Fatigue and failure of a polymer chain under tension

TL;DR

This paper develops a theoretical framework for the probability distribution of rupture rates in a polymer chain under tension, emphasizing the tail of fast collapse rates, and validates it with numerical simulations.

Contribution

It provides the first analytic calculation of the full probability distribution function of polymer chain rupture rates, especially its tail, which was previously unaddressed.

Findings

The tail of the PDF follows a universal power law.

Numerical simulations confirm the theoretical predictions.

The theory offers insights into rare, rapid rupture events.

Abstract

The rupture of a polymer chain maintained at temperature $T$ under fixed tension is prototypical to a wide array of systems failing under constant external strain and random perturbations. Past research focused on analytic and numerical studies of the mean rate of collapse of such a chain. Surprisingly, an analytic calculation of the probability distribution function (PDF) of collapse rates appears to be lacking. Since rare events of rapid collapse can be important and even catastrophic, we present here a theory of this distribution, with a stress on its tail of fast rates. We show that the tail of the PDF is a power law with a {\em universal} exponent that is theoretically determined. Extensive numerics validate the offered theory. Lessons pertaining to other problems of the same type are drawn.