Bimodal distribution function of a 3d wormlike chain with a fixed orientation of one end

TL;DR

This paper analyzes the distribution function of a 3D wormlike chain with one end fixed, revealing a bimodal distribution in the intermediate chain length range and providing analytical results consistent with prior studies.

Contribution

It introduces an exact Green's function approach to study the distribution, highlighting the bimodal shape in intermediate lengths and extending previous analytical results.

Findings

Bimodal distribution observed in intermediate chain lengths

Analytical results match previous studies for short and long chains

Exact representation using quantum rigid rotator Green's function

Abstract

We study the distribution function of the three dimensional wormlike chain with a fixed orientation of one chain end using the exact representation of the distribution function in terms of the Green's function of the quantum rigid rotator in a homogeneous external field. The transverse 1d distribution function of the free chain end displays a bimodal shape in the intermediate range of the chain lengths ($1.3L_{p},...,3.5L_{p}$). We present also analytical results for short and long chains, which are in complete agreement with the results of previous studies obtained using different methods.