Statistical mechanical theory for steady state systems. V. Nonequilibrium probability density

The phase space probability density for steady heat flow is given. This generalizes the Boltzmann distribution to a nonequilibrium system. The expression includes the nonequilibrium partition function, which is a generating function for statistical averages and which can be related to a nonequilibrium free energy. The probability density is shown to give the Green-Kubo formula in the linear regime. A Monte Carlo algorithm is developed based upon a Metropolis sampling of the probability distribution using an umbrella weight. The nonequilibrium simulation scheme is shown to be much more efficient for the thermal conductivity of a Lennard-Jones fluid than the Green-Kubo equilibrium fluctuation method. The theory for heat flow is generalized to give the generic nonequilibrium probability densities for hydrodynamic transport, for time-dependent mechanical work, and for nonequilibrium quantum statistical mechanics.     

Statistical mechanical theory for steady state systems. IV. Transition probability and simulation algorithm demonstrated for heat flow

Two microscopic transition theorems are given for the probability of nonequilibrium work performed on a subsystem of a thermal reservoir along the trajectory in phase space of the subsystem. The resultant transition probability is applied to the case of heat flow down an applied temperature gradient. A combined molecular dynamics and Monte Carlo algorithm is given for such a nonequilibrium steady state. Results obtained for the thermal conductivity are in good agreement with previous Green-Kubo and nonequilibrium molecular dynamics results.     

Equilibrium and nonequilibrium molecular dynamics simulations of the thermal conductivity of molten alkali halides

The thermal conductivity of molten NaCl and KCl was calculated through the Evans-Gillan nonequilibrium molecular dynamics (NEMD) algorithm and Green-Kubo equilibrium molecular dynamics (EMD) simulations. The EMD simulations were performed for a "binary" ionic mixture and the NEMD simulations assumed a pure system for reasons discussed in this work. The cross thermoelectric coefficient obtained from Green-Kubo EMD simulations is discussed in terms of the homogeneous thermoelectric power or Seebeck coefficient of these materials. The thermal conductivity obtained from NEMD simulations is found to be in very good agreement with that obtained through Green-Kubo EMD simulations for a binary ionic mixture. This result points to a possible cancellation between the neglected "partial enthalpy" contribution to the heat flux associated with the interdiffusion of one species through the other and that part of the thermal conductivity related to the coupled fluxes of charge and heat in "binary" ionic mixtures.     

On calculation of thermal conductivity from Einstein relation in equilibrium molecular dynamics

In equilibrium molecular dynamics, Einstein relation can be used to calculate the thermal conductivity. This method is equivalent to Green-Kubo relation and it does not require a derivation of an analytical form for the heat current. However, it is not as commonly used as Green-Kubo relationship. Its wide use is hindered by the lack of a proper definition for integrated heat current (energy moment) under periodic boundary conditions. In this paper, we developed an appropriate definition for integrated heat current to calculate thermal conductivity of solids under periodic conditions. We applied this method to solid argon and silicon based systems; compared and contrasted with the Green-Kubo approach.     

Thermal conductivity of solid argon at high pressure and high temperature: a molecular dynamics study

The thermal conductivity of solid argon at high-pressure (up to 50 GPa) and high-temperature (up to 2000 K) has been calculated by equilibrium molecular dynamics simulations using the Green-Kubo formalism and an exponential-6 interatomic potential. A simple empirical expression is given for its pressure and temperature dependence. The results are compared with predictions based on kinetic theory. The relative change of the thermal conductivity lambda with density rho is found to be consistent with a partial differential ln lambda/ partial differential ln rho slope of approximately 6 in a wide range of pressures and temperatures, in good agreement with predictions based on kinetic theory.     

Transport and Helfand moments in the Lennard-Jones fluid. II. Thermal conductivity

The thermal conductivity is calculated with the Helfand-moment method in the Lennard-Jones fluid near the triple point. The Helfand moment of thermal conductivity is here derived for molecular dynamics with periodic boundary conditions. Thermal conductivity is given by a generalized Einstein relation with this Helfand moment. The authors compute thermal conductivity by this new method and compare it with their own values obtained by the standard Green-Kubo method. The agreement is excellent.     

Molecular dynamics simulations of the mechanisms of thermal conduction in methane hydrates

The thermal conductivity of methane hydrate is an important physical parameter affecting the processes of methane hydrate exploration,mining,gas hydrate storage and transportation as well as other applications.Equilibrium molecular dynamics simulations and the Green-Kubo method have been employed for systems from fully occupied to vacant occupied sI methane hydrate in order to estimate their thermal conductivity.The estimations were carried out at temperatures from 203.15 to 263.15 K and at pressures from 3 to 100 MPa.Potential models selected for water were TIP4P,TIP4P-Ew,TIP4P/2005,TIP4P-FQ and TIP4P/Ice.The effects of varying the ratio of the host and guest molecules and the external thermobaric conditions on the thermal conductivity of methane hydrate were studied.The results indicated that the thermal conductivity of methane hydrate is essentially determined by the cage framework which constitutes the hydrate lattice and the cage framework has only slightly higher thermal conductivity in the presence of the guest molecules.Inclusion of more guest molecules in the cage improves the thermal conductivity of methane hydrate.It is also revealed that the thermal conductivity of the sI hydrate shows a similar variation with temperature.Pressure also has an effect on the thermal conductivity,particularly at higher pressures.As the pressure increases,slightly higher thermal conductivities result.Changes in density have little impact on the thermal conductivity of methane hydrate.     

Thermal conductivity of molten alkali halides from equilibrium molecular dynamics simulations

The thermal conductivity of molten sodium chloride and potassium chloride has been computed through equilibrium molecular dynamics Green-Kubo simulations in the microcanonical ensemble (N,V,E). In order to access the temperature dependence of the thermal conductivity coefficient of these materials, the simulations were performed at five different state points. The form of the microscopic energy flux for ionic systems whose Coulombic interactions are calculated through the Ewald method is discussed in detail and an efficient formula is used by analogy with the methods used to evaluate the stress tensor in Coulombic systems. The results show that the Born-Mayer-Huggins-Tosi-Fumi potential predicts a weak negative temperature dependence for the thermal conductivity of NaCl and KCl. The simulation results are in agreement with part of the experimental data available in the literature with simulation values generally overpredicting the thermal conductivity by 10%-20%.     

Thermal conductivity of solid argon from molecular dynamics simulations

The thermal conductivity of solid argon in the classical limit has been calculated by equilibrium molecular dynamic simulations using the Green-Kubo formalism and a Lennard-Jones interatomic potential. Contrary to previous theoretical reports, we find that the computed thermal conductivities are in good agreement with experimental data. The computed values are also in agreement with the high-temperature limit of the three-phonon scattering contribution to the thermal conductivity. We find that finite-size effects are negligible and that phonon lifetimes have two characteristic time scales, so that agreement with kinetic theory is obtained only after appropriate averaging of the calculated phonon lifetimes.     

Transport properties of Mie(14,7) fluids: molecular dynamics simulation and theory

An extensive computer simulation study is presented for the self-diffusion coefficient, the shear viscosity, and the thermal conductivity of Mie(14,7) fluids. The time-correlation function formalism of Green-Kubo is utilized in conjunction with molecular dynamics (MD) simulations. In addition to molecular simulations, the results of a recent study [A. Eskandari Nasrabad, J. Chem. Phys. 128, 154514 (2008)] for the mean free volume are applied to calculate the self-diffusion coefficients within a free volume theory framework. A detailed comparison between the MD simulation and free volume theory results for the diffusion coefficient is given. The density fluctuation theory of shear viscosity is used to compute the shear viscosity and the results are compared to those from MD simulations. The density and temperature dependences of different time-correlation functions and transport coefficients are studied and discussed.     

甲烷水合物导热机理的分子动力学模拟

甲烷水合物导热系数是甲烷水合物勘探、开采、储运以及其他应用过程中一个十分重要的物理参数.我们采用平衡分子动力学（EMD）方法Green-Kubo理论计算温度203.15～263.15K、压力范围3～100MPa、晶穴占有率为0～1的sI甲烷水合物的导热系数,采用的水分子模型包括TIP4P、TIP4P-Ew、TIP4P-FQ、TIP4P/2005、TIP4P/Ice.研究了主客体分子、外界温压条件等对甲烷水合物导热性能的影响.研究结果显示甲烷水合物的低导热性能由主体分子构建的sI笼型结构决定,而客体分子进入笼型结构后,使得笼型结构导热性能增强,同时进入笼型结构的客体分子越多,甲烷水合物导热性能越强.研究结果还显示在高温区域（T〉TDebye/3）内不同温度作用下,所有sI水合物具有相似的导热规律.压力对导热系数有一定影响,尤其是在较高压力条件下,压力越高,导热系数越大.而在不同温度和不同压力作用过程中,密度的改变对导热系数的增大或减小几乎没有影响.     

Validation of intermolecular pair potential model of SiH4: molecular-dynamics simulation for saturated liquid density and thermal transport properties

We demonstrate a validation of the intermolecular pair potential model of SiH(4), which is constructed from ab initio molecular-orbital calculations and expressed as the sum of the exponential and the London dispersion terms. The saturated liquid densities of SiH(4) are calculated for temperatures from 100 to 225 K by molecular-dynamics (MD) simulation. The average deviation between the experiment and the MD simulation using the present potential model is 3.9%, while the deviations exceed 10% for other well-known potential models such as the five-center Lennard-Jones (LJ) model. Subsequently, the shear viscosity, the thermal conductivity, and the self-diffusion coefficient of liquid SiH(4) are calculated by an equilibrium MD simulation with the Green-Kubo formula from 100 to 225 K. The average deviations from experiment are 11.8% and 13.7% for the shear viscosity and the thermal conductivity, respectively. Comparing the present model with an empirical one-center LJ model, it turns out that the rotational energy transfer through the intermolecular potential energy, which comes from the anisotropic potential energy, plays an important role in the thermal conductivity of liquid SiH(4). These results indicate that the present intermolecular potential model has an ability to give realistic pictures for liquid SiH(4) through molecular simulations.     

Constructing a force interaction model for thermal conductivity computation using molecular dynamics simulation: ethylene glycol as an example

This study aims to construct a force interaction model for thermal conductivity computation and to analyze the liquid properties in atomic level for liquid ethylene glycol (EG) using molecular dynamic simulation. The microscopic details of the molecular system and the macroscopic properties of experimental interest are connected by Green-Kubo relations. In addition, the major contributions of heat transfer modes for thermal conductivity due to convection, interaction, and torque are obtained quantitatively. This study reveals that the intramolecular interaction force fields result in different conformations of the EG in the liquid and thus the molecular shapes. The trans∕gauche ratio for EG's O-Me-Me-O torsional angle and the number of intermolecular∕intramolecular H-bonds are found to be important parameters affecting the thermal conductivity.     

Mechanisms for thermal conduction in hydrogen hydrate

Extensive equilibrium molecular dynamics simulations have been performed to investigate thermal conduction mechanisms via the Green-Kubo approach for (type II) hydrogen hydrate, at 0.05 kbar and between 30 and 250 K, for both lightly filled H(2) hydrates (1s4l) and for more densely filled H(2) systems (2s4l), in which four H(2) molecules are present in the large cavities, with respective single- and double-occupation of the small cages. The TIP4P water model was used in conjunction with a fully atomistic hydrogen potential along with long-range Ewald electrostatics. It was found that substantially less damping in guest-host energy transfer is present in hydrogen hydrate as is observed in common type I clathrates (e.g., methane hydrate), but more akin in to previous results for type II and H methane hydrate polymorphs. This gives rise to larger thermal conductivities relative to common type I hydrates, and also larger than type II and H methane hydrate polymorphs, and a more crystal-like temperature dependence of the thermal conductivity.     

Determination of thermal parameters of one-dimensional nanostructures through a thermal transient method

We present an improved methodology for a thermal transient method enabling simultaneous measurement of thermal conductivity and specific heat of nanoscale structures with one-dimensional heat flow. The temporal response of a sample to finite duration heat pulse inputs for both short (1 ns) and long (5 μs) pulses is analyzed and exploited to deduce the thermal properties. Excellent agreement has been obtained between the recovered physical parameters and computational simulations through choosing an optimized pulse width.     

Development of a thermal conductivity cell with nanolayer coating for thermal conductivity measurement of fluids

Various techniques and methodologies of thermal conductivity measurement have been based on the determination of the rate of directional heat flow through a material having a unit temperature differential between its opposing faces. The constancy of the rate depends on the material density, its thermal resistance and the heat flow path itself. The last of these variables contributes most significantly to the true value of steady-state axial and radial heat dissipation depending on the magnitude of transient thermal diffusivity along these directions. The transient hot-wire technique is broadly used for absolute measurements of the thermal conductivity of fluids. Refinement of this method has resulted in a capability for accurate and simultaneous measurement of both thermal conductivity and thermal diffusivity together with the determination of the specific heat. However, these measurements, especially those for the thermal diffusivity, may be significantly influenced by fluid radiation. Recently developed corrections have been used to examine this assumption and rectify the influence of even weak fluid radiation. A thermal conductivity cell for measurement of the thermal properties of electrically conducting fluids has been developed and discussed.     

Mesoscopic simulations of phase distribution effects on the effective thermal conductivity of microgranular porous media

This paper analyzes the phase distribution effects on the effective thermal conductivity (ETC) of multi-phase microgranular porous media using mesoscopic statistics based numerical methods. A multi-parameter random generation-growth method, quartet structure generation set (QSGS), is developed for replicating microstructures of multi-phase granular porous media based on the macroscopic statistical information, such as the volume fractions and the phase interactions. The phase distribution characteristics and the interphase connections are controlled by adjusting the related parameters. Then the energy transport equations through porous media are solved by a lattice Boltzmann method developed by us with multi-phase conjugate heat transfer considered. The results indicate that a smaller average particle size could lead to a larger effective thermal conductivity of two-phase porous media for a certain porosity. For the anisotropic media, if the larger directional growth probability is along the direction of temperature gradient, the effective thermal conductivity in the parallel direction is enhanced as a result, and that in the vertical direction will be weakened. For multi-phase porous media, the degree of phase conglomeration is determined by the phase interactions. A larger liquid-liquid interaction leads to a higher degree of liquid phase conglomeration and therefore a larger effective thermal conductivity of the porous media.     

Heat transfer in polymer composites filled with inorganic hollow micro-spheres: A theoretical model

The heat transfer mechanisms in inorganic hollow micro-spheres filled polymer composites are analyzed in the present paper. This heat transfer includes mainly three mechanisms: (1) thermal conduction between solid and gas; (2) thermal radiation between the hollow micro-sphere surfaces; and (3) natural thermal convection of the gas in the micro-hollow spheres. A theoretical model of heat transfer in polymer/inorganic hollow micro-sphere composites is established based on the law of minimal thermal resistance and the equal law of the specific equivalent thermal conductivity, and a corresponding equation of effective thermal conductivity is derived. The effective thermal conductivity (k_eff) of hollow glass bead-filled polypropylene composites is estimated by using this equation, and is compared with the numerical simulations by means of a finite element method. The results show that the variation of the theoretical estimations of k_eff are similar to the numerical simulations at lower filler volume fraction (φ_f20%). Moreover, k_eff decreases linearly with increasing φ_f, and reduces somewhat with increase of filler size.     

Thermal relaxation mechanism and role of chemical functionalization in fullerene solutions

Using molecular-dynamics simulations we investigate thermal relaxation of C60 and C84 molecules suspended in octane liquid. Pristine fullerenes exhibit relatively slow relaxation due to weak thermal coupling with the liquid. A comparison of the interfacial transport characteristics obtained from relaxation simulations with those obtained from equilibrium simulations and fluctuation-dissipation theorem analysis demonstrates that the relaxation process involves two main steps: (i) energy flow from high- to low-frequency modes within the fullerene, and (ii) energy flow from low-frequency fullerene modes to the liquid. Functionalization of fullerenes with alkene chains leads to significant reduction of the thermal relaxation time. The relaxation time of functionalized fullerenes becomes independent from the functionalizing chain length beyond approximately 10 carbon segments; this can be understood in terms of thermal conductivity along the chain and heat transfer between the chain and the solvent.