Relationship between the nonexponentiality 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, beta, and the relaxation time, tau, are commonly related: log(tau) is an approximately linear function of 1/beta, 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 beta and tau is that the two quantities are governed by the same parameter, the liquid elasticity length, d el. The increase of d el on lowering temperature increases tau and decreases beta, resulting in the observed common relationship between beta and tau. In this picture, we also discuss the crossovers of beta and tau at low temperature.