Improvement of integral equation theories for mixtures

A comprehensive study of integral equation theories for binary mixtures is presented. The mixture components differ primarily in size (the diameters d iffer by 10%, 20%, and 30%) and interact either via hard potentials or via Lennard-Jones potentials. For the latter, variation with energy parameter ( epsilon) is considered. This article focuses on improving the accuracy of t he theories by systematic inclusion of bridge diagrams into the closure rel ationships. Specifically, the first two orders of bridge diagrams are exact ly evaluated for these mixtures. A general Monte Carlo integration scheme f or diagram evaluation is discussed and applied. Comparisons with diagrams o btained from a Legendre expansion technique are made in order to assess whe ther this approach is practical. The approximation of higher order diagrams has been considered. Specifically, techniques for approximation of all hig her order diagrams, which were successful for single component fluids, were found to be problematic for mixtures. However, a simple algorithm for appr oximate third order diagrams is presented and found to lead to improvements . A detailed analysis of the bridge diagram variation with the nature of th e mixture is presented and may be useful in extending the present results t o related mixtures. The spatial dependence of the diagrams has also been ex amined and found to be extremely well reproduced by simple polynomial expan sions. In addition, physical arguments have been applied to extract large s eparation limits of the diagrams. The accuracy of the integral equation the ories with order of bridge diagrams is assessed by comparing pressure estim ates from the virial expansion and from the integration of compressibilitie s. With this measure, the quality of the integral equation theories for eac h mixture is assessed at 18 state points. In all cases, the thermodynamic c onsistency improves smoothly and rapidly with the order of bridge diagram i ncluded in the theory. This result, together with the general Monte Carlo a lgorithm and the detailed structural and spatial analysis, shows that direc t bridge diagram evaluation is practical and consistently improves the qual ity of the theory for these mixtures. (C) 1999 American Institute of Physic s. [S0021-9606(99)52622-6].