An integral equation approach to effective interactions between polymers in solution

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We use the thread model for linear chains of interacting monomers, and the ``polymer reference interaction site model'' (PRISM) formalism to determine the monomer-monomer pair correlation function hmm(r) for dilute and semi-dilute polymer solutions, over a range of temperatures from very high (where the chains behave as self-avoiding walks) to below the θ temperature, where phase separation sets in. An inversion procedure, based on the HNC integral equation, is used to extract the effective pair potential between ``average'' monomers on different chains. An accurate relation between hmm(r), hcc(r) [the pair correlation function between the polymer centers of mass (c.m.)], and the intramolecular form factors is then used to determine hcc(r), and subsequently extract the effective c.m.-c.m. pair potential vcc(r) by a similar inversion procedure. vcc(r) depends on temperature and polymer concentration, and the predicted variations are in reasonable agreement with recent simulation data, except at very high temperatures, and below the θ temperature.