Long-Wavelength Anomalies in the Asymptotic Behavior of Mode-Coupling Theory

We discuss the dynamic behavior of a tagged particle close to a classical localization transition in the framework of the mode-coupling theory of the glass transition. Asymptotic results are derived for the order parameter as well as the dynamic correlation functions and the mean-squared displacement close to the transition. The influence of an infrared cutoff is discussed.Comment: 15 pages, 8 figures, to appear in J Phys Condens Matte

Universal and non-universal features of glassy relaxation in propylene carbonate

It is demonstrated that the susceptibility spectra of supercooled propylene carbonate as measured by depolarized-light-scattering, dielectric-loss, and incoherent quasi-elastic neutron-scattering spectroscopy within the GHz window are simultaneously described by the solutions of a two-component schematic model of the mode-coupling theory (MCT) for the evolution of glassy dynamics. It is shown that the universal beta-relaxation-scaling laws, dealing with the asymptotic behavior of the MCT solutions, describe the qualitative features of the calculated spectra. But the non-universal corrections to the scaling laws render it impossible to achieve a complete quantitative description using only the leading-order-asymptotic results.Comment: 37 pages, 16 figures, to be published in Phys. Rev.

Reorientational relaxation of a linear probe molecule in a simple glassy liquid

Within the mode-coupling theory (MCT) for the evolution of structural relaxation in glass-forming liquids, correlation functions and susceptibility spectra are calculated characterizing the rotational dynamics of a top-down symmetric dumbbell molecule, consisting of two fused hard spheres immersed in a hard-sphere system. It is found that for sufficiently large dumbbell elongations, the dynamics of the probe molecule follows the same universal glass-transition scenario as known from the MCT results of simple liquids. The $\alpha$-relaxation process of the angular-index-j=1 response is stronger, slower and less stretched than the one for j=2, in qualitative agreement with results found by dielectric-loss and depolarized-light-scattering spectroscopy for some supercooled liquids. For sufficiently small elongations, the reorientational relaxation occurs via large-angle flips, and the standard scenario for the glass-transition dynamics is modified for odd-j responses due to precursor phenomena of a nearby type-A MCT transition. In this case, a major part of the relaxation outside the transient regime is described qualitatively by the $\beta$-relaxation scaling laws, while the $\alpha$-relaxation scaling law is strongly disturbed.Comment: 40 pages. 10 figures as GIF-files, to be published in Phys. Rev.

Alpha-Relaxation Processes in Binary Hard-Sphere Mixtures

Molecular-dynamics simulations are presented for two correlation functions formed with the partial density fluctuations of binary hard-sphere mixtures in order to explore the effects of mixing on the evolution of glassy dynamics upon compressing the liquid into high-density states. Partial-density-fluctuation correlation functions for the two species are reported. Results for the alpha-relaxation process are quantified by parameters for the strength, the stretching, and the time scale, where the latter varies over almost four orders of magnitude upon compression. The parameters exhibit an appreciable dependence on the wave vector; and this dependence is different for the correlation function referring to the smaller and that for the larger species. These features are shown to be in semi-quantitative agreement with those calculated within the mode-coupling theory for ideal liquid-glass transitions.Comment: 14 pages, 20 figures, RevTe

Effect of Composition Changes on the Structural Relaxation of a Binary Mixture

Within the mode-coupling theory for idealized glass transitions, we study the evolution of structural relaxation in binary mixtures of hard spheres with size ratios $\delta$ of the two components varying between 0.5 and 1.0. We find two scenarios for the glassy dynamics. For small size disparity, the mixing yields a slight extension of the glass regime. For larger size disparity, a plasticization effect is obtained, leading to a stabilization of the liquid due to mixing. For all $\delta$, a decrease of the elastic moduli at the transition due to mixing is predicted. A stiffening of the glass structure is found as is reflected by the increase of the Debye-Waller factors at the transition points. The critical amplitudes for density fluctuations at small and intermediate wave vectors decrease upon mixing, and thus the universal formulas for the relaxation near the plateau values describe a slowing down of the dynamics upon mixing for the first step of the two-step relaxation scenario. The results explain the qualitative features of mixing effects reported by Williams and van Megen [Phys. Rev. E \textbf{64}, 041502 (2001)] for dynamical light-scattering measurements on binary mixtures of hard-sphere-like colloids with size ratio $\delta=0.6$

Higher order glass-transition singularities in colloidal systems with attractive interactions

The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line, and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third order bifurcation point, i.e. in a A_3 (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth order A_4 (swallow-tail) singularity at a critical well width. Close to the A_3 and A_4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.Comment: 19 pages, 12 figures, Phys. Rev. E, in prin