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Triangle Distribution and Equation of State for Classical Rigid Disks

Dorothea K. Stillinger·Frank H. Stillinger·Salvatore Torquato·Thomas M. Truskett·Pablo G. Debenedetti
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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.

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Dorothea K. Stillinger, Frank H. Stillinger, Salvatore Torquato, Thomas M. Truskett, Pablo G. Debenedetti. 1999-10-27. Triangle Distribution and Equation of State for Classical Rigid Disks. https://arxiv.org/abs/cond-mat/9910451

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