Adsorbed self-avoiding walks subject to a force

TL;DR

This paper analyzes a polymer adsorption model with a force applied at the polymer's end, establishing the existence of a free energy limit, its convexity, and characterizing the phase transition between adsorbed and desorbed states.

Contribution

It provides a rigorous mathematical framework for understanding how an applied force influences polymer adsorption and desorption, including phase boundary properties.

Findings

Existence of a limiting free energy in the presence of force and surface potential.

Convexity of the free energy with respect to relevant variables.

Identification and bounds of the phase boundary between adsorbed and desorbed phases.

Abstract

We consider a self-avoiding walk model of polymer adsorption where the adsorbed polymer can be desorbed by the application of a force. In this paper the force is applied normal to the surface at the last vertex of the walk. We prove that the appropriate limiting free energy exists where there is an applied force and a surface potential term, and prove that this free energy is convex in appropriate variables. We then derive an expression for the limiting free energy in terms of the free energy without a force and the free energy with no surface interaction. Finally we show that there is a phase boundary between the adsorbed phase and the desorbed phase in the presence of a force, prove some qualitative properties of this boundary and derive bounds on the location of the boundary.