Grafted polymers under the influence of external fields

Abstract

The structure of grafted polymer ‘‘brushes’’ may be profoundly modified by the action of ‘‘external fields’’—local shifts in chemical potential due to, e.g., interfacial effects at the grafting surface. We discuss the strong-stretching limit of the self-consistent mean-field theory for a brush exposed to an arbitrary external potential, a simple scaling law for the brush height arises in the case where the external field pushes monomers towards the surface. In contrast, repulsive interactions can lead to ‘‘exclusion zones’’ or regions from which polymer ends are repelled, leading to a breakdown of the simple scaling formula. We exactly solve the self-consistent theory of the brush in a repulsive square well where an exclusion zone always appears. Our results describe a brush in the case where a thin layer of one component of a binary solvent that is a worse solvent for the polymer than is the bulk mixture wets the grafting surface. We also discuss the effects of thermal fluctuations and chain polydispersity on our results, and estimate the effects of various interfacial phenomena on the brush structure.