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An integral equation approach to effective interactions between polymers in solution

V. Krakoviack·B. Rotenberg·J. -P. Hansen
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Abstract

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 $h_{mm}(r)$ 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 $h_{mm}(r)$, $h_{cc}(r)$ [the pair correlation function between the polymer centers of mass (c.m.)], and the intramolecular form factors is then used to determine $h_{cc}(r)$, and subsequently extract the effective c.m.-c.m. pair potential $v_{cc}(r)$ by a similar inversion procedure. $v_{cc}(r)$ 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.

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V. Krakoviack, B. Rotenberg, J. -P. Hansen. 2003-12-16. An integral equation approach to effective interactions between polymers in solution. https://doi.org/10.1021/jp036800o

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