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 in 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 \ensuremath{\tau}($T$) collected from dielectric spectroscopy and dynamic light scattering covering a range 10${}^{\ensuremath{-}12}$ s \ensuremath{\tau}($T$) 10${}^{2}$ s. 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 ${E}_{\ensuremath{\infty}}$ and a low-temperature regime for which ${E}_{\mathrm{coop}}$($T$) \ensuremath{\equiv} $E$($T$)--${E}_{\ensuremath{\infty}}$ increases exponentially while cooling. A scaling is introduced, specifically ${E}_{\mathrm{coop}}$($T$)/${E}_{\ensuremath{\infty}}$ \ensuremath{\propto} exp[--\ensuremath{\lambda}($T$/${T}_{\mathrm{A}}$--1)], where \ensuremath{\lambda} is a fragility parameter and ${T}_{\mathrm{A}}$ a reference temperature proportional to ${E}_{\ensuremath{\infty}}$. In order to describe \ensuremath{\tau}($T$) still the attempt time ${\ensuremath{\tau}}_{\ensuremath{\infty}}$ has to be specified. Thus, a single interaction parameter ${E}_{\ensuremath{\infty}}$ describing the high-temperature regime together with \ensuremath{\lambda} controls the temperature dependence of low-temperature cooperative dynamics.