A semiflexible polymer chain under geometrical restrictions: Only bulk behaviour and no surface adsorption

TL;DR

This study models a semiflexible polymer confined between two stair-shaped impenetrable surfaces in two dimensions, revealing that such geometrical restrictions lead to purely bulk behavior with no surface adsorption.

Contribution

It provides an exact analytical model showing that geometrical constraints prevent surface adsorption of a semiflexible polymer in two dimensions.

Findings

Polymer exhibits only bulk behavior under constraints.

No surface adsorption occurs due to geometrical restrictions.

Exact partition function derived for the confined polymer.

Abstract

We analyse the conformational behaviour of a linear semiflexible homo-polymer chain confined by two geometrical constraints under a good solvent condition in two dimensions. The constraints are stair shaped impenetrable surfaces. The impenetrable surfaces are lines in a two dimensional space. The infinitely long polymer chain is confined in between such two (A and B) surfaces. A lattice model of a fully directed self-avoiding walk is used to calculate the exact expression of the partition function, when the chain has attractive interaction with one or both the constraints. It has been found that under the proposed model, the chain shows only a bulk behaviour. In other words, there is no possibility of adsorption of the chain due to restrictions imposed on the walks of the chain.