  We present a theory to predict the structure and thermodynamics of mixtures
of colloids of different diameters, building on our earlier work [J. Chem.
Phys. 145, 074904 (2016)] that considered mixtures with all particles
constrained to have the same size. The patchy, solvent particles have
short-range directional interactions, while the solute particles have
short-range isotropic interactions. The hard-sphere mixture without any
association site forms the reference fluid. An important ingredient within the
multi-body association theory is the description of clustering of the reference
solvent around the reference solute. Here we account for the physical,
multi-body clusters of the reference solvent around the reference solute in
terms of occupancy statistics in a defined observation volume. These occupancy
probabilities are obtained from enhanced sampling simulations, but we also
present statistical mechanical models to estimate these probabilities with
limited simulation data. Relative to an approach that describes only up to
three-body correlations in the reference, incorporating the complete reference
information better predicts the bonding state and thermodynamics of the
physical solute for a wide range of system conditions. Importantly, analysis of
the residual chemical potential of the infinitely dilute solute from molecular
simulation and theory shows that whereas the chemical potential is somewhat
insensitive to the description of the structure of the reference fluid the
energetic and entropic contributions are not, with the results from the
complete reference approach being in better agreement with particle
simulations.
