Origin of the Kohlrausch exponent

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.