An integral equation approach to effective interactions between polymers in solution

TL;DR

This paper develops an integral equation approach using PRISM and HNC methods to determine effective interactions between polymers in solution, accounting for temperature and concentration effects, with results aligning well with simulations.

Contribution

It introduces a novel inversion procedure to extract effective monomer-monomer and center-of-mass pair potentials from correlation functions in polymer solutions.

Findings

Effective pair potentials vary with temperature and concentration.

Predicted potentials agree with simulation data in most conditions.

Method provides a systematic way to analyze polymer interactions.

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 $\theta$ 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 $\theta$ temperature.