Triangle Distribution and Equation of State for Classical Rigid Disks
Abstract
The triangle distribution function f^(3) for three mutual nearest neighbors in the plane describes basic aspects of short-range order and statistical thermodynamics in two-dimensional many-particle systems. This paper examines prospects for constructing a self-consistent calculation for the rigid-disk system f^(3). We present several identities obeyed by f^(3). A rudimentary closure suggested by scaled-particle theory is introduced. In conjunction with three of the basic identities, this closure leads to a unique f^(3) over the entire density range. The pressure equation of state exhibits qualitatively correct behavior in both the low density and the close-packed limits, but no intervening phase transition appears. We discuss extensions to improved disk closures, and to the three-dimensional rigid sphere system.
Keywords
Cite
@article{arxiv.cond-mat/9910451,
title = {Triangle Distribution and Equation of State for Classical Rigid Disks},
author = {Dorothea K. Stillinger and Frank H. Stillinger and Salvatore Torquato and Thomas M. Truskett and Pablo G. Debenedetti},
journal= {arXiv preprint arXiv:cond-mat/9910451},
year = {2007}
}
Comments
40 pages, 8 Figures (To appear in the Journal of Statistical Physics)