Logarithmic coarsening and glassy behavior in a polymer model with mass-dependent diffusion

TL;DR

This paper introduces a polymer growth and diffusion model with mass-dependent energy barriers, exhibiting non-universal logarithmic coarsening and glassy dynamics, supported by simulations, scaling theories, and analytical solutions.

Contribution

It presents a novel polymer model with mass-dependent diffusion barriers that captures glassy behavior and non-universal coarsening, supported by multiple analytical and numerical methods.

Findings

Logarithmic coarsening depends on the exponent gamma.

Strong-glass behavior observed in polymer disappearance times.

Analytical solutions match numerical simulations.

Abstract

We present a model of polymer growth and diffusion with frustration mechanisms for density increase and with diffusion rates of Arrhenius form with mass-dependent energy barriers Gamma(m) ~ (m-1)^gamma. It shows non-universal logarithmic coarsening involving the exponent gamma. Strong-glass behavior is found in the typical times for disappearance of all polymers up to a given length, without reference to the equilibrium states of the macroscopic system. These features are predicted by numerical simulations, scaling theories and an analytic solution of the master equation within an independent interval approximation, which also provides the cluster size distribution.