Active Microrheology of Networks Composed of Semiflexible Polymers. II. Theory and comparison with simulations

TL;DR

This paper develops a theoretical model for bead motion in semiflexible polymer networks, confirming simulation results and predicting scaling laws and concentration dependence consistent with experiments.

Contribution

It introduces a theoretical framework that explains bead dynamics in semiflexible networks, extending previous simulations with analytical predictions.

Findings

Bead displacement scales as t^0.5 at intermediate times and t^1 at long times.

Compliance varies with concentration as c^(-4/3), matching experimental data.

The theory reveals an osmotic restoring force due to filament piling up.

Abstract

Building on the results of our computer simulation (ArXiv cond-mat/0503573)we develop a theoretical description of the motion of a bead, embedded in a network of semiflexible polymers, and responding to an applied force. The theory reveals the existence of an osmotic restoring force, generated by the piling up of filaments in front of the moving bead and first deduced through computer simulations. The theory predicts that the bead displacement scales like x ~ t^alfa with time, with alfa=0.5 in an intermediate- and alfa=1 in a long-time regime. It also predicts that the compliance varies with concentration like c^(-4/3) in agreement with experiment.