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

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

2006-02-24

arxiv.org/abs/cond-mat/0602571v1

Phys. Rev. E 74, 011503 (2006)

Physics

Condensed Matter

Statistical Mechanics

15 pages, 9 figures

Scientific paper

10.1103/PhysRevE.74.011503

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.

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