Topological derivation of shape exponents for stretched exponential relaxation

Abstract

In homogeneous (ideal) glasses, the important dimensionless stretched-exponential shape parameter β is described by magic (not adjusted) simple fractions derived from fractal configuration spaces of effective dimension d * determined by 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 β estimates are fully supported by the results of relaxation measurements involving many different glassy materials and probe methods. The present unique topological predictions for β typically agree with observed values to ∼1% and indicate that for field-forced conditions β should be constant for appreciable ranges of such exogenous variables as temperature and ionic concentration, as indeed observed using appropriate frequency-domain data analysis. The present approach can also be inverted and used to test sample homogeneity and quality.