Tension dynamics in semiflexible polymers. Part I: Coarse-grained equations of motion

TL;DR

This paper develops a coarse-grained, nonlinear dynamic model for semiflexible polymers based on the wormlike chain model, revealing deterministic tension relaxation behavior through perturbation analysis.

Contribution

It introduces a novel coarse-grained equation of motion for weakly bending semiflexible polymers, highlighting the deterministic nature of tension dynamics.

Findings

Derived a partial integro-differential equation for tension relaxation.

Predicted nonlinear response characteristics of semiflexible polymers.

Established a length-scale separation in the weakly-bending limit.

Abstract

Based on the wormlike chain model, a coarse-grained description of the nonlinear dynamics of a weakly bending semiflexible polymer is developed. By means of a multiple scale perturbation analysis, a length-scale separation inherent to the weakly-bending limit is exploited to reveal the deterministic nature of the spatio-temporal relaxation of the backbone tension and to deduce the corresponding coarse-grained equation of motion. From this partial integro-differential equation, some detailed analytical predictions for the non-linear response of a weakly bending polymer are derived in an accompanying paper (Part II, cond-mat/0609638).