Monte Carlo cluster algorithm for fluid phase transitions in highly size-asymmetrical binary mixtures

TL;DR

This paper introduces an efficient Monte Carlo cluster algorithm embedded in a restricted Gibbs ensemble to study fluid phase transitions in highly size-asymmetrical binary mixtures, enabling accurate analysis of phase behavior.

Contribution

The authors develop and detail a rejection-free geometrical cluster algorithm for simulating highly size-asymmetrical mixtures within a restricted Gibbs ensemble, improving simulation efficiency and accuracy.

Findings

Adding small particles decreases the critical temperature by ~50%.

Critical density drops by ~30% with small particle addition.

The method reveals that small particles reduce net attraction between large particles.

Abstract

Highly size-asymmetrical fluid mixtures arise in a variety of physical contexts, notably in suspensions of colloidal particles to which much smaller particles have been added in the form of polymers or nanoparticles. Conventional schemes for simulating models of such systems are hamstrung by the difficulty of relaxing the large species in the presence of the small one. Here we describe how the rejection-free geometrical cluster algorithm (GCA) of Liu and Luijten [Phys. Rev. Lett 92, 035504 (2004)] can be embedded within a restricted Gibbs ensemble to facilitate efficient and accurate studies of fluid phase behavior of highly size-asymmetrical mixtures. After providing a detailed description of the algorithm, we summarize the bespoke analysis techniques of Ashton et al. [J. Chem. Phys. 132, 074111 (2010)] that permit accurate estimates of coexisting densities and critical-point parameters. We apply our methods to study the liquid--vapor phase diagram of a particular mixture of Lennard-Jones particles having a 10:1 size ratio. As the reservoir volume fraction of small particles is increased in the range 0--5%, the critical temperature decreases by approximately 50%, while the critical density drops by some 30%. These trends imply that in our system, adding small particles decreases the net attraction between large particles, a situation that contrasts with hard-sphere mixtures where an attractive depletion force occurs.