Interplay of Polymer Structure, Solvent Ordering, and Charge Fluctuations in Polyelectrolyte Solution Thermodynamics

Abstract

We develop a polymer field-theoretic model that incorporates explicit treatment of semiflexibility and polar solvents, providing a framework to determine the impact of solvent ordering and concentration fluctuations on the thermodynamic behavior of polyelectrolyte solutions. We study the effect of dipole ordering on the electrostatic potential near a charged surface and the phase behavior of oppositely charged symmetric polyelectrolytes. The phase diagrams, incorporating quadratic-order concentration fluctuation corrections, are determined using different approximations of the chain structure factor for semiflexible polymers. While wormlike-chain statistics provides the most broadly accurate prediction for phase behavior, a Gaussian-rigid interpolation remains an adequate approximation for quadratic-order fluctuation corrections for many experimentally relevant systems. However, our theory provides the basis for predicting the impact of higher-order concentration fluctuations, which requires chain statistics that cannot be rendered from existing approximate methods.

Exploration of Phase Behavior in Asymmetric Semiflexible Polyelectrolyte Mixtures Using Polymer Field Theory

“…Building upon the self-consistent field theory presented in our previous paper, 61 we have broadened our analysis to encompass the phase behavior of polyelectrolyte solutions exhibiting varying degrees of asymmetry. The theoretical model we previously developed is specifically designed for a solution of polyelectrolytes within a polar solvent, with the aim of accurately capturing polymer structure and solvent ordering at the nanoscale.…”

“…A more detailed derivation of the chemical potential equations can be found in our previous paper. 61 The solution to these nonlinear equations is determined under the constraints of incompressibility and charge neutrality in each phase, resulting in a system of nine equations with 11 unknowns (five component volume fractions per phase and the Galvani potential). To enhance computational efficiency, we reduce this system to five equations with seven unknowns by applying the incompressibility and electroneutrality constraints to relate the volume fractions to each other directly.…”

“…The solvent coupling matrix M γ 1 ... γ n false( n false) gives the coupling between solvent and dipole conjugate fields W ϕ (S) and W⃗ D false( normalS false) , respectively, within the expansion terms. For a more detailed explanation, we refer the reader to our previous paper …”

“…For a more detailed explanation, we refer the reader to our previous paper. 61 Both the positive and negative ionic species share the same form. For example, positive ionic species result in an expansion in the form…”

“…Incorporating the WLC model within the RPA framework facilitates a more precise understanding of how polymer structure and interactions influence the phase behavior in polyelectrolyte systems . In our previous paper, we confirm that the Gaussian chain model overpredicts the phase separating domain for semiflexible polymers by undercounting the small length-scale fluctuation effects, which have been previously explored …”