  Polymer chains in colloid-polymer mixtures can be coarse-grained by replacing
them with single soft particles interacting via effective polymer-polymer and
polymer-colloid pair potentials. Here we describe in detail how
Ornstein-Zernike inversion techniques, originally developed for atomic and
molecular fluids, can be generalized to complex fluids and used to derive
effective potentials from computer simulations on a microscopic level. In
particular, we consider polymer solutions for which we derive effective
potentials between the centers of mass, and also between mid-points or
end-points from simulations of self-avoiding walk polymers. In addition, we
derive effective potentials for polymers near a hard wall or a hard sphere. We
emphasize the importance of including both structural and thermodynamic
information (through sum-rules) from the underlying simulations. In addition we
develop a simple numerical scheme to optimize the parameterization of the
density dependent polymer-polymer, polymer-wall and polymer-sphere potentials
for dilute and semi-dilute polymer densities, thus opening up the possibility
of performing large-scale simulations of colloid-polymer mixtures. The methods
developed here should be applicable to a much wider range effective potentials
in complex fluids.
