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.     

Statistical mechanical theory for steady state systems. VII. Nonlinear theory

The second entropy theory for nonequilibrium thermodynamics is extended to the nonlinear regime and to systems of mixed parity (even and odd functions of molecular velocities). The steady state phase space probability density is given for systems of mixed parity. The nonlinear transport matrix is obtained and it is shown to yield the analog of the linear Onsager-Casimir reciprocal relations. Its asymmetric part contributes to the flux and to the production of second entropy. The nonlinear transport matrix is not simply expressible as a Green-Kubo fluctuation equilibrium time correlation function. However, here the first nonlinear correction to the transport coefficient is given explicitly as a type of the Green-Kubo equilibrium time correlation function. The theory is illustrated by application to chemical kinetics.     

Statistical mechanical theory for steady-state systems. III. Heat flow in a Lennard-Jones fluid

A statistical mechanical theory for heat flow is developed based upon the second entropy for dynamical transitions between energy moment macrostates. The thermal conductivity, as obtained from a Green-Kubo integral of a time correlation function, is derived as an approximation from these more fundamental theories, and its short-time dependence is explored. A new expression for the thermal conductivity is derived and shown to converge to its asymptotic value faster than the traditional Green-Kubo expression. An ansatz for the steady-state probability distribution for heat flow down an imposed thermal gradient is tested with simulations of a Lennard-Jones fluid. It is found to be accurate in the high-density regime at not too short times, but not more generally. The probability distribution is implemented in Monte Carlo simulations, and a method for extracting the thermal conductivity is given.     

Transport Properties of Simple Fluids from the Soft‐Core Double Yukawa Potential

The present work is concerned with checking a new and simple pair potential function (soft‐core double Yukawa potential) for noble gases by calculation of the transport properties. The viscosity, thermal conductivity and self diffusion coefficient in dilute gas limit in the temperature range of 298‐1400 K are calculated and agreement with the measurements is, in general, within the experimental error. A comparison of the calculated and experimental values of the viscosity, thermal conductivity and the diffusion coefficients yields an average absolute deviation of 0.5%, 1.5% and 1.2%, respectively. Also, the calculated transport properties from this potential have been compared with those calculations via the accurate experimental potential and also the corresponding state.     

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.     

Transport Coefficients Of Ar—Kr Mixtures by Molecular Dynamics Computer Simulation

Abstract

Equilibrium molecular dynamics computer simulations have been used to determine the transport coefficients of model Ar—Kr mixtures, which are represented by Lennard-Jones pair potentials with Lorentz—Berthelot rules for the cross-species interactions. The component self-diffusion and mutual-diffusion coefficients are calculated from time correlation functions and mean square displacements. Time correlation functions are used to evaluate the shear and bulk viscosity, thermal conductivity and the thermal diffusion coefficient (Soret/Dufour coefficient). In the case of the thermal transport coefficients, the partial enthalpy of the two species is required at each state point to define the heat flux rigorously. We obtain this and the partial volume (and species resolved chemical potential) using particle-exchange (and particle insertion) techniques implemented in separate [NPT] simulations at the same state point.

The viscoelasticity of the fluids is characterised by the relaxation times for bulk and shear stress relaxation. The results are for dense liquids close to the triple point temperature and density. Agreement with experiment and previous simulation is particularly good for the density of the mixtures, the shear modulus, shear viscosity, shear stress relaxation time and thermal conductivity. As for the single component noble gas fluids (simulated and experiment) there is a significant qualitative difference in the temperature and, for mixtures, composition dependence of the bulk viscosity.     

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.     

Molecular dynamics simulations of the structure and transport properties of tetra-butylphosphonium amino acid ionic liquids

Systematic molecular dynamics simulations are used to study the structure, dynamics and transport properties of the ionic liquids composed of the tetra-butylphosphonium ([TBP](+), or [P(C(4)H(9))(4)](+)) cation with six amino acid ([AA](-)) anions. The structural features of these ionic liquids were characterized by calculating the partial site-site radial distribution functions, g(r), and computing the dihedral angle distribution of n-butyl side chains in the [TBP](+) cations. The dynamics of the ionic liquids are described by studying the velocity autocorrelation function (VACF) and the mean-square displacement (MSD) for the centers of mass of the ions at different temperatures. The ionic diffusion coefficients and the electrical conductivities were evaluated from both the Einstein and Green-Kubo methods. The cross-correlation terms in the electric-current autocorrelation functions, which are an indication of the ion pair correlations, are investigated. The cationic transference numbers were also estimated to study the contributions of the anions and cations to the transport of charge in these ionic liquids. We determined the role of the amino acid anion structures on the dynamical behavior and the transport coefficients of this family of ionic liquids. In general, the MSD and self-diffusion coefficients of the relatively heavier non-planar [TBP](+) cations are smaller than those of the lighter amino acid anions. Introducing polar functional groups (acid or amide) in the side chain of [AA](-) decreases the diffusion coefficient and electrical conductivity of AAILs. The major factors for determining the magnitude of the transport coefficients are the chemical functionality and the length of the alkyl side chain of the [AA](-) anion of these [TBP][AA] ionic liquids.     

Viscosity and thermal conductivity of some refrigerants at moderate and high densities on the basis of Rainwater–Friend theory and the corresponding states principle

The initial density dependence of viscosity and thermal conductivity was formulated on the basis of Rainwater–Friend (RF) theory. In this work, we have first focused on the calculation of viscosity and thermal conductivity of moderately dense argon by using RF theory and an accurate ab initio potential function. This theory which was originally presented for spherical potentials have been adapted for calculation of viscosity and translational contribution of thermal conductivity of some refrigerants by introducing the corresponding states correlations for the second transport virial coefficients. Then the internal states contribution for the thermal conductivity has been determined based on the Mason–Monchick and modified Enskog theories. So, we have calculated the viscosity and thermal conductivity of some refrigerants, R32, R14, R12, R13, R22, R134a, R143a, R125, R123, R142b, at moderate densities up to about 2 mol dm⁻³. At high densities, beyond the validity range of RF theory, we have applied correlation expressions for the viscosity and thermal conductivity residual functions to calculate the viscosity and thermal conductivity of supercritical refrigerants and then compared with the available experimental data. In conclusion, we have shown that the RF theory in conjunction with the corresponding states residual functions present the reliable model for calculation of viscosity and thermal conductivity of refrigerants over a comparatively wide temperature and pressure range up to 65 MPa within the experimental errors.     

NMR relaxation parameters of a Lennard-Jones fluid from molecular-dynamics simulations

Ensembles of soft spheres or of Lennard-Jones atoms were studied by molecular dynamics at reduced temperatures from 0.8 to 3, and radial distribution functions, diffusion coefficients, and magnetic dipole-dipole correlation functions were measured as functions of system size. The expected relation between the values of the correlation functions at zero lag time and the integrals of the radial distribution was verified for each system. The measured correlation functions were compared with theoretical expressions derived by [Ayant et al., J. Phys. (Paris) 36, 991 (1975)] and by [Hwang and Freed, J. Chem. Phys. 63, 4017 (1975)]. It was shown that, in order to recover the long-time behavior characteristic of diffusion-controlled relaxation processes, the simulation must comprise at least 10 000 particles. By fitting the simulation results to the Hwang-Freed function, independent values of the diffusion coefficient were obtained, similar but not identical to those computed using the Green-Kubo formalism. The spectral densities of the dipole-dipole interaction were computed as Fourier transforms of the correlation functions. These quantities are less sensitive to model imperfections and reproduce quite well the values derived from theory. The dimensionless spin-lattice and spin-spin relaxation rates were derived from the spectral densities. It was shown that the spin-lattice (longitudinal) relaxation rate goes through a maximum as the temperature increases, while the spin-spin (transverse) rate decreases monotonously.     

Cutoff radius effect of isotropic periodic sum method for transport coefficients of Lennard-Jones liquid

Molecular dynamics simulations of a Lennard-Jones (LJ) liquid were applied to compare the isotropic periodic sum (IPS) method [X. Wu and B. R. Brooks, J. Chem. Phys. 122, 044107 (2005)], which can reduce the calculation cost of long-range interactions, such as the Lennard-Jones and Coulombic ones, with the cutoff method for the transport coefficients which includes the self-diffusion coefficient, bulk viscosity, and thermal conductivity. The self-diffusion coefficient, bulk viscosity, and thermal conductivity were estimated with reasonable accuracy if the cutoff distance of the LJ potential for the IPS method was greater than 3sigma. The IPS method is an effective technique for estimating the transport coefficients of the Lennard-Jones liquid in a homogeneous system.     

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.     

Ab initio intermolecular potential energy surface and thermophysical properties of hydrogen sulfide

A six-dimensional potential energy hypersurface (PES) for two interacting rigid hydrogen sulfide molecules was determined from high-level quantum-mechanical ab initio computations. A total of 4016 points for 405 different angular orientations of two molecules were calculated utilizing the counterpoise-corrected supermolecular approach at the CCSD(T) level of theory and extrapolating the calculated interaction energies to the complete basis set limit. An analytical site-site potential function with eleven sites per hydrogen sulfide molecule was fitted to the interaction energies. The PES has been validated by computing the second pressure virial coefficient, shear viscosity, thermal conductivity and comparing with the available experimental data. The calculated values of volume viscosity were not used to validate the potential as the low accuracy of the available data precluded such an approach. The second pressure virial coefficient was evaluated by means of the Takahashi and Imada approach, while the transport properties, in the dilute limit, were evaluated by utilizing the classical trajectory method. In general, the agreement with the primary experimental data is within the experimental error for temperatures higher than 300 K. For lower temperatures the lack of reliable data indicates that the values of the second pressure virial coefficient and of the transport properties calculated in this work are currently the most accurate estimates for the thermophysical properties of hydrogen sulfide.     

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.     

Proton transport properties in an ionic liquid having a hydroxyl group

An ionic liquid having a hydroxyl group, choline bis(trifluoromethylsulfonyl)amide ([N(111(2OH))][N(Tf)(2)]), was synthesized to investigate the effect of hydroxyl groups on the proton transport. 1,1,1-Trifluoro-N-(trifluoromethylsulfonyl)methanesulfoneamide (HN(Tf)(2)) as a proton source was mixed with the choline derivative at various molar ratios. Their thermal properties, viscosities, and ionic conductivities were investigated. [N(111(2OH))][N(Tf)(2)] showed a melting point at 27 °C, and its thermal stability was higher than 400 °C. The viscosity of [N(111(2OH))][N(Tf)(2)]/HN(Tf)(2) mixtures increased as the acid molar fraction increased. The ionic conductivity of [N(111(2OH))][N(Tf)(2)] was 2.1 × 10(-3) S cm(-1) at 25 °C; the ionic conductivity monotonously decreased as the acid molar fraction increased. There was a clear correlation between the ionic conductivity and the viscosity for the mixtures of the choline derivative and the acid. PFG-NMR measurements were carried out to investigate the diffusion behavior of protons. Although the acid and the hydroxyl group were indistinguishable by (1)H NMR, the self-diffusion coefficient of the (1)H of the hydroxyl group and the acid was larger than those of other (1)H nuclei. This difference suggests that a fast intermolecular proton transfer exists between the hydroxyl group and the acid.     

Correlation energy functionals dependent on an effective number of electrons: charged species and equilibrium geometries

Recently proposed spin-dependent and spin-independent correlation energy functionals [Perez-Jimenez et al., J. Chem. Phys. 116, 10571 (2002)] based on an effective number of electrons N are extended to deal with charged systems. By introducing the concept of an effective atomic number Z analogous to N, the spin-dependent functional in combination with Becke's exchange [Becke, Phys. Rev. A 38, 3098 (1988)] yields a mean absolute error (MAE) of 5.4 kcal/mol for the 88 ionization potentials and 58 electron affinities included in the extended G2 set, and a MAE of 4.1 kcal/mol for the 312 data comprising the above plus the 148 enthalpies of formation of the extended G2 set and the 18 total energies of the neutral atoms H through Ar. Geometry optimizations performed on the 53 molecules of the G2-1 test set with the above combination of exchange and correlation functionals yield MAEs of 0.017 A and 1.5 degrees for the 68 bond lengths and 29 angles analyzed as compared with the experimental estimates.     

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%.     

Phoretic forces on convex particles from kinetic theory and nonequilibrium thermodynamics

In this article we derive the phoretic forces acting on a tracer particle, which is assumed to be small compared to the mean free path of the surrounding nonequilibrium gas, but large compared to the size of the surrounding gas molecules. First, we review and extend the calculations of Waldmann [Z. Naturforsch. A 14A, 589 (1959)] using half-sphere integrations and an accommodation coefficient characterizing the collision process. The presented methodology is applied to a gas subject to temperature, pressure, and velocity gradients. Corresponding thermophoretic, barophoretic, and rheophoretic forces are derived, and explicit expressions for spherical particles are compared to known results. Second, nonequilibrium thermodynamics is used to join the diffusion equation for the tracer particle with the continuum equations of nonisothermal hydrodynamics of the solvent. So doing, the distinct origin of the thermophoretic and barophoretic forces is demonstrated. While the latter enters similarly to an interaction potential, the former is given by flux-flux correlations in terms of a Green-Kubo relation, as shown in detail.     

The Ne-Ne interatomic potential revisited

The neon-neon interaction has been re-examined in the light of new data, both theoretical and experimental. Because of recent interest in solids at very high pressures, a new accurate potential is presented with particular interest paid to its highly repulsive region. A potential in HFD-B form incorporating the most recent dispersion coefficients was fitted to accurate viscosity data and high-energy scattering beam data. The potential is able to predict a wide range of macroscopic (second virial coefficients, viscosity, thermal conductivity, diffusion and 0 K binding energy) and microscopic properties (spectroscopic differential and high-energy total cross sections). The potential is extended to very short range by extrapolating to united atom perturbation results.     

Ar—Kr溶液扩散系数的分子动力学模拟及其与温度的关系

用分子动力学模拟方法研究确定Ａｒ－Ｋｒ溶液的自扩散系数Ｄ１、Ｄ２和互扩散系数Ｄ１２以及它们随温度变化的规律。结果表明，分别用Ｇｒｅｅｎ－Ｋｕｂｏ法和Ｅｉｎｓｔｅｉｎ法得到的扩散系数在数值上一致；该溶液的３种扩散系数均满足Ｄ＝Ｄ０ｅ＾Ｅ／ＲＴ关系。