A theoretical treatment of deeply supercooled liquids is difficult because their properties emerge from spatial inhomogeneities that are self-induced, transient, and nanoscopic. I use computer simulations to analyse self-induced static and dynamic heterogeneity in equilibrium systems approaching the experimental glass transition. I characterise the broad sample-to-sample fluctuations of salient dynamic and thermodynamic properties in elementary mesoscopic systems. Findings regarding local lifetimes and distributions of dynamic heterogeneity are in excellent agreement with recent single molecule studies. Surprisingly broad thermodynamic fluctuations are also found, which correlate well with dynamics fluctuations, thus providing a local test of the thermodynamic origin of slow dynamics.

Using x-ray tomography, we experimentally investigate granular packings subject to mechanical tapping for three types of beads with different friction coefficients. We validate the Edwards volume ensemble in these three-dimensional granular systems and establish a granular version of thermodynamic zeroth law. Within the Edwards framework, we also explicitly clarify how friction influences granular statistical mechanics by modifying the density of states, which allows us to determine the entropy as a function of packing fraction and friction. Additionally, we obtain a granular jamming phase diagram based on geometric coordination number and packing fraction.

Due to their unique structural and mechanical properties, randomly cross-linked polymer networks play an important role in many different fields, ranging from cellular biology to industrial processes. In order to elucidate how these properties are controlled by the physical details of the network (e.g., chain-length and end-to-end distributions), we generate disordered phantom networks with different cross-linker concentrations C and initial densities ρ init and evaluate their elastic properties. We find that the shear modulus computed at the same strand concentration for networks with the same C, which determines the number of chains and the chain-length distribution, depends strongly on the preparation protocol of the network, here controlled by ρ init. We rationalize this dependence by employing a generic stress−strain relation for polymer networks that does not rely on the specific form of the polymer end-to-end distance distribution. We find that the shear modulus of the networks is a nonmonotonic function of the density of elastically active strands, and that this behavior has a purely entropic origin. Our results show that if short chains are abundant, as it is always the case for randomly cross-linked polymer networks, the knowledge of the exact chain conformation distribution is essential for correctly predicting the elastic properties. Finally, we apply our theoretical approach to literature experimental data, qualitatively confirming our interpretations.

We use ab initio molecular dynamics simulations to investigate the properties of the dry surface of pure silicaand sodium silicate glasses. The surface layers are defined based on the atomic distributions along the direction(z direction) perpendicular to the surfaces. We show that these surfaces have a higher concentration of danglingbonds as well as two-membered (2M) rings than the bulk samples. Increasing the concentration of Na 2 O reducesthe proportion of structural defects. From the vibrational density of states, one concludes that 2M rings have aunique vibrational signature at a frequency ≈850 cm −1 , compatible with experimental findings. We also findthat, due to the presence of surfaces, the atomic vibration in the z direction is softer than for the two otherdirections. The electronic density of states shows clearly the differences between the surface and interior and wecan attribute these to specific structural units. Finally, the analysis of the electron localization function allows toget insight on the influence of local structure and the presence of Na on the nature of chemical bonding in theglasses.

We propose a novel model for a glass-forming liquid which allows to switch in a continuous manner froma standard three-dimensional liquid to a fully connected mean-field model. This is achieved by introducingk additional particle-particle interactions which thus augments the effective number of neighbors of eachparticle. Our computer simulations of this system show that the structure of the liquid does not changewith the introduction of these pseudo neighbours and by means of analytical calculations, we determine thestructural properties related to these additional neighbors. We show that the relaxation dynamics of thesystem slows down very quickly with increasing k and that the onset and the mode-coupling temperaturesincrease. The systems with high values of k follow the MCT power law behaviour for a larger temperaturerange compared to the ones with lower values of k. The dynamic susceptibility indicates that the dynamicheterogeneity decreases with increasing k whereas the non-Gaussian parameter is independent of it. Thus weconclude that with the increase in the number of pseudo neighbours the system becomes more mean-field like.By comparing our results with previous studies on mean-field like system we come to the conclusion that thedetails of how the mean-field limit is approached are important since they can lead to different dynamicalbehavior in this limit.