Studies in Molecular Dynamics. II. Behavior of a Small Number of Elastic Spheres

TLDR

The existence of a first‑order phase transition in hard‑sphere systems remains unresolved without larger system studies. The study derives the equation of state and collision rate for hard‑sphere systems containing 4 to 500 particles. The results demonstrate that particle number strongly affects the equation of state, enabling comparison with analytical theories to delineate their validity and to determine the particle count required at various densities for quantitative accuracy.

Abstract

The equation of state and the collision rate for systems ranging in size from four to 500 particles are described. The dependence of the results on the number of particles is qualitatively discussed and in this way insight is gained as to what is required of more accurate analytical theories. By comparing the results to various analytical theories now available their region of validity is established. The number of particles necessary at various densities to obtain a quantitative description of the equilibrium properties is delineated. Whether a first-order phase transition exists for hard spheres remains open until larger systems are investigated.