present in the sample as determined by TGA. The initial LSZ-SWNT dispersions had over 99% 
of the native LSZ activity. This is greater than that observed by Ding et al. who achieved a 
maximum of 90% of native LSZ activity in the presence of silica nanotubes.218 Furthermore, 
Merli et al. found that covalently bonding LSZ to MWNT via EDC/NHS actually increased 
activity,141 however covalent functionalization has the disadvantages of reducing SWNT 
mechanical and electrical properties.21 The activity of the supernatants being lower than that of 
the mixture was most likely due to the removal of excess LSZ during centrifugation thereby 
leaving only bound LSZ which could be sterically hindered when compared with the unbound 
LSZ in mixture dispersions. It is hypothesized that if the solid assemblies were normalized to the 
surface bound LSZ, and not to the total LSZ quantity which is not readily accessible, the activity 
would much higher. Therefore the major difference between the dispersions and solid assemblies 
is likely to be surface to volume ratio and LSZ accessibility dependent. In addition, some studies 
have shown SWNT have inherent antimicrobial activity, therefore the reduced SWNT 
concentration may also have contributed to the reduced activity in the supernatant.219-220 The 
LSZ-TTAB-SWNT dispersions show a similar trend as the LSZ-SWNT dispersions, however, 
the supernatant loses less activity. At this time, the reason for this decreased loss in activity is 
unknown but is likely due to a synergistic interaction between LSZ, SWNT, and TTAB, as there 
201 
 
was no indication of any such relationship between the LSZ and TTAB as seen in Figure 83. The 
concentrated mixture LSZ-TTAB-SWNT fiber maintains the highest degree of activity when 
compared with the LSZ-TTAB-SWNT fibers in PVA. The reasoning for this is likely due to the 
increased steric hindrance caused by incorporation of PVA which prevents the interaction of the 
LSZ active site with the bacterial cell wall. 
 
Figure 84. Lytic activity analysis of LSZ-SWNT and LSZ-TTAB-SWNT dispersions and 
macroscopic assemblies. Activity was tested against M. lysodeikticus and normalized for the 
mass of LSZ present in each sample. It should be noted that the calculated error for each sample 
was less than that of the UV-vis, therefore, the error shown is that inherent of the UV-vis used in 
characterization. 
 
202 
 
It should be noted that the loss in activity from LSZ-SWNT mixture dispersion to the resultant 
fiber (not shown) is approximately 60%, whereas the loss in activity from LSZ-TTAB-SWNT 
mixture to the least active resultant fiber is approximately 32%. The reasoning for this is unclear, 
however, likely involves the increased stability of the LSZ-TTAB-SWNT dispersions over the 
LSZ-SWNT dispersions. Overall, although there is a loss in activity, this data confirms the 
ability to process LSZ-SWNT dispersions into macroscopic assemblies which maintain 
antibacterial activity. Furthermore, it should be noted that a commercially available mouthwash 
containing LSZ maintains only 28.5% of native LSZ activity.221-222 Therefore, although the loss 
of activity in LSZ-SWNT fibers seems significant, it is less than that of currently available 
commercial products. 
  
203 
 
5. CONCLUSIONS 
The goal of this research was to expand on the previous research and exploit the 
properties of both LSZ and SWNT to create dispersions capable of macroscopic assembly for 
tailorable applications. These results were achieved through processing of LSZ and SWNT from 
dispersion to fiber or film. In order to fully realize this, the interaction, phase behavior, rheology, 
stabilization, and macroscopic assembly of LSZ-SWNT dispersions were analyzed and 
understood. This study led to antibacterial, mechanically robust fibers and films capable of being 
tailored to specific applications. 
The research presented here has shown that LSZ not only disperses SWNT as individuals 
or small bundles, but molecularly interacts through a ?-? bond between the sidewall of SWNT 
and the hydrophobic tryptophan of LSZ, which maintains native antibacterial activity. Sharp van 
Hove singularities in the UV-vis absorbance of LSZ-SWNT dispersions between 1.6 eV and 2.4 
eV qualitatively showed the characteristics of individuals or small bundles of SWNT. SEM 
images showed 10 nm bundles of SWNT surrounded by LSZ. These images qualitatively verify 
that LSZ molecularly interacts with SWNT, and quantitatively verifies that LSZ disperses 
SWNT as individuals or small bundles. In addition to LSZ being able to disperse SWNT through 
a molecular interaction, the research presented here shows that LSZ maintains its? structure and 
activity when coupled with SWNT. UV-CD spectra of LSZ and LSZ-SWNT show that each 
contain characteristic alpha helix peaks at 205 nm and 215 nm wavelengths verifying that the 
secondary structure of LSZ does not adversely change when coupled with SWNT. Furthermore, 
turbidimetric analysis in the presence of M. lysodeikticus verifies that the antibacterial properties 
of LSZ are maintained in LSZ-SWNT dispersion mixtures, supernatants, and macroscopic 
assemblies. 
204 
 
 The phase behavior of LSZ-SWNT dispersions has been shown to be complex. 
Dispersions transition from dilute isotropic liquids to concentrated physical gels. Through optical 
microscopy the phase transition can qualitatively be seen when the number and size of SWNT 
aggregates increases due to depletion interactions. Quantitatively the transition is shown through 
rheological analysis of the frequency sweep tests combined with the deviation of Cox-Merz rule 
and the viscosity increase. It was then shown that through the addition of a surfactant (TTAB) 
the LSZ-SWNT dispersion was able to be electrostatically stabilized to a higher degree reducing 
the amount of SWNT aggregation at a given concentration. Furthermore, the phase behavior was 
shown to be capable of being altered through the addition of natural or synthetic polymers 
without the loss of antibacterial activity. Understanding of the phase behavior of LSZ-SWNT 
dispersions was of extreme importance for determining methods of macroscopic assembly. Until 
now, no extensive experimental phase behavior or rheological characterization has been done on 
spherical biomolecule-dispersed SWNT solutions such as LSZ-SWNT. 
 Fibers and films of LSZ-SWNT dispersions have been shown to be possible through wet 
and dry fiber spinning and film casting. The mechanical, electrical, and optical properties have 
been shown to be tailorable depending on dispersion constituents, dispersion state, and 
processing methods. This was done using a combination of mechanical testing, electrical 
resistivity testing, UV-vis and Raman spectroscopy, SEM, and optical microscopy. Furthermore, 
to the author?s knowledge, the mechanical toughness has been shown to be greater than any 
previously made SWNT or SWNT-composite fiber. Finally, in addition to record toughness, the 
fibers and films were shown to be antibacterial through turbidimetric analysis. 
The research presented here has wide ranging potential applications. The antibacterial 
maintained by all the dispersions would lend for the use of fibers or films in hospitals, airports, 
205 
 
train stations, or any high traffic area as a coating on common surfaces to prevent the spread of 
communicable illnesses such as the flu and the common cold. The toughness demonstrated by 
the LSZ-TTAB-SWNT in PVA fibers would make them a useful material for ballistics, aviation, 
automotive, or any application in which energy absorption is important. These potential 
applications will only be possible through further research on the foundation that has been 
presented in this research. Optimization of the fiber spinning or film casting process will only 
increase the mechanical robustness of the materials. Furthermore, understanding the interactions 
collectively taking place in LSZ-TTAB-SWNT in PVA dispersions will allow for incremental 
increases in SWNT concentration prior to aggregation which should result in better mechanical 
properties. In addition, this research lays the foundation for a route for experimental 
determination of interactions between biomolecules and SWNT, furthers basic understanding of 
particle and phase behavior theory of cylinder-sphere systems by helping to extend it to a 
polydisperse, interacting system, and shows a method for increasing SWNT concentration of 
kinetically stable dispersions through synergistic effects of compatible dispersants. 
  
206 
 
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