A theoretical perspective is provided on the glass transition in molecular liquids at thermal equilibrium, on the spatially heterogeneous and aging dynamics of disordered materials, and on the rheology of soft glassy materials. We start with a broad introduction to the field and emphasize its connections with other subjects and its relevance. The important role played by computer simulations in studying and understanding the dynamics of systems close to the glass transition at the molecular level is given. The recent progress on the subject of the spatially heterogeneous dynamics that characterizes structural relaxation in materials with slow dynamics is reviewed. The main theoretical approaches are presented describing the glass transition in supercooled liquids, focusing on theories that have a microscopic, statistical mechanics basis. We describe both successes and failures and critically assess the current status of each of these approaches. The physics of aging dynamics in disordered materials and the rheology of soft glassy materials are then discussed, and recent theoretical progress is described. For each section, an extensive overview is given of the most recent advances, but we also describe in some detail the important open problems that will occupy a central place in this field in the coming years.

Theoretical perspective on the glass transition and amorphous materials

Journal of Physics Condensed Matter: Preface

The elastic properties, elastic models and elastic perspectives of metallic glasses

We review the random first-order transition theory of the glass transition, emphasizing the experimental tests of the theory. Many distinct phenomena are quantitatively predicted or explained by the theory, both above and below the glass transition temperature Tg. These include the following: the viscosity catastrophe and heat-capacity jump at Tg, and their connection; the nonexponentiality of relaxations and their correlation with the fragility; dynamic heterogeneity in supercooled liquids owing to the mosaic structure; deviations from the Vogel-Fulcher law, connected with strings or fractal cooperative rearrangements; deviations from the Stokes-Einstein relation close to Tg; aging and its correlation with fragility; and the excess density of states at cryogenic temperatures owing to two-level tunneling systems and the Boson peak.

Theory of structural glasses and supercooled liquids.

Amorphous metal oxides are useful in optical, electronic and electrochemical devices. The bonding arrangement within these glasses largely determines their properties, yet it remains a challenge to manipulate their structures in a controlled manner. Recently, we developed synthetic protocols for incorporating nanocrystals that are covalently bonded into amorphous materials. This 'nanocrystal-in-glass' approach not only combines two functional components in one material, but also the covalent link enables us to manipulate the glass structure to change its properties. Here we illustrate the power of this approach by introducing tin-doped indium oxide nanocrystals into niobium oxide glass (NbOx), and realize a new amorphous structure as a consequence of linking it to the nanocrystals. The resulting material demonstrates a previously unrealized optical switching behaviour that will enable the dynamic control of solar radiation transmittance through windows. These transparent films can block near-infrared and visible light selectively and independently by varying the applied electrochemical voltage over a range of 2.5 volts. We also show that the reconstructed NbOx glass has superior properties-its optical contrast is enhanced fivefold and it has excellent electrochemical stability, with 96 per cent of charge capacity retained after 2,000 cycles.

https://www.pkusz.edu.cn/uploadfile/2013/0824/20130824114836947.pdf

Tunable near-infrared and visible-light transmittance in nanocrystal-in-glass composites

That the dynamical properties of a glass-forming liquid at high temperature are different from behaviour in the supercooled state has already been established. Numerical simulations now suggest that the static length scale over which spatial correlations exist also changes on approaching the glass transition. Supercooled liquids exhibit a pronounced slowdown of their dynamics on cooling1 without showing any obvious structural or thermodynamic changes2. Several theories relate this slowdown to increasing spatial correlations3,4,5,6. However, no sign of this is seen in standard static correlation functions, despite indirect evidence from considering specific heat7 and linear dielectric susceptibility8. Whereas the dynamic correlation function progressively becomes more non-exponential as the temperature is reduced, so far no similar signature has been found in static correlations that can distinguish qualitatively between a high-temperature and a deeply supercooled glass-forming liquid in equilibrium. Here, we show evidence of a qualitative thermodynamic signature that differentiates between the two. We show by numerical simulations with fixed boundary conditions that the influence of the boundary propagates into the bulk over increasing length scales on cooling. With the increase of this static correlation length, the influence of the boundary decays non-exponentially. Such long-range susceptibility to boundary conditions is expected within the random first-order theory4,9,10 (RFOT) of the glass transition. However, a quantitative account of our numerical results requires a generalization of RFOT, taking into account surface tension fluctuations between states.

Thermodynamic signature of growing amorphous order in glass-forming liquids

Glasses are amorphous solids, in the sense that they display elastic behaviour. In crystalline solids, elasticity is associated with phonons, which are quantized vibrational excitations. Phonon-like excitations also exist in glasses at very high (terahertz; 10(12) Hz) frequencies; surprisingly, these persist in the supercooled liquids. A universal feature of such amorphous systems is the boson peak: the vibrational density of states has an excess compared to the Debye squared-frequency law. Here we investigate the origin of this feature by studying the spectra of inherent structures (local minima of the potential energy) in a realistic glass model. We claim that the peak is the signature of a phase transition in the space of the stationary points of the energy, from a minima-dominated phase (with phonons) at low energy to a saddle-point-dominated phase (without phonons). The boson peak moves to lower frequencies on approaching the phonon-saddle transition, and its height diverges at the critical point. Our numerical results agree with the predictions of euclidean random matrix theory on the existence of a sharp phase transition between an amorphous elastic phase and a phonon-free one.

Phonon interpretation of the 'boson peak' in supercooled liquids

We use results derived in the framework of the replica approach to study the liquid-glass thermodynamic transition. The main results are derived without using replicas and applied to the study of the Lennard-Jones binary mixture introduced by Kob and Andersen. We find that there is a phase transition due to the entropy crisis. We compute both analytically and numerically the value of the phase transition point ${T}_{K}$ and the specific heat in the low temperature phase.

Thermodynamical Liquid-Glass Transition in a Lennard-Jones Binary Mixture

We compute the thermodynamic properties of the glass phase in a binary mixture of soft spheres. Our approach is a generalization to mixtures of the replica strategy, recently proposed by Mezard and Parisi, providing a first principle statistical mechanics computation of the thermodynamics of glasses. The method starts from the interatomic potentials, and translates the problem into the study of a molecular liquid. We compare our analytical predictions to numerical simulations, focusing onto the values of the thermodynamic transition temperature and the configurational entropy.

/pdf/thermodynamics-of-binary-mixture-glasses-50uawx6s7c.pdf

Thermodynamics of binary mixture glasses

According to the mosaic scenario, relaxation in supercooled liquids is ruled by two competing mechanisms: surface tension, opposing the creation of local excitations, and entropy, providing the drive to the configurational rearrangement of a given region. We test this scenario through numerical simulations well below the Mode Coupling temperature. For an equilibrated configuration, we freeze all the particles outside a sphere and study the thermodynamics of this sphere. The frozen environment acts as a pinning field. Measuring the overlap between the unpinned and pinned equilibrium configurations of the sphere, we can see whether it has switched to a different state. We do not find any clear evidence of the mosaic scenario. Rather, our results seem compatible with the existence of a single (liquid) state. However, we find evidence of a growing static correlation length, apparently unrelated to the mosaic one.

https://arxiv.org/pdf/cond-mat/0607817.pdf

Paolo Verrocchio

Papers

Thermodynamic signature of growing amorphous order in glass-forming liquids

Phonon interpretation of the 'boson peak' in supercooled liquids

Thermodynamical Liquid-Glass Transition in a Lennard-Jones Binary Mixture

Thermodynamics of binary mixture glasses

Mosaic multistate scenario versus one-state description of supercooled liquids.