# The conformation of a semiflexible filament in a quenched random potential

## TL;DR

This paper investigates the conformational behavior of a semiflexible filament in a quenched random potential, combining theoretical analysis with simulations to understand how cross-linking influences filament shape and energy storage.

## Contribution

It introduces a theoretical framework for the conformational statistics of semiflexible filaments in random potentials and compares predictions with Brownian dynamics simulations.

## Key findings

- Curvature distribution depends on potential correlation length and strength.
- Theoretical predictions align with simulation results.
- Replica field techniques' applicability is discussed.

## Abstract

Motivated by the observation of the storage of excess elastic free energy - (prestress) -- in cross linked semiflexible networks, we consider the problem of the conformational statistics of a single semiflexible polymer in a quenched random potential. The random potential, which represents the effect of cross linking to other filaments is assumed to have a finite correlation length $\xi$ and mean strength $V_{0}$. We examine statistical distribution of curvature in filament with thermal persistence length $\ell_{P}$ and length $L_0$ in the limit that $\ell_{P} \gg L_0$. We compare our theoretical predictions to finite element Brownian dynamics simulations. Lastly we comment on the validity of replica field techniques in addressing these questions.