The Cole-Cole Law for Critical Dynamics in Glass-Forming Liquids

TL;DR

This paper explores the application of the Cole-Cole law within mode-coupling theory to describe critical dynamics in glass-forming liquids, successfully explaining experimental optical-Kerr-effect data and spectral features in benzophenone.

Contribution

It introduces a Cole-Cole law for susceptibilities in MCT, providing a better description of dynamics outside the transient regime and explaining experimental observations.

Findings

The Cole-Cole law accounts for susceptibilities below the microscopic excitation band.

It explains the alpha-peak wing observed in benzophenone's spectra.

The leading-order MCT formulas describe the crossover in spectral features.

Abstract

Within the mode-coupling theory (MCT) for glassy dynamics, the asymptotic low-frequency expansions for the dynamical susceptibilities at critical points are compared to the expansions for the dynamic moduli; this shows that the convergence properties of the two expansions can be quite different. In some parameter regions, the leading-order expansion formula for the modulus describes the solutions of the MCT equations of motion outside the transient regime successfully; at the same time, the leading- and next-to-leading order expansion formulas for the susceptibility fail. In these cases, one can derive a Cole-Cole law for the susceptibilities; and this law accounts for the dynamics for frequencies below the band of microscopic excitations and above the high-frequency part of the alpha-peak. It is shown that this scenario explains the optical-Kerr-effect data measured for salol and benzophenone (BZP). For BZP it is inferred that the depolarized light-scattering spectra exhibit a wing for the alpha-peak within the Gigahertz band. This wing results from the crossover of the von Schweidler-law part of the alpha-peak to the high-frequency part of the Cole-Cole peak; and this crossover can be described quantitatively by the leading-order formulas of MCT for the modulus.