Tension dynamics in semiflexible polymers. Part II: Scaling solutions and applications

TL;DR

This paper provides analytical solutions for tension dynamics in semiflexible polymers, revealing how tension propagates and relaxes under external forces, with implications for understanding polymer behavior in experimental settings.

Contribution

It introduces explicit analytical solutions for tension relaxation in semiflexible polymers, extending previous coarse-grained models to include detailed tension dynamics and applications.

Findings

Tension relaxation follows specific power-law behaviors.

Analytical predictions match experimental tension propagation.

End-to-end distance dynamics are characterized explicitly.

Abstract

In Part I of this contribution, a systematic coarse-grained description of the dynamics of a weakly-bending semiflexible polymer was developed. Here, we discuss analytical solutions of the established deterministic partial integro-differential equation for the spatio-temporal relaxation of the backbone tension. For prototypal experimental situations, such as the sudden application or release of a strong external pulling force, it is demonstrated that the tensile dynamics reflects the self-affine conformational fluctuation spectrum in a variety of intermediate asymptotic power laws. Detailed and explicit analytical predictions for the tension propagation and relaxation and corresponding results for common observables, such as the end-to-end distance, are obtained.