End-To-End Distribution Function Function of Stiff Polymers for all Persistence Lengths

TL;DR

This paper develops a recursive method to compute the end-to-end distance distribution of stiff polymers across all persistence lengths, providing an analytic expression that matches simulations and transitions smoothly between stiff and flexible regimes.

Contribution

It introduces a new recursive approach to derive the full distribution function of wormlike chains for any stiffness, unifying stiff and flexible limits.

Findings

Analytic distribution matches Monte Carlo data for stiff chains.

Distribution transitions smoothly to Gaussian for low stiffness.

Method applicable in any dimension, here demonstrated in 3D.

Abstract

We set up recursion relations for calculating all even moments of the end-to-end distance of a Porod-Kratky wormlike chains in $D$ dimensions. From these moments we derive a simple analytic expression for the end-to-end distribution in three dimensions valid for all peristence lengths. It is in excellent agreement with Monte Carlo data for stiff chains and goes properly over into the Gaussian random-walk distributions for low stiffness.