  The self- and mutual-avoiding walk used in conventional lattice models for
polymeric systems requires that all lattice sites, polymer segments, and
solvent molecules (unoccupied lattice sites) have the same volume. This
incorrectly accounts for the solvent entropy (i.e., size ratio between polymer
segments and solvent molecules), and also limits the coarse-graining capability
of such models, where the invariant degree of polymerization controlling the
system fluctuations is too small (thus exaggerating the system fluctuations)
compared to that in most experiments. Here we show how to properly account for
the solvent entropy in the recently proposed lattice models with multiple
occupancy of lattice sites [Q. Wang, Soft Matter 5, 4564 (2009)], and present a
quantitative coarse-graining strategy that ensures both the solvent entropy and
the fluctuations in the original systems are properly accounted for using such
lattice models. Although proposed based on homogeneous polymer solutions, our
strategy is equally applicable to inhomogeneous systems such as polymer brushes
immersed in a small-molecule solvent.
