A directed walk model of a long chain polymer in a slit with attractive walls

TL;DR

This paper provides exact solutions for directed walk models of long polymers confined in a slit with attractive walls, revealing phase behavior and forces relevant to colloidal stabilization and flocculation.

Contribution

It introduces exact solutions for directed walk polymer models in a slit with attractive walls, analyzing phase diagrams and forces in the large width limit.

Findings

Large width phase diagram differs from half-plane case

Polymer induces forces indicating stabilization or flocculation

Asymptotic behaviour of free energy characterized for large widths

Abstract

We present the exact solutions of various directed walk models of polymers confined to a slit and interacting with the walls of the slit via an attractive potential. We consider three geometric constraints on the ends of the polymer and concentrate on the long chain limit. Apart from the general interest in the effect of geometrical confinement this can be viewed as a two-dimensional model of steric stabilization and sensitized flocculation of colloidal dispersions. We demonstrate that the large width limit admits a phase diagram that is markedly different from the one found in a half-plane geometry, even when the polymer is constrained to be fixed at both ends on one wall. We are not able to find a closed form solution for the free energy for finite width, at all values of the interaction parameters, but we can calculate the asymptotic behaviour for large widths everywhere in the phase plane. This allows us to find the force between the walls induced by the polymer and hence the regions of the plane where either steric stabilization or sensitized flocculation would occur.