Mode coupling, universality, and the glass transition

Abstract

We investigate the current status of the mode-coupling theory (MCT) of the glass transition by making a comparison with two recent sets of experiments: the scaling data resulting from the dielectric measurements of Dixon et et al. et al. [Phys. Rev. Lett. 65, 1108 (1990)] and the neutron-scattering data. Our main conclusions include the following. (a) Experiments do show the sequence of time scales in the relaxation predicted by MCT. In particular, we believe that the high-frequency tail of the data of Nagel and co-workers is the realization of the so-called von Schweidler relaxation predicted by MCT in the frequency regime. (b) The nature of scaling discovered by Dixon et al. is quite different from and more universal than that predicted by MCT, which is basically a time-temperature superposition. Furthermore, the dielectric measurements show that there exists a universal relation between the exponent b governing von Schweidler relaxation and the exponent β governing a stretched exponential: 1+b=3/4(1+β). (c) Dixon et al. find no evidence for the existence of a special temperature ${\mathit{T}}_0$ (well above the phenomenological glass-transition temperature ${\mathit{T}}_{\mathit{g}}$) above and below which the relaxation dynamics is substantially different. This constitutes a discrepancy between the two sets of experiments since neutron-scattering experiments have been interpreted as confirming the existence of such a temperature well above ${\mathit{T}}_{\mathit{g}}$. A possible reinterpretation of MCT is suggested so as to reconcile these two sets of experiments and MCT.