On the corrections to Strong-Stretching Theory for end-confined, charged polymers in a uniform electric field

TL;DR

This paper extends the strong-stretching theory for end-confined, charged polymers by deriving corrections for weakly charged chains and validating these with numerical self-consistent field theory, revealing deviations from classical parabolic profiles.

Contribution

It introduces corrections to the Milner-Witten-Cates theory for charged polymers and compares these with numerical solutions, enhancing understanding of charge effects in polymer brush systems.

Findings

Corrections to MWC theory are derived for weakly charged chains.

Monomer-density profiles deviate from the classical parabolic shape due to charge.

Theoretical predictions are validated against numerical self-consistent field results.

Abstract

We investigate the properties of a system of semi-diluted polymers in the presence of charged groups and counter-ions, by means of self-consistent field theory. We study a system of polyelectrolyte chains grafted to a similarly, as well as an oppositely charged surface, solving a set of saddle-point equations that couple the modified diffusion equation for the polymer partition function to the Poisson-Boltzmann equation describing the charge distribution in the system. A numerical study of this set of equations is presented and comparison is made with previous studies. We then consider the case of semi-diluted, grafted polymer chains in the presence of charge-end-groups. We study the problem with self-consistent field as well as strong-stretching theory. We derive the corrections to the Milner-Witten-Cates (MWC) theory for weakly charged chains and show that the monomer-density deviates from the parabolic profile expected in the uncharged case. The corresponding corrections are shown to be dictated by an Abel-Volterra integral equation of the second kind. The validity of our theoretical findings is confirmed comparing the predictions with the results obtained within numerical self-consistent field theory.