Scaling in rupture of polymer chains

TL;DR

This paper investigates how polymer chain rupture dynamics depend on chain length and force propagation, revealing that rupture force decreases with chain length and saturates, with analytical results confirmed by simulations.

Contribution

It introduces a detailed analysis of rupture dynamics considering non-Markovian effects and force propagation delays in polymer chains, highlighting the dominant role of force propagation slowdown.

Findings

Rupture force decreases with chain length as f_{max} ~ const - (ln(N/r))^{2/3}.

Rupture force saturates at a value independent of chain length.

Analytical results are validated by extensive numerical simulations.

Abstract

We consider the rupture dynamics of a homopolymer chain pulled at one end at a constant loading rate r. Compared to single bond breaking, the existence of the chain introduces two new aspects into rupture dynamics: the non-Markovian aspect in the barrier crossing and the slow-down of the force propagation to the breakable bond. The relative impact of both these processes is investigated, and the second one was found to be the most important at moderate loading rates. The most probable rupture force is found to decrease with the number of bonds as f_{max} const-(ln(N/r))^(2/3) and finally to approach a saturation value independent on N. All our analytical findings are confirmed by extensive numerical simulations.