Self‐Consistent Integral Equation Theory for Semiflexible Polyelectrolytes in Poor Solvent

Abstract

AbstractSelf‐consistent hybrid MC/PRISM method is presented for calculating properties of polyelectrolytes in semidilute and more concentrated regimes in a poor solvent. The static structure and conformational behavior of salt‐free polyelectrolyte solutions composed of semiflexible polyions and monovalent counterions are studied using the approach which combines the traditional Monte‐Carlo (MC) simulation with the numerical solution of the polymer integral PRISM equation. The MC technique is applied to generate the configurations of a single chain molecule and obtain the averaged intrapolymer correlation function. The PRISM equation is then numerically solved for a given monomer density to obtain the various correlation functions and the medium‐induced intrapolymer potential. This is used in a single chain MC simulation, where the polymer sites interact via the bare Coulomb potential together with the short range attractive potential and a self‐consistently determined medium‐induced potential. The monomer‐monomer pair correlation functions and static structure factors are calculated for a large variety of parameters. Conformational properties such as the radius of gyration and visual images are obtained as a function of attractive short‐range interaction, monomer density, Bjerrum length, and chain stiffness. The MC/PRISM study predicts that there is a range of hydrophobicity and monomer density for which polyion chains can form the toroidal structure in a poor solvent. Nonmonotonic dependence of the chain size on monomer density is predicted over the entire range of parameters. Polyion structure factor peak position as a function of density is described. Two concentration regimes in which the polyion structure factors exhibit physically different peaks were found. Over the entire concentration regime considered polyelectrolyte chains undergo strong compression with Rg ∝ l.Conformation of a polyion chain for lB = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.imageConformation of a polyion chain for lB = 2, ε = 0.18 at ρ* = 0.2 and α = 10°.