Origin of the Kohlrausch exponent

TL;DR

This paper proposes a theoretical relation for the Kohlrausch beta exponent based on the Adam-Gibbs conjecture, linking it to structural entropy and flow barriers, supported by numerical data for Lennard-Jones potentials.

Contribution

It introduces a new relation for the Kohlrausch beta exponent derived from the Adam-Gibbs conjecture and structural entropy considerations.

Findings

Beta values between 0.3 and 0.6 predicted

Relation connects beta to structural entropy and flow barriers

Supports the idea that local forces govern glass dynamics

Abstract

According to a recent numerical finding, the dynamics of a glass former is exclusively due to the forces within the first coordination shell. This implies that the Kohlrausch beta should be understandable in terms of the effective nearest-neighbor potential. The present paper proposes a relation for the Kohlrausch beta based on the Adam-Gibbs conjecture of a flow barrier proportional to the number of atoms or molecules in a cooperatively rearranging region. The conjecture implies that beta is given by the ratio of the structural entropy increase per particle to the barrier increase per particle. Making use of a recent numerical determination of the structural entropy per particle in Lennard-Jones-like potentials, one can show that the relation leads to values between 0.3 and 0.6.