Fluids of hard convex molecules i. Basic theory

Document Type

Article

Publication Date

10-20-1994

Abstract

We consider the excess Helmholtz free energy A/l for a system of hard convex molecules without additional soft interactions. The starting point is the expansion of —∆A in irreducible graphs of Mayer/bonds. For such a system, differential and integral geometry can be used to obtain a reformulation in which the use of two-body geometry, as implicit in the/function, is replaced by one-body geometry. A graph point with n incident bonds (n-point) requires a set of n-point measures of one-body geometry. An example is an old (1936) result of Santalo and Blaschke, which expresses the second virial coefficient in terms of the 1-point measures volume, surface, and integral mean curvature. We obtain the corresponding result for the next simplest class of graphs, the rings, which contain only 2-points. This results in an enormous reduction in complexity, especially for mixtures. We define the set of 2-point measures required to compute the ring graphs. For graphs which contain n-points with n > 2, the added complexity of multi-point measures countervails the simplification in going from 2-body to 1-body geometry. © Taylor & Francis Group, LLC.

Publication Title

Molecular Physics

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