Generic van der Waals Equation of State, Modified Free Volume Theory of Diffusion, and Viscosity of Simple Liquids Rozita Laghaei, Afshin Eskandari Nasrabad, and Byung Chan Eu* Department of Chemistry and le Regroupement Quebecois sur les Materiaux de Pointe (RQMP), McGill UniVersity, 801 Sherbrooke Street West, Montreal, Quebec H3A 2K6, Canada ReceiVed: NoVember 11, 2004; In Final Form: January 20, 2005 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 (R) 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. 1. Introduction The density and temperature dependence of transport coef- ficients of liquids is of considerable interest and importance from the viewpoint of the molecular theory, namely, nonequi- librium statistical mechanics, of liquids because they provide information on not only the structures of liquids but also dynamic processes occurring in condensed phase of matter. Experiments show that they are generally strong functions of density and temperature, which are rather difficult to calculate in reliable accuracy by means of statistical mechanics. Molecular dynamics simulation methods 1-4 seem to be the only reliable means to calculate them at present. However, the computer simulation methods have their own limitations. In a previous series of articles 5-10 on the theory of transport coefficients of liquids, it has been shown that density fluctuations within the intermolecular interaction force range give rise to momentum and energy transfer between molecules interacting through intermolecular forces, and such momentum and energy transfer are responsible for the viscosity and thermal conductivity of liquids. The theory may be termed the density fluctuation theory, and we will henceforth use the terminology in this work. In the density fluctuation theory, the transport coefficients, such as shear viscosity, bulk viscosity, and thermal conductivity, are given in terms of the self-diffusion coefficient and the pair correlation function as well as the intermolecular force of the liquid of interest. Their relations to the self-diffusion coefficient are rather reminiscent of the well-known Stokes-Einstein (SE) relation 11 between the viscosity of the liquid and the diffusion coefficient of the particle tracing through the medium. Such relations have also been found to give rise to relations between transport coefficients, such as that akin to the Eucken relation, 12 which are well-established in the gas kinetic theory, but new to the kinetic theory of liquids. Thus, the aforementioned relations between the transport coefficients of liquids are generalizations to liquids of the gas kinetic theory relations between transport coefficients of dilute gases. 12 By use of such relations, it has been possible to calculate the shear viscosity, bulk viscosity, and thermal conductivity of simple liquids from the experimental or simulation data on self- diffusion coefficients of liquids, if the latter are available in the literature on liquids. The transport coefficients thus calcu- lated have been shown to be in excellent accord with the experimental data available in the literature. Thus, the density fluctuation theory holds out the tantalizing possibility of calculating transport coefficients from an entirely molecular viewpoint and without relying on empirical self-diffusion coefficients, if the latter can be calculated by means of a statistical mechanical method. Self-diffusion coefficients of liquids, however, have been difficult to calculate in a reliable accuracy in the liquid density range by means of statistical mechanics; there have been some theories reported in the literature, 13-15 but they are limited to a relatively low density or are of unreliable accuracy. For this reason, molecular dynamics simulation methods have been the only practical nonexperimental source of information on self-diffusion coef- ficients of liquids, although they are not only rather time- consuming to compute but also limited in their scope of applicability in practice for various reasons. Therefore, there is room to develop a statistical mechanical theory of diffusion that has a reliable accuracy and is practical from the viewpoint of currently available computational resources. Free volume theories 16-19 of diffusion have attractive features from the conceptual standpoint. In particular, the free volume * Author to whom correspondence should be addressed. Phone: (514) 398-6929. Fax: (514) 398-3797. E-mail: Byung.Eu@McGill.Ca. 5873 J. Phys. Chem. B 2005, 109, 5873-5883 10.1021/jp0448245 CCC: $30.25 © 2005 American Chemical Society Published on Web 03/08/2005