Analytical results of the extensible freely jointed chain model

TL;DR

This paper provides analytical formulas for the extension and fluctuations of an extensible freely jointed chain model under force, validated by simulations and offering insights into polymer behavior.

Contribution

It introduces new analytical expressions for the extension and fluctuations of an extensible freely jointed chain, including high force approximations, validated against Langevin simulations.

Findings

Analytical formulas accurately fit simulation data.

High force approximation effectively describes chain behavior.

Comparison with phenomenological models highlights improvements.

Abstract

Based on classical statistical mechanics, we calculate analytically the length extension and the fluctuations, under a pulling force, of a polymer modelled as a freely jointed chain with extensible bonds, the latter considered as harmonic springs. We obtain an analytical formula for the partition function, and derive both the extension curve of the chain and the fluctuations as a function of the force. An independent high force approximation has been also evaluated. The analytical formulas have been validated by analysing the exactness of their fit on data obtained from Langevin simulations, and compared with the phenomenological expressions largely used in the past literature.