Hard ellipsoids: analytically approaching the exact overlap distance

TL;DR

This paper improves the analytical approximation of the overlap distance for hard ellipsoids, demonstrating that the modified BP equation closely matches the exact numerical solutions and enabling detailed study of phase transitions.

Contribution

It introduces a simple modification to the Berne-Pechukas approximation that accurately predicts the overlap distance for hard ellipsoids across aspect ratios.

Findings

MBP equation matches exact solutions well

Estimated isotropic-nematic transition at volume fraction 0.343

Determined nematic-solid transition between 0.592 and 0.635

Abstract

Following previous work (JCP 134, 201103 (2011)), the replica exchange Monte Carlo technique is used to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. Here, in addition to the analytical approximation of the overlap distance given by Berne and Pechukas (BP) and the exact numerical solution of Perram and Wertheim, we tested a simple modification of the original BP approximation (MBP) which corrects the known T-shape mismatch of BP for all aspect-ratios. We found that the MBP equation of state shows a very good quantitative agreement with the exact solution. The MBP analytical expression allowed us to study size effects on the previously reported results. For the thermodynamic limit, we estimated the exact 1:5 hard ellipsoid isotropic-nematic transition at the volume fraction 0.343(3), and the nematic-solid transition in the volume fraction interval 0.592(6)-0.634(8).