Equation of State for Parallel Rigid Spherocylinders

TL;DR

This paper derives the equation of state for parallel rigid spherocylinders using Shinomoto's method and compares two approaches, finding good agreement with simulations for elongated particles.

Contribution

It extends Shinomoto's method to spherocylinders and compares two routes for deriving the equation of state, highlighting their validity ranges.

Findings

Shinomoto's original route is valid for nearly spherical spherocylinders.

The virial route agrees well with numerical simulations for elongated spherocylinders.

The equation of state accurately models pressure for different aspect ratios.

Abstract

The pair distribution function of monodisperse rigid spherocylinders is calculated by Shinomoto's method, which was originally proposed for hard spheres. The equation of state is derived by two different routes: Shinomoto's original route, in which a hard wall is introduced to estimate the pressure exerted on it, and the virial route. The pressure from Shinomoto's original route is valid only when the length-to-width ratio is less than or equal to 0.25 (i.e., when the spherocylinders are nearly spherical). The virial equation of state is shown to agree very well with the results of numerical simulations of spherocylinders with length-to-width ratio greater than or equal to 2.