A. Latz

A theory for the beta -relaxation process near the liquid-to-glass crossover

The mode coupling theory for supercooled liquid dynamics finds a beta -relaxation regime on mesoscopic timescales. It is caused by the interplay between nonlinear interactions of density fluctuations and phonon-assisted hopping transport. In this regime all correlation functions and spectra can be expressed in terms of a single beta -correlator G, which is a homogeneous function of time and two relevant control parameters. For temperatures T sufficiently above the critical value Tc hopping effects can be neglected and a stretched susceptibility minimum, is found as a crossover from von Schweidler decay to critical decay. For T near Tc hopping effects balance the cage effect and this results on logarithmic scales in a rather abrupt crossover from the high-frequency alpha -peak tail to the critical spectrum. For T below Tc there appears a frequency window between two knees in the susceptibility spectrum, where hopping effects suppress the enhanced fractal spectra. There occurs a crossover from Debye relaxation to white noise. The resulting susceptibility minimum in the strongly supercooled state exhibits a subtle power law dependence on the separation parameter T-Tc.

β Relaxation theory for simple systems : some addenda

The evolution of the tagged particle probability density for a hard sphere system is evaluated within the β-relaxation window. Relaxation curves obtained by molecular dynamics studies by Barrat, Hansen and Roux for a binary mixture are analyzed quantitatively with β-relaxation scaling formulae. The dynamical light scattering data obtained by Pusey and van Megen for colloidal suspensions are described by the combined α- and β-relaxation scaling results. The range of validity of asymptotic expressions near a glass transition singularity is discussed for the Debye-Waller factor as a function of packing fraction. The applied theoretical formulae are those of the mode coupling theory for the liquid to glass transition.

On the theory of light scattering in molecular liquids

Abstract:The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities ρlm(q) with l = 0 and l = 2. l, m denote indices of spherical harmonics. To account for all observed hydrodynamic singularities, a generalization of the theory of Schilling and Scheidsteger [1] for these correlation functions is presented, which is capable to describe the light scattering experiments from the liquid regime to the glassy state. As a microscopic theory it fulfills all sum rules contrary to previous phenomenological theories. We emphasize the importance of the helicity index m for the microscopic theory by showing, that only the existence of m = 1 components lead to the well known Rytov dip in liquids and to the appearance of transversal sound waves in VH symmetry in the deeply supercooled liquid and the glass. Exact expressions for the phenomenological frequency dependent rotation translation coupling coefficients of previous theories are derived.The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities

Light-scattering study of β-relaxation in CaKNO3 and salol near the liquid-glass transition: idealized and extended mode coupling theory analysis☆

\rho_{lm}(q)

Light scattering spectroscopy of the liquid-glass transition : comparison with idealized and extended mode coupling theory

with

α-relaxation in a supercooled binary mixture

l=0

Light scattering at the liquid to glass transition

and

Microscopic dynamics of hard ellipsoids in their liquid and glassy phase

l=2

Light-scattering spectra of supercooled molecular liquids

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Bogoliubov–Born–Green–Kirkwood–Yvon hierarchy methods for sums of Lyapunov exponents for dilute gases

l