Bimodal probability density characterizes the elastic behavior of a semiflexible polymer in 2D under compression

TL;DR

This paper provides an exact probabilistic analysis of a semiflexible polymer's elastic response under compression, revealing a bimodal distribution near buckling and highlighting differences between clamped and free polymers.

Contribution

It introduces exact solutions for the probability densities of a wormlike chain under compression, uncovering bimodal shapes linked to buckling and semiflexibility effects.

Findings

Bimodal probability density near buckling force

Distinct configurations for clamped polymers under compression

Symmetric distributions for free polymers under compression and stretching

Abstract

We explore the elastic behavior of a wormlike chain under compression in terms of exact solutions for the associated probability densities. Strikingly, the probability density for the end-to-end distance projected along the applied force exhibits a bimodal shape in the vicinity of the critical Euler buckling force of an elastic rod, reminiscent of the smeared discontinuous phase transition of a finite system. These two modes reflect the almost stretched and the S-shaped configuration of a clamped polymer induced by the compression. Moreover, we find a bimodal shape of the probability density for the transverse fluctuations of the free end of a cantilevered polymer as fingerprint of its semiflexibility. In contrast to clamped polymers, free polymers display a circularly symmetric probability density and their distributions are identical for compression and stretching forces.