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

By analyzing the experimental data for various glass-forming liquids and polymers, we find that non-exponentiality $\beta$ and the relaxation time $\tau$ are uniquely related: $\log(\tau)$ is an approximately linear function of $1/\beta$, followed by a crossover to a higher linear slope. We rationalize the observed relationship using a recently developed approach, in which the problem of the glass transition is discussed as the elasticity problem.