The generic van der Waals equation of state and self-diffusion coefficients of liquids

Abstract

In this paper we use the generic van der Waals equation of state to define the free volume of liquids along the liquid–vapor coexistence line (liquids curve) in the case of liquid argon and along three isotherms in the high-pressure regime in the case of liquid methane. With the free volume computed from the cavity function obtained by means of a Monte Carlo simulation method, we have calculated the self-diffusion coefficients of liquid argon and liquid methane. The Cohen–Turnbull free volume theory is used to calculate them. With the empirical parameter appearing in the Cohen–Turnbull theory suitably adjusted, the theoretical and experimental values of the self-diffusion coefficients agree very well with regard to the density and temperature dependence for the cases of available data compared. A pair of analytic formulas for density dependence of the self-diffusion coefficient is obtained by using the approximate cavity functions for hard spheres and tested against the experimental data on methane. A comparison of the analytic formulas with experiment is also very good.

Relation of Tracer Diffusion Coefficient and Solvent Self-Diffusion Coefficient

“…Benzened 6 (99.5%) was obtained from Sigma (St. Louis, MO) and used as received. For the tracer diffusion coefficient measurements in benzene, 1% (w/w) tracer solutions were prepared in benzened 6 . The benzene self-diffusion coefficient was measured with 1% (w/w) benzene-h 6 in benzene-d 6 solution.…”

Diffusion of aromatic compounds in nonaqueous solvents: A study of solute, solvent, and temperature dependences

“…Free volume theory, which has affinity with the kinetic theory, has received considerable attention in the past few decades, and there are many reports on the successful use of that theory for the study of diffusion in the literature. 51,61,[91][92][93][94][95][96] There are different approaches of using the free volume theory, and the simplest is probably the one given by Hildebrand. 91 Based on Batschinski's equation 97 for viscosity, Hiddebrand suggested for self diffusivity D s the following:…”

Prediction of Self-Diffusion Coefficients of Fluids Based on Friction and Free Volume Theories

“…The best expression of the free volume is given by the CarnahanStarling (CS) EOS [20]. Considering the expression for the free volume of the hardsphere fluid by the CS EOS, the free volume and cavity function of a hard-sphere fluid could be described as follows [2,8]:…”

“…With the GvdW EOS, an equation for the self-diffusion coefficient based on the Cohen-Turnbull free volume theory has been proposed [2] as follows:…”

“…Self-diffusion and mutual diffusion coefficients, which are the most widely used transport properties in practical engineering applications and other related areas, provide the basic time scales for non-equilibrium phenomena [2]. The self-diffusion coefficient refers to the diffusion behavior in a single-component fluid; such behavior describes the molecular motion in the absence of a chemical potential gradient.…”