One of the most important and interesting unsolved problems of science is the nature of glassy dynamics and the glass transition. It is quite an old problem, and starting from the early20th century there have been many efforts towards a sound understanding of the phenomenon. As a result, there are a number of theories in the field, which do not entirely contradict each other, but between which the connection is not entirely clear. In the last couple of decades or so, there has been significant progress and currently we do understand many facets of the problem. But a unified theoretical framework for the varied phenomena associated with glassiness is still lacking. Mode-coupling theory, an extreaordinarily popular approach, came from Götze and co-workers in the early eighties. The theory was originally developed to describe the two¬ step decay of the time-dependent correlation functions in a glassy fluid observed near the glass transition temperature(Tg). The theory went beyond that and made a number of quantitative predictions that can be tested in experiments and simulations. However, one of the drawback of the theory is its prediction of a strong ergodic to non-ergodic transition at a temperature TMCT; no such transition exists in real systems at the temperatures at which MCT predicts it. Consequently, the predictions of the theory like the power-law divergences of the transport quantities (e.g., viscosity and relaxation time) fail at low enough temperature and the theory can not be used below TMCT. It is well understood now that MCT is some sort of a mean-field theory of the real phenomenon, and in real systems the transition predicted by MCT is at best avoided due to finite dimensions and activated processes, neither of which is taken into account in standard MCT. Despite its draw backs, even the most severe critic of the theory will be impressed by its power and the predictions in a regime where it works. Even though the non-ergodic transition predicted by the theory is averted, the MCT mechanism for the increase of viscosity and relaxation time is actually at work in real systems. The status of MCT for glass transition is ,perhaps, similar to the Curie-Weiss theory of magnetic phase transition and it will require hard work and perhaps a conceptual breakthrough to go beyond this mean-field picture. Discussion of such a theoretical framework and its possible directions are, however, beyond the scope of this thesis. In the first part of this work, we have extended the mode coupling theory to three important physical situations: the properties of fluids under strong confinement, a sheared fluid and for the growth kinetics of glassy domains. In the second part, we have studied a different class of non equilibrium phenomenon in arrested systems, the fluctuation relations for yielding. In the first chapter, we talk about some general phenomenology of the glass transition problem and a few important concepts in the field. Then we briefly discuss the physical problems to be addressed in detail later on in the thesis followed by a brief account of some of the important existing theories in the field. This list is by no means exhaustive but is intended to give a general idea of the theoretical status of the problem. We conclude this chapter with a detailed derivation of MCT and its successes and failures. This derivation is supposed to serve as a reference for the details of the calculations in later chapters. The second chapter deals with a simple theory of an important problem of lubrication and dynamics of fluid at nanoscopic scales. When a fluid is confined between two smooth surfaces down to a few molecular layers and an normal force is applied on the upper surface, it is found that one layer of fluid gets squeezed out of the geometry at a time. The theory to explain this phenomenon came from Persson and Tosatti. However, due to a mathematical error, the in-plane viscosity term played no role in the original calculation. We re-do this calculation and show that the theory is actually more powerful than was suggested originally by its proponents. In the third chapter, we work out a detailed theory for the dynamics of fluid under strong planar confinement. This theory is based on mode-coupling theory. The walls in our theory enter in terms of an external potential that impose a static inhomogeneous background density. The interaction of the density fluctuation with this static background density makes the fluid sluggish. The theory explains how the fluid under strong confinement can undergo a glassy transition at a higher temperature or lower density than the corresponding bulk fluid as has been found in experiments and simulations. One of the interesting findings of the theory is the three-step relaxation that has also been found in a variety of other cases. The fourth chapter consists of a mode-coupling calculation of a sheared fluid through the microscopic approach first suggested by Zaccarelli et al[J. Phys.: Condens. Matter 14,2413(2002)]. The various assumptions of the theory are quite clear in this approach. The main aim of this calculation is to understand how FDR enters with in the theory. The only new result is the modified form of Yvon-Born-Green(YBG) equations for a sheared fluid. Then we extend the theory for the case of a confined fluid under steady shear and show that a confined fluid will show shear thinning at a much lower shear rate than the bulk fluid. When a system is quenched past a phase transition point, phase ordering kinetics begins. The properties of the system show “aging” with time, and the characteristic length scale of the quenched system grows as one waits. The analogous question for glasses has also been asked in the contexts of various numerical and experimental works. We formulate a theory in chapter five for rationalizing these findings. We find that MCT, surprisingly, offers an answer to this key question in glass forming liquids. The challenge of this theory is that care must be taken in using some equilibrium relations like the fluctuation-dissipation relation(FDR), which is one of the key steps in most of the derivations of MCT. We find that the qualitative, and some times even the quantitative, picture is in agreement with numerical findings. A similar calculation for the spin-glass case also predicts increase of the correlation volume with the waiting time, but with a smaller exponent than the structural glass case. We extended this theory to the case of shear and find that shear cuts off the growth of the length-scale of glassy correlations when the waiting time becomes of the order of the inverse shear rate. For the case of sheared fluid, if we take the limit of the infinite waiting time, the system will reach a steady state. Then, the resulting theory will describe a fluid in sheared steady state. The advantage of this theory over the existing mode-coupling theories for a sheared fluid is that FDR has not been used in any stage. This is an important development since the sheared steady state is driven away from equilibrium. Interestingly, the theory captures a suitably-defined effective temperature and gives results that are consistent with numerical experiments of steady state fluids(both glass and granular materials). We give the details of a theoretical model for jamming and large deviations in micellar gel in the sixth chapter. This theory is motivated by experiments. Through the main ingredient of the attachment-detachment kinetics and some simple rules for the dynamics, the theory is capable of capturing all the experimental findings. The novel prediction of this work is that in a certain parameter range, the fluctuation relations may be violated although the large deviation function exists. We argue that a wider class of physical systems can be understood in terms of the present theory. In the final chapter, we summarize the problems studied in this thesis and point out some future directions.

De récentes études expérimentales de la dynamique de colloïdes illuminés par une figure d'interférence optique aléatoire (tavelures ou speckle) ont montré l'existence de phénomènes de sous-diffusion, de piégeage, ou de ségrégation dans le cas de mélanges, sous l'effet de cet environnement désordonné. L'objet de ce travail de doctorat est d'approfondir la compréhension de ces phénomènes par une étude théorique. Dans ce but, une version de la théorie de couplage de modes (MCT), initialement développée pour les fluides confinés dans des solides poreux désordonnés, a été appliquée au cas d'un fluide plongé dans un potentiel aléatoire gaussien de covariance gaussienne. La résolution numérique des équations asymptotiques de cette théorie a permis la construction de diagrammes d'état, lesquels reproduisent, par exemple, le comportement réentrant non trivial de la diffusivité observé dans les expériences, dont une interprétation physique simple est proposée.Les résultats suggèrent en outre une forte dépendance de la dynamique du système par rapport à la longueur de corrélation du désordre. Une étude détaillée de la relaxation du fluide a été effectuée, dans le but d'apporter une compréhension de la dynamique à toutes les échelles de temps. En parallèle, il a été montré que de nombreuses approximations classiques utilisées dans le calcul des propriétés structurales des fluides conduisent à des résultats non physiques dans le cas présent.Finalement, un programme de simulation Monte Carlo a été développé, et les premiers résultats sont comparés à la théorie et aux expériences. / Recent experimental studies of the dynamics of colloids beamed by a random light pattern (speckle) showed the existence of subdiffusion, trapping, or mixture separation phenomena, under the action of that disordered environment.To this end, a version of the Mode Coupling Theory (MCT), initially developed for fluids in confinement in sol id porous matrices has been applied to the case of a fluid plunged in a random Gaussian potential with a Gaussian correlation function.The aim of this PhD work is to further improve the understanding of these phenomena by the addition of a theoretical study.The numerical resolution of the asymptotic equations of this theory leads to the construction o phase diagrams, which reproduce for example the non trivial reentrent behaviour of the diffusivity, observed in related experiments, for which a physical interpretation is proposed. Furthermore, results suggest a strong depend ence of the dynamics on the disorder correlation length. A detailed study of the relaxation of the fluid has been made, in order to bring an understandin( of the dynamics at ali timescales. Simultaneously, it has been showed that a number of common approximations used in the calculation of the structural properties of fluids lead in the present case to non-physical results. Finally, a Monte-Carlo simulation program has been developed, and the first results are compared to theory and experiments.

No description available.

La théorie de couplage de mode (MCT) est l'une des méthodes les plus utilisées pour étudier les transitions vitreuses dans les fluides classiques. Ses prédictions sont en général en accord semi quantitatif avec les simulations. Sa mise en oeuvre nécessite la détermination de la structure statique, généralement par résolution des équations d'Orsntein-Zernike avec une fermeture adéquate. Partant de fermetures utilisant des fonctions « bridges » déduites de la fonctionnelle de référence du mélange de sphères dures, notre travail a consisté d'abord à étudier l'influence de la qualité de cette structure statique sur les prédictions relatives aux états non ergodiques dans des mélanges binaires dissymétriques. Nous avons ensuite considéré les résultats de la théorie du couplage de modes dans sa version naïf (NMCT ) et complète, afin d'analyser les mécanismes d'arrêt, les comparer au fluide effectif et aux approches stochastiques (équations de Langevin généralisées). Enfin, nous proposons une version pragmatique de cette méthode qui fournit des prédictions en meilleur accord quantitatif avec les résultats des simulations pour une variété de potentiels d'interaction / The mode coupling theory (MCT) is one of the most widely used methods for studying the glass transition in classical fluids. Its predictions are usually in semi-quantitative agreement with simulation. Its implementation requires the determination of the static structure usually from the Ornstein-Zernike equations with a suitable closure. Starting from closures that use bridge functions deduced from the hard-sphere reference functional, our work consisted first in studying the influence of the quality of this static structure on the predictions concerning the non-ergodic states in asymmetric binary mixtures. We next considered the results of the mode coupling theory in its naive and full versions, in order to analyze the arrest mechanisms and compare them to the effective fluid and the stochastic approaches (generalized Langevin equations). Finally, we propose a pragmatic version of this method that provides predictions in better quantitative agreement with simulations for a variety of interaction potentials

In this thesis, theoretical and computer simulation studies of vibrational phase relaxation in various molecular liquids are presented. That includes liquid nitrogen, both along the coexistence line and the critical isochore, binary liquid mixture and liquid water. The focus of the thesis is to understand the dependence of the vibrational relaxation on the density, temperature, composition and the role of different interactions among the molecules. The density fluctuation of the solute particles in a solvent is studied systematically, where the computer simulation results are compared with the mode coupling theory (MCT). The classical density functional theory (DFT) is used to study the vibrational relaxation dynamics in molecular liquids with an aim to understand the heterogeneous nature of the dynamics commonly observed in experiments. Chapter 1 contains a brief overview of the earlier relevant theories, their successes and shortcomings in the light of the problems discussed in this thesis. This chapter discusses mainly the basic features of the vibrational dynamics of molecular liquids and portrays some of the theoretical frameworks and formalisms which are widely recognized to have contributed to our present understanding. Vibrational dephasing of nitrogen molecules is known to show highly interesting anomalies near its gas–liquid critical point. In Chapter 2, we present the results of extensive computer simulation studies and theoretical analysis of the vibrational phase relaxation of nitrogen molecules both along the critical isochore and the gas–liquid coexistence line. The simulation includes the different contributions (density (ρ), vibration–rotation (VR), and resonant transfer (Rs)) and their cross–correlations. Following Everitt and Skinner, we have included the vibrational coordinate (q) dependence of the inter–atomic potential, which is found to have an important contribution. The simulated results are in good agreement with the experiments. The linewidth (directly proportional to the rate of the vibrational phase relaxation) is found to have a lambda shaped temperature dependence near the critical point. As observed in the experimental studies, the calculated lineshape becomes Gaussian–like as the critical temperature (Tc) is approached while being Lorentzian–like at the temperatures away from Tc. Both the present simulation and a mode coupling theory (MCT) analysis show that the slow decay of the enhanced density fluctuations near the critical point (CP), probed at the sub–picosecond timescales by the vibrational frequency modulation, and an enhanced vibration–rotation coupling, are the main causes of the observed anomalies. Dephasing time (тv) and the root mean square frequency fluctuation (Δ) in the supercritical region are calculated. The principal results are: 1. a crossover from a Lorentzian–like to a Gaussian–like lineshape is observed as the critical point is approached along the critical isochore, 2. the root mean square frequency fluctuation shows a non–monotonic dependence on the temperature along the critical isochore, 3. the temperature dependent linewidth shows a divergence–like (λ–shaped) behavior along the coexistence line and the critical isochore. It is found that the linewidth calculated from the time integral of the normal coordinate time correlation function (CQ(t)) is in good agreement with the known experimental results. The origin of the anomalous temperature dependence of linewidth can be traced to simultaneous effects of several factors, (i) the enhancement of the negative cross–correlations of ρ with VR and Rs and (ii) the large density fluctuations as the critical point (CP) is approached. Due to the negative cross–correlations of ρ with VR and Rs the total decay becomes faster (correlation times are in the femtosecond scale). The reason for the negative cross–correlation between ρ and VR is explored in detail. A mode coupling theory (MCT) analysis shows a slow decay of the enhanced density fluctuations near the critical point. The MCT analysis demonstrates that the large enhancement of VR–coupling near CP may arise from a non–Gaussian behavior of the equilibrium density fluctuations. This enters through a non–zero value of the triplet direct correlation function. Many of the complex systems found in nature and used routinely in industry are multi–component systems. In particular, binary mixtures are highly non–ideal and play an important role in the industry. The dynamic properties are strongly influenced by composition fluctuations which are absent in the one component liquids. In Chapter 3, isothermal–isobaric (NPT) ensemble molecular dynamics simulation studies of vibrational phase relaxation (VPR) in a model system are presented. The model considers strong attractive interaction between the dissimilar species to prevent phase separation. The model reproduces the experimentally observed non–monotonic, nearly symmetric, composition dependence of the dephasing rate. In addition, several other experimentally observed features, such as the maximum of the frequency modulation correlation time (т c) at a mole fraction near 0.5 and the maximum rate enhancement by a factor of about 3 above the pure component value, are also reproduced. The product of the mean square frequency modulation ((Δω2(0))) with тc indicates that the present model is in the intermediate regime of the inhomogeneous broadening. The non–monotonic composition (χ) dependence of тv is found to be primarily due to the non–monotonic χ dependence of тc, rather than due to a similar dependence in the amplitude of (Δω2(0)). The probability distribution of Δω shows a markedly non–Gaussian behavior at intermediate composition (χ - 0.5). We have also calculated the composition dependence of the viscosity (η∗) in order to explore the correlation between the viscosity with that of тv and тc. It is found that both the correlation times essentially follow the nature of the composition dependence of the viscosity. A mode coupling theory (MCT) analysis is presented to include the effects of the composition fluctuations in binary mixture. Water is an interesting and attractive object for research, not only because of its great importance in life processes but also due to its unusual and intriguing properties. Most of the anomalous properties of water are related to the presence of a three–dimensional network of hydrogen bonds, which is constantly changing at ultrafast, sub–picosecond timescales. Vibrational spectroscopy provides the means to study the dynamics of processes involving only certain chemical bonds. The dynamics of hydrogen bonding can be probed via its reflection on molecular vibrations, e.g., the stretching vibrational mode of the O–H bond. Recently developed femtosecond infrared vibrational spectroscopy has proved to be valuable to study water dynamics because of its unique temporal resolution. Recent studies have shown that the vibrational relaxation of the O–H stretch of HDO occurs at an extremely fast timescale with time constant being less than 100 femtosecond. Here, in Chapter 4, we investigate the origin of this ultrafast vibrational dephasing using computer simulation and appropriate theoretical analysis. In addition to the usual fast vibrational dynamics due to the hydrogen bonding excitations, we find two additional reasons: (a) the large amplitude of angular jumps of the water molecules (with 30–40 fs time intervals) provide large contribution to the mean square vibrational frequency and (b) the projected force along the O–H bond due to the solvent molecules, on the oxygen (FO(t)) and hydrogen (FH (t)) atoms of the O–H bond exhibit a large negative cross–correlation (NCC) between FO(t) and FH (t). This NCC is shown to be partly responsible for a weak, non–Arrhenius temperature dependence of the relaxation rate. In the concluding note, Chapter 5 starts with a brief summary of the outcome of this thesis and ends up with suggestions of a few relevant problems that may prove worthwhile to be addressed in the future.

Comprendre l’origine microscopique du ralentissement de la dynamique au voisinage de la transition vitreuse reste l’un des problèmes fondamentaux de la physique de la matière condensée. Au cours de ce travail, nous introduisons un nouveau modèle de liquide, appelé liquide de Voronoï, et dont les interactions sont directement reliées aux propriétés géométriques des tessellations de Voronoï. Pour cette classe de liquides, les interactions sont à plusieurs corps et agissent de telle sorte que le système est toujours sous tension tout en restant stable. Le but de ce travail est d’étudier un mélange binaire du liquide de Voronoï et de voir de quelles façons ces interactions exotiques affectent le scénario habituel de la transition vitreuse. Tout au long de ce travail, nous caractérisons le liquide de Voronoï bidisperse théoriquement et par le biais des simulations numériques. Nous proposons également des comparaisons avec des liquides de Lennard-Jones surfondus bien décrit dans la littérature. / Understanding the origin of the important slowing down of the dynamics near glass transition is still one of the remaining fundamental problems of condensed matter physics. During this work we introduced a brand-new model of liquids named Voronoi liquid, whose interactions are directly related to the geometrical properties of Voronoi tessellations. For these class of liquids interactions are intrinsically manybody and act in such a way that the liquid is always under tension but remains stable. The aim of this work is to use a binary mixture of the Voronoi liquid to see to what extend these exotic interactions may affect the classical scenario of glass transition. Throughout this work we characterize theoretically and by mean of numerical simulation the bidisperse Voronoi liquid. Comparisons with well-known Lennard-Jones glass formers are systematically performed.

À l'approche de la transition vitreuse les fondus de polymères montrent une augmentation importante de la viscosité de plusieurs ordres de grandeur. Le but de cette étude est d'acquérir une compréhension plus profonde des propriétés viscoélastiques des fondus de polymères vitrifiables. Les polymères sont modélisés comme des chaînes flexibles en utilisant un modèle de bille-ressort. Les propriétés dynamiques sont analysées dans le cadre de la théorie de couplage de mode idéale. Nous constatons que la température critique de couplage de mode varie avec l'inverse de la longueur de chaîne. En étudiant la fonction de relaxation de cisaillement, nous constatons que les processus de relaxation polymériques, ne sont pas modifiés, mais décalés vers des temps plus importants en approchant la transition vitreuse. / Polymer melts show a remarkable increase of their viscosity by many orders of magnitude on approaching the glass transition. The aim of this study is to gain a deeper insight into the viscoelastic properties of glass forming polymer melts. The polymers are modeled as flexible chains using a bead-spring model. The dynamic properties are analyzed in the framework of the ideal mode-coupling theory. We find that the critical temperature of the ideal mode-coupling theory scales with the reciprocal chain length. By studying the shear relaxation function we find that the polymer relaxation processes are not altered but shifted to later times in the approach of the glass transition.