Molecular theory of thermal conductivity of the Lennard-Jones fluid

In this paper the thermal conductivity of the Lennard-Jones fluid is calculated by applying the combination of the density-fluctuation theory, the modified free volume theory of diffusion, and the generic van der Waals equation of state. A Monte Carlo simulation method is used to compute the equilibrium pair-correlation function necessary for computing the mean free volume and the coefficient in the potential-energy and virial contributions to the thermal conductivity. The theoretical results are compared with our own molecular dynamics simulation results and with those reported in the literature. They agree in good accuracy over wide ranges of density and temperature examined in molecular dynamics simulations. Thus the combined theory represents a molecular theory of thermal conductivity of the Lennard-Jones fluid and by extension simple fluids, which enables us to compute the nonequilibrium quantity by means of the Monte Carlo simulations for the equilibrium pair-correlation function.     

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.     

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.     

Equation of state of simple dense fluids. Thermal pressure coefficients and effective hard sphere diameters

The thermal pressure coefficient of a fluid may be simply related to the hard sphere term in a van der Waals type of equation of state. Experimental data for liquid argon and simulation results for a Lennard-Jones 12-6 fluid have been used to give information about the temperature dependence of the hard sphere diameter. The implications of this behaviour have been briefly discussed.     

Theoretical scheme for the shear viscosity of Lennard-Jones fluids

We use the shear viscosity expression from the Enskog theory of dense gases in a perturbative scheme for the Lennard-Jones (LJ) fluid. This perturbative scheme is formulated by combining the analytic rational function approximation method of Bravo Yuste and Santos [Phys. Rev. A 43, 5418 (1991)] for the radial distribution function of hard-sphere fluids and the well known Mansoori-Canfield/Rasaiah-Stell perturbation theory to determine an effective diameter for the LJ fluid. The scheme is reliable on a wide range of temperatures and densities, and is very accurate around the critical point. Using this information, we build an accurate empirical formula for the shear viscosity in the liquid phase, which fits the recent data [K. Meier et al., J. Chem. Phys. 121, 3671 (2004)] in the whole simulation range.     

Theory of transport in liquid metals: III. Calculation of shear viscosity coefficients of binary alloys

A theoretical procedure for the calculation of the shear viscosity coefficients of liquid binary alloys is proposed based on the simulation of an alloy by a hypothetical single-component hard-sphere liquid and treatment of the latter according to a corrected Enskog approach. The Enskog result is corrected according to a corresponding states principles developed by the authors in a previous work. The pair correlation function at contact necessary for the Enskog calculation is obtained from the solution of the Carnahan and Starling equation of state for single component hard-sphere fluids. The proposed theory is tested numerically by comparing its viscosity results for fifteen alloys with experimental data and with the corresponding results of the Eyring approach and the Tham and Gubbins theory. The latter theory is implemented numerically with pair-correlation values at contact satisfying exactly the Carnahan and Starling equation of state for binary hard-sphere fluids. These values result from analytic and closed-form expressions for the pair-correlation function developed presently through a correction of the corresponding Lebowitz expressions.     

Modified graessley theory for non-newtonian viscosities of polydimethylsiloxanes and their solutions

A deviation from Graessley's theory of entanglement viscosity appears at very high shear rates when the flow of polydimethylsiloxanes of various molecular weights and their solutions with various concentrations is measured by the capillary method. In order to explain this deviation, a modified Graessley theory is proposed according to the previously reported suggestion that frictional viscosity appears not to be negligible at high shear rates. A reducing procedure taking a frictional viscosity parameter into account was performed. All of the reduced data are combined to give a master curve in spite of a wide range of molecular weight, concentration, and shear rate (from the lower Newtonian to very highest non-Newtonian flow region). The findings from the reducing procedure completely explain the mechanism of non-Newtonian flow for the bulk polymers with various molecular weights, including those below the critical molecular weight for entanglement, and for polymer solutions at any concentration. The viscosity of the linear polymer system consists of the shear-dependent entanglement term η_ent proposed by Graessley and the shear-independent frictional term η_fric. The non-Newtonian behavior depends on the ratio of η_ent/η_fric at the shear rate of measurement. The ratio of zero-shear entanglement viscosity η_ent,0 to η_fric and the critical shear rate for onset of the non-Newtonian flow may be used as a measure of the non-Newtonian behavior of the system and a measure of capability for its rising, respectively. The Graessley theory is to be included in the present modified theory and is applicable to the case of η_entη_fric ? 1.     

羟乙基皂仁胶水溶胶和凝胶体系流变性的研究——不含交联剂溶胶体系的粘度

研究了羟乙基皂仁胶水溶胶体系的粘度对浓度、温度和切变速率的依赖性。溶胶的表观粘度进行了非牛顿校正,其表观粘度的切变速率依赖性可用幂律模型描述。采用Spencer-Dillon方程求得的体系零切粘度与浓度的关系可用Onogi公式描述。对于溶剂和较稀溶液,温度对粘度的影响可用Andrade公式描述,但对较浓溶液,此式不再适用。     

Excluded volume in the generic van der Waals equation of state and the self-diffusion coefficient of the Lennard-Jones fluid

In the previous papers applying the generic van der Waals equation of state the mean excluded volume was defined with the contact diameter of particles at which the potential energy is equal to zero-the size parameter in the case of the Lennard-Jones potential. This parameter appears as the upper limit of the integral for the generic van der Waals parameter B (mean excluded volume divided by the density) in the generic van der Waals equation of state. Since the choice is not unique, in this paper we reexamine the manner of defining the upper limit and propose another choice for the upper limit. We also propose an interpretation of the free volume overlap factor alpha appearing in the free volume theory of diffusion and a method of estimating it in terms of the intermolecular potential energy only. It is shown that with the so-estimated free volume overlap factor and the new choice of the upper limit of the integral for B the self-diffusion coefficient in the modified free volume theory of diffusion not only acquires a better accuracy than before, but also becomes calculable in terms of only the intermolecular interaction potential without an adjustable parameter. We also assess some of effective diameters of molecules proposed in the literature for their ability to predict the self-diffusion coefficient within the framework of the modified free volume theory of diffusion.     

Chemical potential perturbation: a method to predict chemical potentials in periodic molecular simulations

A new method, called chemical potential perturbation (CPP), has been developed to predict the chemical potential as a function of density in periodic molecular simulations. The CPP method applies a spatially varying external force field to the simulation, causing the density to depend upon position in the simulation cell. Following equilibration the homogeneous (uniform or bulk) chemical potential as a function of density can be determined relative to some reference state after correcting for the effects of the inhomogeneity of the system. We compare three different methods of approximating this correction. The first method uses the van der Waals density gradient theory to approximate the inhomogeneous Helmholtz free energy density. The second method uses the local pressure tensor to approximate the homogeneous pressure. The third method uses the Triezenberg-Zwanzig definition of surface tension to approximate the inhomogeneous free energy density. If desired, the homogeneous pressure and Helmholtz free energy can also be predicted by the new method, as well as binodal and spinodal densities of a two-phase fluid region. The CPP method is tested using a Lennard-Jones (LJ) fluid at vapor, liquid, two-phase, and supercritical conditions. Satisfactory agreement is found between the CPP method and an LJ equation of state. The efficiency of the CPP method is compared to that for Widom's method under the tested conditions. In particular, the new method works well for dense fluids where Widom's method starts to fail.     

Relations between transport coefficients and their density and temperature dependence

Nonequilibrium statistical mechanics via density fluctuation theory predicts relations between the bulk and shear viscosity, thermal conductivity, and self-diffusion coefficient of a fluid. In this Feature Article, we discuss such relations holding for fluids over wide ranges of density and temperature experimentally studied in the laboratory. It is discussed how such relations can be used to successfully compute the density and temperature dependence on the basis of intermolecular interaction potential models with the help of the modified free volume theory and the generic van der Waals equation of state once the parameters in them are determined at a low density or at a subcritical temperature. Although some approximations have been made to derive them, they represent a reliable molecular theory of transport coefficients over the entire density and temperature ranges of fluids--namely, gases and liquids--a theory hitherto unavailable in the kinetic theory of liquids and dense gases.     

Generalized van der Waals Theory of Interfaces in Simple Fluid Mixtures

An efficient implementation of the generalized van der Waals theory of fluids is presented for the calculation of surface tension in simple fluid mixtures. While detailed correlation analysis is avoided the dominant binding energy contribution and the negative contribution due to the nonlocal entropy are accounted for in the free energy density functional by simple physical approximations of the type originally introduced by van der Waals. Efficient computation is achieved by the use of a single-parameter optimization of a tanh-shaped profile representing the total density as well as the composition variation across the interface. This simple profile nevertheless incorporates the expected adsorption to the interface of the volatile component. Application is made to argon/krypton mixtures represented by Lennard-Jones potentials and Lorentz-Berthelot combining rules. Surface tension predictions compare well with both experimental observations and computer simulation results which also indicated close agreement in particle density profiles, especially if the Berthelot rule is amended with a binary interaction parameter slightly (3%) less than unity. Copyright 2001 Academic Press.     

Study on Non-Newtonian Behaviors of Lennard-Jones Fluids via Molecular Dynamics Simulations

Using nonequilibrium molecular dynamics simulations, we study the non-Newtonian rheological behaviors of a monoatomic fluid governed by the Lennard-Jones potential. Both steady Couette and oscillatory shear flows are investigated. Shear thinning and normal stress effects are observed in the steady Couette flow simulations. The radial distribution function is calculated at different shear rates to exhibit the change of the microscopic structure of molecules due to shear. We observe that for a larger shear rate the repulsion between molecules is more powerful while the attraction is weaker, and the above phenomena can also be confirmed by the analyses of the potential energy. By applying an oscillatory shear to the system, several findings are worth mentioning here:First, the phase difference between the shear stress and shear rate increases with the frequency. Second, the real part of complex viscosity first increases and then decreases while the imaginary part tends to increase monotonically, which results in the increase of the proportion of the imaginary part to the real part with the increasing frequency. Third, the ratio of the elastic modulus to the viscous modulus also increases with the frequency. These phenomena all indicate the appearance of viscoelasticity and the domination of elasticity over viscosity at high oscillation frequency for Lennard-Jones fluids.     

Transient molecular dynamics simulations of viscosity for simple fluids

A transient molecular dynamics (TMD) method has been developed for simulation of fluid viscosity. In this method a sinusoidal velocity profile is instantaneously overlaid onto equilibrated molecular velocities, and the subsequent decay of that velocity profile is observed. The viscosity is obtained by matching in a least-squares sense the analytical solution of the corresponding momentum transport boundary-value problem to the simulated decay of the initial velocity profile. The method was benchmarked by comparing results obtained from the TMD method for a Lennard-Jones fluid with those previously obtained using equilibrium molecular dynamics (EMD) simulations. Two different constitutive models were used in the macroscopic equations to relate the shear rate to the stress. Results using a Newtonian fluid model agree with EMD results at moderate densities but exhibit an increasingly positive error with increasing density at high densities. With the initial velocity profiles used in this study, simulated transient velocities displayed clear viscoelastic behavior at dimensionless densities above 0.7. However, the use of a linear viscoelastic model reproduces the simulated transient velocity behavior well and removes the high-density bias observed in the results obtained under the assumption of Newtonian behavior. The viscosity values obtained using the viscoelastic model are in excellent agreement with the EMD results over virtually the entire fluid domain. For simplicity, the Newtonian fluid model can be used at lower densities and the viscoelastic model at higher densities; the two models give equivalent results at intermediate densities.     

Influence of polydispersity and long chain branching on the melt viscosity of polycarbonate

The Newtonian and non-Newtonian melt viscosities of bisphenol A polycarbonate (PC) at 280°C were treated according to the generalized multivariable power function, where the average molecular weights, polydispersity degree and branching degree are considered as variables. The shear rate was also considered as a variable for non-Newtonian conditions. In the same way, the melt fluidity was treated as a multivariable power function. It has been found that the same melt flow properties of polymer can be obtained by an appropriate combination of Newtonian melt viscosity (being a function of molecular weight) and long chain branching. The experimental data on PC agree with the theoretical approach of Bucche and Graessley.     

A perturbation method for the Ornstein-Zernike equation and the generic van der Waals equation of state for a square well potential model

We calculate the generic van der Waals parameters A and B for a square well model by means of a perturbation theory. To calculate the pair distribution function or the cavity function necessary for the calculation of A and B, we have used the Percus-Yevick integral equation, which is put into an equivalent form by means of the Wiener-Hopf method. This latter method produces a pair of integral equations, which are solved by a perturbation method treating the Mayer function or the well width or the functions in the square well region exterior to the hard core as the perturbation. In the end, the Mayer function times the well width is identified as the perturbation parameter in the present method. In this sense, the present perturbation method is distinct from the existing thermodynamic perturbation theory, which expands the Helmholtz free energy in a perturbation series with the inverse temperature treated as an expansion parameter. The generic van der Waals parameters are explicitly calculated in analytic form as functions of reduced temperature and density. The van der Waals parameters are recovered from them in the limits of vanishing density and high temperature. The equation of state thus obtained is tested against Monte Carlo simulation results and found reliable, provided that the temperature is in the supercritical regime. By scaling the packing fraction with a temperature-dependent hard core, it is suggested to construct an equation of state for fluids with a temperature-dependent hard core that mimicks a soft core repulsive force on the basis of the equation of state derived for the square well model.     

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.     

Non-hard sphere thermodynamic perturbation theory

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of f(ex-ref), chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established.     

Theoretical and computational investigations on thermodynamic properties, effective site diameters, and molecular free volume of carbon disulfide fluid

A newly proposed theory [R. Laghaei et al., J. Chem. Phys. 124, 154502 (2006)] was extended to polyatomics and applied to compute the density and temperature dependence of the effective site diameters of carbon disulfide fluids. The generic van der Waals (GvdW) theory was also extended to polyatomics in order to calculate the GvdW parameters and the molecular free volume using the effective site diameters as the repulsion-attraction separation distance. A three-site Lennard-Jones potential available in the literature was slightly modified and used in Monte Carlo simulations to obtain the functions appearing in the effective site diameter and GvdW expressions. The interaction potential was examined to reproduce the fluid phase thermodynamic properties using Gibbs ensemble Monte Carlo simulations and also the equation of state in the liquid phase using NVT Monte Carlo (NVT-MC) simulations. Comparison between the simulation results and experimental data shows excellent agreement for the densities of the coexisting phases, the vapor pressure, properties of the predicted critical point, and the equation of state. NVT-MC simulations were performed over a wide range of densities and temperatures in sub- and supercritical regions to compute the effective site diameters, the GvdW parameters, and the molecular free volume. The molecular structure in terms of the site-site pair correlation functions, the density dependence of the effective site diameters, and the density and temperature dependence of the GvdW parameters and molecular free volume were studied and discussed. The GvdW parameters were fitted to empirical expressions as a function of density and temperature. The computed molecular free volume will be used in future investigations to study the transport properties of carbon disulfide.