Equation of state of hard oblate ellipsoids by replica exchange Monte Carlo

TL;DR

This study uses replica exchange Monte Carlo simulations to determine the equation of state of hard oblate ellipsoids with an aspect ratio of 1:5, capturing phase transitions across a wide density range.

Contribution

It applies both analytical and numerical overlap solutions to accurately model phase behavior of oblate ellipsoids using replica exchange Monte Carlo.

Findings

Identifies isotropic-nematic transition at volume fraction 0.341.

Detects nematic-crystal transition between 0.584 and 0.605.

Provides equation of state data across a broad density spectrum.

Abstract

We implemented the replica exchange Monte Carlo technique to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. For this purpose, we considered the analytical approximation of the overlap distance given by Bern and Pechukas and the exact numerical solution given by Perram and Wertheim. For both cases we capture the expected isotropic-nematic transition at low densities and a nematic-crystal transition at larger densities. For the exact case, these transitions occur at the volume fraction 0.341, and in the interval $0.584-0.605$, respectively.