On the behaviour of short Kratky-Porod chain

TL;DR

This paper analytically derives short chain expansions for the worm-like chain model, providing detailed corrections to the stiff rod limit for the distribution function, scattering, and extension-force relations.

Contribution

It introduces a method to resum moment expansions of the end-to-end distance distribution for short chains, extending the accuracy to seventh order in chain length.

Findings

Derived short chain expansion for the distribution function

Extended scattering function analysis for short chains

Analyzed extension-force relation with high-order corrections

Abstract

Using the exact computation of a large number of moments of the distribution function of the end-to-end distance $G(r,N)$ of the worm-like chain, we have established the analytical form of the coefficients in Taylor expansions of the moments for short chain lengths $N$. The knowledge of these coefficients enabled us to resummate the moment expansion of $G(r,N)$ by taking into account consecutively the deviations of the moments from their stiff rod limit. Within this procedure we have derived the short chain expansion for $G(r,N)$, the scattering function, and the extension-force relation, which take into account the deviations of the moments from their stiff rod limit to the seventh order in $N$.