Elastic behavior of a semiflexible polymer in 3D subject to compression and stretching forces

TL;DR

This paper provides exact solutions for the elastic response of semiflexible polymers in 3D under force, revealing a smooth transition from stretched to buckled states and highlighting differences between 2D and 3D confinement.

Contribution

It offers a precise analytical description of the force-extension behavior of semiflexible polymers in 3D, contrasting with classical buckling theory and including effects of thermal fluctuations.

Findings

Force-extension relation exhibits a smooth crossover rather than buckling.

Susceptibility peaks near the Euler buckling force.

2D confinement enhances the polymer's resistance to applied force.

Abstract

We elucidate the elastic behavior of a wormlike chain in 3D under compression and provide exact solutions for the experimentally accessible force-extension relation in terms of generalized spheroidal wave functions. In striking contrast to the classical Euler buckling instability, the force-extension relation of a clamped semiflexible polymer exhibits a smooth crossover from an almost stretched to a buckled configuration. In particular, the associated susceptibility, which measures the strength of the response of the polymer to the applied force, displays a prominent peak in the vicinity of the critical Euler buckling force. For increasing persistence length, the force-extension relation and the susceptibility of semiflexible polymers approach the behavior of a classical rod, whereas thermal fluctuations permit more flexible polymers to resist the applied force. Furthermore, we find that semiflexible polymers confined to 2D can oppose the applied force more strongly than in 3D.