Multiscale Model for the Dielectric Permittivity

Abstract

Abstract:We present a generalisation of the Debye relaxation model for the dielectric permittivity in the case in which the global relaxation process is the result of many elementary excitations. The relaxation dynamics is in this case non-Markovian. In the case of many events, for which the central limit theorem holds and Gaussianity as well as the assumption of independency are both plausible, the global relaxation time is given by a log-normal function. The hierarchy of relaxation times leads to a generalised expression of the dielectric permittivity.

Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields

“…Mode-Coupling Theory (MCT), are able to account for the coupling of each molecule to collective degrees of freedom [17,18], but do not explicitly address the simultaneous effect of the AC field on the dynamics of both the single molecule and all the other molecules which provide the memory effect in dielectric relaxation. The GLE derived here will open the possibility of describing both these effects at the same time, within MCT type approaches [17] or within the GLE picture that has been proposed more recently to deal with hierarchy of relaxation times in liquids and glasses [19][20][21]. Furthermore, the GLE derived here can be used as the starting point for a more microscopic description of nonlinear dielectric response of supercooled liquids under strong fields [22], for which a microscopic picture is currently lacking [23].…”