Bundling in brushes of directed and semiflexible polymers

TL;DR

This paper investigates how attractive interactions between aligned, grafted polymers can cause a homogeneous polymer brush to become unstable and form bundles, breaking translational symmetry and creating density modulations.

Contribution

It introduces a theoretical analysis of bundling instability in polymer brushes due to attractive interactions, considering both directed and semiflexible polymer models.

Findings

Homogeneous polymer brushes can become unstable and form bundles due to attractive interactions.

The instability leads to density modulations with a finite wavelength.

The analysis applies to both directed polymers and weakly bending chains.

Abstract

We explore the effect of an attractive interaction between parallel-aligned polymers, which are perpendicularly grafted on a substrate. Such an attractive interaction could be due to, e.g., reversible cross-links. The competition between permanent grafting favoring a homogeneous state of the polymer brush and the attraction, which tends to induce in-plane collapse of the aligned polymers, gives rise to an instability of the homogeneous phase to a bundled state. In this latter state the in-plane translational symmetry is spontaneously broken and the density is modulated with a finite wavelength, which is set by the length scale of transverse fluctuations of the grafted polymers. We analyze the instability for two models of aligned polymers: directed polymers with a line tension and weakly bending chains with a bending stiffness.