Elastic traits of the extensible discrete wormlike chain model

TL;DR

This paper derives analytical and numerical formulas for the end-to-end distance of an extensible discrete worm-like chain polymer under force, improving data fitting accuracy for experimental measurements of semi-flexible polymers.

Contribution

It provides a new analytical approximation for the force-extension relationship of extensible worm-like chains, enhancing the interpretation of experimental data.

Findings

Analytical formulas match experimental data well

Numerical transfer matrix method provides exact results

Improved accuracy in elastic parameter estimation

Abstract

Polymer models play the special role of elucidating the elementary features describing the physics of long molecules and become essential to interpret the measurements of their magnitudes. In this work the end-to-end distance of an extensible discrete worm-like chain polymer as a function of the applied force has been calculated both numerically and analytically, the latter as an effective approximation. The numerical evaluation uses the Transfer Matrix formalism to obtain an exact calculation of the partition function, while the analytic derivations generalize the simple phenomenological formulas largely used up to now. The obtained formulas are simple enough to be implemented in the fit analysis of experimental data of semi-flexible extensible polymers, with the result that the elastic parameters obtained are compatible with previous measurements, and more, their accuracy strongly improves in a large range of chain extensibility.