Self-avoiding walks adsorbed at a surface and subject to a force

TL;DR

This paper studies self-avoiding walks attached to a surface and subjected to a force, showing that the free energy and critical force criteria are the same whether the force is applied at the top vertices or the last vertex.

Contribution

It proves that the free energy and critical force behavior are identical for forces applied at the top vertices or the last vertex of the walk.

Findings

Free energy is the same for both force application methods.

Critical force-temperature curve is identical in both cases.

Response to pushing the walk is equivalent regardless of force application point.

Abstract

We consider self-avoiding walks terminally attached to an impenetrable surface at which they can adsorb. We call the vertices farthest away from this plane the top vertices and we consider applying a force at the plane containing the top vertices. This force can be directed away from the adsorbing surface or towards it. In both cases we prove that the free energy (in the thermodynamic limit) is identical to the free energy when the force is applied at the last vertex. This means that the criterion determining the critical force - temperature curve is identical for the two ways in which the force is applied and the response to pushing the walk is also the same in the two cases.