Topological derivation of shape exponents for stretched exponential relaxation

TL;DR

This paper introduces a topological method to predict the shape parameter beta in stretched exponential relaxation for glasses, linking it to fractal configuration spaces and validated by experimental data.

Contribution

It presents a novel topological framework deriving beta from fractal dimensions and axioms, providing accurate predictions supported by experimental relaxation measurements.

Findings

Beta values are accurately predicted within ~1% using topological rules.

Beta remains constant over a range of external conditions like temperature and ionic concentration.

The approach can test sample homogeneity and quality through its predictions.

Abstract

In homogeneous glasses, values of the important dimensionless stretched-exponential shape parameter beta are shown to be determined by magic (not adjusted) simple fractions derived from fractal configuration spaces of effective dimension d* by applying different topological axioms (rules) in the presence (absence) of a forcing electric field. The rules are based on a new central principle for defining glassy states: equal a priori distributions of fractal residual configurational entropy. Our approach and its beta estimates are fully supported by the results of relaxation measurements involving many different glassy materials and probe methods. The present unique topological predictions for beta typically agree with observed values to ~ 1% and indicate that for field-forced conditions beta should be constant for appreciable ranges of such exogenous variables as temperature and ionic concentration, as indeed observed using appropriate data analysis. The present approach can also be inverted and used to test sample homogeneity and quality.