Using molecular dynamics simulations, we study the static and dynamic properties of spherical nanoparticles (NPs) embedded in a disordered and polydisperse polymer network. Purely repulsive and weakly attractive polymer–NP interactions are considered. It is found that for both types of particles, the NP dynamics at intermediate and long times is controlled by the confinement parameter C = σN/λ, where σN is the NP diameter and λ is the dynamic localization length of the cross-links. Three dynamical regimes are identified: (i) for weak confinement (C ≲ 1), the NPs can freely diffuse through the mesh; (ii) for strong confinement (1 ≲ C ≲ 3), NPs proceed by means of activated hopping; (iii) for extreme confinement (C ≳ 3), the mean-squared displacement shows on intermediate time scales a quasi-plateau because the NPs are trapped by the mesh for very long times. Escaping from this local cage is a process that depends strongly on the local environment, thus giving rise to an extremely heterogeneous relaxation dynamics. The simulation data are compared with the two main theories for the diffusion process of NPs in gels. Both theories give a very good description of the C dependence of the NP diffusion constant but fail to reproduce the heterogeneous dynamics at intermediate time scales.

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.