Optimization of the anisotropic united atoms intermolecular potential for n-alkanes: improvement of transport properties

The parameters of the anisotropic united atom (AUA) intermolecular potential for n-alkanes originally proposed by Toxvaerd [J. Chem. Phys. 93, 4290 (1990)] [AUA(3)] was optimized by Ungerer et al. [J. Chem. Phys. 112, 5499 (2000)] [AUA(4)] on the basis of equilibrium properties (vapor pressures, vaporization enthalpies, and liquid densities). In this work we analyze the influence of the torsion potential in the internal and collective dynamics of the AUA model. The modified potential [AUA(4m)] preserves all the intermolecular parameters and only explores an increment in the trans-gauche and gauche(+)-gauche(-) transition barrier of the torsion potential. This modification better reproduce different transport properties (shear viscosity, self-diffusion coefficient, and internal relaxation times), keeping the accuracy achieved in our previous work for equilibrium properties. An extensive investigation of the shear viscosity of ethane, n-pentane, n-dodecane, and n-eicosane in a wide range of pressures and temperatures shows that the AUA(4m) improves the accuracy of the original AUA(4), reducing the absolute average deviation from 30% to 14.5%. Finally, the self-diffusion coefficient of n-hexane computed with the new model in the range of 223-333 K and from 0.1 to 295 MPa is in better agreement with respect to the experimental data than the original model.     

Quantum computation of the properties of helium using two-body and three-body intermolecular potentials: a molecular dynamics study

We have performed the molecular dynamics simulation to obtain energy, pressure, and self-diffusion coefficient of helium at different temperatures and densities using Lennard–Jones (LJ), Hartree–Fock dispersion-Individual damping (HFD-ID) potential, and the HFD-like potential which has been obtained with an inversion of viscosity data at zero pressure supplemented by quantum corrections following the Feynman–Hibbs approach. The contribution of three-body interactions using an accurate simple relationship reported by Wang and Sadus between two-body and three-body interactions has been also involved for non-effective potentials (HFD-ID and HFD-like) in simulation. Our results show a good agreement with corresponding experimental data. A comparison of our simulated results with other molecular simulations using different potentials is also included.     

Computation of some thermodynamics, transport, structural properties, and new equation of state for fluid neon using a new intermolecular potential from molecular dynamics simulation

A new pair potential energy function of neon has been determined via the inversion of reduced viscosity collision integrals at zero pressure and fitted to obtain an analytical potential form. The pair potential reproduces the second virial coefficient, viscosity, thermal conductivity, and self-diffusion coefficient of neon in a good accordance with experimental data over wide ranges of temperature and density. We have also performed molecular dynamics simulation to obtain some thermodynamics, transport, and structural properties of fluid neon at different temperatures and densities using our calculated pair potential supplemented by quantum corrections following the Feynman–Hibbs approach. The significance of this work is that the three-body expression of Wang and Sadus (J Chem Phys 125:144509–1, 2006) can be used to improve the prediction of the pressures of neon without requiring an expensive three-body calculation. The molecular dynamics simulation of neon has been also used to determine a new equation of state for neon. Our results are in a good agreement with experiment and literature values.     

Modified free volume theory of self-diffusion and molecular theory of shear viscosity of liquid carbon dioxide

In previous work on the density fluctuation theory of transport coefficients of liquids, it was necessary to use empirical self-diffusion coefficients to calculate the transport coefficients (e.g., shear viscosity of carbon dioxide). In this work, the necessity of empirical input of the self-diffusion coefficients in the calculation of shear viscosity is removed, and the theory is thus made a self-contained molecular theory of transport coefficients of liquids, albeit it contains an empirical parameter in the subcritical regime. The required self-diffusion coefficients of liquid carbon dioxide are calculated by using the modified free volume theory for which the generic van der Waals equation of state and Monte Carlo simulations are combined to accurately compute the mean free volume by means of statistical mechanics. They have been computed as a function of density along four different isotherms and isobars. A Lennard-Jones site-site interaction potential was used to model the molecular carbon dioxide interaction. The density and temperature dependence of the theoretical self-diffusion coefficients are shown to be in excellent agreement with experimental data when the minimum critical free volume is identified with the molecular volume. The self-diffusion coefficients thus computed are then used to compute the density and temperature dependence of the shear viscosity of liquid carbon dioxide by employing the density fluctuation theory formula for shear viscosity as reported in an earlier paper (J. Chem. Phys. 2000, 112, 7118). The theoretical shear viscosity is shown to be robust and yields excellent density and temperature dependence for carbon dioxide. The pair correlation function appearing in the theory has been computed by Monte Carlo simulations.     

Computation of some thermodynamic properties of nitrogen using a new intermolecular potential from molecular dynamics simulation

A new pair-potential energy function of nitrogen has been determined via the inversion of reduced viscosity collision integrals and fitted to obtain an analytical potential form. The pair-potential reproduces the second virial coefficient, viscosity, thermal conductivity, self-diffusion coefficient, and thermal diffusion factor of nitrogen in a good accordance with experimental data over wide ranges of temperatures and densities. We have also performed the molecular dynamics simulation to obtain pressure, internal energy, heat capacity at constant volume, and self-diffusion coefficient of nitrogen at different temperatures and densities using our calculated pair-potential and some other potentials. The molecular dynamics of the nitrogen molecules has been also used to determine nitrogen equation of state in two (low and high) pressure ranges. Our results are in a good agreement with experiment and literature values.     

Static and dynamic critical behavior of a symmetrical binary fluid: a computer simulation

A symmetrical binary, A+B Lennard-Jones mixture is studied by a combination of semi-grand-canonical Monte Carlo (SGMC) and molecular dynamics (MD) methods near a liquid-liquid critical temperature T(c). Choosing equal chemical potentials for the two species, the SGMC switches identities (A-->B-->A) to generate well-equilibrated configurations of the system on the coexistence curve for TT(c). A finite-size scaling analysis of the concentration susceptibility above T(c) and of the order parameter below T(c) is performed, varying the number of particles from N=400 to 12 800. The data are fully compatible with the expected critical exponents of the three-dimensional Ising universality class. The equilibrium configurations from the SGMC runs are used as initial states for microcanonical MD runs, from which transport coefficients are extracted. Self-diffusion coefficients are obtained from the Einstein relation, while the interdiffusion coefficient and the shear viscosity are estimated from Green-Kubo expressions. As expected, the self-diffusion constant does not display a detectable critical anomaly. With appropriate finite-size scaling analysis, we show that the simulation data for the shear viscosity and the mutual diffusion constant are quite consistent both with the theoretically predicted behavior, including the critical exponents and amplitudes, and with the most accurate experimental evidence.     

Generic van der Waals equation of state, modified free volume theory of diffusion, and viscosity of simple liquids

The shear viscosity formula derived by the density fluctuation theory in previous papers is computed for argon, krypton, and methane by using the self-diffusion coefficients derived in the modified free volume theory with the help of the generic van der Waals equation of state. In the temperature regime near or above the critical temperature, the density dependence of the shear viscosity can be accounted for by ab initio calculations with the self-diffusion coefficients provided by the modified free volume theory if the minimum (critical) free volume is set equal to the molecular volume and the volume overlap parameter (alpha) is taken about unity in the expression for the self-diffusion coefficient. In the subcritical temperature regime, if the density fluctuation range parameter is chosen appropriately at a temperature, then the resulting expression for the shear viscosity can well account for its density and temperature dependence over the ranges of density and temperature experimentally studied. In the sense that once the density fluctuation range is fixed at a temperature, the theory can account for the experimental data at other subcritical temperatures on the basis of the intermolecular force only; the theory is predictive even in the subcritical regime of temperature. Theory is successfully tested in comparison with experimental data for self-diffusion coefficients and shear viscosity for argon, krypton, and methane.     

Rotational and translational self-diffusion in concentrated suspensions of permeable particles

In our recent work on concentrated suspensions of uniformly porous colloidal spheres with excluded volume interactions, a variety of short-time dynamic properties were calculated, except for the rotational self-diffusion coefficient. This missing quantity is included in the present paper. Using a precise hydrodynamic force multipole simulation method, the rotational self-diffusion coefficient is evaluated for concentrated suspensions of permeable particles. Results are presented for particle volume fractions up to 45% and for a wide range of permeability values. From the simulation results and earlier results for the first-order virial coefficient, we find that the rotational self-diffusion coefficient of permeable spheres can be scaled to the corresponding coefficient of impermeable particles of the same size. We also show that a similar scaling applies to the translational self-diffusion coefficient considered earlier. From the scaling relations, accurate analytic approximations for the rotational and translational self-diffusion coefficients in concentrated systems are obtained, useful to the experimental analysis of permeable-particle diffusion. The simulation results for rotational diffusion of permeable particles are used to show that a generalized Stokes-Einstein-Debye relation between rotational self-diffusion coefficient and high-frequency viscosity is not satisfied.     

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.     

Dynamics of fluids near the consolute critical point: a molecular-dynamics study of the Widom-Rowlinson mixture

Molecular-dynamics simulations are presented for the dynamic behavior of the Widom-Rowlinson mixture [B. Widom, and J. S. Rowlinson, J. Chem. Phys. 52, 1670 (1970)] at its critical point. This model consists of two components where like species do not interact and unlike species interact via a hard-core potential. Critical exponents are obtained from a finite-size scaling analysis. The self-diffusion coefficient shows no anomalous behavior near the critical point. The shear viscosity and thermal conductivity show no divergent behavior for the system sizes considered, although there is a significant critical enhancement. The mutual diffusion coefficient, D(AB), vanishes as D(AB) approximately xi(-1.26 +/- 0.08), where xi is the correlation length. This is different from the renormalization-group (D(AB) approximately xi(-1.065)) mode coupling theory (D(AB) approximately xi(-1)) predictions. The theories and simulations can be reconciled if we assume that logarithmic corrections to scaling are important.     

Transport coefficients of square-well fluids

We analyze the analytical form of the velocity time correlation function of a hard sphere system obtained by employing generalized Langevin equation for a square-well fluid. The self-diffusion coefficient and shear viscosity have been calculated using this analytical form of velocity tcf for a square-well fluid. The addition of an attractive square-well potential in place of hard sphere leads to a substantial influence on transport coefficients. Unlike harmonic model diffusion coefficient no longer vanishes. A breakdown of the Stokes–Einstein relation is observed at low densities for a square-well fluid.     

Pair correlation functions and the self-diffusion coefficient of Lennard-Jones liquid in the modified free volume theory of diffusion

In this paper, we apply the Matteoli-Mansoori empirical formula for the pair correlation function of simple fluids obeying the Lennard-Jones potential to calculate reduced self-diffusion coefficients on the basis of the modified free volume theory. The self-diffusion coefficient thus computed as functions of temperature and density is compared with the molecular dynamics simulation data and the self-diffusion coefficient obtained by the modified free volume theory implemented with the Monte Carlo simulation method for the pair correlation function. We show that the Matteoli-Mansoori empirical formula yields sufficiently accurate self-diffusion coefficients in the supercritical regime, provided that the minimum free volume activating diffusion is estimated with the classical turning point of binary collision at the mean relative kinetic energy 3k(B)T/2, where k(B) is the Boltzmann constant and T is the temperature. In the subcritical regime, the empirical formula yields qualitatively correct, but lower values for the self-diffusion coefficients compared with computer simulation values and those from the modified free volume theory implemented with the Monte Carlo simulations for the pair correlation function. However, with a slightly modified critical free volume, the results can be made quite acceptable.     

Structural and dynamical properties of a core-softened fluid in a supercritical region

We present a theoretical study of the structural, thermodynamic, and transport properties of a supercritical fluid comprising particles interacting via isotropic attractive core-softened potential. The shear viscosity and self-diffusion coefficient are computed on the basis of the mode-coupling theory, with required structural input obtained from the thermodynamically self-consistent integral equation theory. We also consider dilute solutes in a core-softened fluid and use the anisotropic integral equation theory to obtain the solute-solute potential of mean force, which yields the second virial coefficient. We analyze its dependence on the solvent density and solute-solvent interaction strength.     

A mode-coupling theory treatment of the transport coefficients of the Lennard-Jones fluid

We apply mode-coupling theory to study shear viscosity and self-diffusion coefficient of the Lennard-Jones fluid throughout the entire fluid region of the phase diagram. Theoretical results are compared with the extensive simulation data and good agreement is found. In addition, theory is compared to the experimental data on the transport coefficients of inert gas fluids.     

Sulfur hexafluoride's liquid-vapor coexistence curve, interfacial properties, and diffusion coefficients as predicted by a simple rigid model

We present here molecular-dynamics simulation results of the vapor-liquid coexistence curve, surface tension, and self-diffusion coefficients of sulfur hexafluoride. Sulfur hexafluoride is modeled as a rigid molecule, following the model proposed by Pawley [Mol. Phys. 43, 1321 (1981)]. Vapor-liquid coexistence curve and surface tension are obtained through direct molecular-dynamic simulations in the NVT ensemble. Simulation results are able to reproduce the qualitative shape of the vapor-liquid envelope. However, lower densities, a higher critical temperature, and an overestimated surface tension are obtained here. Those deviations are explained on the basis of the rigidity of the molecular model used. Self-diffusion coefficients are calculated from simulations in the NVE ensemble for different gas states at atmospheric pressure. The rigid model performs better for dynamical properties since simulation results provide very good agreement with available experimental data in this case.     

Waterlike dynamic anomalies in a liquid described by a core-softened potential

We present a theoretical study of transport properties of a liquid comprised of particles interacting via isotropic core-softened potential. Shear viscosity and self-diffusion coefficient are computed on the basis of the mode-coupling theory, with required structural input obtained from thermodynamically self-consistent integral equation theory. Both self-diffusion coefficient and viscosity display waterlike anomalous density dependence, with diffusivity increasing and viscosity decreasing with density within a particular density range along several isotherms below a certain temperature. Our theoretical results for both transport coefficients are in good agreement with the simulation data.     

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.     

A viscosity equation for polyatomic fluids under normal and high pressures

In this work, we relate the self-diffusion coefficient to the residual entropy of the system according to the free volume theory and scaling principle. The viscosity equation for a freely jointed Lennard-Jones chain fluid is then obtained from the expression of self-diffusion coefficient by applying the Stokes–Einstein equation. The real polyatomic compounds are modeled as chains of tangent Lennard-Jones segments. The segment size and energy parameter as well as chain length (expressed by the number of segments) are obtained from the experimental viscosity data. The proposed viscosity equation reproduces the experimental viscosity data with an average absolute deviation of 5.12% for 18 polyatomic compounds (1600 data points) over wide ranges of temperature and pressure. For engineering applications, the generalized model parameters for normal alkanes with the number of carbon atoms n > 3 are proposed. The segment energy parameter is suggested to be evaluated from the critical temperature, and the segment size parameter and chain length are correlated with the number of carbon atoms in an alkane molecule.     

Empirical Relationships between Transport Coefficients of Liquid Metals over a Range of Thermodynamic States

Abstract

Assuming the Wiedemann-Franz law, measured data for electrical conductivity α of liquid Cs and Rb is converted to λ_e , the electronic contribution to the thermal conductivity A. While the major part of the measured thermal conduction is thereby accounted for, the “residual” ionic contribution, denned as (^λ-1—λ_e ^?1)^?1, does not simply increase as the metal-insulator transition is approached along the coexistence curve.

Since λ is dominated by _λe, it is surprising that a hard sphere model, which predicts λ/n = 5k_B/2M with n the shear viscosity and M the ionic mass, still gives correctly a relatively constant ratio, though a difference in behaviour of λ/n as a function of thermodynamic state is noted for liquid Rb and Cs compared with liquid argon.

A generalization of Andrade's formula for shear viscosity at the melting point is also discussed, including the work of Zwanzig relating the self-diffusion coefficient D to n via the bulk viscosity.     

Bulk Viscosity and the Relation between Transport Coefficients

Abstract

The longitudinal and bulk viscosity of the fluid Argon is calculated using its relation with self diffusion coefficient. This relation was derived by developing the relation between coherent and incoherent scattering functions. The results obtained are compared with recent simulation data of bulk viscosity. A good agreement is achieved for a wide range of temperatures at the triple point density. Our results successfully explain the increase in bulk viscosity with decrease in temperature near the triple point. The validity of the relation between diffusion and longitudinal viscosity is also tested for liquid metals. The results obtained for liquid metals of the longitudinal viscosity, at their melting points, are not found to be in agreement with experimental results. A relation between thermal conductivity and self-diffusion coefficient is proposed.