Exact analytical solution of the extensible freely jointed chain model

Abstract

Based on classical statistical mechanics, we calculate analytically the length extension under a pulling force of a polymer modeled as a freely jointed chain with extensible bonds, the latter being considered as harmonic springs. We obtain an exact formula for the extension curve, as well as an independent high force approximation. These formulas can reproduce with high precision the experimental extension/force curves also at low values of the elastic constant of the spring, where previous proposals differ substantially. We successfully validate the analytical results together with the phenomenological expressions used in the literature by analyzing the precision of their fit on data obtained from Langevin simulations.