# Local versus global stretched mechanical response in a supercooled liquid near the glass transition

## TL;DR

This study uses molecular dynamics simulations to analyze local and global mechanical responses in a supercooled liquid near the glass transition, revealing consistent Cole-Davidson spectra and size-dependent relaxation behaviors.

## Contribution

It demonstrates that local and global spectra follow the Cole-Davidson formula with size-independent stretching, and explains size effects via the elastic shoving model.

## Key findings

- Spectra fit Cole-Davidson formula across scales
- Stretching exponent remains constant regardless of region size
- Size dependence of relaxation explained by elastic shoving model

## Abstract

Amorphous materials have a rich relaxation spectrum, which is usually described in terms of a hierarchy of relaxation mechanisms. In this work, we investigate the local dynamic modulus spectra in a model glass just above the glass transition temperature by performing a mechanical spectroscopy analysis with molecular dynamics simulations. We find that the spectra, at the local as well as on the global scale, can be well described by the Cole-Davidson formula in the frequency range explored with simulations. Surprisingly, the Cole-Davidson stretching exponent does not change with the size of the local region that is probed. The local relaxation time displays a broad distribution, as expected based on dynamic heterogeneity concepts, but the stretching is obtained independently of this distribution. We find that the size dependence of the local relaxation time and moduli can be well explained by the elastic shoving model.