Improved Approximations for Some Polymer Extension Models

TL;DR

This paper introduces highly accurate approximations for the force-extension relationships in polymer models like FJC and WLC, facilitating better data fitting in molecular force spectroscopy experiments.

Contribution

It presents novel approximations with less than 1% error for key polymer models, improving the accuracy of force-extension data analysis.

Findings

Less than 1% relative error in approximations

Applicable to fitting experimental force-extension curves

Useful for complex spring geometries in experiments

Abstract

We propose approximations for force-extension dependencies for the freely jointed chain (FJC) and worm-like chain (WLC) models as well as for extension-force dependence for the WLC model. Proposed expressions show less than 1% relative error in the useful range of the corresponding variables. These results can be applied for fitting force-extension curves obtained in molecular force spectroscopy experiments. Particularly they can be useful for cases where one has geometries of springs in series and/or in parallel where particular combination of expressions should be used for fitting the data. All approximations have been obtained following the same procedure of determining the asymptotes and then reducing the relative error of that expression by adding an appropriate term obtained from fitting its absolute error.