MEMBRANE SEPARATION IN SUPERCRITICAL ANTISOLVENT PROCESS FOR NANOPARTICLE PRODUCTION Except where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my advisory committee. This thesis does not include proprietary or classified information. Kayoko Ono Certificate of Approval: W. Robert Ashurst Assistant Professor Chemical Engineering Ram B. Gupta, Chair Professor Chemical Engineering Yoon Y. Lee Professor Chemical Engineering Joe F. Pittman Interim Dean Graduate School MEMBRANE SEPARATION IN SUPERCRITICAL ANTISOLVENT PROCESS FOR NANOPARTICLE PRODUCTION Kayoko Ono A Thesis Submitted to the Graduate Faculty of Auburn University in Partial Fulfillments of the Degree of Master of Science Auburn, Alabama December 15, 2006 iii MEMBRANE SEPARATION IN SUPERCRITICAL ANTISOLVENT PROCESS FOR NANOPARTICLE PRODUCTION Kayoko Ono Permission is granted to Auburn University to make copies of this thesis at its discretion, upon request of individuals or institutions and at their expense. The author reserves all publications rights. Signature of Author Date of Graduation iv VITA Kayoko Ono, daughter of Hatsuo and Remiko Ono, was born September 22, 1981, in Kumamoto prefecture, Japan. She graduated from Seiseiko High School in March, 2000. She entered Tohoku University in Sendai, Japan in April, 2000 and graduated with a Bachelor of Engineering (Applied Chemistry) in March, 2004. In August, 2004, she entered the Graduate School, Auburn University, in Auburn, Alabama to pursue MS degree in Chemical Engineering. v THESIS ABSTRACT MEMBRANE SEPARATION IN SUPERCRITICAL ANTISOLVENT PROCESS FOR NANOPARTICLE PRODUCTION Kayoko Ono Master of Science, December 2006 (B.S., Tohoku University, Sendai, 2004) 103 Typed Pages Directed by Ram B. Gupta In supercritical antisolvent process to produce pharmaceutical nanoparticles, drug solution is injected into supercritical carbon dioxide. CO 2 rapidly extracts the solvent, causing the drug to precipitate as micro- and nano-particles. A portion of drug dissolves in CO 2 /organic solvent mixture. For the recovery of drug nanoparticles from the precipitation vessel, CO 2 /organic solvent is removed through a filter. As much as 50% of the drug is typically lost in the process, in dissolved and un-retained particle forms. Hence a better method to separate CO 2 /organic solvent is needed. In this work, a polymer membrane based separation of CO 2 /organic solvent is proposed and tested. Gas and vapor separations using non-porous polymer membranes have been brought to focus in the past 30 years. Very recently, amorphous Teflon (TeflonAF, vi DuPont, Wilmington, DE) polymers have been introduced which are copolymers consisting of 2,2-bistrifluoromethyl-4,5-difluoro-1,3-dioxole (PDD) and tetrafluoroethylene (TFE). Teflon AF 2400 contains 87 mol% PDD and 13 mol% TFE with Tg = 240 o C, whereas Teflon AF 1600 contains 65 mol% PDD and 35 mol% TFE with Tg = 160 o C. Both the copolymers have a high temperature stability and chemical resistance, as well as high free volume compared to the conventional glassy polymers. Permeability coefficients of CO 2 in Teflon AF 2400, Teflon AF 1600, and poly(tetrafluoroethylene) (PTFE) are measured, at varying feed pressure and temperature. The permeability increased in the order of PTFE < Teflon AF 1600 < Teflon AF 2400. This can be explained by the fact that PTFE is a semicrystalline polymer and Teflon AFs are glassy polymers with a high free volume. In addition, the reuse of the membrane for second and third time resulted in enhancement of the permeability, which can be attributed to the CO 2 plasticization of the membrane. Further understanding of the transport of CO 2 through the membranes is investigated by applying solution-diffusion model. In the presence of CO 2 , acetone solvent has a high permeability through Teflon AF. And no permeability of larger drug molecule tetracycline is observed through Teflon AF when dissolved in acetone. vii ACKNOWLEDGEMENT The author would like to thank Prof. Ram B. Gupta for guiding this research work. The work would not have been completed without his advice. Also, gratitude is given toward my colleagues for their advice and help. Last but not least, thanks are due to my parents and my friends, Irais, Suhaila, Zahra and Ken?ichi for their support. viii TABLE OF CONTENTS CHAPTER 1: INTRODUCTION 1 CHAPTER 2: AMOURPHOUS TEFLON MEMBRANE 27 CHAPTER 3: EXPERIMENTAL METHODS 34 CHAPTER 4: PERMEABILITY OF CARBON DIOXIDE 55 CHAPTER 5: PERMEABILITY OF ACETONE 68 CHAPTER 6: PERMEABILITY OF TETRACYCLINE 86 CONCLUSIONS 87 REFERENCES 89 ix LIST OF FIGURES Fig. 1-1. Phase diagram of carbon dioxide 1 Fig. 1-2. Density dependence of carbon dioxide 2 Fig. 1-3. Schematic of rapid expansion of supercritical solution (RESS) 3 Fig. 1-4. Schematic of supercritical antisolvent (SAS) Process 4 Fig. 1-5. Amorphous and crystalline portion in a polymer 6 Fig. 1-6. Chemical structures of elastomers 7 Fig. 1-7. Chemical structure of high free volume glassy polymer (PTMSP) 8 Fig. 1-8. Chemical structure of polytetrafluoroethylene (PTFE) 10 Fig. 1-9. Schematic of molecules transporting through a nonporous membrane 12 Fig. 1-10a. Sorption isotherm for gases in elastomers 13 Fig. 1-10b. Sorption isotherm for organic vapor/liquids in polymers 14 Fig. 1-10c. Sorption isotherm for gases in glassy polymers 15 Fig. 1-11. Schematic of sorption isotherms for dual sorption theory 16 Fig. 1-12a. Schematic of constant pressure/variable volume method 23 Fig. 1-12b. Schematic of constant volume/variable pressure method 23 Fig. 1-13. Schematic of a SAS process with membrane separation 25 Fig. 2-1. Chemical structure of Teflon AF products 27 Fig. 2-2. Micrograph of Teflon AF 2400 taken by SEM 28 Fig. 3-1. Schematic of the membrane set-up for CO 2 permeation 35 x Fig. 3-2a. An example of a plot of permeate pressure vs time 38 Fig. 3-2b. An example of a plot of ln(p feed -p permeate ) vs time 38 Fig. 3-3. Schematic of the set-up for verification of the system 39 Fig. 3-4a. Schematic of the membrane-set up for acetone + CO 2 permeation 46 Fig. 3-4b. Enlargement of the schematic of the membrane holder 46 Fig. 3-5. Schematic of the tetracycline permeation test 54 Fig. 4-1a. Permeate pressure vs time for CO 2 permeation 57 Fig. 4-1b. Logarithm of the pressure difference vs time for CO 2 permeation 57 Fig. 4-2. CO 2 permeability in Teflon AF 2400, AF1600 and PTFE 60 Fig. 4-3a. Temperature dependence of CO 2 permeability in Teflon AF 2400 64 Fig. 4-3b. Arrhenius plot of CO 2 permeability in Teflon AF 2400 film 65 Fig. 4-4a. Plasticization effect on CO 2 permeability in Teflon AF 2400 66 Fig. 4-4b. Plasticization effect on CO 2 permeability in Teflon AF 1600 67 Fig. 5-1. Acetone calibration curve 69 xi LIST OF TABLES Table 1-1. Glass transition temperature of polymers 8 Table 1-2. Solubility of gases in natural rubber 19 Table 2-1. CO 2 permeability in various polymers studied previously 32 Table 2-2. CO 2 Permeability in Teflon AF 2400 studied previously 33 Table 4-1. CO 2 permeability in Teflon AF 2400, AF 1600 and PTFE 59 Table 4-2. CO 2 Permeability coefficients in Teflon AF 2400 63 Table 5-1. Verification of set-up for acetone + CO 2 permeation 74 Table 5-2. Acetone permeation through Teflon AF 1600 77 Table 5-3. Acetone permeability coefficient in Teflon AF 1600 85 1 CHAPTER 1 INTRODUCTION Supercritical Fluids A fluid is supercritical when it is compressed beyond its critical pressure and heated beyond its critical temperature. For example, carbon dioxide is supercritical if it is heated above 31.1 o C and simultaneously compressed above 72.8 atm. The supercritical region can be depicted as shows in Fig. 1-1. P-T diagram 72.8 atm 31.1 ?C Pr es su r e Temperature Pr es su r e Pr es su r e Fig. 1-1. Phase diagram of carbon dioxide. 2 No amount of compression can liquefy the supercritical fluid. In fact pressure can be used to continuously change the density from gas-like conditions to liquid-like conditions. Near the critical region, small changes in the pressure can give rise to large changes in the density. Fig. 1-2 shows how density of carbon dioxide is varied by pressure at different isotherms. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 50 100 150 200 Pressure (bar) Density (gm/ml) 33 C 35 C 40 C 50 C 70 C 100 C Fig. 1-2. Density dependence of carbon dioxide. In addition to density, diffusivity of the supercritical fluids is higher than that of liquid solvents, and can be easily varied. For typical conditions, diffusivity in supercritical fluids is of the order of 10 -3 cm 2 /s as compared to 10 -1 for gases and 10 -5 for liquids. Typical viscosity of supercritical fluids is of the order of 10 -4 g/cm?s, similar to that of gases, and about 100 fold lower than that of liquids. High diffusivity and low viscosity provide rapid equilibration of the fluid to the mixture. As a supercritical fluid, CO 2 is 3 often used due to its low critical temperature and pressure as well as its availability and benign character. Over the past two decades, supercritical carbon dioxide (above 31.1 o C and 72.8 atm) has emerged as a medium for the formation of micro- and nano-particles of pharmaceutical compounds, due to its adjustable solvent properties, high diffusivity, non- flammability, and non-toxicity. Depending upon the solubility in supercritical CO 2 , two classes of processes have emerged: (a) rapid expansion of supercritical solution (RESS) for CO 2 -soluble materials, and (b) supercritical antisolvent (SAS) for CO 2 -insoluble materials. Schematic of RESS process is shown in Fig. 1-3. In RESS process, the drug material is first dissolved in supercritical CO 2 and then expanded through a nozzle to rapidly precipitate as particles. Since the expansion occurs as fast as the speed of sound, the material comes out as small microparticles. But due to the limited solubility of drugs in supercritical CO 2 , RESS process had limited utility so far. In a recently developed RESS-SC process [Thakur and Gupta, 2006] by using menthol solid co-solvent, the solubility has been enhanced by several hundred fold. The presence of the solid cosolvent also hinders the particle growth; hence the particles in nanometer size range are easily obtained. Menthol is later removed by sublimation, yielding pure drug nanoparticles. Rapid expansion CO2+drug material Nozzle Fig. 1-3. Schematic of rapid expansion of supercritical solution (RESS) 4 Schematic of an experimental set-up for a SAS process is shown in Fig. 1-4. In SAS process, the drug material is first dissolved in an organic solvent. The solution is then injected into supercritical CO 2 , resulting in the extraction of solvent by supercritical CO 2 and precipitation of the material. Since the speed of extraction is fast due to the high (gas-like) diffusivity of supercritical CO 2 , the small microparticles of the material are obtained. Recently, the extraction speed was enhanced by ultrasonic mixing which results in nanoparticles [Gupta and Chattopadhyay, 2003]. In the new process, the particle size is easily controlled by the extent of ultrasonic power supplied. The strong extraction ability of supercritical CO 2 allows the production of pure drug nanoparticles, free of any residual solvent or additives. Valve CO2 pump Coil CO2 inlet outlet nozzle Liquid pump solution reservoir CO2 cylinder Precipitation vessel Pressure gauge filter Drug + solvent Fig. 1-4. Schematic of supercritical antisolvent (SAS) process Supercritical fluid processing has been applied to a wide variety of compounds [Arai et al., 2002; Yeo et al., 2004]. However, in these processes, low yield of particle collection has been a problem [Taylor, 1996, Yeo et al., 2004]. This is mainly due to the 5 failure in separating the particles or dissolved material from the CO 2 /solvent mixture. The material loss is a great disadvantage considering the expensive price of many drugs. In addition, pressurization of supercritical fluid, in many cases CO 2 , is costly especially looking at it on an industrial scale [Carlson et al., 2005; Bolzan et al., 2001]. Meanwhile, in the field of gas and vapor separations, use of polymer membranes has been brought to focus in the past 30 years and has been investigated heavily since [Mulder, 1996]. There are several researches that have combined these two prevailing technologies: supercritical fluid processing and membrane technology. Membrane Technology Polymer as a membrane A membrane is a barrier used to separate two or more components. Membranes can be made from different materials. It can be from natural or synthetic materials. Synthetic membranes can be either organic or inorganic. Inorganic membranes can be ceramics (alumina, zirconia, titania, etc.), glass membranes made from silica and zeolites. Organic membranes are polymers which is a macromolecule whose basic unit is called a monomer. The monomers build up to make a large chain resulting in large molecular weight. A polymer that consists of one type of monomer is called a homopolymer, whereas a polymer that consists of two or more types of monomers is called a copolymer. When the monomers are sequenced in a random way, the copolymer is called a random copolymer. 6 Polymers have a portion at which the molecular segments are lined up and a portion at which they are placed randomly (Fig. 1-5). A polymer that contains a large portion of crystalline region is called a (semi-) crystalline polymer. On the other hand, a polymer that has no crystalline portion is called an amorphous polymer. Heating a solid amorphous polymer would change the state of the polymer. As the heat is added, segments in the amorphous region start vibrating and as a result, free volume increases. Free volume refers to the void volume that is not occupied by the polymer chains. The temperature at which this occurs is called a glass transition temperature (Tg) and the state after the transition is called a rubbery state. Polymers that are in the rubbery state at ambient condition, i.e. polymers that have a glass transition temperature below the ambient temperature are called elastomers. Polyethylene (PE) and polydimethylsiloxane (PDMS; silicon rubber) are examples of elastomers (Fig. 1-6). Crystalline Amorphous Fig. 1-5. Amorphous and crystalline portion in a polymer 7 CH3 Si CH3 O Polydimethylsiloxane (PDMS; silicon rubber) CC HH HH Polyethylene (PE) Fig. 1-6. The chemical structures of the elastomers Table 1-1 shows the glass transition temperature of some of the polymers. In the glassy state, free volume does not change with temperature, but in the rubbery state, free volume increases as the temperature increases. Since for rubbery polymers, polymer flexibility increases due to the vibrating motion, free volume is increased and hence, most rubbery polymers (elastomers) have larger permeabilities than glassy polymers. However, the highest permeability measured so far is for polytrimethylsilylpropyne (PTMSP), which is a high free-volume glassy polymer (Fig. 1-7). Many research have been conducted to learn the permeation properties of this highly permeable polymer. 8 Table 1-1. Glass transition temperature of polymers (Schouten, 1987) Polymer Glass transition temperature (Tg) [?C] Polydimethylsiloxane (PDMS) -123 Polyethylene (PE) -120 Natural rubber -72 Polystyrene 100 Polytetrafluoroethylene (PTFE) 126 Polyetheretherketone (PEEK) 143 Polycarbonate 150 Polysulfone 190 Polyimide (Kapton) 300 Poly 1-trimethylsilyl-1-propyne (PTMSP) C = C CH3 CH3 Si CH3 H3C Fig. 1-7. Chemical structure of a high free volume glassy polymer (PTMSP) 9 Free volume can be quantified by a measure called fractional free volume, FFV: V VV 0 FFV ? = where V is the molar volume and V 0 the volume occupied by the polymer chains. V can be calculated by dividing the MW of the polymer by the density which can be determined experimentally. ? MW V = V 0 can be calculated using Bondi [1968]?s approximation which is as follows: w VV ?= 3.1 0 where V w is the van der Waals volume. V w can be calculated using a group contribution method [Krevelen, 1990]. Bos et al. [1999] measured free volume on several polymers such as polysulfone, polyethersulfone, polyetherimide, polycarbonate, polyimide (Matrimid 5218), etc. The values ranged from 0.138 to 0.225 with Matrimid the largest value. Porous and nonporous membranes In terms of the pore size, membranes can be classified into two: porous and nonporous membranes. Pores exist in nonporous membranes, but their sizes are of a molecular scale and a lot smaller than those of the porous membranes. In general, membranes that have pore size of less than 5-6 ? are considered nonporous, and membranes with pore sizes larger than those are considered porous. 5-6 ? is about the 10 size of simple molecules. From a statistical point of view, membranes that have fixed pores would be porous and membranes that have pores that appear and disappear transiently would be nonporous. Porous membranes are used for microfiltration and ultrafiltration. Microfiltration is the separation done in the range of 0.1-10 ?m and ultrafiltration is in the range of 2-100 nm (0.002-0.1 ?m). Porous membranes contain fixed pores larger than those of the nonporous membranes. The main problem in micro/ultrafiltration is flux decline due to concentration polarization, adsorption, pore-plugging and gel-layer formation [Mulder, 1996]. Examples of polymers for microfiltrations are polycarbonate, polytetrafluoroethylene (PTFE), polypropylene, polyamide, cellulose-ester, polysulfone (PSf), and polyetheretherketone (PEEK). Polytetrafluoroethylene (PTFE) is a hydrophobic material which is highly crystalline and has a high thermal stability and chemical resistance, originally developed by DuPont with Teflon trademark. The chemical structure of PTFE is shown in Fig. 1-8. CC FF FF Polytetrafluoroethylene (PTFE) Fig. 1-8. Chemical structure of polytetrafluoroethylene (PTFE) 11 When the sizes of the molecules are small and are in the same order of magnitude, porous membranes cannot do the separation and nonporous membranes should be used. Hence, nonporous membranes are used in gas/vapor separation and pervaporation. Pervaporation is a liquid permeation method having vacuum at the permeate-side, where the permeants immediately evaporate as vapor. Insight into the transport mechanism through membranes is needed to determine the performance of the membrane. For porous membranes, several models such as Knudsen flow and Hagen-Poiseuille flow exist [Mulder, 1996]. Knudsen flow is applied when the pores are small compared to the mean free path of the penetrants. Mean free path is the average distance a molecule travel before colliding into another molecule. Hence, in a Knudsen flow, interaction between the molecule and the pore wall is greater than the interaction between the molecules. On the other hand, Hagen-Poiseuille flow, which is also called the viscous flow, is applied when the pores are larger compared to the mean free path, indicating that the interaction between the molecules is greater than that of the molecule and the pore wall. Patil et al. [2006] measured permeation of supercritical CO 2 through polymeric hollow fiber membranes and reached the conclusion that the permeation profile followed Hagen-Poiseuille model. For nonporous membranes, solution-diffusion model is employed. Since in this work, nonporous membrane is used, transport through nonporous membranes will be discussed in depth by following the solution-diffusion model. 12 Transport mechanism through nonporous membranes Transport through nonporous membranes depends on the membrane material. The schematic of molecules transporting through a nonporous (dense) membrane is shown in Fig. 1-9. Nonporous (dense) membrane Flow direction Feed Permeate Fig. 1-9. Schematic of molecules transporting through a nonporous (dense) membrane The transport mechanism can be described by a solution-diffusion model [Wijmans et al., 1995]. Permeability can be written: SDP ?= where P is permeability coefficient, D is diffusion coefficient, and S is solubility. In this model, first, penetrants dissolve into the membrane and then they diffuse through the membrane. Separation is achieved by differences in the amount of penetrants that dissolves in the membrane (i.e., solubility) and the rate at which the penetrants diffuse through the membrane (i.e., diffusivity). 13 The solubility of gases in elastomers is generally very low and can be described by Henry?s law [Mulder, 1996]. Henry?s law describes a linear relationship between the concentration of gases in polymer (c) and the penetrant pressure (p). It can be written as follows: pkc ?= D The proportionality constant, k D , is referred to as the Henry?s law constant. The plot of this relationship is shown in Fig. 1-10a which is called a sorption isotherm. In this case, where the solubility is very low, the diffusion coefficient can be considered constant. For small non-interacting molecules, the diffusion coefficient decreases as the molecular size increases. This system can be called an ideal system, where the solubility and the diffusion coefficient are independent of penetrant concentration. Henry?s law; linear Gases in elastomers c p Fig. 1-10a. Sorption isotherm for gases in elastomers On the other hand, when the penetrants are organic vapors/liquids, the situation is different. Henry?s law is not obeyed and a non-linearity is seen at high pressures (Fig. 1- 10b). 14 Organic vapor/liquids in polymers Highly non-linear at high pressures c p Fig. 1-10b. Sorption isotherm for organic vapor/liquids in polymers The solubility will be high and the diffusion coefficient will be concentration-dependent. This system can be called a non-ideal system, where the solubility and the diffusion coefficient are concentration-dependent. Therefore, two systems should be considered separately: an ideal system where the solubility and the diffusivity coefficient are constants, and non-ideal system where the two measures are concentration-dependent. 15 For glassy polymers, linearity deviates at high pressures (Fig.1-10c). Dual-mode model can be employed to explain this curvature. The theory assumes that there are two types of sorption modes: Henry?s law sorption and Langmuir type sorption as well as two types of diffusion modes [Hu et al., 2003]. The schematic of the sorption isotherm for each sorption type is shown in Fig. 1-11. Concentration of penetrants in polymer is the addition of the two concentrations: HD ccc += where c D is the concentration of the penetrant sorbed onto the polymer by Henry?s law sorption and c H is the concentration of the penetrant sorbed onto the polymer by Langmuir type sorption. Equation becomes: bp bpc pkc + += 1 ' H D where k D is the Henry?s law constant, p the system pressure, ' H c the saturation constant and b the hole affinity constant. Gases in glassy polymers Non-linear c p Fig. 1-10c. Sorption isotherm for gases in glassy polymers 16 Langmuir sorptionHenry?s law c p Dual sorption theory c p Fig. 1-11. Schematic of the sorption isotherm for the dual sorption theory The driving force for transport can be pressure, temperature, concentration, and electromotive force [Wijmans, 1995]. These can all be written in terms of chemical potential gradient. Flux, J, through a plane perpendicular to the direction of diffusion can be expressed as: x LJ d d? ?= where ? is the chemical potential, x the position within the membrane and L a proportionality coefficient. Hence, d?/dx demonstrates the chemical potential gradient in the direction of diffusion. If the driving forces were to be expressed as concentration and pressure gradients, chemical potential will be written as: pvcT d)ln(dRd +?= ?? where c is the molar concentration of the penetrant, ? the activity coefficient, and v the molar volume of the penetrant. 17 The solution-diffusion model assumes that the pressure within a membrane is uniform and that the chemical potential gradient across the membrane is expressed only as a concentration gradient, without the pressure gradient. Hence, x c c TL J d dR ?= Replacing RTL/c with the diffusion coefficient D, the equation becomes the Fick?s first law. x c DJ d d ?= To further discuss transport through a nonporous membrane using this Fick?s law, concentration-independent system (ideal system) and concentration-dependent system (non-ideal) should be discussed separately [Mulder, 1996]. Transport in ideal systems Here, ideal systems where solubility and diffusion coefficient are independent of the concentration are discussed [Mulder, 1996]. In these cases, the penetrants are small non-interacting gases such as helium, hydrogen, argon, nitrogen, oxygen and methane. The solubility of these gases in polymers can be described by Henry?s law. As explained earlier, Henry?s law depicts the linear relationship between the concentration of the penetrant in the polymer (c) and the pressure of the system (p). Henry?s law is written as follows: pSc ?= c is the concentration of the gases in the polymer, S the solubility coefficient, p the pressure of the system. Substituting this equation into Fick?s law, xcDJ d/d?= , 18 x p DSJ d d ?= Integrating this equation across the membrane, for which x = 0 and p = p 1 represent the position and pressure of the feed side respectively and x = L and p = p 2 represent the position and pressure of the permeate side respectively, will give the following: )( 21 pp L DS J ?= Since SDP ?= , )( 21 pp L P J ?= This equation shows the relationship between the flux, J, and the permeability, P. According to this equation, the flux is proportional to the pressure difference across the membrane (p 1 - p 2 ) and inversely proportional to the membrane thickness, L. As permeability depends on solubility and diffusivity, we will further look into these two measures for ideal systems. The diffusion coefficient increases as the size of the gas molecules decreases. This can be explained by an equation that shows that the frictional resistance of a molecule (f) increases as the radius of the molecule (r) increases and another equation that shows that the diffusion coefficient is inversely proportional to the frictional resistance [Mulder, 1996]. rf ??6= f kT D = Hence, r kT D ??6 = 19 Therefore, it can be said that the diffusion coefficient decreases as the size of the gas molecules (i.e., r) increases. On the other hand, solubility increases as the size of gas molecules increases. The reason for this is as follows. Since dissolution of penetrants into polymers can be considered as two steps: penetrant condensation and penetrant mixing with the polymer matrix, solubility highly relates with condensability of the penetrant molecules. Solubility increases as condensability increases. Condensability increases as the molecular size increases so large organic vapors/liquids have a higher condensability than small non- interacting gas molecules. Therefore, it can be said that the solubility increases as molecular size increases. Table 1-2 shows the critical temperature, T c , and the solubility coefficient S of different gases in natural rubber [Brown et al., 1970]. T c is a measure of condensability, i.e. the higher the T c , the more condensable the substance. It demonstrates that as T c increases, the solubility increases. Table 1-2. Critical temperature and solubility of gases in natural rubber (Brown et al., 1970) Gas T c [K] S [cm 3 /(cm 3 cmHg)] H 2 33.3 0.0005 N 2 126.1 0.0010 O 2 154.4 0.0015 CH 4 190.7 0.0035 CO 2 304.2 0.0120 20 Permeability can also depend on temperature, arising both from the dependence of diffusivity and solubility. The temperature dependence of the permeability coefficient can be written: ? ? ? ? ? ? ? ? ?= T E PP R exp p o p E is the activation energy for permeation and o P a temperature independent constant. The temperature dependence of the solubility of small non-interactive gases in polymers can be written: ? ? ? ? ? ? ? ?= T H SS R exp s o s H? is the heat of solution and o S is the temperature-independent constant. Dissolution of a penetrant into a polymer takes two steps: penetrant condensation and penetrant mixing with the polymer matrix. Hence, the heat of solution, s H? , contains both the heat of condensation, oncondensati H? , and the heat of mixing, mixing H? . mixingoncondensatis HHH ?+?=? If s H? is negative, the process is exothermic and if it is positive, the process is endothermic. oncondensati H? is always negative, which indicates a exothermic process, where heat is released when condensation occurs and increases in magnitude as penetrant condensability increases. For small non-interactive gases, the heat of solution has a small positive value which indicates endothermic process and the solubility increases slightly with increasing temperature. 21 The temperature dependence of the diffusivity of small non-interactive gases in polymers can be written: ? ? ? ? ? ? ?= T E DD R exp d o where d E is the activation energy for diffusion and o D a temperature-independent constant. ? ? ? ? ? ? ? ? ?=? ? ? ? ? ? +? ?= T E P T EH SDP R exp R exp p o ds oo For small non-interactive gases, the temperature effect of the permeability coefficient depends on diffusion rather than solubility since the solubility is small and hence, its temperature dependence is small. Transport in non-ideal systems Here, non-ideal systems where solubility and diffusion coefficient are dependent on concentration are discussed [Mulder, 1996]. In these cases, the penetrants are interacting gases such as large gas molecules or organic vapors. As solubility increases with large molecules, the heat of sorption is negative, which indicates an exothermic process and the solubility decreases as temperature increases. On the other hand, diffusivity is dependent on penetrant concentration and therefore is hard to discuss compared to the ideal system. An example of a non-ideal system may be carbon dioxide permeating through a polymer, especially high free volume polymer. Carbon dioxide is considered to plasticize glassy polymers at high pressures. At high pressures, carbon dioxide acts as an agent to swell the polymer and hence, affect the permeability of the 22 polymer. When the pressure reaches what is called a plasticization pressure, the permeability starts increasing as the feed pressure is increased. There are researches done to learn the mechanism of this plasticization effect [Bos et al., 1999]. Permeability Permeability depends on factors such as sample history (the conditions that the polymer membrane encountered during formation) and the test conditions (temperature, pressure, and penetrant) [Mulder, 1996]. Penetrants such as helium, hydrogen, nitrogen, argon and oxygen are non-interacting gases, whereas gases such as carbon dioxide, sulfur dioxide, hydrogen sulfide, ethylene, propylene are interacting gases. Two structural parameters that affect the permeability are: glass transition temperature (T g ) and crystallinity. Glass transition temperature determines whether the polymer is glassy or rubbery whereas crystallinity determines whether the polymer is (semi-) crystalline or amorphous. Transport occurs mainly through the amorphous portions, so it is understandable that the degree of crystallinity affects the permeability. To measure the permeability of a gas through the membrane, there are two available methods. First one is the constant pressure/variable volume method as shown in Fig. 1- 12a. In this method, the feed side will be pressurized with the penetrant gas at a constant pressure. Gas permeation flux will be measured by a mass flowmeter or a soap film flowmeter. 23 Feed Membrane Permeate Fig. 1-12a. Schematic of constant pressure/variable volume method The second method shown in Fig. 1-12b utilizes an apparatus that has a fixed volume on the permeate side which is pressurized by the penetrant that permeated through the membrane. This method is termed as constant volume/variable pressure method. The rate of increase in pressure on the permeate side will be monitored by a pressure transducer or a pressure gauge. FeedPermeate Membrane PI Fig. 1-12b. Schematic of constant volume/variable pressure method 24 Membrane Technology with Supercritical Fluids There are several researches that have combined the two technologies: supercritical fluid processing and membrane technology. Semenova et al. [1992] conducted separation between supercritical CO 2 and ethanol using an asymmetric polyimide membrane in the purpose of recovering ethanol. Also with the asymmetric polyimide membrane, Higashijima et al. [1994] performed separation between supercritical CO 2 and petroleum components for enhanced oil recovery. In both of these researches, the major component of the retentate stream was supercritical CO 2 . In comparison, several studies are done where supercritical CO 2 was the permeate and the solute was the retentate. In these researches, apparatus was designed which contained an extraction column followed by a membrane set-up. Spricigo et al. [2001] have reported on the separation of nutmeg essential oil and dense CO 2 using a cellulose acetate membrane. High retention factor of nutmeg essential oil and high CO 2 flux were obtained in their experiments. Tan et al. [2003] designed an apparatus where the extraction column was followed by a membrane set-up. Separation of caffeine and supercritical CO 2 was performed by means of a nanofilter M5 hollow membrane (Tech-Sep Co.), which consists of a thin layer of ZrO 2 -TiO 2 coated on a carbon substrate. The inorganic layer had an average pore size of 3 nm. When the transmembrane pressure was kept constant at 0.2 MPa and temperature at 308 K, they obtained caffeine rejection of 100% and the highest CO 2 permeation flux at the feed pressure of 7.95 MPa. Peinemann et al. [2004] developed a method using a composite membrane of polyether imide being the porous support membrane and Teflon AF 2400 being the nonporous selective membrane in order to separate tocopherolacetate from supercritical CO 2 . Teflon AFs are licensed products of 25 DuPont, which are amorphous, glassy copolymers consisting of 2,2-bistrifluoromethyl- 4,5-difluoro-1,3-dioxole (PDD) and tetrafluoroethylene (TFE) [Buck et al., 1993]. Carlson et al. [2005] investigated separation of D-limonene from supercritical CO 2 using reverse osmosis membranes. They observed that 70% of the CO 2 can be recycled with the need of only small amount of pressurization, which would contribute greatly to the reduction of recompression cost. Work in This Thesis In this work, use of a nonporous polymer membrane was proposed to raise the particle collection yield in SAS process. The membrane would be placed at the outlet of the precipitation cell so as to let supercritical CO 2 and solvent permeate through the membrane and retaining the particles in the retentate (Fig.1-13). Drug + Solvent Supercritical CO2 + Solvent Membrane Supercritical CO2 Particles Fig. 1-13. Schematic of a supercritical antisolvent (SAS) process with membrane separation Therefore, as a first step, permeation tests of CO 2 through Teflon AF products were conducted. Teflon AF was selected due to its high gas and solvent permeability as well as 26 its chemical and thermal inertness. In addition, its nonporosity is favored in this situation to prevent particle clogs to occur and to make this process viable for any range of particle size. The gas/vapor permeability property of this copolymer has been investigated earlier by several researchers, but most of the work has been performed at low pressures [Pinnau et al., 1996; Alentiev et al., 1997; Merkel et al., 1999; Polyakov et al., 2003]. In this work, CO 2 permeability data was obtained at higher pressures and compared with the data acquired for semicrystalline polytetrafluoroethylene (PTFE). As a second step, the permeability of an organic solvent with CO 2 was measured. Acetone was chosen as the organic solvent. Lastly, the permeability of drug particles in organic solvent was investigated. Tetracycline was chosen as the drug particles and methanol as the solvent to dissolve the drug. 27 CHAPTER 2 AMORPHOUS TEFLON MEMBRANE Teflon AF products (DuPont, Wilmington, DE) are amorphous, glassy random copolymers consisting of 2,2-bistrifluoromethyl-4,5-difluoro-1,3-dioxole (PDD) and tetrafluoroethylene (TFE). The chemical structure of this copolymer is shown in Fig. 2-1. CC FF FF F CF3 CF3 F O O TFE PDD xy Fig. 2-1. Chemical structure of Teflon AF product: amorphous, glassy random copolymer of 2,2-bistrifluoromethyl-4,5-difluoro-1,3-dioxole (PDD) and tetrafluoroethylene (TFE). x = 13 mol %, y = 87 mol % for Teflon AF 2400 and x = 35 mol %, y = 65 mol % for Teflon AF 1600 28 Teflon AF 2400 contains 87 mol% PDD and 13 mol% TFE with the transition temperature of 240 o C, whereas Teflon AF 1600 contains 65 mol% PDD and 35 mol% TFE with Tg = 160 o C. Teflon AFs have high temperature stability and chemical resistance, as well as high free volume compared to other glassy polymers [Buck, 1993]. It is a nonporous (dense) membrane as shown in the micrograph taken by a scanning electron microscope (SEM) (Fig. 2-2). The micrograph on the right shows the edge of a film which has a thickness of approximately 60 ?m. The micrograph on the left is at higher magnification and there were no pores seen. Fig. 2-2. Micrograph of a Teflon AF 2400 film taken by a scanning electron microscope In Teflon AF, the side chains on the dioxole contribute to its high free volume. Free volume can be quantified by a measure called fractional free volume, FFV: V VV 0 FFV ? = 29 where V is the molar volume and V 0 the volume occupied by the polymer chains. V can be calculated by dividing the MW of the polymer by the density which can be determined experimentally. ? MW V = V 0 can be calculated using Bondi [1968]?s approximation which is as follows: w VV ?= 3.1 0 where V w is the van der Waals volume. V w can be calculated using a group contribution method [Krevelen, 1990]. The values of FFV for Teflon AF 2400 obtained by Pinnau et al. [1996] was 0.327 respectively. This value is in the same range as that of poly1- trimethylsilyl-1-propyene (PTMSP) which was measured as 0.34 by Alentiev et al. [1997], but higher than those of other glassy polymers which are typically in the range of 0.14-0.23 [Bos et al., 1999]. The permeability property of this copolymer has been investigated earlier by several researchers, but most of the work has been performed mainly at low pressures [Pinnau et al., 1996; Alentiev et al., 1997; Merkel et al., 1999; Polyakov et al., 2003]. Pinnau et al. [1996] have made Teflon AF 2400 film from solvent-cast method and obtained films with thickness of 14-20 ?m. The permeation measurements were tested with a membrane of surface area of 12.6 cm 2 by a constant pressure/variable volume method. Pure gas permeation measurements were performed at 25-60 ?C and a pressure difference of 20-120 psig across the membrane (atmospheric pressure at the permeate side). Gas flow rates were monitored by a soap film flowmeter. The calculation was done by the following equations: 30 ? ? ? ? ? ? = t Vp TA J d d 76 273 atm 12 pp LJ P ? ? = where J is the permeation flux, P atm the atmospheric pressure, A the membrane surface area, T the absolute temperature, and dV/dt the volumetric flow rate monitored by the soap film flowmeter. P is the permeability coefficient, p 2 the feed/retentate (upstream) pressure, p 1 the permeate (downstream) pressure (atmospheric), and L the membrane thickness. Gas mixture permeation measurements were performed at 25 ?C and a pressure difference of 200 psig. The compositions of the retentate and the permeate were analyzed by a gas chromatograph with a TCD detector. They observed that Teflon AF 2400 showed a higher permeability than other glassy polymers, although less than that of poly 1-trimethylsilyl-1-propyne (PTMSP). Teflon AF 2400 showed higher permeability for small gas molecules than large, condensable gases. This indicates that the diffusion coefficient is high for the small gas molecules, resulting in high permeability. On the other hand, PTMSP showed higher permeability for large, condensable gases than small gas molecules. This indicates that PTMSP exhibits higher permeability mainly due to high solubility whereas Teflon AF 2400 exhibits high permeability mainly due to high diffusion coefficient. The temperature dependence of the gas permeability of Teflon AF 2400 was very weak. The vapor permeability of Teflon AF 2400 increased greatly with the vapor activity, indicating plasticization of the polymer. Alentiev et al. [1997] made Teflon AF 2400 and Teflon AF 1600 film using solvent-cast method in which the films were cast from 2 wt % of perfluorotoluene solutions. For Teflon AF 2400, the solvent was evaporated at 55 ?C whereas for Teflon 31 AF 1600, the solvent was evaporated at ambient temperature. Then, the films were dried in vacuum at 40-50 ?C. Permeability and diffusion coefficient were measured by a mass spectrometric method for different gases such as He, H 2 , O 2 , N 2 , CO 2 , and hydrocarbons C 1 -C 3 . The measurements were conducted at 22 ?C with pressure difference of 0.0013- 0.027 MPa across the membrane (vacuum on the permeate side). They found that high permeability was exhibited especially for lighter gases, i.e. He and H 2 . No dependence of permeability on feed pressure was seen. A value of 2600 barrer was obtained for CO 2 permeability. Also, they have estimated and measured the free volume of the perfluorodioxole copolymers by Bondi?s method [Krevelen, 1990] and positron annihilation lifetime (PAL) method respectively. Merkel et al. [1999] have made Teflon AF 2400 film from solvent-cast method and obtained films with thickness of 50 ?m. The permeation measurements were tested with a membrane of surface area of 13.8 cm 2 by a constant pressure/variable volume method. Pure gas permeation measurements were performed at 25-60 ?C and a pressure difference of 15-240 psig across the membrane (atmospheric at the permeate side). The calculation was done in the same way as Pinnau et al. [1996]. They obtained the CO 2 permeability value of 2200 barrer at 35 ?C. They have compared the permeability of Teflon AF 2400 with that of PTMSP and polysulfone (PSF). The value for Teflon AF 2400 fell between the two: larger than that of PSF and smaller than that of PTMSP. PSF is a size-sieving, low free volume glassy polymer whereas PTMSP is a weakly size- sieving, high free volume glassy hydrocarbon-rich polymer. Since size-sieving character is affected by the polymer?s diffusion coefficient, it can be said that the diffusion coefficient of Teflon AF 2400 affects its permeability to a larger extent compared to 32 PTMSP and to a smaller extent compared to PSF. This is similar to observation of Pinnau et al. [1996], where it was shown that the high diffusion coefficient of Teflon AF 2400 largely contributed to its high permeability. Table 2-1 shows the CO 2 permeability through various polymer membranes studied by researchers previously. Table 2-1. CO 2 permeability coefficients in different polymers studied previously Polymer P [barrer] T [?C] p f [psig] p? (psi) Reference PTMSP 30000 25 50 50 I. Pinnau, 1993 Polycarbonate 8 25 50 50 H. J. Bixler, 1971 PTFE 12 S. M. Nemser, 1991 Matrimid 5218 34 50 1465.5 1465.5 S. Damle, 2003 PDMS 3200 40 I. Blume Polysulfone 5-8 35 14.7-132.3 C. Hu, 2003 IPC 3016-6032 40 1217.8 43.5 V. E. Patil, 2006 PVA 2180-4360 40 1130.8 43.5 V. E. Patil, 2006 PTMSP : poly1-trimethylsilyl-1-propyne PTFE : polytetrafluoroethylene Matrimid 5218 : commercial polyimide PDMS : polydimethylsiloxane IPC : polyamide copolymer PVA : polyvinyl alcohol 33 Table 2-2 shows the CO 2 permeability through Teflon AF 2400. The differences in the permeability coefficient values are considered to be coming from the differences in the condition at which the films were formed. Table 2-2. CO 2 Permeability coefficients in Teflon AF 2400 studied previously Reference P [barrer] T [?C] p f [MPa] p? [MPa] S. M. Nemser, 1991 2800 25 1.7 1.6 I. Pinnau, 1996 3900 25 0.45 0.35 A. Y. Alentiev, 1997 2600 22 0.013-0.037 0.013-0.037 T. C. Merkel, 1999 2200 35 0 S. M. Nemser, 1991 : melt-pressed I. Pinnau, 1996 : solvent cast from perfluoro-N-methyl morpholine (PF 5052), air-dried overnight at ambient condition, dried in a vacuum oven at 150 ?C for 3 days A. Y. Alentiev, 1997 : cast from perfluorotoluene, dried at 55 ?C, dried in a vacuum oven at 40-50 ?C T. C. Merkel, 1999 : cast from PF 5060, dried at ambient condition 34 CHAPTER 3 EXPERIMENTAL METHODS Polytetrafluoroethylene (PTFE) film was purchased from Small Parts, Inc., Miami Lakes, FL. It has a high crystallinity and a high melting temperature. Teflon AF 2400 and Teflon AF 1600 films of thickness ranging from 40-60 ?m were obtained from Random Technologies, San Francisco, CA, under license from DuPont (reference 040225-0004 and 060221-0001). AF 2400 is a copolymer of 87 mol% 2,2-bistrifluoromethyl-4,5- difluoro-1,3-dioxole (PDD) and 13 mol% tetrafluoroethylene (TFE), having a glass transition temperature of 240 o C. AF 1600 is a copolymer consisting of 65 mol% PDD and 35 mol% TFE, having a Tg of 160 ?C. These copolymers have a high free volume compared to other glassy polymers. Carbon dioxide used in the experiments had a purity of 99.9999% purchased from Airgas South, Inc., Atlanta, GA. (1-a) Membrane set-up for CO 2 permeation test using constant volume method The schematic of the membrane set-up is shown in Fig.3-1. CO 2 was pressurized by a syringe pump (Model 500D, Teledyne ISCO, Lincoln, NE) and feed pressure was measured by a pressure gauge (High Pressure Equipment, Erie, PA) indicated PI 1 in Fig. 3-1. The polymer membrane film was set inside a stainless steel filter holder (model XX45 025 00, Millipore, Billerica, MA) between the Buna-N resin O-ring and the filter 35 support screen, and was sealed by hand with a hex wrench. The thickness of the membrane was measured with a micrometer before the placement into the holder. At high pressures, PTFE O-rings were inserted above and beneath the membrane to decrease the force put on the membrane surface due to tightening and to let the membrane have some space for expansion due to plasticization. A high-pressure vessel was attached to the permeate side of the filter holder so as to increase the permeate volume. Permeate pressure was measured by a pressure gauge (PI 2). The feed and the permeate side were bypassed by a valve to let gradual increase or decrease in pressure occur in the case of pressurization/depressurization. The system was maintained at a desired temperature by an Isotemp immersion circulator (Model 730, Fisher Scientific, Pittsburgh, PA) immersed in a water bath. Valve Bypass valve Exit valve PI 1 CO2 pump CO2 cylinder PI 2 Water bath maintained at constant temperature Filter holder with membrane Ballast volume Coil Constant pressure Closed Feed sidePermeate side Constant volume/variable pressure method Fig. 3-1. Schematic of the membrane set-up for CO 2 permeation test 36 First, with the inlet valve and the bypass valve opened and the exit valve closed, the system was pressurized to the desired pressure. Then, the inlet and bypass valves were closed, and the pump was run at a pressure approximately 100 psi higher than the previous run. The experiment was initiated by opening the inlet valve and pressurizing the feed side to create pressure difference across the membrane, which will be the driving force for permeation. While the feed pressure was maintained constant by the pump, pressure increase in the constant permeate-side volume was recorded as a function of time. Permeation tests were performed up to the feed pressure of 1270 psig for Teflon AF 2400 and PTFE, and up to 630 psig for AF 1600. Permeability was given in the units of Barrer, which is equivalent to 10 -10 cm 3 (STP) . cm /(s . cm 2. cmHg). The calculation of the permeability coefficient is described in the following section. (1-b) Theory: CO 2 permeation test The permeate flux in moles [mol /(s . cm 2 )] J can be calculated by: t n A J d d 1 p = where n p is the number of moles of penetrant (CO 2 ) on the permeate side and A is the area of the membrane [cm 2 ]. Permeability coefficient is defined as: p LJ P ? ? = where L is the membrane thickness [cm 2 ] and p? is the pressure difference across the membrane [cmHg]. The permeability was calculated as follows: 37 TznVp R ppp = Assuming z to be constant and taking derivatives on both sides, t p Tz V t n d d Rd d ppp = Hence, the molar flux, J, will be: t p TzA V J d d R pp = And the permeability coefficient, P, will be: ? ? ? ? ? ? ?? ? ? = cmHgcms cmmol d d R 2 pp t p pTzA LV P Noting pf ppP ?=? and arranging, () ( ) t pp ppTzA LV P d d R pf pf p ? ? ?= ( ) t pp TzA LV d lnd R pfp ? ?= Changing the units from mol to cm 3 (STP), () ( ) ? ? ? ? ? ? ?? ?? ? ?= cmHgcms cmSTPcm d lnd STPR MW 2 3 COp 2 t p TzA LV P ? For the units of permeability of gases and vapors, barrer is frequently used: 1 ( ) cmHgcms cmSTPcm 10barrer 2 3 10 ?? ? = ? From the above equation of P, it can be found that the slope, m, of the plot of p?ln versus t (dln?p/dt) is necessary to determine P. Fig. 3-2a shows the graph obtained from the CO 2 permeation experiment and the permeate pressure is plotted against time. In Fig. 38 3-2b, the plot of the logarithm of the pressure difference ?p versus t is shown. An equation fitted linearly to this plot can give the slope of this plot. And the permeability coefficient can be calculated. Time p pe r m e a t e Fig. 3-2a. An example of a plot of permeate pressure vs time Time ln (p fe e d -p pe r m e a t e ) Fig. 3-2b. An example of a plot of logarithm of pressure difference vs time 39 (2-a) Set-up for verification of the system for acetone + CO 2 permeation Material balance of the acetone was checked on the membrane set-up for the acetone + CO 2 permeation. This is to ensure that the calculation is done properly and that the data obtained is trustable. Also, it is useful for verifying that there is no leak in the system, although leaks were easily detectable by monitoring the system immersed in the water bath (If there were any leaks, air bubbles would have come out of the loose connections). This was done by analyzing the flow at the 6-port valve by a ultraviolet (UV)-visible (Vis) spectrophotometer (Genesys 2, Thermo Electron, Waltham, MA) and comparing the value obtained with the amount of acetone fed into the system. The schematic of the set-up is shown in Fig. 3-3. restrictor PI 1 CO2 pump CO2 cylinder PI 2 Water bath maintained at constant temperature 40 ?C Filter holder without membrane coil Liquid pump 70 ?C valve 2-position 6-port valve Liquid reservoir 40 ?C Constant pressure/variable volume method Constant flow rate Constant pressure Opened Loop Fig. 3-3. Schematic of the set-up for verification of acetone + CO 2 permeation system CO 2 was pumped by a syringe pump (Model 500D, Teledyne ISCO, Lincoln, NE) and acetone was pumped by a liquid pump (Scientific Systems, Inc. LabAlliance, State College, PA). The combined flow passed through a coil immersed in the water bath 40 maintained at 40 ?C by an Isotemp immersion circulator (Model 730, Fisher Scientific, Pittsburgh, PA). The flow passed through the stainless steel filter holder (model XX45 025 00, Millipore, Billerica, MA) which did not have a membrane film inserted in between. System pressure was monitored by pressure gauges PI 1 and PI 2, both of which should have shown the same value due to absence of the membrane. After passing through a valve, the flow entered the 2-position 6-port valve (Model 7010, Rheodyne, Rohnert Park, CA) and exited to flow through the coil maintained at approximately 70 ?C and finally flowed through a 75 ?m polyetheretherketone-silica (PEEKsil) tubing which acted as a flow restrictor. The sampling was done at the 6-port valve when the loop of the valve was isolated from the rest of the system. The acetone collected in the isolated loop was slowly depressurized and washed with water to collect all of the acetone. The experimental steps are as follows. The valve at the position after the filter holder was kept open throughout the experiment. CO 2 was continuously flowing in advance to acetone. It was run at constant pressure in the range of 8-10 MPa. After the CO 2 flow reached steady state, acetone flow was started at a constant flow rate ranging in 0.10-0.25 mL/min. Once enough time was given for the CO 2 and acetone flow to reach steady state, sampling was initiated at the 6-port valve by turning the valve to the position that would isolate the loop. The permeate stream contained in the loop was depressurized by opening the sampling valve and was collected in distilled water to absorb the acetone in the stream. Then, the loop was washed with distilled water to completely remove the acetone from the loop. After the sampling was complete, the 6-port valve was returned back to the position at which the loop was connected to the system again. The collected sample solution was analyzed by UV spectrophotometry to determine the acetone 41 concentration using the calibration curve made from known concentrations of acetone solutions. The absorption at 500 nm was recorded followed by the absorption at 266 nm. The calculation following this experiment is summarized in the following section. (2-b) Theory: Verification of the system for acetone + CO 2 permeation Amount of acetone collected at the 6-port valve was calculated from ultraviolet (UV) spectrophotometry analysis. For the solution collected, the absorption at 500 nm was first measured and then at 266 nm. The difference between these two values is considered the net absorption. From the calibration curve prepared with the solutions of known concentration, the concentration of the sample solution is calculated. Multiplying this concentration by the weight of the solution will give the amount of acetone in the solution. To ensure that 100 % of the acetone fed into the system was maintained within the system, the amount of acetone experimentally collected (by UV) inside the loop of the 6-port valve will be compared with the amount of acetone that should be collected in the loop, which can be calculated from the amount of acetone fed into the system. The amount of acetone that should be collected in the loop according to the amount of acetone fed into the system will be calculated as follows. First, the mole fraction of acetone in the acetone + CO 2 feed flow, fedacetone, y , will be calculated. The mass flow rate of acetone fed, fedacetone, m , was calculated from the volumetric flow rate of feed acetone at 27 ?C, C27 fedacetone, ? v : C27 fedacetone, C27 acetonefedacetone, ?? ?= vm ? 42 Next, the molar flow rate of acetone fed, fedacetone, n , was calculated: acetone fedacetone, fedacetone, MW m n = The mass and molar flow rates of CO 2 will be calculated in the same way. The mass flow rate of CO 2 fed, fed,CO 2 m , was calculated from the volumetric flow rate of CO 2 at 40 ?C and the system pressure p, p v C,40 fed,CO 2 ? : pp vm C,40 fed,CO C,40 COfed,CO 222 ?? ?= ? The molar flow rate of CO 2 fed, fed,CO 2 n , was calculated: 2 2 2 CO fed,CO fed,CO MW m n = Using the molar flow rates of acetone and CO 2 , the molar fraction of acetone that was fed into the system can be calculated: fed,COfedacetone, fedacetone, fedacetone, 2 nn n y + = From pressure, p, temperature, T (40 ?C), and acetone mole fraction in the acetone + CO 2 feed flow, fedacetone, y , the compressibility factor, z, can be calculated using Peng-Robinson Equation of State (PR-EOS), which is shown below. 2 m 2 mm 2 R bbVV a bV T p ?+ ? ? = ? c 2 c 2 R45724.0 P T a = c c .07780R0 P T b = 43 ()( ) 2 0.5 r 2 126992.054226.137464.01 T??++= ??? c r T T T = where V m is the molar volume, T c the critical temperature, P c the critical pressure, R the gas constant, ? the acentric factor, T r the reference temperature. After obtaining z using the PR-EOS program, the molar volume of the acetone + CO 2 feed mixture, mixtmol, v , can be calculated from the compressibility equation: p Tz v R mixtmol, = Inverse of mixtmol, v is the molar density, mixtmol, ? : mixtmol, mixtmol, 1 v =? The weight density, mixtg, ? , can be obtained by multiplying the molecular weight of the mixture, mixt MW . First, the molecular weight of the mixture, mixt MW , can be calculated as: ))((MW)()(MWMW fed,COCOfedacetone,acetonemixt 22 yy += Hence, the weight density of the mixture, mixtg, ? , can be calculated: )MW)(( mixtmixtmol,mixtg, ?? = If the assumption is made that the acetone fed was 100 % maintained within the system, from the weight density of the mixture, mixtg, ? , and the acetone mole fraction in the combined flow, fedacetone, y , the weight of acetone that should be collected in the loop of the 6-port valve, d_loopacetone_fe w , can be calculated as: 44 mixt acetonefedacetone,loopmixtureg, d_loopacetone_fe MW )MW)()()(( yv w ? = This acetone amount is the value that should be obtained at the loop of the 6-port valve, according to the amount of acetone fed into the system. This value, d_loopacetone_fe w , should be compared with the amount obtained from UV analysis, _loopacetone_UV w . Percentage of the acetone collected in the loop of the 6-port valve is: 100Percentage d_loopacetone_fe _loopacetone_UV ?= w w (3-a) Membrane set-up for acetone + CO 2 permeation test The schematic of the membrane set-up is shown in Fig. 3-4. CO 2 was fed by a syringe pump (Model 500D, Teledyne ISCO, Lincoln, NE) and acetone was pumped by a liquid pump (Scientific Systems, Inc. LabAlliance, State College, PA). CO 2 flow was diversed into two streams: one merging with the acetone flow and the other flowing to the permeate side of the membrane. This was done to keep the permeate pressure the same as the retentate pressure. The CO 2 flow that was combined with the acetone flow passed through a coil immersed in a water bath maintained at 40 ?C by an Isotemp immersion circulator (Model 730, Fisher Scientific, Pittsburgh, PA). The fluid inlet fitting was specially modified as shown in Fig. 3-4b so that there was enough space for 1/16? stainless steel tubings to go through and be set at positions near the membrane on both the feed/retentate and the permeate side. On the feed/retentate side, this modification allowed the acetone feed + CO 2 flow to pass through the outside 45 of the tubing and the retentate flow to pass through the inside of the tubing, which flowed to the retentate restrictor. On the permeate side, CO 2 flowed through the outside of the 1/16? stainless steel tubing and the permeate stream flowed through the inside of the tubing, which flowed to the 6-port valve. The feed/retentate pressure was measured by a pressure gauge (High Pressure Equipment, Erie, PA) indicated PI 1. The polymer membrane film was set inside a stainless steel filter holder (model XX45 025 00, Millipore, Billerica, MA) between the Buna-N resin O-ring and the filter support screen, and was sealed by hand with a hex wrench. The thickness of the membrane was measured with a micrometer before the placement into the holder. At high pressures, PTFE O-rings were inserted above and beneath the membrane to decrease the force put onto the membrane surface due to tightening and to let the membrane have some space for expansion due to plasticization. Permeate pressure was measured by a pressure gauge indicated PI 2. The permeate flow passed through a valve, then entered a 2-position 6- port valve (Model 7010, Rheodyne, Rohnert Park, CA), and flowed through the coil which was heated to approximately 70 ?C in order to prevent CO2 freezing at the outlet due to expansion. Finally, the stream flowed through a 75 ?m polyetheretherketone-silica (PEEKsil) tubing which acted as a flow restrictor. CO 2 flow rate was measured by inversing a graduated cylinder in the water bath and collecting the flow that came out the restrictor during a certain amount of time. The system was maintained at 40 ?C by an Isotemp immersion circulator (Model 730, Fisher Scientific, Pittsburgh, PA) immersed in a water bath. The sampling was done at the 6-port valve when the loop of the valve was isolated from the rest of the system. The acetone collected in the isolated loop was slowly depressurized into distilled water and washed additionally with water to collect all of the 46 acetone in the loop. The collected sample solution was analyzed by an ultraviolet-visible (UV-Vis) spectrophotometer (Genesys 2, Thermo Electron, Waltham, MA) to determine the acetone concentration from the calibration curve previously made. restrictors PI 1 CO2 pump CO2 cylinder PI 2 Water bath maintained at constant temperature 40 ?C coil Purge valve Liquid pump 70 ?C Valve Liquid resevoir permeate retentate 2-position 6-port valve loop Filter holder with membrane Constant flow rate Constant pressure Constant pressure/variable volume method Fig. 3-4a. Schematic of the membrane-set up for acetone + CO 2 permeation Arrows: flow direction Membrane holder Enlargement 1/16? stainless steel tubingMembrane film Sintered metal support O-ring Retentate (CO2 + Acetone)Permeate (CO2 + Acetone) CO2 CO2 + Acetone CO2 CO2 + Acetone Feed/retentatePermeate To the 6-port valve To the retentate restrictor Fig. 3-4b. Enlargement of the schematic of the membrane holder 47 The experimental steps are as follows. The purge valve was kept closed, and the retentate and the permeate valve were kept open throughout the experiment. CO 2 was continuously flowed in advance to acetone and after reaching steady state, acetone flow was started at 0.50 mL/min. Once enough time was given for the CO 2 and acetone flow to reach steady state, sampling was initiated at the 6-port valve by turning the valve to the position that would isolate the loop. The permeate stream contained in the loop was depressurized by opening the sampling valve and was collected in distilled water to absorb the acetone in the stream. Then, the loop was washed with distilled water to completely remove the acetone from the loop. The collected sample solution was analyzed by UV spectrophotometry to determine the acetone concentration from the calibration curve previously made. The absorption at 500 nm was recorded followed by the absorption at 266 nm. The calculation following this experiment is summarized in the next section. (3-b) Theory: CO 2 + acetone permeation test Calculation of the percentage of acetone collected at the permeate side The calculation for the CO 2 and acetone permeation test is the same as in the verification experiment for the set-up. Amount of acetone collected at the 6-port valve will be calculated from ultraviolet (UV) spectrophotometry analysis. For the solution collected, the absorption at 500 nm was first measured and then at 266 nm. The difference between these two values was considered as the net absorption. From the 48 calibration curve prepared beforehand with the solutions of known concentration, the concentration of the sample solution was calculated. Multiplying this concentration by the weight of the solution will give the amount of acetone in the solution. To calculate what percentage of the feed permeated through the membrane, the amount of acetone collected inside the loop of the 6-port valve by UV analysis should be compared with the amount of acetone that will be collected in the loop when 100 % permeation was occurring, which can be calculated from the amount fed into the system. The latter value (amount of acetone that is to be collected in the loop when 100 % permeation occurs) will be calculated as follows. First, the mole fraction of acetone in the combined (acetone + CO 2 ) feed flow, fedacetone, y , will be calculated from the volumetric flow rate of feed acetone at 25 ?C, C25 fedacetone, ? v , and the volumetric flow rate of feed CO 2 at 40 ?C and 1 atm, C,1atm40 fed,CO 2 ? v : 2 22 CO C,1atm40 fed,CO C,1atm40 CO acetone C25 fedacetone, C25 acetone acetone C25 fedacetone, C25 acetone fedacetone, MW ))(( MW ))(( MW ))(( ???? ?? + = vv v y ?? ? From pressure, p, temperature, T, and acetone mole fraction in the feed, fedacetone, y , the compressibility factor, z, can be calculated using Peng-Robinson Equation of State (PR- EOS). After obtaining z using the PR-EOS program, the molar volume of the combined feed mixture, mixtmol, v , can be calculated from the compressibility equation: p Tz v R mixtmol, = 49 Inverse of mixtmol, v is the molar density, mixtmol, ? : mixtmol, mixtmol, 1 v =? The weight density, mixtg, ? , can be obtained by multiplying the molecular weight of the mixture, mixt MW , with the molar density mixtmol, ? . First, the molecular weight of the feed mixture, mixt MW , will be calculated: ))(MW())(MW(MW fed,COCOfedacetone,acetonemixt 22 yy += Hence, the weight density, mixtg, ? , can be calculated: )MW)(( mixtmixtmol,mixtg, ?? = If 100 % of the feed acetone permeated through the membrane, using the weight density of the mixture, mixtg, ? , and the acetone mole fraction in the combined feed flow, fedacetone, y , the weight of feed acetone that will be collected in the loop, d_loopacetone_fe w , can be calculated: mixt acetonefedacetone,loopmixtg, d_loopacetone_fe MW )MW)()()(( yv w ? = This acetone amount should be compared with the amount obtained from UV analysis. Percentage of the acetone that permeated through the membrane is calculated: 100Percentage d_loopacetone_fe _loopacetone_UV ?= w w 50 Calculation of the permeation flux and the permeability coefficient of acetone The following will be the calculation of the permeation flux of acetone and the permeability coefficient of acetone. The CO 2 flow rate at the permeate and the retentate side was measured with inversed cylinder at the exit of the restrictors in the 40 ?C water bath. Hence, the CO 2 flow rates measured were values at 40 ?C and ambient pressure (1 atm). These volumetric flow rates can be converted into mass flow rate by multiplying the CO 2 density at that condition. The value of the density of CO 2 at the certain pressure and 40 ?C was obtained from NIST webbook (webbook.nist.gov). The mass flow rate on the permeate and the retentate side of the membrane will be calculated: C,1atm40 CO C,1atm40 permeatepermeate,CO 22 ?? ?= ?vm C,1atm40 CO C,1atm40 retentateretentate,CO 22 ?? ?= ?vm Multiplying the CO 2 mass permeation rate, permeate,CO 2 m , with the CO 2 density at 40 ?C and the system pressure, p, CO 2 volumetric flow rate can be obtained at the system condition: pp mv ,C40 COpermeate,CO ,C40 permeate,CO 222 ?? ?= ? From the UV analysis, the weight of acetone collected in the sample loop of the 6-port valve at the permeate side, _loopacetone_UV w , was obtained. Dividing this value by the sample loop volume will give the concentration (w/v) of acetone in the acetone + CO 2 solution collected in the loop. loop _loopacetone_UV ,C40 permeateacetone, v w c p = ? Assuming that the acetone exist only a sparing amount compared to CO 2 , the CO 2 flow rate at the system condition, p v ,C40 permeate,CO 2 ? , can be considered as the total (acetone + CO 2 ) 51 flow rate, p v ,C40 permeate,COacetone 2 ? + . Multiplying the acetone concentration, p e c ,C40 permeatacetone, ? , with the total volumetric flow rate, p v ,C40 permeate,COacetone 2 ? + , gives the mass flow rate of acetone that permeated through the membrane, permeateacetone, m . pp vcm ,C40 permeate,COacetone ,C04 permeateacetone,permeateacetone, 2 ? + ? ?= p v v w m ,C40 permeate,CO loop _loopacetone_UV permeateacetone, 2 ? ?= The volumetric flow rate of acetone fed into the system at 25 ?C, C25 acetone ? v , can be converted to the mass flow rate of acetone, feedacetone, m , by multiplying the acetone density at 25 ?C, C25 acetone ? ? : C25 acetone C25 acetonefeedacetone, ?? ?= ?vm Hence, the mass flow rate of acetone that was retained within the retentate side, retentateacetone, m , will be: permeateacetone,feedacetone,retentateacetone, mmm ?= Next, to calculate the partial pressures of acetone in the CO 2 + acetone flow on the permeate and the retentate side, the mass flow rate of acetone on each side ( retentateacetone,permeateacetone, , mm ) will be converted to molar flow rate by dividing the value by the molecular weight of acetone, acetone MW . acetone permeateacetone, permeateacetone, MW m n = acetone permeateacetone, permeateacetone, MW m n = 52 The acetone mole fraction in the CO 2 + acetone flow on the permeate and the retentate side will be calculated: permeate,COpermeateacetone, permeateacetone, permeateacetone, 2 nn n y + = retentate,COretentateacetone, retentateacetone, retentateacetone, 2 nn n y + = The partial pressure of acetone in each side will be obtained by multiplying the system pressure with the acetone mole fractions, permeateacetone, y retentateacetone, y . permeateacetone,permeateacetone, ypp ?= retentateacetone,retentateacetone, ypp ?= Hence, the pressure difference of acetone across the membrane, acetone p? , can be calculated: permeateacetone,retentateacetone,acetone ppp ?=? Defining J as the mass flux of acetone permeating through the membrane, the mass flow rate of acetone that permeated, permeateacetone, m , should be divided by the membrane surface area A. A m J permeateacetone, permeateacetone, = The acetone permeability, P acetone,permeate , is calculated by multiplying the membrane thickness, L, and dividing by the acetone pressure difference across the membrane, ?p acetone : 53 acetone permeateacetone, permeateacetone, p LJ P ? ? = (4) Tetracycline permeability test The permeability coefficient of tetracycline was determined to test if large drug molecules can be retained by the membrane. The schematic of this test is shown in Fig. 3- 5. Approximately 43 mg of tetracycline was dissolved into 15 mL of methanol. Teflon AF 1600 film was inserted between the two plates of the stainless steel filter holder. On the side that were to be the permeate side, pure methanol was injected by a syringe to fill the space. On the other hand, the tetracycline/methanol solution was injected by a syringe on the side that were to be the feed side. Both ends were plugged and was positioned vertically so that the feed side was at the top and the permeate side at the bottom. It was placed that way overnight to see if there was any permeation of tetracycline occurring. Twenty-four hours later, the solution on the permeate side was analyzed by UV spectrophotometry since tetracycline is detectable by UV. The absorption of the solution was compared with that of pure methanol at 286 nm and 266 nm. 54 Membrane holder enlargement Membrane film Sintered metal support O-ring Filled with methanol Filled with tetracycline + methanol Feed Permeate Fig. 3-5. Schematic of tetracycline permeation test 55 CHAPTER 4 PERMEABILITY OF CARBON DIOXIDE Calculation of the permeability coefficient of CO 2 The calculation of the permeability coefficient P will be shown below for the data collected at 45 ?C and the feed pressure of 231 psig for a Teflon AF 2400 film with a thickness of 63.5 ?m. The initial pressure difference ?p was 100 psi, which was the same for all experimental runs. The membrane surface area that was available for permeation was 2.2 cm 2 . The volume on the permeate side was measured to be 14 cm 3 . First, the calculation of the compressibility factor, z, will be reviewed. Since the permeate pressure (p p ) was varying over time, 3 values of permeate pressure were chosen to calculate z for each permeate pressure. The CO 2 density values of the corresponding permeate pressures were used for the calculation. The 3 calculated compressibility factors were averaged to give one value of z. To get a good average value of z, the first value of the permeate pressure was taken from the beginning of the experiment, the second from the middle of the experiment, and the third from the end of the experiment. The permeate pressure (p p ) chosen as a first value was 138.8 psig, which was taken from the start of the experiment. The calculation of z using this p p value will be shown as follows. The CO 2 density at 45 ?C and 138.8 psig was 0.01841 g/cm 3 . Converting the units of the temperature to K, 56 318.15K45)K(273.15C45 =+=?=T Converting the units of the permeate pressure to Pa, Pa101.058 bar Pa10 14.51psia bar 14.7)psia(138.8138.8psig 6 5 p ?= ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?+==p Also converting the units of the CO 2 density into g/m 3 , 3 4 3 36 3 gC,138.8psi45 CO m g 101.841 m cm10 cm g 0.01841 2 ?= ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = ? ? Using the definition of z, z was calculated: gC,138.8psi45 CO COp 2 2 R MW ? ? ? = ?T p z () () 0.956 m g 101.841318.15K Kmol mPa 8.314 mol g 44Pa101.058 3 4 3 6 = ? ? ? ? ? ? ?? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? =z The first value of z was calculated as 0.956. The other two values were calculated in the same way. The three values was averaged to give one value of z. Averaging, z was obtained to be 0.943. Next, the value of the slope of the logarithm of the pressure difference vs time, m, will be determined. The graphs are shown in Fig. 4-1a and 4-1b. As the slope of the line, the value of -0.0265 min -1 was obtained. Converting this units from min -1 to sec -1 , sec 1042.4 sec60 min min 0265.0 4? ?? = ? ? ? ? ? ? ? ? ? ? ? ? ?? =m 57 135 145 155 165 175 185 195 205 215 225 235 0 1020304050607080 Time[min] P p erm e a t e[ p s i g ] Fig. 4-1a. A graph of permeate pressure vs time for CO 2 permeation through Teflon AF 2400 film with thickness of 63.5 ?m. Temperature = 45 ?C. Feed pressure = 231 psig. Initial pressure difference = 100 psi. y = -0.0265x + 4.5296 R 2 = 1 0 1 2 3 4 5 6 0 1020304050607080 Time[min] l n (P f eed -P p e rm ea t e ) Fig. 4-1b. A graph of logarithm of the pressure difference vs time for CO 2 permeation through Teflon AF 2400 film with thickness of 63.5 ?m. Temperature = 45 ?C. Feed pressure = 231 psig. Initial pressure difference = 100 psi. 58 Finally, the permeability coefficient, P, can be calculated. The CO 2 density at STP condition is 0.001977g/cm 3 . The gas constant, R, should be converted to K)/(molcmcmHg 3 ?? . Kmol cmcmHg 6237 L cm10 atm 76cmHg Kmol Latm 0.08206R 333 ? ? = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = Converting the units of the film thickness, L, from micrometers (?m) to centimeters (cm), () cm106.35 ?m10 cm m63.5 3 4 ? ?= ? ? ? ? ? ? ? ? ?= ?L The permeability coefficient, P, can be calculated: () ( ) ? ? ? ? ? ? ?? ? ? ?? ?= cmHgcms cmSTPcm STPR MW 2 3 CO COp 2 2 ?TzA mLV P ()( ) ( ) ()() () ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?? ?= ? ? 3 3 2 4 33 cm g 0.001977318.15K Kmol cmcmHg 62372.2cm0.943 sec 104.42- mol g 44cm106.3514cm P () ? ? ? ? ? ? ?? ? ?= ? cmHgcms cmSTPcm 1012.2 2 3 7 []barrer2120= The permeability of CO 2 through Teflon AF 2400 film with thickness of 63.5 ?m was calculated as cmHg)cmcm/(s(STP)cm1012.2 237 ???? ? or 2120 barrer while the feed pressure of CO 2 was maintained at 231 psig. 59 CO 2 permeability in Teflon AF 2400, AF1600 and PTFE The permeability coefficients of CO 2 in Teflon AF 2400, 1600, and PTFE at 45 ?C are tabulated in Table 4-1 and plotted against feed pressure in Fig. 4-2. Table 4-1. CO 2 permeability coefficients in different membranes vs feed pressure at 45 ?C and initial pressure difference of 100 psi Teflon AF 2400 Pfeed [psig] 231 430 629 829 1173 1270 Permeability [barrer] 2120 2450 3100 3680 3350 2700 Teflon AF 1600 Pfeed [psig] 230 428 627 Permeability [barrer] 630 1210 1820 PTFE Pfeed [psig] 232 1273 Permeability [barrer] 16 16 60 0 1000 2000 3000 4000 0 250 500 750 1000 1250 1500 Feed Pressure [psig] P e r m e a b i l i ty C o e ffi c i e n t [Ba r r e r ] AF 2400 AF 1600 PTFE Fig. 4-2. CO 2 permeability coefficients in different membranes vs feed pressure at 45 ?C and initial pressure difference of 100 psi Teflon AF 2400 had a permeability value ranging in 2100-3700 barrer for the feed pressures of 230-1270 psig. Up to the feed pressure of 830 psig, the permeability coefficient increased as the feed pressure increased, but for 1170 psig, the value dropped and dropped further for 1270 psig. It can be said that a maximum value for the permeability coefficient exists between 830 psig and 1170 psig. Between these pressures, critical pressure of CO 2 exists. This type of maximum permeability of CO 2 was observed by Patil et al [2006] as well. They observed a maximum permeability of CO 2 through 1-2 ?m thick polyvinyl alcohol (PVA) membrane and 0.5-1 ?m thick polyamide copolymer (IPC) membrane at the pressure very close to the critical pressure of CO 2 when the experiment was performed at the temperature of 40 ?C and pressure difference of 0.3 MPa. Their 61 conclusion was that the transport mechanism through the membrane followed the Hagen- Poiseuille model [Bird et al., 2002; Mulder, 1996], which is generally applied for viscous flow where the interaction between the molecules is more dominant than the interaction between the molecules and the pore wall. Hagen-Poiseuille equation is: p MWL r J ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? = ? ? ? ? 8 2 where J is the flux of the penetrant, ? the porosity, ? the pore tortuosity, ? the density of the penetrant, ? the absolute viscosity of the penetrant, r the pore radius, L the membrane thickness, MW the molecular weight of the penetrant and ?p the pressure difference across the membrane. Since Hagen-Poiseuille equation generally describes the scheme of the flow through pipes, it can be said that the assumption was made for the pores to have a cylindrical structure and equal radius. In seen in the equation, the ratio of the density to viscosity (inverse of the kinematic viscosity) is a critical parameter. The density of CO 2 drastically changes about the critical pressure and so does the viscosity. The rates at which density and viscosity change with feed pressure affect the value of the ratio and hence, the permeability. This may have lead to the existence of maximum in the permeability value. From the permeability data of CO 2 and N 2 through IPC membrane, they have back-calculated the membrane pore size and obtained the value of 1.9 nm and 1.7 nm respectively. It is assumed that the pore size of Teflon AFs is in the range of 5.9-6.4 ? [Alentiev et al., 1997] and is smaller than 1.7 nm (17 ?) so Hagen-Poiseuille model may not be appropriate to apply. Further discussion will be required to explain the existence of maximum permeability. 62 Teflon AF 1600 had a permeability value ranging in 630-1820 barrer for the feed pressures of 230-630 psig. The permeability coefficient increased as the feed pressure increased. Polytetrafluoroethylene (PTFE) had a permeability value of 16 barrer at the feed pressure of 230 psig and 1270 psig. There was scarcely any permeation compared to the Teflon AF products. Comparing the permeability among the three polymers, it can be easily seen that Teflon AF 2400 has the highest permeability among the three, followed by AF 1600 and then PTFE. The fact that Teflon AF 2400 has a higher permeability than AF 1600 can be explained by the difference in the amount of free volume in the polymers. AF 2400 has higher free volume than AF 1600. The large difference in the permeability of Teflon AF products and PTFE can be explained by the degree of crystallinity. As gas/vapor transport occurs through the amorphous part of the polymer, the portion at which this can happen is limited for PTFE. This permeability result can be comprehended in terms of the amount of tetrafluoroethylene (TFE) in the polymer that the permeability decreases as the ratio of tetrafluoroethylene increases. In terms of the amount of 2,2-bistrifluoromethyl-4,5- difluoro-1,3-dioxole (PDD) in the polymer, the permeability increases as the ratio of PDD increases. Hence, it can be said that the PDD structure contributes to the decrease in crystallinity and increase in free volume, leading to an increase in CO 2 permeability. 63 In Table 4-2, the permeability coefficient of Teflon AF 2400 obtained by previous studies was organized along with the value obtained in this work. The value obtained in the current work fell in the same range as the values obtained by other researchers. The differences in the values obtained can be attributed to the difference in the formation of the membrane and the difference in the experimental condition or method. Table 4-2. CO 2 Permeability coefficients in Teflon AF 2400 studied previously Reference P [barrer] T [?C] p f [MPa] p? [MPa] Current work 2440 50 2.9 0.69 Current work 2450 45 3.1 0.69 Current work 2590 40 3.2 0.69 Current work 2740 35 3.3 0.69 S. M. Nemser, 1991 2800 25 1.7 1.6 I. Pinnau, 1996 3900 25 0.45 0.35 A. Y. Alentiev, 1997 2600 22 0.013-0.037 0.013-0.037 T. C. Merkel, 1999 2200 35 0 Current work, 2006: polymer purchased from Random Technologies S. M. Nemser, 1991: melt-pressed I. Pinnau, 1996: solvent cast from perfluoro-N-methyl morpholine (PF 5052), air-dried overnight at ambient condition, dried in a vacuum oven at 150 ?C for 3 days A. Y. Alentiev, 1997: cast from perfluorotoluene, dried at 55 ?C, dried in a vacuum oven at 40-50 ?C T. C. Merkel, 1999: cast from PF 5060, dried at ambient condition 64 Temperature dependence of CO 2 permeability through Teflon AF 2400 Fig. 4-3a depicts the permeability coefficients in Teflon AF 2400 versus feed pressure (220-830 psig) at various temperatures (35-50 ?C) to see if there is any temperature dependence of the permeability. Fig. 4-3b is the Arrhenius plot of CO 2 permeability in Teflon AF 2400. From the graphs obtained, it can be said that there is not a significant dependence on temperature, although there seems to be a slight decrease in permeability as the temperature increases. This matches with Pinnau et al. (1996)?s work where they have found that only a weak temperature dependence of permeability is shown for Teflon AF 2400. 1500 2000 2500 3000 3500 4000 4500 0 250 500 750 1000 Feed Pressure [psig] P e r m e a b i l i ty C o e ffi c i e n t [Ba r r e r ] 50C 45C 40C 35C Fig. 4-3a. Temperature dependence of CO 2 permeability in Teflon AF 2400 film at varying feed pressure. Initial pressure difference = 100 psi. 65 1000 10000 0.00305 0.00310 0.00315 0.00320 0.00325 0.00330 1/T [K-1] P e r m e a b i l i ty C o e ffi c i e n t [Ba r r e r ] pf=222psig pf=438psig pf=636psig pf=834psig Fig. 4-3b. Arrhenius plot of CO 2 permeability in Teflon AF 2400 film at varying feed pressure. Initial pressure difference = 100 psi. CO 2 plasticization effect on Teflon AF 2400 and AF 1600 Bos et al. [1999] defined plasticization as an increase in permeability as a function of feed pressure. The pressure at which plasticization occurs is called the plasticization pressure. Fig. 4-4a shows the plasticization effect of CO 2 on Teflon AF 2400 and Fig. 4- 4b shows for AF 1600 at 45 ?C. First-time-use membrane showed a profile that increased as the feed pressure increased, but as the membrane is used for the second run, third run, and so on, the permeability coefficients became independent of the feed pressure. Although to a smaller degree, the same trend can be seen for AF 1600, where the permeability coefficients became less dependent on the feed pressure as the membrane is used more. This plasticization phenomenon can be attributed to CO 2 acting as a swelling agent and increasing segmental mobility of the polymer, resulting in an increase of free 66 volume. The difference in the degree of plasticization between AF 2400 and AF 1600 may be due to the difference in the amount of free volume in the polymers. Since 2,2- bistrifluoromethyl-4,5-difluoro-1,3-dioxole (PDD) in the polymer contributes greatly to the amount of free volume, with AF 2400 having 87% PDD and AF 1600 having 65% PDD, the free volume is higher for AF 2400. The higher free volume led to a higher degree of plasticization, even reaching the point where the permeability became independent of the feed pressure. 1000 2000 3000 4000 5000 0 250 500 750 1000 Feed Pressure [psig] Pe r m e a b i l i ty C o e ffi c i e n t [B a r r e r ] 1st 2nd 3rd 4th Fig. 4-4a. Plasticization effect on CO 2 permeability in Teflon AF 2400 film at 45 ?C. Initial pressure difference = 100 psi. 67 500 1000 1500 2000 2500 0 250 500 750 Feed Pressure [psig] P e r m e a b i l i ty C o e ffi c i e n t [Ba r r e r ] 1st 2nd 3rd 4th 5th Fig. 4-4b. Plasticization effect on CO 2 permeability in Teflon AF 1600 film at 45 ?C. Initial pressure difference = 100 psi. 68 CHAPTER 5 PERMEABILITY OF ACETONE Verification of the measurement The verification of the measurement was performed on the set-up for the acetone + CO 2 permeation test at 40 ?C. The sample solution (acetone + CO 2 ) collected at the 6- port valve was analyzed by UV spectrophotometry to determine the weight of acetone collected. This value was then compared with the theoretical value that should have been collected in the loop of the 6-port valve, applying the assumption that 100 % of acetone fed was maintained within the system. Fig. 5-1 shows the calibration curve for acetone solutions of known concentrations. The net absorption was taken on the x-axis and the acetone concentration in the units of grams acetone per grams solution (g acetone/g solution) was taken on the y-axis. The net absorption refers to the difference in absorptivity measured at 500 nm and 266 nm. (Acetone shows absorption at 266 nm.) The equation for the calibration line turned out to be 5 1030033.0 ? ??= xy with the linearity being very high. 69 y = 0.0033x - 3E-05 R 2 = 1 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 0.000 0.100 0.200 0.300 0.400 0.500 0.600 Net Absorbance (266nm A - 500 nm A) A c et o n e c o nc ent ra t i o n [ g ac et o n e / g so l u t i o n ] Fig. 5-1. UV calibration curve for acetone Using this calibration line, the concentration of the solution (y) collected at the 6-port valve was determined from the net absorption (x) obtained by the ultraviolet (UV) spectrophotometic analysis. The calculation for the percentage of acetone collected at the 6-port valve will be shown below. First, the amount of acetone fed into the system will be calculated to determine the mole fraction of acetone in the acetone + CO 2 feed flow acetone y . The mass flow rate of acetone fed, fedacetone, m , was calculated from the volumetric flow rate of acetone at 27 ?C, C27 fedacetone, ? v : C27 fedacetone, C27 acetonefedacetone, ?? ?= vm ? min g 0.1958 min mL 0.25 mL g 0.783 fedacetone, = ? ? ? ? ? ? ? ? ? ? ? ? ? =m 70 The mass flow rate of acetone that was fed, fedacetone, m , was calculated as 0.1958 g/min. Next, the molar flow rate of acetone fed, fedacetone, n , was calculated: acetone fedacetone, fedacetone, MW m n = min mol 0.003376 mol g 58 min g 0.1958 fedacetone, ==n The molar flow rate of acetone that was fed into the system, fedacetone, m , was calculated as 0.003376 mol/min. The mass and molar flow rate of CO 2 fed into the system was calculated in the same way. The system pressure p was 8.51 MPa and the CO 2 volumetric flow rate at 40 ?C and 8.51 MPa, C,8.51MPa40 fed,CO 2 ? v , was 4.3 mL/min. The CO 2 density at that condition, 1MPa5.8C,40 CO 2 ? ? , was 0.356 g/mL. C,8.51MPa40 fed,CO 1MPa5.8C,40 COfed,CO 222 ?? ?= vm ? min g 1.53 min mL 4.3 mL g 0.356 fed,CO 2 = ? ? ? ? ? ? ? ? ? ? ? ? ? =m The mass flow rate of CO 2 fed into the system, fed,CO 2 m , was calculated as 1.53 g/min. 2 2 2 CO fed,CO fed,CO MW m n = min mol 0.0348 mol g 44 min g 1.53 fed,CO 2 ==n 71 The molar flow rate of CO 2 fed into the system, fed,CO 2 n , was calculated as 0.0348 mol/min. Now, the mole fraction of acetone in acetone + CO 2 feed flow, fedacetone, y ,can be calculated: fed,COfedacetone, fedacetone, fedacetone, 2 nn n y + = 0.0884 min mol 0.0348 min mol 0.00338 min mol 0.00338 fedacetone, = + =y The mole fraction of acetone in acetone + CO 2 feed flow, fedacetone, y , was calculated as 0.0884. From pressure p (8.51 MPa), temperature T (40 ?C) and acetone mole fraction in the acetone + CO 2 feed flow, fedacetone, y , the compressibility factor z can be calculated using Peng-Robinson Equation of State (PR-EOS). Using the PR-EOS program, z was calculated as 0.2019. The molar volume of the feed mixture (acetone + CO 2 ), mixtmol, v , can be calculated from the compressibility equation. The conversions were done in advance. Converting the system pressure p = 8.51 MPa into the units of atm, () atm 84.0 Pa101.013 atm MPa Pa10 8.51MPa 5 6 = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?=p The molar volume of the feed mixture, mixtmol, v , will be calculated: p Tz v R mixtmol, = 72 () () mol L 0618.0 atm0.84 K15.313 Kmol Latm 08206.0202.0 mixtmol, = ? ? ? ? ? ? ? ? =v Changing the units from L/mol to cm 3 /mol, mol cm 61.8 L cm10 mol L 0.0618 333 mixtmol, = ? ? ? ? ? ? ? ? ? ? ? ? ? ? =v The molar volume of the feed mixture, mixtmol, v , was calculated as 61.77 cm 3 /mol. Inverse of mixtmol, v is the molar density, mixtmol, ? : mixtmol, mixtmol, 1 v =? 3 3 mixtmol, cm mol 0.0162 mol cm 61.8 1 = ? ? ? ? ? ? ? ? =? To calculate the weight density of the mixture, the molecular weight of the feed mixture needs to be calculated. The molecular weight of the mixture, mixt MW , can be calculated as: ))(MW())((MWMW fed,COCOfedacetone,acetonemixt 22 yy += ))(1MW())((MWMW fedacetone,COfedacetone,acetonemixt 2 yy ?+= mol g 45.20.0884))(1 mol g (44(0.0884) mol g 58MW mixt =?+ ? ? ? ? ? ? = Now, the weight density of the feed mixture, mixtg, ? , can be calculated: )MW)(( mixtmixtmol,mixtg, ?? = 33 mixtg, cm g 0.732 mol g 45.2 cm mol 0.0162 = ? ? ? ? ? ? ? ? ? ? ? ? =? 73 If the assumption is made that the acetone fed was 100 % maintained within the system, from the weight density of the mixture, mixtg, ? , and the acetone mole fraction, fedacetone, y , in the combined flow, the amount of acetone that should have been collected in the sample loop volume of 0.19 cm 3 , d_loopacetone_fe w , can be calculated as: mixt acetonefedacetone,loopmixtg, d_loopacetone_fe MW )MW)()()(( yv w ? = 0.0158g mol g 45.2 ) mol g 58)(0.0884)((0.19cm cm g 0.732 3 3 d_loopacetone_fe = ? ? ? ? ? ? ? ? ? ? ? ? =w This is the value of the weight of acetone that should have been collected at the loop of the 6-port valve, calculated from the amount of acetone fed into the system and assuming that 100 % of the acetone fed into the system was maintained within the system, and it was calculated as 0.0158 g. This acetone amount was compared with the amount that was collected at the 6-port valve and analyzed by UV experimentally. The weight of acetone in the loop obtained from UV analysis was 0.0162 g. Therefore, the percentage of the acetone collected at the 6-port valve is: %100Percentage d_loopacetone_fe _loopacetone_UV ?= w w 103%100% 0.0158g 0.0162g Percentage =?= In Table 5-1, the result is summarized for the set-up verification experiments. The percentage of the acetone collected ranged from 103-110 %. It can be said that there was no leak in the system and the data obtained in this method is trustable. 74 Table 5-1. Verification of set-up for acetone + CO 2 permeation Run number Pressure [MPa] CO 2 feed flow rate at 40?C, p MPa [mL/min] Acetone feed flow rate at 27?C [mL/min] Acetone collected [g] Acetone fed [g] Percentage collected [%] 1 8.508 4.3 0.25 0.0162 0.0158 103 2 8.644 3.8 0.25 0.0173 0.0164 105 3 9.607 2.3 0.10 0.00791 0.0072 110 4 8.247 4.1 0.10 0.00760 0.0071 107 Measurement of acetone permeation Calculation of the percentage of feed acetone that permeated through the membrane Acetone permeation test was performed on Teflon AF 1600 film with thickness of 40.6 ?m at 40 ?C. The calculation of the percentage of acetone that permeated through Teflon AF 1600 film will be shown below. To calculate what percentage of the feed acetone permeated through the membrane, the amount of acetone collected at the 6-port valve on the permeate side will be compared with the amount of acetone fed into the system. The amount of acetone fed into the system will be calculated as follows. The calculation will be shown here for the experiment in which the volumetric flow rate of the feed acetone was 0.50 mL/min at 25 ?C and the volumetric flow rate of the feed CO 2 was 227 mL/min at 40 ?C and 1 atm. The CO 2 pressure on both the permeate and the retentate side was maintained at 3.21 MPa. The density of the acetone at 25 ?C was 0.783 g/mL and the density of CO 2 at 40 ?C and 1 atm was 0.00172 g/mL 75 (http://webbook.nist.gov). First, the mole fraction of acetone in the CO 2 + acetone feed flow, fedacetone, y , will be calculated as: 2 ,22 CO C,1atm40 fed,CO C,1atm40 CO acetone C25 fedacetone, C25 acetone acetone C25 fedacetone, C25 acetone fedacetone, MW ))(( MW ))(( MW ))(( ?? ?? ?? + = v v v y ? ? ? 0.4321 mol g 44 min mL 227 mL g 0.00172 mol g 58 min mL 0.50 mL g 0.783 mol g 58 min mL 0.50 mL g 0.783 fedacetone, = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? =y From pressure, p, temperature, T, and acetone mole fraction in the feed flow, fedacetone, y , the compressibility factor, z, can be calculated using Peng-Robinson Equation of State (PR-EOS). After obtaining z using the PR-EOS program, the molar volume of the feed mixture, mixtmol, v , can be calculated from the compressibility equation. First, converting the system pressure p = 3.21 MPa into the units of atm, () 31.7atm Pa101.013 atm MPa Pa10 MPa21.3 5 6 = ? ??=p The molar volume of the feed mixture, mixtmol, v , can be calculated: p zRT v = mixtmol, 76 () () mol L 0.0647 31.7atm 313.15K Kmol Latm 0.082060.07984 mixtmol, = ? ? ? ? ? ? ? ? =v Changing the units from L/mol to cm 3 /mol, mol cm 64.7 L cm10 mol L 0.0647 333 mixtmol, = ? ? ? ? ? ? ? ? ? ? ? ? ? ? =v Inverse of mixtmol, v is the molar density, mixtmol, ? : mixtmol, mixtmol, 1 v =? 33 mixtmol, cm mol 0.0155 mol cm 64.7 1 ==? The weight density, mixtg, ? , can be obtained by multiplying the molecular weight of the mixture mixt MW with the molar density mixtmol, ? . First, the molecular weight of the mixture will be calculated: ))(MW())(MW(MW fed,COCOfedacetone,acetonemixt 22 yy += )1)(MW())(MW( fedacetone,COfedacetone,acetone 2 yy ?+= mol g 50.10.432))(1 mol g (44)(0.432) mol g 58(MW mixt =?+= Hence, the weight density of the mixture, mixtg, ? , can be calculated: )MW)(( mixtmixtmol,mixtg, ?? = 33 mixtg, cm g 0.773) mol g )(50.1 cm mol (0.0155 ==? 77 If the assumption is made that 100 % of the feed acetone permeated through the membrane, from the weight density of the mixture, mixtg, ? , and the acetone mole fraction in the combined feed flow, fedacetone, y , the weight of acetone that is to be collected in the loop, d_loopacetone_fe w , can be calculated as: mixt acetonefedacetone,loopmixtg, d_loopacetone_fe MW ))(MW)()(( yv? w = 0.0736g mol g 50.1 ) mol g 8)(0.432)(5)(0.19cm cm g (0.773 3 3 d_loopacetone_fe ==w This acetone amount should be compared with the amount obtained from UV analysis. Percentage of acetone that permeated through the membrane is calculated: 100Percentage d_loopacetone_fe _loopacetone_UV ?= w w 7%100% 0.0736g 0.00517g Percentage =?= Table 5-2. shows the percentage of feed acetone that permeated through Teflon AF 1600 film of 40.6 ?m thickness. Table 5-2. Acetone amount collected in 0.19 mL volume and percentage of feed acetone that permeated through Teflon AF 1600 film of 40.6 ?m thickness at 40 ?C Pressure [MPa] CO 2 feed flow rate at 40?C,1atm [mL/min] Acetone feed flow rate at 25?C [mL/min] Acetone permeated [g] Acetone fed [g] Percentage permeated [%] 3.21 227 0.50 0.00517 0.0735 7 78 Calculation of acetone permeation flux and permeability coefficient The following will be the calculation of the permeation flux and the permeability coefficient of acetone through Teflon AF 1600 film. The CO 2 flow rate at the permeate and the retentate side were measured with inversed cylinder at the exit of the restrictors in the 40 ?C water bath. Hence, the CO 2 volumetric flow rates on the permeate and the retentate side were measured at 40 ?C and ambient pressure (1 atm). The volumetric flow rate at 40 ?C and 1 atm was 180 mL/min for the permeate side and 47 mL/min for the retentate side of the membrane. min mL 180 C,1atm40 permeate,CO 2 = ? v min mL 47 C,1atm40 retentate,CO 2 = ? v These volumetric flow rates can be converted into mass flow rates by multiplying the CO 2 density at that condition (40 ?C and 1 atm). The values of the density of CO 2 at the certain pressure and 40 ?C were obtained from NIST webbook. From the density of CO 2 at 40 ?C and 1 atm, C,1atm40 CO 2 ? ? , which is 0.00172 g/mL, C,1atm40 CO C,1atm40 permeate,COpermeate,CO 222 ?? ?= ?vm min g 0.3096 mL g 0.00172 min mL 180 permeate,CO 2 = ? ? ? ? ? ? ? ? ? ? ? ? ? =m C,1atm40 CO C,1atm40 retentate,COretentate,CO 222 ?? ?= ?vm min g 0.08084 mL g 0.00172 min mL 47 retentate,CO 2 = ? ? ? ? ? ? ? ? ? ? ? ? ? =m 79 The mass flow rate of CO 2 on the permeate side, permeate,CO 2 m , and the retentate side, retentate,CO 2 m , were calculated as g/min3096.0 and g/min08084.0 respectively. Dividing the CO 2 mass flow rate on the permeate side by the CO 2 density at the system condition (40 ?C and 3.21 MPa), CO 2 volumetric flow rate can be obtained at the system condition: MPa21.3,C40 CO permeate,CO C,3.21MPa40 permeate,CO 2 2 2 ? ? = ? m v min mL 4.85 mL g 0.06378 min g 0.3096 C,3.21MPa40 permeate,CO 2 = ? ? ? ? ? ? ? ? ? ? ? ? = ? v Hence, the CO 2 volumetric flow rate on the permeate side at the system condition, C,3.21MPa40 permeate,CO 2 ? v , was calculated as mL/min85.4 . From the UV analysis, the weight of acetone collected in the sample loop of the 6- port valve at the permeate side was obtained. The amount of acetone collected in the sample loop volume of 0.19 mL at 3.21 MPa and 40 ?C, _loopacetone_UV w , was 0.00517 g. Dividing this amount by the sample loop volume will give the concentration (w/v) of acetone in the CO 2 + acetone solution collected in the loop. loop _loopacetone_UV C,3.21MPa40 permeateacetone, v w c = ? mL g 0.02721 0.19mL 0.00517g C,3.21MPa40 permeateacetone, == ? c 80 Assuming that acetone is sparing amount compared to CO 2 , the CO 2 volumetric flow rate can be considered as the volumetric flow rate of the CO 2 + acetone flow at the system condition. min mL 854.4 C,3.21MPa40 permeate,CO C,3.21MPa40 permeateacetone,CO 22 == ?? + vv Multiplying the acetone concentration, C,3.21MPa40 permeateacetone, ? c , with the volumetric flow rate C,3.21MPa40 permeateacetone,CO 2 ? + v gives the mass flow rate of acetone that permeated through the membrane permeateacetone, m . C,3.21MPa40 permeateacetone,CO MPa21.3,C40 permeateacetone,permeateacetone, 2 ? + ? ?= vcm min g 0.132 min mL 4.854 mL g 0.02721 permeateacetone, = ? ? ? ? ? ? ? ? ? ? ? ? ? =m Next, the acetone amount that was fed to the feed side will be considered. The mass flow rate of acetone fed into the system by the liquid pump at ambient temperature, feedacetone, m , can be calculated using the acetone density value at ambient temperature, 25 ?C ( C25 acetone ? ? = 0.7855 g/mL). Since acetone was run at 0.50 mL/min at 25 ?C, C25 acetone C25 acetonefeedacetone, ?? ?= ?vm min g 0.393 mL g 0.7855 min mL 0.50 feedacetone, = ? ? ? ? ? ? ? ? ? ? ? ? ? =m The mass flow rate of acetone fed to the feed side, feedacetone, m , was calculated as 0.393 g/min. 81 Hence, the mass flow rate of acetone that was retained within the retentate side retentateacetone, m will be: permeateacetone,feedacetone,retentateacetone, mmm ?= min g 0.261 min g 0.132 min g 0.393 retentateacetone, = ? ? ? ? ? ? ? ? ? ? ? ? ? =m The mass flow rate of acetone retained at the retetate side, retentateacetone, m , was calculated as 0.261 g/min. To calculate the permeability coefficient, the value of the driving force is required. In this case, the driving force can be written as the difference in partial pressure of acetone on the permeate and the retentate side of the membrane. To calculate the partial pressures of acetone in the CO 2 + acetone flow on the permeate and the retentate side, the mass flow rate of acetone on each side ( retentateacetone,permeateacetone, , mm ) as well as the mass flow rate of CO 2 on each side ( permeate,CO 2 m , retentate,CO 2 m ) should be converted to molar flow rate by dividing the value by the molecular weight of acetone ( acetone MW ) and CO 2 ( 2 CO MW ) respectively. First, the molar flow rate of acetone on the permeate side will be calculated: acetone permeateacetone, permeateacetone, MW m n = min mol 0.00228 mol g 58 min g 0.132 permeateacetone, = ? ? ? ? ? ? ? ? ? ? ? ? =n The molar flow rate of CO 2 on the permeate side will be: 82 2 2 2 CO permeate,CO permeate,CO MW m n = min mol 0.00704 mol g 44 min g 0.310 permeate,CO 2 = ? ? ? ? ? ? ? ? ? ? ? ? =n The acetone mole fraction in the CO 2 + acetone flow on the permeate side will be calculated: permeate,COpermeateacetone, permeateacetone, permeateacetone, 2 nn n y + = 245.0 min mol 00704.0 min mol 00228.0 min mol 00228.0 permeateacetone, = ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? =y The calculation was done the same way for the retentate side. The molar flow rate of acetone on the retentate side will be: acetone retentateacetone, retentateacetone, MW m n = min mol 00450.0 mol g 58 min g 261.0 retentateacetone, = ? ? ? ? ? ? ? ? ? ? ? ? =n The molar flow rate of CO 2 on the retentate side will be: 2 2 2 CO retentate,CO retentate,CO MW m n = 83 min mol 00184.0 mol g 44 min g 0808.0 retentate,CO 2 = ? ? ? ? ? ? ? ? ? ? ? ? =n The acetone mole fraction in the CO 2 + acetone flow on the retentate side will be: retentate,COretentateacetone, retentateacetone, retentateacetone, 2 nn n y + = 710.0 min mol 00184.0 min mol 00450.0 min mol 00450.0 retentateacetone, = ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? =y Hence, the molar fraction of acetone in the CO 2 + acetone flow on the permeate side, permeateacetone, y , and the retentate side, retentateacetone, y , were calculated as 0.245 and 0.710 respectively. The partial pressure of acetone on the permeate and the retentate side will be obtained by multiplying the system pressure (p = 3.21 MPa) with the acetone mole fractions permeateacetone, y retentateacetone, y respectively. permeateacetone,permeateacetone, ypp ?= () MPa785.0245.0MPa208.3 permeateacetone, =?=p retentateacetone,retentateacetone, ypp ?= () MPa28.2710.0MPa208.3 retentateacetone, =?=p The partial pressure of acetone on the permeate and the retentate side were calculated to be 0.785 MPa and 2.28 MPa respectively. 84 Hence, the pressure difference of acetone across the membrane acetone p? can be calculated: permeateacetone,retentateacetone,acetone ppp ?=? ()( ) MPa49.1MPa785.0MPa28.2 acetone =?=?p Converting the units to cmHg from MPa, () cmHg1119 atm 76cmHg Pa10013.1 atm MPa Pa10 MPa49.1 5 6 acetone = ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?=?p The partial pressure difference of acetone across the membrane acetone p? was calculated to be 1119 cmHg. Next, the acetone flux was calculated. First, the units of the acetone mass permeation rate, permeateacetone, m , should be converted from mL/min to mL/sec, sec g 20.2 sec60 min min g 132.0 permeateacetone, = ? ? ? ? ? ? ? ? ? ? ? ? ? =m Defining mass flux of acetone that permeated through the membrane, J acetone,permeate , as: A m J permeateacetone, permeateacetone, = () 22 permeateacetone, cmsec g 00.1 cm2.2 sec g 20.2 ? = ? ? ? ? ? ? =J The mass flux of acetone that permeated through the membrane, J acetone_permeate, was calculated as 1.00 )cmg/(sec 2 ? . Converting the units of the membrane thickness L = 40.6 ?m to centimeters, 85 () cm00406.0 ?m10 cm ?m6.40 4 = ? ? ? ? ? ? ? ? ?=L Finally, the acetone permeability is calculated as: p LJ P ? ? = permeateacetone, permeateacetone, () () cmHgcmsec cmg 1063.3 cmHg1119 cm00406.0 cmsec g 00.1 2 6 2 permeateacetone, ?? ? ?= ? ? ? ? ? ? ? ? = ? P 6 1063.3 ? ? cmHg)cmg/(sec 2 ?? was obtained as a value for acetone permeability through Teflon AF 1600 film with thickness of 40.6 ?m and surface area of 2.2 cm 2 at 40 ?C and 3.21 MPa. Table 5-3. shows the result along with the experimental condition. Table 5-3. Acetone permeability through Teflon AF 1600 film with thickness of 40.6 ?m and surface area of 2.2 cm 2 at 40 ?C and 3.21 MPa Pressure [MPa] CO 2 permeate flow rate at 40?C,1atm [mL/min] CO 2 retentate flow rate at 40?C,1atm [mL/min] Acetone feed flow rate at 25?C [mL/min] Acetone permeability [g?cm/(sec?cm 2 ?cmHg)] 3.21 180 47 0.50 3.63?10 -6 86 CHAPTER 6 PERMEABILITY OF TETRACYCLINE The permeability of tetracycline through Teflon AF 1600 was measured. The feed side contained a methanol solution in which tetracycline was dissolved. The initial concentration of the solution was approximately 2.9 mg/min. The permeate side was filled with pure methanol. After 24 hours, the solution on the permeate side was analyzed by ultraviolet (UV) spectrophotometry by comparing the absorptivity of the solution with that of pure methanol. As a result, the absorption was the same as the one for pure methanol at 286 nm and 266 nm. Therefore, it can be concluded that there is no permeation of tetracycline through the membrane. 87 CONCLUSIONS A membrane set-up to measure the permeability of CO 2 and a set-up to measure the permeability of acetone with CO 2 were designed and built. The latter set-up was verified by checking that 100% of acetone fed was collected at the permeate side in the case without the membrane. Permeation tests were performed for CO 2 , acetone and tetracycline. CO 2 permeation was conducted for Teflon AF 2400, AF 1600 and polytetrafluoroethylene (PTFE). CO 2 , acetone and tetracycline permeation were conducted for Teflon AF 1600. The permeability of CO 2 through Teflon AF 2400, AF 1600 and PTFE was measured by monitoring the pressure increase on the permeate side of the membrane while running CO 2 at constant flow rate. The permeability value was obtained for different feed pressures (psig) while maintaining the pressure difference across the membrane at 100 psig. The permeability coefficient decreased in the order Teflon AF 2400 > AF 1600 > PTFE. This is due to the increase of free volume and decrease of the degree of crystallinity in this order. Also the CO 2 plasticization effect on Teflon AF 2400 and AF 1600 were seen. The CO 2 permeability through Teflon AF 2400 became independent of the feed pressure as the polymer was used repeatedly. To a smaller extent, the same effect was seen for Teflon AF 1600, i.e. the CO 2 permeability became less 88 dependent on feed pressure upon repeated use. Temperature dependence of CO 2 permeability through Teflon AF 2400 was not significant. 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