Aging phenomena in nonlinear dissipative chains: Application to polymer

TL;DR

This paper investigates energy relaxation in a nonlinear dissipative chain model for polymers, revealing long-lived localized modes, quasi-stationary states, and aging effects similar to glasses, with implications for understanding polymer dynamics.

Contribution

It introduces a phenomenological nonlinear lattice model with dissipative couplings to explain aging and relaxation phenomena in polymers, highlighting the role of localized modes.

Findings

Existence of quasi-stationary states with non-zero energy at high dissipation.

Observation of stretched exponential relaxation laws.

Strong dependence of correlation functions on waiting time, similar to glassy systems.

Abstract

We study energy relaxation in a phenomenological model for polymer built from rheological considerations: a one dimensional nonlinear lattice with dissipative couplings. These couplings are well known in polymer's community to be possibly responsible of beta-relaxation (as in Burger's model). After thermalisation of this system, the extremities of the chain are put in contact with a zero-temperature reservoir, showing the existence of surprising quasi-stationary states with non zero energy when the dissipative coupling is high. This strange behavior, due to long-lived nonlinear localized modes, induces stretched exponential laws. Furthermore, we observe a strong dependence on the waiting time tw after the quench of the two-time intermediate correlation function C(tw+t,tw). This function can be scaled onto a master curve, similar to the case of spin or Lennard-Jones glasses.