  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 characterized 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 behavior 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 behavior 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.
