Relationship between non-exponentiality of relaxation and relaxation time in the problem of glass transition

By analyzing the experimental data for various glass-forming liquids and polymers, we find that the nonexponentiality, β, and the relaxation time, τ, are commonly related: log(τ) is an approximately linear function of 1/β, followed in most cases by a crossover to a higher linear slope. We rationalize this relationship in the recently developed elastic approach to the glass transition. The key to the observed common relationship between β and τ is that the two quantities are governed by the same parameter, the liquid elasticity length, del. The increase of del on lowering temperature increases τ and decreases β, resulting in the observed common relationship between β and τ. In this picture, we also discuss the crossovers of β and τ at low temperature