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The mode-coupling theory for ideal liquid-glass transitions is extended so that the structural relaxation for the reorientational degrees of freedom of a linear molecule, which is immersed in a system of spherical particles, can be described. Closed equations of motion for the correlation functions formed with tensor density fluctuations are derived, which deal with the molecule's translational and reorientational motion. From these equations the nonergodicity parameters of a hard dumbbell molecule are calculated, which quantify its arrest in a hard-sphere glass. For top-down symmetric molecules it is shown that the odd-angular-momentum variables can exhibit an ergodic-to-nonergodic transition, characterized by a continuous increase of the Edwards-Anderson parameters near the critical points.

The \ensuremath{\alpha}-relaxation dynamics in a hard-sphere system is studied solving microscopic-mode-coupling equations. The solutions for coherent and incoherent dynamical structure factors, the transversal correlation functions, and the moduli are presented for all wave vectors. The wave-vector dependence of fitted Kohlrausch exponents \ensuremath{\beta} and of the relaxation times \ensuremath{\tau} is discussed. Recent experiments on the \ensuremath{\alpha} relaxation of colloidal systems are quantitatively analyzed.

In der vorliegenden Arbeit wird, ausgehend von einem schematischen Modenkopplungsmodell, die Dynamik und das Fließverhalten von kolloidalen Dispersionen unter stationärer Scherung nahe am Glasübergang untersucht. Bei dem gewählten Zugang werden sowohl analytische als auch numerische Methoden eingesetzt. Die wichtigsten Kontrollparameter des Modells sind die Scherrate und der Separationsparameter, welcher den Abstand zum Glasübergangspunkt misst. Ein negativer Separationsparameter definiert einen flüssigkeitsartigen Zustand während ein positiver Wert für den Separationsparameter zu einem glasartigen Zustand führt. Nach Diskussion der grundlegenden Eigenschaften des Modells und des dazugehörigen numerischen Algorithmus gliedert sich der Hauptteil der Arbeit in drei Kapitel:Der beta-ProzessNach Einführung der Bewegungsgleichung und Diskussion des Gültigkeitsbereiches wird eine sehr nützliche Eigenschaft, das Zweiparameterskalengesetz, diskutiert. Dies erlaubt eine präzise Definition des Flüssigkeits-, Übergangs- und Glasbereiches und die Einführung natürlicher Zeitskalen. Es werden analytische Ausdrücke zur Beschreibung der Dynamik in den drei Bereichen für alle relevanten Zeitskalen abgeleitet und die Ergebnisse werden numerisch überprüft. Die Dynamik kann durch verschiedene verallgemeinerte Potenzreihen und einer Exponentialfunktion beschrieben werden. Vier dieser Potenzreihen sind notwendig um die Dynamik im Flüssigkeitsbereich zu beschreiben. Die Dynamik im Übergangsbereich kann durch zwei Potenzreihen beschrieben werden. Um die Dynamik im Glasbereich auf allen Zeitskalen zu beschrieben, werden drei Potenzreihen und eine Exponentialfunktion benötigt. Die Kurzzeitasymptoten und die scherdominierte Langzeitasymptoten hängen nicht vom Separationsparameter ab.FließkurvenIn diesem Kapitel wird die stationäre Scherspannung als Funktion der Scherrate untersucht. Nach Diskussion der grundlegenden Eigenschaften der Fließkurven führt eine asymptotische Entwicklung unter Zuhilfenahme des analytischen Ergebnisses für die Langzeitdynamik und des Zweiparameterskalengesetzes für den beta-Prozess auf einen analytischen Ausdruck für die Fließkurven, dem Lambda-Modell. Dieses Modell kann in drei Spezialfällen analytisch ausgewertet werden. Die Ergebnisse sind Potenzreihen mit nicht ganzzahligen Exponenten. Im allgemeinen Fall sind Näherungen durch numerisch motivierte Formeln notwendig. Für kleine positive Separationsparameter beschreibt das Lambda-Modell die Fließkurven für hinreichend kleine Scherraten korrekt. Für kleine negative Separationsparameter beschreibt das Lambda-Modell die Fließkurven in endlichen Fenstern für die Scherrate korrekt. Schließlich wird der bei negativen Separationsparametern und bei doppelt logarithmischer Auftragung der Fließkurven auftretender Wendepunkt untersucht. Die Approximation der Fließkurve durch die entsprechende Wendetangente führt zu einem effektiven Potenzgesetz.Analyse experimenteller DatenIm letzten Kapitel werden experimentelle Daten zum Fließverhalten und zur linearen Viskoelastizität einer thermosensitiven Kern-Mantel-Dispersion analysiert. Es wird ein erweitertes schematisches Modell eingeführt um die Fließkurven und das Speicher- und Verlustmodul simultan an die Daten anzupassen. Die allgemeinen Eigenschaften dieses erweiterten Modells und das Verfahren zur Datenanpassung werden ausfühlich erläutert. Bei niedrigen effektiven Packungsbrüchen und hinreichend großen Scherraten beziehungsweise Frequenzen, bei denen die Probe keine Kristallisation aufweist, können die Fließkurven und die dazugehörigen Module unter Verwendung des erweiterten schematischen Modells qualitativ und quantitativ korrekt an die experimentellen Daten angepasst werden.

The question about the existence of a structural glass transition in two dimensions is studied using mode coupling theory (MCT). We determine the explicit d-dependence of the memory functional of mode coupling for one-component systems. Applied to two dimensions we solve the MCT equations numerically for monodisperse hard discs. A dynamic glass transition is found at a critical packing fraction phi_c^{d=2} = 0.697 which is above phi_c^{d=3} = 0.516 by about 35%. phi^d_c scales approximately with phi^d_{\rm rcp} the value for random close packing, at least for d=2, 3. Quantities characterizing the local, cooperative 'cage motion' do not differ much for d=2 and d=3, and we e.g. find the Lindemann criterion for the localization length at the glass transition. The final relaxation obeys the superposition principle, collapsing remarkably well onto a Kohlrausch law. The d=2 MCT results are in qualitative agreement with existing results from MC and MD simulations. The mean squared displacements measured experimentally for a quasi-two-dimensional binary system of dipolar hard spheres can be described satisfactorily by MCT for monodisperse hard discs over four decades in time provided the experimental control parameter Gamma (which measures the strength of dipolar interactions) and the packing fraction phi are properly related to each other., Comment: 14 pages, 15 figures

A colloidal system of spheres interacting with both a deep and narrow attractive potential and a shallow long-ranged barrier exhibits a prepeak in the static structure factor. This peak can be related to an additional mesoscopic length scale of clusters and/or voids in the system. Simulation studies of this system have revealed that it vitrifies upon increasing the attraction into a gel-like solid at intermediate densities. The dynamics at the mesoscopic length scale corresponding to the prepeak represents the slowest mode in the system. Using mode coupling theory with all input directly taken from simulations, we reveal the mechanism for glassy arrest in the system at 40% packing fraction. The effects of the low-q peak and of polydispersity are considered in detail. We demonstrate that the local formation of physical bonds is the process whose slowing down causes arrest. It remains largely unaffected by the large-scale heterogeneities, and sets the clock for the slow cluster mode. Results from mode-coupling theory without adjustable parameters agree semi-quantitatively with the local density correlators but overestimate the lifetime of the mesoscopic structure (voids).

We consider the nonlinear rheology of dense colloidal suspensions under a time-dependent simple shear flow. Starting from the Smoluchowski equation for interacting Brownian particles advected by shearing (ignoring fluctuations in fluid velocity) we develop a formalism which enables the calculation of time-dependent, far-from-equilibrium averages. Taking shear-stress as an example we derive exactly a generalized Green-Kubo relation, and an equation of motion for the transient density correlator, involving a three-time memory function. Mode coupling approximations give a closed constitutive equation yielding the time-dependent stress for arbitrary shear rate history. We solve this equation numerically for the special case of a hard sphere glass subject to step-strain., 4 pages

Large scale molecular dynamics simulations are performed to study the steady state yielding dynamics of a well established simple glass. In contrast to the supercooled state, where the shear stress, $\sigma$, tends to zero at vanishing shear rate, $\gammadot$, a stress plateau forms in the glass which extends over about two decades in shear rate. This strongly suggests the existence of a finite dynamic yield stress in the glass, $\sigma^+ (T) \equiv \sigma(T; \gammadot \to 0) >0$. Furthermore, the temperature dependence of $\sigma^+$ suggests a yield stress discontinuity at the glass transition in agreement with recent theoretical predictions. We scrutinize and support this observation by testing explicitly for the assumptions (affine flow, absence of flow induced ordering) inherent in the theory. Also, a qualitative change of the flow curves enables us to bracket the glass transition temperature $T_c$ of the theory from above and (for the first time in simulations) {\it from below}. Furthermore, the structural relaxation time in the steady state behaves quite similar to the system viscosity at all studied shear rates and temperatures., Comment: 4 pages, 5 figures

The dynamical heterogeneities (DH) in non-ergodic states of an attractive colloidal glass are studied, as a function of the waiting time. Whereas the fluid states close to vitrify showed strong DH, the distribution of squared displacements of the glassy states studied here only present a tail of particles with increased mobility for the lower attraction strength at short waiting times. These particles are in the surface of the percolating cluster that comprises all of the particles, reminiscent of the fastest particles in the fluid. The quench deeper into the attractive glass is dynamically more homogeneous, in agreement with repulsive glasses (i.e. Lennard-Jones glass)., Comment: Proceedings of 5th IDMRCS - Lille 2005

The predictions of the mode-coupling theory of the glass transition (MCT) for the tagged-particle density-correlation functions and the mean-squared displacement curves are compared quantitatively and in detail to results from Newtonian- and Brownian-dynamics simulations of a polydisperse quasi-hard-sphere system close to the glass transition. After correcting for a 17% error in the dynamical length scale and for a smaller error in the transition density, good agreement is found over a wide range of wave numbers and up to five orders of magnitude in time. Deviations are found at the highest densities studied, and for small wave vectors and the mean-squared displacement. Possible error sources not related to MCT are discussed in detail, thereby identifying more clearly the issues arising from the MCT approximation itself. The range of applicability of MCT for the different types of short-time dynamics is established through asymptotic analyses of the relaxation curves, examining the wave-number and density-dependent characteristic parameters. Approximations made in the description of the equilibrium static structure are shown to have a remarkable effect on the predicted numerical value for the glass-transition density. Effects of small polydispersity are also investigated, and shown to be negligible., Comment: 20 pages, 23 figures

A first principles approach to the nonlinear flow of dense suspensions is presented which captures shear thinning of colloidal fluids and dynamical yielding of colloidal glasses. The advection of density fluctuations plays a central role, suppressing the caging of particles and speeding up structural relaxation. A mode coupling approach is developed to explore these effects., 4 pages, 2 figures; slightly corrected version; Phys. Rev. Lett., to be published (2002)

A mode-coupling theory for dense polymeric systems is developed which unifyingly incorporates the segmental cage effect relevant for structural slowing down and polymer chain conformational degrees of freedom. An ideal glass transition of polymer melts is predicted which becomes molecular-weight independent for large molecules. The theory provides a microscopic justification for the use of the Rouse theory in polymer melts, and the results for Rouse-mode correlators and mean-squared displacements are in good agreement with computer simulation results., Comment: 4 pages, 3 figures, Phys. Rev. Lett. in press

Um den Glasübergang (GT) zu studieren, wurde eine zweidimensionale (2D) binäre paramagnetische PMMA Kolloidmischung untersucht. Die Monolage bildete sich aus, weil die Teilchen an eine vollkommen flach eingestellte Wasser-Luft-Grenzfläche sedimentierten. Von den ca. 100000 Kolloiden wurden die zeitabhängigen Positionen von etwa 1000 Teilchen videomikroskopisch beobachtet. Mit einem von außen veränderbaren Magnetfeld B, senkrecht zur Wasser-Luft-Grenzfläche angelegt, wechselwirkten die Kolloide über ein repulsives 1/r^3 Dipol-Potential. Das System wird durch einen Wechselwirkungsparameter Gamma beschrieben, der proportional zu B^2/kT ist. Danach entspricht Gamma einer von B abhängigen inversen Systemtemperatur Tsys. - Für verschiedene Tsys wurden radiale Paar-Verteilungsfunktionen und mittlere quadratische Verschiebungen gemessen und mit denen anderer Glasbildner verglichen. Somit wurde das hier benutzte System als 2D Glas identifiziert. Änderungen der Teilchenanordnungen wurden mit 3-Punktkorrelationsfunktionen und mit Dreiecken der zueinander nächsten Nachbarteilchen betrachtet. Für die vier 3-Teilchenkombinationen der großen und kleinen Kolloide wurde jeweils ein lokal-dichteoptimiertes gleichschenkliges Dreieck, die sogenannten Elementardreiecke, gefunden. Für hohe Tsys und zunehmende Wartezeiten neigen gleiche Elementardreiecke dazu, sich zu Kristallit-Clustern zusammenzulagern, bzw. diese Kristallit-Cluster wiederum, Multi-Kristallit-Cluster zu bilden. Die 2D Packung der Dreiecke der zueinander nächsten Nachbarteilchen wurde zeitabhängig und für verschiedene Tsys untersucht. Die Beobachtungen führten auf das Konzept lokal-dichteoptimierter Kristallit-Cluster, das den GT als Perkolation lokal-dichteoptimierter Elementardreiecke erklärt, wobei das System über die lokal-dichteoptimierten Kristallit-Cluster stabilisiert wird. Zwischen den Kristallit-Clustern liegen ungeordnete, voneinander getrennte Gebiete, deren strukturelle Relaxationen eingefroren sind.

Using computer simulations, we identify the mechanisms causing aggregation and structural arrest of colloidal suspensions interacting with a short-ranged attraction at moderate and high densities. Two different non-ergodicity transitions are observed. As the density is increased, a glass transition takes place, driven by excluded volume effects. In contrast, at moderate densities, gelation is approached as the strength of the attraction increases. At high density and interaction strength, both transitions merge, and a logarithmic decay in the correlation function is observed. All of these features are correctly predicted by mode coupling theory.

The colloidal gel and glass transitions are investigated using the idealized mode coupling theory (MCT) for model systems characterized by short-range attractive interactions. Results are presented for the adhesive hard sphere and hard core attractive Yukawa systems. According to MCT, the former system shows a critical glass transition concentration that increases significantly with introduction of a weak attraction. For the latter attractive Yukawa system, MCT predicts low temperature nonergodic states that extend to the critical and subcritical region. Several features of the MCT nonergodicity transition in this system agree qualitatively with experimental observations on the colloidal gel transition, suggesting that the gel transition is caused by a low temperature extension of the glass transition. The range of the attraction is shown to govern the way the glass transition line traverses the phase diagram relative to the critical point, analogous to findings for the fluid-solid freezing transition., 11 pages, 7 figures; to be published in Phys. Rev. E (1 May 1999)

Depolarized light scattering spectra of orthoterphenyl showing the emergence of the structural relaxation below the oscillatory microscopic excitations are described by solutions of a schematic mode--coupling--theory model.

Within 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 a-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!#. @S1063-651X~98!09609-3#

Depolarized light-scattering spectra of propylene carbonate were obtained in the frequency range 0.2 GHz--4 THz at temperatures from 350 to 135 K. Analysis of the resulting susceptibility spectra revealed reasonable agreement with the predictions of the idealized mode coupling theory, yielding critical exponents a=0.29, b=0.50, and an exponent parameter \ensuremath{\lambda}=0.78\ifmmode\pm\else\textpm\fi{}0.05. A scaling analysis demonstrated critical slowing down of the scaling frequencies from both above and below ${\mathit{T}}_{\mathit{C}}$, with the scaling frequency extrapolating to zero at ${\mathit{T}}_{\mathit{C}}$=187\ifmmode\pm\else\textpm\fi{}5 K. The \ensuremath{\alpha}-relaxation peak was fit to a Kohlrausch function, which gave \ensuremath{\beta}=0.77\ifmmode\pm\else\textpm\fi{}0.05 for 210\ensuremath{\le}T\ensuremath{\le}350 K with no sign of systematic temperature dependence. An extended mode coupling theory analysis was also carried out which corroborated the results obtained with the idealized version. Polarized Brillouin spectra were also obtained, and were analyzed with a generalized hydrodynamics approach using low-frequency sound velocity values determined separately in an ultrasonics experiment. The results indicate that the Cole-Davidson function is not an adequate model for the structural relaxation due to the neglect of \ensuremath{\beta}-relaxation processes, so that this analysis cannot provide a meaningful estimate of ${\mathit{T}}_{\mathit{C}}$. Furthermore, the \ensuremath{\alpha}-relaxation time associated with Brillouin scattering was found to be about five times shorter than that probed by depolarized light scattering.

Recently reported light-scattering studies of CaKNO3 and Salol are reanalyzed, using the extended version of the mode-coupling theory of the liquid-glass transition including activated transport or hopping effects. Problems found in the original fits due to the neglect of hopping terms are largely corrected, and quantitative predictions for the susceptibility minimum below the crossover temperature Tc are found. The results are also shown to accurately explain the CaKNO3 neutron spin-echo data reported by Mezei [J. Non-Cryst. Solids 131 133, 317 (1991)].

The light scattering spectra of molecular liquids are derived within a generalized hydrodynamics. The wave vector and scattering angle dependences are given in the most general case and the change of the spectral features from liquid to solidlike is discussed without phenomenological model assumptions for (general) dielectric systems without long-ranged order. Exact microscopic expressions are derived for the frequency-dependent transport kernels, generalized thermodynamic derivatives and the background spectra., Comment: 12 pages

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., 19 pages, 12 figures, Phys. Rev. E, in print