The Slowly Formed Guiselin Brush

TL;DR

This paper develops a theory for polymer layers formed by slow, irreversible adsorption, revealing a layered structure with a density profile that differs from the instantaneous Guiselin brush, depending on the experiment duration.

Contribution

It introduces a model for slowly formed polymer brushes, extending Guiselin's theory to account for finite adsorption times and resulting in a layered density profile.

Findings

Inner layer thickness scales as t_final^{-5/3}

Outer layer extends up to height ~ N^{5/6}

Density decay follows z^{-2/5} profile

Abstract

We study polymer layers formed by irreversible adsorption from a polymer melt. Our theory describes an experiment which is a ``slow'' version of that proposed by Guiselin [Europhys. Lett., v. 17 (1992) p. 225] who considered instantaneously irreversibly adsorbing chains and predicted a universal density profile of the layer after swelling with solvent to produce the ``Guiselin brush.'' Here we ask what happens when adsorption is not instantaneous. The classic example is chemisorption. In this case the brush is formed slowly and the final structure depends on the experiment's duration, $t_{final}$. We find the swollen layer consists of an inner region of thickness $z^* \sim t_{final}^{-5/3}$ with approximately constant density and an outer region extending up to height $h \sim N^{5/6}$ which has the same density decay $\sim z^{-2/5}$ as for the Guiselin case.