From boiling point to glass transition temperature: transport coefficients in molecular liquids follow three-parameter scaling

Abstract

The phenomenon of the glass transition is an unresolved problem of condensed matter physics. Its prominent feature, the super-Arrhenius temperature dependence of the transport coefficients remains a challenge to be described over the full temperature range. For a series of molecular glass formers, we combined tau(T) from dielectric spectroscopy and dynamic light scattering covering the range 10_-12 s < tau(T) < 10^2s. Describing the dynamics in terms of an activation energy E(T), we distinguish a high-temperature regime characterized by an Arrhenius law with a constant activation energy E_inf and a low-temperature regime for which E_coop(T):= E(T) - E_inf increases while cooling. A two-parameter scaling is introduced, specifically E_coop(T)/E_inf = f[lambda(T/T_A -1)], where f is an exponential function, lambda a dimensionless parameter, and T_A a reference temperature proportional to E_inf. In order to describe tau(T), in addition, the attempt time tau_inf has to be specified. Thus, a single interaction parameter E_inf extracted from the high-temperature regime together with lambda controls the temperature dependence of low-temperature cooperative dynamics.