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An increase in the co-operativity in the motion of particles and a growth of a suitably defined dynamical correlation length seem to be generic features exhibited by all liquids upon supercooling. These features have been observed both in experiments and in numerical simulations of glass-forming liquids. Specially designed NMR experiments have estimated that the rough magnitude of this correlation length is of the order of a few nanometers near the glass transition. Simulations also predict that there are regions in the system which are more liquid-like than other regions. A complete theoretical understanding of this behaviour is not available at present. In recent calculations, Berthier, Biroli and coworkers [1, 2] extended the simple mode coupling theory (MCT) to incorporate the effects of dynamic heterogeneity and predicted the existence of a growing dynamical correlation length associated with the cooperativity of the dynamics. MCT also predicts a power law divergence of different dynamical quantities at the mode coupling temperature and at temperatures somewhat higher than the mode coupling temperature, these predictions are found to be consistent with experimental and simulation results. The system size dependence of these quantities should exhibit finite size scaling (FSS) similar to that observed near a continuous phase transition in the temperature range where they show power law growth. Hence we have used the method of finite size scaling in the context of the dynamics of supercooled liquids. In chapter 2, we present the results of extensive molecular dynamics simulations of a model glass forming liquid and extract a dynamical correlation length ξ associated with dynamic heterogeneity by performing a detailed finite size scaling analysis of a four-point dynamic susceptibility χ4(t) [3] and the associated Binder cumulant. We find that although these quantities show the “normal” finite size scaling behaviour expected for a system with a growing correlation length, the relaxation time τ does not. Thus glassy dynamics can not be fully understood in terms of “standard” critical phenomena. Inspired by the success of the empirical Adam-Gibbs relation [4] which relates dynamics with the configurational entropy, we have calculated the configurational entropy for different system sizes and temperatures to explain the nontrivial scaling behaviour of the relaxation time. We find that the behaviour of the relaxation time τ can be explained in terms of the Adam-Gibbs relation [4] for all temperatures and system sizes. This observation raises serious questions about the validity of the mode coupling theory which does not include the effects of the potential energy (or free energy) landscape on the dynamics. On the other hand, in the “random first order transition” theory (RFOT), introduced by Wolynes and coworkers [5], the configurational entropy plays a central role in determining the dynamics. So we also tried to explain our simulation results in terms of RFOT. However, this interpretation has the drawback that the value of one of the exponents of this theory extracted from our numerical results does not satisfy an expected physical bound, and there is no clear explanation for the obtained values of other exponents. Thus we find puzzling values for the exponents relevant to the applicability of RFOT, which are in need of explanation. This can be due to the fact that RFOT focuses only near the glass transition, while all our simulation results are for temperatures far above the glass transition temperature (actually, above the mode coupling temperature). Interestingly, results similar to ours were obtained in a recent analysis [6] of experimental data near the laboratory glass transition, on a large class of glass-forming materials. Thus right now we do not have any theory which can explain our simulation data consistently from all perspectives. There have been some attempts to extend the RFOT analysis to temperatures above the mode coupling temperature [7, 8] and to estimate a length scale associated with the configurational entropy at such temperatures. We compare our results with the predictions arising from these analyses. In chapter 3, we present simulation results that suggest that finite size scaling analysis is probably the only feasible method for obtaining reliable estimates of the dynamical correlation length for supercooled liquids. As mentioned before, although there exists a growing correlation length, the behaviour of all measured quantities (specifically, the relaxation time) is not in accordance with the behaviour expected in “standard” critical phenomena. So one might suspect the results for the correlation length extracted from the scaling analysis. To find out whether the results obtained by doing finite size scaling are correct, we have done simulations of very large system sizes for the same model glass forming liquid. In earlier studies, the correlation length has been extracted from the wave vector dependence of the dynamic susceptibility in the limit of zero wave vector, but to estimate the correlation length with reasonable accuracy one needs data in the small wave vector range. This implies that one needs to simulate very large systems. But as far as we know, in all previous studies typical system sizes of the order of 10, 000 particles have been used to do this analysis. In this chapter we show by comparing results for systems of 28, 000 and 350, 000 particles that these previous estimates are not reliable. We also show that one needs to simulate systems with at least a million particles to estimate the correlation length correctly near the mode coupling temperature and this size increases with decreasing temperature. We compare the correlation length obtained by analyzing the wave vector dependence of the dynamic susceptibility for a 350, 000particle system with the results obtained from the finite size scaling analysis. We were only able to compare the results in the high temperature range due to obvious reasons. However the agreement in the high temperature range shows that the finite size scaling analysis is robust and also establishes the fact that finite size scaling is the only practical method to extract reliable correlation lengths in supercooled liquids. In chapter 4, we present a free energy landscape analysis of dynamic heterogeneity for a monodisperse hard sphere system. The importance of the potential energy landscape for particles interacting with soft potentials is well known in the glass community from the work of Sastry et al. [9] and others, but the hard sphere system which does not have any well defined potential energy landscape also exhibits similar slow dynamics in the high density limit. Thus it is not clear how to treat the hard sphere systems within the same energy landscape formalism. Dasgupta et al. [10, 11, 12, 13, 14, 15] showed that one can explain the slow dynamics of these hard core systems in term of a free energy landscape picture. They and other researchers showed that these system have many aperiodic local minima in its free energy landscape, with free energy lower than that of the liquid. Using the Ramkrishnan-Yussouff free energy functional, we have performed multi parameter variational minimizations to map out the detailed density distribution of glassy free energy minima. We found that the distribution of the widths of local density peaks at glassy minima is spatially heterogeneous. By performing hard sphere event driven molecular dynamics simulation, we show that there exists strong correlation between these density inhomogeneity and the local Debye-Waller factor which provides a measure of the dynamic heterogeneity observed in simulations. This result unifies the system of hard core particles with the other soft core particles in terms of a landscapebased description of dynamic heterogeneity. In chapter 5, we extend the same free energy analysis to a polydisperse system and show that there is a critical polydispersity beyond which the crystal state is not stable and glassy states are thermodynamically stable. We also found a reentrant behaviour in the liquid-solid phase transition within this free-energy based formalism. These results are in qualitative agreement with experimental observations for colloidal systems.

Water is “the matrix of life” for its fascinating properties. The well-known simple water molecule consists of one oxygen atom and two hydrogen atoms, covering most of planet earth’ssurface. It is the most studied element in science; however, its properties are still not fully understood. Another essential building block of life is proteins, which manifest naturally in aqueous environments. The protein activity is controlled by the protein folding process that is dependent on the surrounding environment. It is hypothesized that the hydrogen bond network of water plays an important role in the folding process. Here, we investigate the protein lysozyme in liquid water as well as in the crystalline state ice Ih, exploring various temperatures, using FT-IR and XRD. Our main finding is that a transition occurs at approximately T=210 K, indicative of the hypothesised protein dynamic “glass” transitionobserved by previous studies in supercooled water at similar temperatures.

Desenvolvemos dois modelos estatísticos para água, nos quais diferentes aspectos de sua estrutura são considerados. O modelo geométrico permite diferentes números de coordenação. Em uma aproximação de campo médio mostramos que sob pressão o modelo apresenta linha de coexistência entre fases de baixa e alta densidade, e ponto crítico. A entropia das ligações de hidrogênio tem papel fundamental na definição da inclinação da linha de coexistência. O comportamento do modelo pode estar realcionado como segundo ponto crítico da água super resfriada e com transições líquido-líquido em geral.O modelo da água quadrada é uma versão térmica do modelo do gelo, no qual considera-se a direcionalidade das ligações de hidrogênio. O modelo foi estudado na rede de Bethe e através de simulações de Monte Carlo em três situações diferentes: para a água pura e na presença de solutos polares e apolares. A água quadrada pura não apresenta transição de fase. No modelo para solvente com solutos apolares, medidas de frequência relativa de ligações e do tempo de correlação mostram que o modelo apresenta estruturação da camada de hidratação. Medidas de correlação temporal no modelo de Ising mostram comportamento oposto. Em um estudo preliminar para uma solução com solutos que realizam ligações de hidrogênio não conseguimos encontrar diagramas de coexistência com círculo fechado, para o conjunto de parâmetros utilizados, possivelmente devido à ausência de buracos. / We have developed two statistical models for water in which different features of water structure are considered. In the geometrical model different coordination numbers are present and the model allows for translational disorder. A mean-field treatment shows that under pressure the model exhibits phases of different densities and a coexistence line ending in a critical point. Entropy of the hydrogen network plays an essential role in defining the slope of the coexistence line. The model behavior might be related with the second critical point in supercooled water and to liquid-liquid transitions in general. The square water model is a thermal version of the ice model, and takes into account the directionality of the hydrogen bonds. The model was studied on a Bethe lattice and through Monte Carlo simulations, for three different situations: as pure water and in the presence of polar and apolar solutes. Pure square water does not present a phase transition. In the presence of apolar solutes, first shell square water presents ordering, as shown from comparison of relative frequency of bonds, as well as from study of time correlations. The latter was shown to present opposite behavior in case of an Ising system. In a preliminary study for a solution of hydrogen bonding solutes we were unable to find a closed loop for the sets of parameters chosen. Vacancies might need to be included.

Lorsqu’un liquide est refroidit suffisamment vite, la cristallisation peut être évitée. On a alors un liquide surfondu dont le temps de relaxation augmente fortement quand la température diminue vers la température de transition vitreuse Tg. En-dessous de Tg, le systèmeest dans l’état vitreux. Il vieillit : son temps de relaxation augmente au cours du temps. L’existence d’une longueur de corrélation croissante associée au ralentissement de la dynamique des liquides surfondus (ou des verres) est une des grandes questions toujours ouvertes dans la physique de la transition vitreuse. Des arguments théoriques très généraux ont montré que la mesure de la susceptibilité alternative non linéaire d’ordre trois des liquides surfondus (ou des verres) donnait directement accès à la longueur de corrélation dynamique. Nous avons mis au point une expérience à haute sensibilité permettant d’accéder à deux susceptibilités diélectriques non linéaires d’ordre trois près de Tg. Nos résultats obtenus sur du glycrol surfondu sont quantitativement en très bon accord avec les prédictions théoriques. Ils montrent que la longueur de corrélation dynamique augmente lorsque T diminue vers Tg. En dessous de Tg, l’étude du vieillissement d’une des susceptibilités non linéaires nous a permis de mettre en évidence que la longueur de corrélation dynamique augmente au cours du temps. Ces résultats renforcent le scénario selon lequel la transition vitreuse serait liée à un point critique sous-jacent, ce qui expliquerait l’ubiquité du comportement vitreux dans la nature. / Upon fast enough cooling, a liquid avoids crystallization and enters in a supercooled state. The relaxation time of this supercooled liquid increases extremely fast when the temperature decreases towards the glass transition temperature Tg. Below Tg, the system is in the glassy state. It ages : the relaxation time increases with time. The existence of a growing correlation length associated to the slowing down of supercooled liquids (or of glasses) is one of the main open issues in the physics of the glass transition. On very general theoretical arguments, it has been shown that the third order a.c. nonlinear susceptibility around Tg gives direct access to the dynamical correlation length. We have developped a high sensibility experiment to measure, close to Tg, two nonlinear dielectric susceptibilities of the third order. Our results performed on supercooled glycerol are quantitatively in very good agreement with theoretical predictions. They show that the dynamical correlation length increases when T decreases towards Tg. Below Tg, aging experiments of one of the nonlinear susceptibilities reveal that the dynamical correlation length increases with time. These results clearly evidence the collective character of glassy dynamics and reinforce the picture of an underlying critical point, which would explain the ubiquity of the glass transition in Nature.

The understanding of complex condensed matter systems is an area of intense study. In this thesis, some properties of simple liquids with strong preference for tetrahedral local ordering are explored. These liquids are amenable to supercooling, and give complex crystalline structures on eventual crystallisation. All liquids studied are simple, monatomic and are similar to real metallic liquids. The vibrational density of states of a glass created in simulation is calculated. We show a correspondence between the vibrational properties of the crystal and the glass, indicating that the vibrational spectra of crystals can be used to understand the more complex vibrational spectra of the glass of the same substance. The dynamics of supercooled liquids is investigated using a previously not implemented comprehensive measure of structural relaxation. This new measure decays more slowly in the deeply supercooled domain than the commonly used measure. A new atomic model for octagonal quasicrystals is presented. The model is based on findings from a molecular dynamics simulation that resulted in 45˚ twinned β-Mn. A decoration is derived from the β-Mn unit cell and the unit cell of the intermediate structure found at the twinning interface. Extensive simulations are used to explore the phase diagram of a liquid at low densities. The resulting phase diagram shows a spinodal line and a phase coexistence region between a liquid and a crystalline phase ending in a critical point. This contradicts the old conclusion of the Landau theory -- that continuous transitions between liquids and crystals cannot exist The same liquid is explored at higher densities. Upon cooling the liquid performs a first order liquid-liquid phase transition. The low temperature liquid is shown to be strong and to have very good glass forming abilities. This result offers new insights into fragile to strong transitions and suggests the possibility of a good metallic glass former. / At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 2: Submitted. Paper 3: In progress.

Phase transitions and other intrinsic properties (shape, size, architecture) of molecularly structured aerosol particles are important for understanding their role in planetary atmospheres and for technical applications. By combining bath gas cooling with time resolved mid-infrared spectroscopy and modeling, information is obtained on dynamic processes and intrinsic properties of fluoroform and ethane aerosol particles. The distinct infrared spectral features of fluoroform aerosol particles make it a particularly suitable model system. Homogeneous crystallization rates of the sub-micron sized aerosol particles are determined (JV = 10⁸ - 10¹⁰ cm-³s-¹ or JS = 10³ – 10⁵ cm-²s-¹ at a temperature of T = 78 K), and the controversial question regarding volume versus surface nucleation in freezing aerosols is addressed. It is demonstrated that current state of the art measurements of droplet ensembles cannot distinguish between the two mechanisms due to inherent experimental uncertainties. The evolution of particle shape from spherical supercooled droplets to cube-like crystalline particles and eventually to elongated crystalline particles is recorded and analyzed in detail with the help of vibrational exciton model calculations. Phase behaviour of pure ethane aerosols and ethane aerosols formed in the presence of other ice nuclei under conditions mimicking Titan’s atmosphere provide evidence for the formation of supercooled liquid ethane aerosol droplets, which subsequently crystallize. The observed homogeneous freezing rates (JV = 10⁷ – 10⁹ cm-³s-¹) imply that supercooled ethane could play a similar role in ethane rich regions of Titan’s atmosphere as supercooled water does in the Earth’s atmosphere.

Phase transitions and other intrinsic properties (shape, size, architecture) of molecularly structured aerosol particles are important for understanding their role in planetary atmospheres and for technical applications. By combining bath gas cooling with time resolved mid-infrared spectroscopy and modeling, information is obtained on dynamic processes and intrinsic properties of fluoroform and ethane aerosol particles. The distinct infrared spectral features of fluoroform aerosol particles make it a particularly suitable model system. Homogeneous crystallization rates of the sub-micron sized aerosol particles are determined (JV = 10⁸ - 10¹⁰ cm-³s-¹ or JS = 10³ – 10⁵ cm-²s-¹ at a temperature of T = 78 K), and the controversial question regarding volume versus surface nucleation in freezing aerosols is addressed. It is demonstrated that current state of the art measurements of droplet ensembles cannot distinguish between the two mechanisms due to inherent experimental uncertainties. The evolution of particle shape from spherical supercooled droplets to cube-like crystalline particles and eventually to elongated crystalline particles is recorded and analyzed in detail with the help of vibrational exciton model calculations. Phase behaviour of pure ethane aerosols and ethane aerosols formed in the presence of other ice nuclei under conditions mimicking Titan’s atmosphere provide evidence for the formation of supercooled liquid ethane aerosol droplets, which subsequently crystallize. The observed homogeneous freezing rates (JV = 10⁷ – 10⁹ cm-³s-¹) imply that supercooled ethane could play a similar role in ethane rich regions of Titan’s atmosphere as supercooled water does in the Earth’s atmosphere.

A model is proposed to predict the heat spreading behaviour experienced by laminate materials when heated over only a part of the domain, which is broken up into two regions, known as the heated and fin regions. The 2D, steady-state, two-region fin model is unique in its treatment of multilayer conduction heat transfer, giving the exact solution in the heat-spreading layer only, in both Cartesian and cylindrical coordinates. The experimentally and numerically validated two region fin model can help designers to assess improved heat transfer rates for laminate pouches for use to encapsulate supercooled salt hydrate phase change materials for long-term heat storage. Waste aseptic cartons (e.g. Tetra Brik) are a potentially useful resource for making laminate heat storage pouches since value-added end-uses are largely absent in Canada and in many other countries. The model is also useful for assessing improved temperature uniformity in heat spreading devices with applied heat fluxes.