Monte Carlo simulations of the solid-liquid transition in hard spheres and colloid-polymer mixtures

TL;DR

This study uses Monte Carlo simulations to analyze the coexistence and interfacial properties of solid-liquid transitions in hard spheres and colloid-polymer mixtures, providing quantitative data on coexistence pressures and interfacial stiffness.

Contribution

It introduces a simulation approach to determine coexistence and interfacial properties in hard sphere and colloid-polymer systems, including the effects of polymer-induced attractions.

Findings

Coexistence pressure for hard spheres: 11.576 k_BT/σ^3

Coexistence pressure for AO model: 8.0 k_BT/σ^3

Interfacial stiffness for (100) plane: 0.49 and 0.95 k_BT/σ^2

Abstract

Monte Carlo simulations at constant pressure are performed to study coexistence and interfacial properties of the liquid-solid transition in hard spheres and in colloid-polymer mixtures. The latter system is described as a one-component Asakura-Oosawa (AO) model where the polymer's degrees of freedom are incorporated via an attractive part in the effective potential for the colloid-colloid interactions. For the considered AO model, the polymer reservoir packing fraction is eta_p^r=0.1 and the colloid-polymer size ratio is q=sigma_p/\sigma=0.15 (with sigma_p and sigma the diameter of polymers and colloids, respectively). Inhomogeneous solid-liquid systems are prepared by placing the solid fcc phase in the middle of a rectangular simulation box creating two interfaces with the adjoined bulk liquid. By analyzing the growth of the crystalline region at various pressures and for different system sizes, the coexistence pressure p_co is obtained, yielding p_co=11.576 k_BT/sigma^3 for the hard sphere system and p_co=8.0 k_BT/sigma^3 for the AO model (with k_B the Boltzmann constant and T the temperature). Several order parameters are introduced to distinguish between solid and liquid phases and to describe the interfacial properties. From the capillary-wave broadening of the solid-liquid interface, the interfacial stiffness is obtained for the (100) crystalline plane, giving the values gamma=0.49 k_BT/sigma^2 for the hard-sphere system and gamma=0.95 k_BT/sigma^2 for the AO model.