Integral equation analysis of single-site coarse-grained models for polymer-colloid mixtures

We discuss the reliability of integral equation methods based on several commonly used closure relations in determining the phase diagram of coarse-grained models of soft-matter systems characterised by mutually interacting soft- and hard-core particles. Specifically, we consider a set of potentials appropriate to describe a system of hard-sphere colloids and linear homopolymers in good solvent, and investigate the behaviour when the soft particles are smaller than the colloids, which is the regime of validity of the coarse-grained models. Using computer-simulation results as a benchmark, we find that the hypernetted-chain approximation provides accurate estimates of thermodynamics and structure in the colloid-gas phase in which the density of colloids is small. On the other hand, all closures considered appear to be unable to describe the behaviour of the mixture in the colloid-liquid phase, as they cease to converge at polymer densities significantly smaller than those at the binodal. As a consequence, integral equations appear to be unable to predict a quantitatively correct phase diagram.