A constrained random-force model for weakly bending semiflexible polymers

TL;DR

This paper introduces a constrained version of the random-force model for semiflexible polymers, showing that the constraints modify the force effects and soften the filament under compression, with implications for understanding disordered elastic systems.

Contribution

It proposes a constrained random-force model for semiflexible polymers, analyzing how the constraints affect the system's behavior and force response.

Findings

Constraints reduce the effects of random forces by numerical factors.

Constraints do not change qualitative behavior in the strong stretching regime.

Transverse random forces soften the filament to compression.

Abstract

The random-force (Larkin) model of a directed elastic string subject to quenched random forces in the transverse directions has been a paradigm in the statistical physics of disordered systems. In this brief note, we investigate a modified version of the above model where the total transverse force along the polymer contour and the related total torque, in each realization of disorder, vanish. We discuss the merits of adding these constraints and show that they leave the qualitative behavior in the strong stretching regime unchanged, but they reduce the effects of the random force by significant numerical prefactors. We also show that a transverse random force effectively makes the filament softer to compression by inducing undulations. We calculate the related linear compression coefficient in both the usual and the constrained random force model.