A self-interacting partially directed walk subject to a force

TL;DR

This paper analyzes a two-dimensional self-interacting directed walk model of a homopolymer under tensile force, exploring phase transitions, force-extension behavior, and extending the analysis to three dimensions with various force orientations.

Contribution

It provides a rigorous analysis of the model's key quantities, including the critical point and phase diagram, and extends the model to three dimensions with force restrictions.

Findings

Critical-force temperature curve identified

Rigorous techniques applicable to full model analyzed

Extension to three dimensions with force in preferred plane

Abstract

We consider a directed walk model of a homopolymer (in two dimensions) which is self-interacting and can undergo a collapse transition, subject to an applied tensile force. We review and interpret all the results already in the literature concerning the case where this force is in the preferred direction of the walk. We consider the force extension curves at different temperatures as well as the critical-force temperature curve. We demonstrate that this model can be analysed rigorously for all key quantities of interest even when there may not be explicit expressions for these quantities available. We show which of the techniques available can be extended to the full model, where the force has components in the preferred direction and the direction perpendicular to this. Whilst the solution of the generating function is available, its analysis is far more complicated and not all the rigorous techniques are available. However, many results can be extracted including the location of the critical point which gives the general critical-force temperature curve. Lastly, we generalise the model to a three-dimensional analogue and show that several key properties can be analysed if the force is restricted to the plane of preferred directions.