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.

A mode-coupling theory for the glassy dynamics of a diatomic probe molecule immersed in a simple liquid

Generalizing the mode-coupling theory for ideal liquid-glass transitions, equations of motion are derived for the correlation functions describing the glassy dynamics of a diatomic probe molecule immersed in a simple glass-forming system. The molecule is described in the interaction-site representation and the equations are solved for a dumbbell molecule consisting of two fused hard spheres in a hard-sphere system. The results for the molecule's arrested position in the glass state and the reorientational correlators for angular-momentum index $\ell = 1$ and $\ell = 2$ near the glass transition are compared with those obtained previously within a theory based on a tensor-density description of the molecule in order to demonstrate that the two approaches yield equivalent results. For strongly hindered reorientational motion, the dipole-relaxation spectra for the $\alpha$-process can be mapped on the dielectric-loss spectra of glycerol if a rescaling is performed according to a suggestion by Dixon et al. [Phys. Rev. Lett. {\bf 65}, 1108 (1990)]. It is demonstrated that the glassy dynamics is independent of the molecule's inertia parameters.Comment: 19 pages, 10 figures, Phys. Rev. E, in prin

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.

Propylene Carbonate Reexamined: Mode-Coupling β\beta Scaling without Factorisation ?

The dynamic susceptibility of propylene carbonate in the moderately viscous regime above $T_{\rm c}$ is reinvestigated by incoherent neutron and depolarised light scattering, and compared to dielectric loss and solvation response. Depending on the strength of $\alpha$ relaxation, a more or less extended $\beta$ scaling regime is found. Mode-coupling fits yield consistently $\lambda=0.72$ and $T_{\rm c}=182$K, although different positions of the susceptibility minimum indicate that not all observables have reached the universal asymptotics

The mean-squared displacement of a molecule moving in a glassy system

The mean-squared displacement (MSD) of a hard sphere and of a dumbbell molecule consisting of two fused hard spheres immersed in a dense hard-sphere system is calculated within the mode-coupling theory for ideal liquid-glass transitions. It is proven that the velocity correlator, which is the second time derivative of the MSD, is the negative of a completely monotone function for times within the structural-relaxation regime. The MSD is found to exhibit a large time interval for structural relaxation prior to the onset of the $\alpha$-process which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The $\alpha$-process for molecules with a large elongation is shown to exhibit an anomalously wide cross-over interval between the end of the von-Schweidler decay and the beginning of normal diffusion. The diffusivity of the molecule is predicted to vary non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin

Structural relaxation in a system of dumbbell molecules

The interaction-site-density-fluctuation correlators, the dipole-relaxation functions, and the mean-squared displacements of a system of symmetric dumbbells of fused hard spheres are calculated for two representative elongations of the molecules within the mode-coupling theory for the evolution of glassy dynamics. For large elongations, universal relaxation laws for states near the glass transition are valid for parameters and time intervals similar to the ones found for the hard-sphere system. Rotation-translation coupling leads to an enlarged crossover interval for the mean-squared displacement of the constituent atoms between the end of the von Schweidler regime and the beginning of the diffusion process. For small elongations, the superposition principle for the reorientational $\alpha$-process is violated for parameters and time intervals of interest for data analysis, and there is a strong breaking of the coupling of the $\alpha$-relaxation scale for the diffusion process with that for representative density fluctuations and for dipole reorientations.Comment: 15 pages, 14 figures, Phys. Rev. E in pres

Fluids of hard ellipsoids: Phase diagram including a nematic instability from Percus-Yevick theory

An important aspect of molecular fluids is the relation between orientation and translation parts of the two-particle correlations. Especially the detailed knowledge of the influence of orientation correlations is needed to explain and calculate in detail the occurrence of a nematic phase. The simplest model system which shows both orientation and translation correlations is a system of hard ellipsoids. We investigate an isotropic fluid formed of hard ellipsoids with Percus-Yevick theory. Solving the Percus-Yevick equations self-consistently in the high density regime gives a clear criterion for a nematic instability. We calculate in detail the equilibrium phase diagram for a fluid of hard ellipsoids of revolution. Our results compare well with Monte Carlo Simulations and density functional theory.Comment: 7 pages including 4 figure

Spin models for orientational ordering of colloidal molecular crystals

Two-dimensional colloidal suspensions exposed to periodic external fields exhibit a variety of molecular crystalline phases. There two or more colloids assemble at lattice sites of potential minima to build new structural entities, referred to as molecules. Using the strength of the potential and the filling fraction as control parameter, phase transition to unconventional orientationally ordered states can be induced. We introduce an approach that focuses at the discrete set of orientational states relevant for the phase ordering. The orientationally ordered states are mapped to classical spin systems. We construct effective hamiltonians for dimeric and trimeric molecules on triangular lattices suitable for a statistical mechanics discussion. A mean-field analysis produces a rich phase behavior which is substantiated by Monte Carlo simulations.Comment: 19 pages, 21 figures; misplacement of Fig.3 fixe

Test of mode coupling theory for a supercooled liquid of diatomic molecules.I. Translational degrees of freedom

A molecular dynamics simulation is performed for a supercooled liquid of rigid diatomic molecules. The time-dependent self and collective density correlators of the molecular centers of mass are determined and compared with the predictions of the ideal mode coupling theory (MCT) for simple liquids. This is done in real as well as in momentum space. One of the main results is the existence of a unique transition temperature T_c, where the dynamics crosses over from an ergodic to a quasi-nonergodic behavior. The value for T_c agrees with that found earlier for the orientational dynamics within the error bars. In the beta- regime of MCT the factorization of space- and time dependence is satisfactorily fulfilled for both types of correlations. The first scaling law of ideal MCT holds in the von Schweidler regime, only, since the validity of the critical law can not be confirmed, due to a strong interference with the microscopic dynamics. In this first scaling regime a consistent description within ideal MCT emerges only, if the next order correction to the asymptotic law is taken into account. This correction is almost negligible for q=q_max, the position of the main peak in the static structure factor S(q), but becomes important for q=q_min, the position of its first minimum. The second scaling law, i.e. the time-temperature superposition principle, holds reasonably well for the self and collective density correlators and different values for q. The alpha-relaxation times tau_q^(s) and tau_q follow a power law in T-T_c over 2 -- 3 decades. The corresponding exponent gamma is weakly q-dependent and is around 2.55. This value is in agreement with the one predicted by MCT from the value of the von Schweidler exponent but at variance with the corresponding exponent gammaComment: 14 pages of RevTex, 19 figure

Asymptotic laws for tagged-particle motion in glassy systems

Within the mode-coupling theory for structural relaxation in simple systems the asymptotic laws and their leading-asymptotic correction formulas are derived for the motion of a tagged particle near a glass-transition singularity. These analytic results are compared with numerical ones of the equations of motion evaluated for a tagged hard sphere moving in a hard-sphere system. It is found that the long-time part of the two-step relaxation process for the mean-squared displacement can be characterized by the $\alpha$-relaxation-scaling law and von Schweidler's power-law decay while the critical-decay regime is dominated by the corrections to the leading power-law behavior. For parameters of interest for the interpretations of experimental data, the corrections to the leading asymptotic laws for the non-Gaussian parameter are found to be so large that the leading asymptotic results are altered qualitatively by the corrections. Results for the non-Gaussian parameter are shown to follow qualitatively the findings reported in the molecular-dynamics-simulations work by Kob and Andersen [Phys. Rev. E 51, 4626 (1995)]