Semiflexible polymers: Dependence on ensemble and boundary orientations

TL;DR

This paper investigates how the mechanical properties of semiflexible polymers depend on ensemble choice and boundary orientations, revealing complex behaviors and mappings to quantum models validated by simulations.

Contribution

It introduces a mapping of the worm-like-chain model to a quantum particle on a sphere to analyze boundary and ensemble effects.

Findings

Multiple free energy minima near t=4 persist across boundary conditions

Projected end-to-end vector distribution depends on embedding dimensions

Quantum mapping aligns well with Monte Carlo simulation results

Abstract

We show that the mechanical properties of a worm-like-chain (WLC) polymer, of contour length $L$ and persistence length $\l$ such that $t=L/\l\sim{\cal O}(1)$, depend both on the ensemble and the constraint on end-orientations. In the Helmholtz ensemble, multiple minima in free energy near $t=4$ persists for all kinds of orientational boundary conditions. The qualitative features of projected probability distribution of end to end vector depend crucially on the embedding dimensions. A mapping of the WLC model, to a quantum particle moving on the surface of an unit sphere, is used to obtain the statistical and mechanical properties of the polymer under various boundary conditions and ensembles. The results show excellent agreement with Monte-Carlo simulations.