Critical behaviour and interfacial fluctuations in a phase-separating model colloid-polymer mixture: grand canonical Monte Carlo simulations

By using Monte Carlo simulations in the grand canonical ensemble we investigate the bulk phase behaviour of a model colloid-polymer mixture, the so-called Asakura-Oosawa model. In this model the colloids and polymers are considered as spheres with a hard-sphere colloid-colloid and colloid-polymer interaction and a zero interaction between polymers. In order to circumvent the problem of low acceptance rates for colloid insertions, we introduce a cluster move where a cluster of polymers is replaced by a colloid. We consider the transition from a colloid-poor to colloid-rich phase which is analogous to the gas-liquid transition in simple liquids. Successive umbrella sampling, recently introduced by Virnau and Mueller (2003 Preprint cond-mat/0306678), is used to access the phase-separated regime. We calculate the demixing binodal and the interfacial tension, also in the region close to the critical point. Finite size scaling techniques are used to accurately locate the critical point. Also investigated are the colloid density profiles in the phase-separated regime. We extract the interfacial thickness w from the latter profiles and demonstrate that the interfaces are subject to spatial fluctuations that can be understood by capillary wave theory. In particular, we find that, as predicted by capillary wave theory, w2 diverges logarithmically with the size of the system parallel to the interface