Confining multiple polymers between sticky walls: a directed walk model of two polymers

TL;DR

This paper presents an exact solution for two directed polymers confined between sticky walls, revealing unique entropic force behaviors and limit properties that differ from single polymer systems.

Contribution

It provides the first exact analysis of two polymers in a slit with sticky walls, exploring limit behaviors and entropic forces in this complex confinement scenario.

Findings

Half-plane and slit limits coincide for two polymers.

Only repulsive entropic forces are observed between the walls.

Force range depends on polymer adsorption parameters.

Abstract

We study a model of two polymers confined to a slit with sticky walls. More precisely, we find and analyse the exact solution of two directed friendly walks in such a geometry on the square lattice. We compare the infinite slit limit, in which the length of the polymer (thermodynamic limit) is taken to infinity before the width of the slit is considered to become large, to the opposite situation where the order of the limits are swapped, known as the half-plane limit when one polymer is modelled. In contrast with the single polymer system we find that the half-plane and infinite slit limits coincide. We understand this result in part due to the tethering of polymers on both walls of the slit. We also analyse the entropic force exerted by the polymers on the walls of the slit. Again the results differ significantly from single polymer models. In a single polymer system both attractive and repulsive regimes were seen, whereas in our two walk model only repulsive forces are observed. We do, however, see that the range of the repulsive force is dependent on the parameter values. This variation can be explained by the adsorption of the walks on opposite walls of the slit.