Extension of chains composed of freely joined elastic segments

Abstract

A relatively simple formula for the mean distance between the ends of a model chain composed of elastic freely joined segments as a function of an extending force applied to its ends was derived. It was assumed that the stiffness coefficient, which characterizes the ability of the segment to extend and contract, is rather high. In the limit of infinite stiffness the relationship obtained transforms into the Langevin function. The formula predicts the existence of two Hook regions in the force-relative extension dependence. The first of them is characterized by small extensions, whereas the second one, by extensions exceeding the equilibrium contour length. The existence of the latter is confirmed by recent experiments. The magnitude of fluctuations of the relative extension was estimated. The obtained relationships for the relative extension and its scatter are in close agreement with the results of computer simulations performed using collisional molecular dynamics for chains composed of 25, 50, 100, and 200 segments.