Interfacial Instability of Charged End-Group Polymer Brushes

TL;DR

This paper models the behavior of charged-end polymer brushes under electric fields, revealing how electrostatic forces influence brush height and induce stable lateral undulation patterns with specific wavelengths.

Contribution

It introduces a continuum model to analyze electrostatic effects on polymer brush stability and predicts the formation of stable undulation patterns.

Findings

Brush height varies with electric field and charge end-group.

Electrostatic energy scales linearly with undulation wavenumber.

Stable undulation wavelength depends on system parameters.

Abstract

We consider a polymer brush grafted to a surface (acting as an electrode) and bearing a charged group at its free end. Using a second distant electrode, the brush is subject to a constant electric field. Based on a coarse-grained continuum model, we calculate the average brush height and find that the brush can stretch or compress depending on the applied field and charge end-group. We further look at an undulation mode of the flat polymer brush and find that the electrostatic energy scales linearly with the undulation wavenumber, $q$. Competition with surface tension, scaling as $q^2$, tends to stabilize a lateral $q$-mode of the polymer brush with a well-defined wavelength. This wavelength depends on the brush height, surface separation, and several system parameters.