Molecular dynamics and theory for the contact values of the radial distribution functions of hard-disk fluid mixtures

TL;DR

This study compares molecular dynamics simulation results for contact values of radial distribution functions in binary hard-disk mixtures with two theoretical models, finding both models agree closely, with the higher-order theory performing better at high densities.

Contribution

It provides a detailed comparison of simulation data with existing theoretical models for hard-disk fluid mixtures, highlighting the accuracy and applicability of these theories.

Findings

Both theories agree quantitatively with simulation data.

The Jenkins and Mancini model is simple and effective.

The Santos et al. model offers improvements at high densities.

Abstract

We report molecular dynamics results for the contact values of the radial distribution functions of binary additive mixtures of hard disks. The simulation data are compared with theoretical predictions from expressions proposed by Jenkins and Mancini [J. Appl. Mech. \textbf{54}, 27 (1987)] and Santos et al. [J. Chem. Phys. \textbf{117}, 5785 (2002)]. Both theories agree quantitatively within a very small margin, which renders the former still a very useful and simple tool to work with. The latter (higher-order and self-consistent) theory provides a small qualitative correction for low densities and is superior especially in the high-density domain.