Molecular dynamics studies of phase transition of n-alkanes mixtures, coupling-decoupling mechanism affecting thermal interfacial conductance of n-alkanes and Fokker-Planck theory of lattice thermal conductivity of crystalline solids

Abstract

Renewable energy sources, such as solar energy or geothermal energy, are promising to complement or even substitute unsustainable fossil fuel energy sources in direct thermal energy utilization. The requirement of a reliable and stable supply from renewable energy mandates highly effective energy storage systems that are capable to absorb and release a large amount of heat over a short period of time. This leads to the exploits of various phase change materials (PCM) with complex structures and/or compositions for their potential applications in thermal energy storage. Thermal transport properties of PCM are essential to the effectiveness of the thermal energy storage systems. Despite recent progresses in thermal conductivity measurements and atomistic level numerical simulation techniques, heat transfer mechanisms in nano-structured organic PCM and bulk crystalline PCM near melting temperatures are known only at a qualitative level. In both cases, Hook’s Law-like harmonic interatomic forces is no longer an accurate approximation to describe the atomistic dynamics that governs the heat transfer processes in these materials. Therefore, anharmonic effects that include the contributions of higher-order potential terms were considered. Further improvement of the effectiveness of complex PCM needs a more quantitative understanding of the fundamental mechanisms associated with thermal transport of these intrinsically anharmonic materials. We first performed a set of systematic molecular dynamics (MD) simulations of the structures and bulk thermal conductivity of mixtures of long-chain n-alkane molecules. We identified how the orientation factor of the n-alkane mixtures is affected by the surface during the crystallization process, where the surface can be artificially adjusted to be attractive or repulsive to n-alkane molecules. We further demonstrated that the thermal conductivity of the mixtures correlate strongly with the orientation of n-alkane chains in the solid-state phase, yet it is insensitive to the number ratio of the mixture. Next, we focus on elucidating the microscopic mechanism of heat transfer across the van der Waals (vdW) force bonded molecular interfaces. To simplify our study, we constructed ideal crystal models of n-eicosane, where all molecules are perfectly aligned in the same direction. Knowledge of the interfacial thermal transport in such idealized n-alkane crystals is important to understanding the upper limits of overall thermal conductivity in such nano-structured molecular crystals. It is important to note that the thermal interfacial conductance (TIC) of these perfectly-aligned n-alkanes crystals cannot be predicted by conventional interfacial heat transfer models such as the acoustic mismatch model (AMM) and the diffusive mismatch model (DMM), because both atomic structures and their vibrational dynamics are essentially identical at both sides of the interface when averaged over a long period of time. By analyzing the MD-simulated atomistic dynamics at the single atomic/molecular level, we unveiled a thermal coupling-decoupling mechanism that emerges from stochastic dynamics of atoms. Two parameters, the duration and strength of the thermal coupling, are identified to quantify the TIC from the single atomic level. This coupling-decoupling mechanism explains the temperature-inverse-TIC in n-alkanes and provides new insights into heat transfer across a broad range of flexible interfaces that consist of nano-meter long molecules and weak interfacial forces, such as interfacial self-assembled monolayers or paraffins or lipid types of soft materials. Finally, we expanded our study to develop new transport theories and simulation methods that are applicable for a wide range of solids at the temperature conditions near the solid-to-liquid phase transition, i.e. melting. This study is in part motivated by our findings of the drastic effects of increasing anharmonic interfacial forces on heat transfer properties in n-alkanes near their melting temperatures. The failure of harmonic or quasi-harmonic approximations near melting temperatures is unavoidable in all types of PCM, including both soft molecular materials for near human-body temperature applications and the hard oxides adopted in the high-temperature applications. The widely-adopted phonon gas (PG) model, which requires anharmonic effects are perturbatively small, likely breaks down at such high temperatures. As the first step to develop a unified theoretical model for heat transfer within very anharmonic solids, either strongly-bonded bulk crystals or weakly-bonded molecular nano-materials, we proposed a Fokker-Planck equation (FPE) theory to describe stochastic fluctuations and relaxation processes of lattice vibration for a wide range of conditions, including those beyond the PG limit. Using the time-dependent, multiple state-variable probability function of a vibration FPE, we first derive time-correlation functions of lattice heat currents in terms of correlation functions among multiple vibrational modes, and subsequently predict the lattice thermal conductivity based on the Green-Kubo formalism. When the quasi-particle kinetic transport theories are valid, this vibration FPE not only predicts a lattice thermal conductivity that is identical to the one predicted by the phonon Boltzmann transport equation, but also provides additional microscopic details on the multiple-mode correlation functions. More importantly, when the kinetic theories become insufficient due to the break-down of the PG approximation, this FPE theory remains valid to study the correlation functions among vibrational modes in highly anharmonic lattices with significant mode-mode interactions and/or in disordered lattices with strongly-localized modes. We also discussed the possible MD simulation algorithms that can extract the parameters of vibrational FPE for very anharmonic solids.