Stretching of a Freely Jointed Chain in Two-Dimensions

TL;DR

This paper derives analytical models for the force-extension behavior of a freely-jointed chain confined to two dimensions, validated by simulations, revealing differences based on how force is applied.

Contribution

It provides the first closed-form analytical expressions for 2D chain stretching under different force application modes, validated by Brownian dynamics simulations.

Findings

Distributed force requires more total force than end-applied force.

Force diverges as extension approaches contour length.

Models are validated by simulation results.

Abstract

Although the stretching of polymers and biomolecules is important in numerous settings, their response when confined to two-dimensions is relatively poorly-studied. In this paper, we derive closed-form analytical expressions for the two-dimensional force-extension response of a freely-jointed chain under force control. Our principal results relate end-to-end distance to total force under two modes of stretching: i) when force is applied only to the free of the chain, and ii) when the applied force is distributed uniformly throughout the chain. We have verified both analytical models by Brownian dynamics simulation of molecules adsorbed strongly to a substrate. The total force required is always larger if distributed throughout the chain than when it is only applied to one end of the chain, and the nature of its divergence to infinity as extension approaches contour length is different.