Simulation of nanocolloid chemical potentials in a hard-sphere polymer solution: Expanded ensemble Monte Carlo

Abstract

We present a novel application of the expanded ensemble Monte Carlo (EEMC) simulation method to calculation of the chemical potential of nanocolloidal particles in nanocolloid–polymer mixtures. This approach uses an expanded canonical ensemble in which the colloidal particle diameter is an additional ensemble variable, allowed to vary between zero and the maximum colloid size desired. Using a hard-sphere model system, we demonstrate that this approach is superior to the Widom method for calculating chemical potentials in colloid–polymer systems. Specifically the EEMC leads to lower uncertainties and is capable of calculating accurate colloid chemical potentials for particle sizes where Widom insertion fails due to overlap. The EEMC method is applied to calculate the colloid chemical potential for an infinitely dilute colloidal particle (hard-sphere) in a dilute polymer (hard-sphere chain) solution over a wide range of relative sizes, 0.1<Rg/R<12, where Rg is the polymer radius of gyration and R is the colloid radius. The simulation results are compared to the predictions of models developed by others: an integral equation model (FS) [Fuchs and Schweizer, Europhys. Lett. 51, 621 (2000)] and a field theoretic (FT) approach [Eisenriegler et al., Phys. Rev. E 54, 1134 (1996)]. Very good agreement is observed with the FS model over a wide range of Rg/R values, whereas the FT model agrees well only at large Rg/R. An empirical power law function is found to represent the simulation results well, potentially useful for analysis of free energy data for colloid–polymer mixtures.