Topological origin of stretched exponential relaxation in glass

Abstract

The physical origin of stretched exponential relaxation is considered by many as one of the oldest unsolved problems in science. The functional form for stretched exponential relaxation can be deduced from the axiomatic diffusion-trap model of Phillips. The model predicts a topological origin for the dimensionless stretching exponent, with two "magic" values emerging: β = 3/5 arising from short-range molecular relaxation pathways and β = 3/7 for relaxation dominated by longer-range interactions. In this paper, we report experimental confirmation of these values using microscopically homogeneous silicate glass specimens. Our results reveal a bifurcation of the stretching exponent, with β = 3/5 for stress relaxation and β = 3/7 for structural relaxation, both on macroscopic length scales. These results point to two fundamentally different mechanisms governing stress relaxation versus structural relaxation, corresponding to different effective dimensionalities in configuration space during the relaxation process.