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
Recommended Citation
Wertheim, M.
(1994).
Fluids of hard convex molecules i. Basic theory.
Molecular Physics,
83(3), 519-537.
http://doi.org/10.1080/00268979400101401
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/9115