Fractal approach to the beta relaxation in supercooled liquids

TL;DR

This paper introduces a fractal model for beta relaxation in supercooled liquids, linking mesoscopic cage dynamics to macroscopic behavior and matching some predictions of mode-coupling theory.

Contribution

It develops a fractal-based framework for understanding beta relaxation, connecting cage size distributions with macroscopic response and reproducing MCT scaling relations.

Findings

Scaling exponents are universal across materials.

The model reproduces MCT scaling relations.

Single cage relaxation varies with material structure.

Abstract

In the present work we present a fractal model for the beta relaxation in supercooled liquids. The macroscopic dynamics is obtained by superposition of relaxation of independent mesoscopic regions (cages). Scaling relations and exponents are assumed for the distribution of cage sizes and for the size dependent response of the independent cages. In this way we obtain some scaling relations for the average response, in the time and frequency domain. For a particular choice of the scaling exponents we obtain the scaling relations predicted by the MCT. The comparison with recent light scattering data reveals that the scaling exponents of the distribution of cage sizes are universal but the single cage relaxation depends on the detailed material structure