Correlation functions of classical fluids. I. The radial distribution functions of mixtures of Kihara molecules in the Percus-Yevick approximation and their thermodynamic functions

Abstract

The Percus-Yevick integral equation is solved for systems of molecules interacting with the Kihara potential. Radial distribution functions for the pure fluid systems of argon, krypton, and xenon, and for the binary mixture argon-nitrogen are obtained. For the one-component system, the use of the Kihara potential yields equivalent results in comparison with previous theoretical and experimental studies. For the case of argon, a numerical potential proposed by Dymond and Alder is also employed and the results show superior agreement with the x-ray diffraction data. The solutions of the two-component case cover a wide range of temperatures, densities, and compositions, including those of the liquid state. The variations of the radial distribution functions with density, temperature, and composition are ascertained. It is found that the main features of the radial distribution functions, such as the peak heights, their relative magnitudes, and the zeros of the total correlation functions, vary under quite complex rules, yet in most part are verifiable by experiments. The macroscopic properties of Ar–N2 mixtures, such as the internal energy and the Helmholtz free energy, are also calculated. Hiroike's formula for the calculation of the free energy is adopted which avoids the usual procedure of integrating a pressure term that has two values, one from the virial theorem and the other from the fluctuation-compressibility derivation. Agreements with values derived from the Strobridge equation of state are close for the internal energy and less satisfactory for the Helmholtz free energy. Their variations with temperature, density, and composition are also demonstrated.