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

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.

arXiv comment15 pages, 9 figures

References in corpus (10)

• Asymptotic laws for tagged-particle motion in glassy systems
• Nearly-logarithmic decay of correlations in glass-forming liquids
• Universal and non-universal features of glassy relaxation in propylene carbonate
• Nearly-logarithmic decay in the colloidal hard-sphere system
• Study of the Depolarized Light Scattering Spectra of Supercooled Liquids by a Simple Mode-Coupling Model
• Brillouin Scattering Study of Propylene Carbonate: An Evaluation of Phenomenological and Mode Coupling Analyses
• Structural Relaxation and Mode Coupling in a Simple Liquid: Depolarized Light Scattering in Benzene
• Structural relaxation in orthoterphenyl: a schematic mode coupling theory model analysis
• What can be learned from the schematic mode-coupling approach to experimental data ?
• Equations of structural relaxation

Cited by in corpus (9)

• Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields
• High-frequency dynamics of type-B glass formers investigated by broadband dielectric spectroscopy
• Structural relaxation in the hydrogen-bonding liquids N-methylacetamide and water studied by optical Kerr-effect spectroscopy
• Broadband dielectric spectroscopy on benzophenone: alpha relaxation, beta relaxation, and mode coupling theory
• Dielectric spectroscopy in benzophenone: The beta relaxation and its relation to the mode-coupling Cole-Cole peak
• Crossover behavior and multi-step relaxation in a schematic model of the cut-off glass transition
• Dynamical properties of densely packed confined hard-sphere fluids
• Scaling equations for mode-coupling theories with multiple decay channels
• Asymptotic Description of Schematic Models for CKN