Cluster relaxation dynamics in liquids and solids near the glass-transformation temperature

Abstract

The structural relaxation in glass forming materials is studied near the glass transformation temperature Tg indicated by the heat capacity maximum. The late-time asymptote of the Kohlrausch–Williams–Watts form of the relaxation function is rationalized via the mesoscopic-scale correlated regions in terms of the Debye-type clusters following the dynamic scaling law. It is repeatedly shown that regardless of underlying microscopic realizations in glass formers with site disorder the structural relaxation is driven by local random fields, described via the directed random walks model. The relaxation space dimension ds = 3 at Tg is suggested for relaxing units of fractal dimension d f = 5/2 for quadrupolar-glass clusters in ortho–para hydrogen mixtures, that is compared with entangled-chain clusters in polymers (d f = 1) and solid-like clusters relaxing in supercooled molecular liquids (with ds = 6 and d f = 3). The relaxation dynamics of orientational-glass clusters in plastic crystals is attributed to the model of continuos time random walks in space ds = 6. As a by-product, the expansivity in polymers, molecular liquids and networks is predicted.