Melting of a colloidal crystal

TL;DR

This paper investigates the melting transition of a colloidal crystal modeled by hard spheres with Yukawa interactions, proposing a theoretical approach to determine phase boundaries and comparing results with simulations.

Contribution

It introduces a simple theoretical method to calculate free energies of liquid and solid phases for Yukawa-interacting particles, improving phase boundary predictions.

Findings

The phase boundary is determined by equating pressures and chemical potentials.

The theory's predictions are validated against Monte Carlo simulation results.

A Lindemann criterion is used to identify the first-order transition when the virial expansion fails.

Abstract

A melting transition for a system of hard spheres interacting by a repulsive Yukawa potential of DLVO form is studied. To find the location of the phase boundary, we propose a simple theory to calculate the free energies for the coexisting liquid and solid. The free energy for the liquid phase is approximated by a virial expansion. The free energy of the crystalline phase is calculated in the spirit of the Lenard-Jonnes and Devonshire (LJD) theory. The phase boundary is found by equating the pressures and chemical potentials of the coexisting phases. When the approximation leading to the equation of state for the liquid breakes down, the first order transition line is also obtained by applying the Lindemann criterion to the solid phase. Our results are then compared with the Monte Carlo simulations.