Links between dynamical Frenkel defects and collective diffusion of fluorides in β-PbF2 are explored using Born–Oppenheimer molecular dynamics. The calculated self-diffusion coefficient and ionic conductivity are 3.2 × 10−5 cm2 s−1 and 2.4 Ω−1 cm−1 at 1000 K in excellent agreement with pulsed field gradient and conductivity measurements. The calculated ratio of the tracer-diffusion coefficient and the conductivity-diffusion coefficient (the Haven ratio) is slightly less than unity (about 0.85), which in previous work has been interpreted as providing evidence against collective ‘multi-ion’ diffusion. By contrast, our molecular dynamics simulations show that fluoride diffusion is highly collective. Analysis of different mechanisms shows a preference for direct collinear ‘kick-out’ chains where a fluoride enters an occupied tetrahedral hole/cavity and pushes the resident fluoride out of its cavity. Jumps into an occupied cavity leave behind a vacancy, thereby forming dynamic Frenkel defects which trigger a chain of migrating fluorides assisted by local relaxations of the lead ions to accommodate these chains. The calculated lifetime of the Frenkel defects and the collective chains is approximately 1 ps in good agreement with that found from neutron diffraction.

Silica is known as the archetypal strong liquid, exhibiting an Arrhenius viscosity curve with a high glass transition temperature and constant activation energy. However, given the ideally isostatic nature of the silica network, the presence of even a small concentration of defects can lead to a significant decrease in both the glass transition temperature and activation energy for viscous flow. To understand the impact of trace level dopants on the viscosity of silica, we measure the viscosity-temperature curves for seven silica glass samples having different impurities, including four natural and three synthetic samples. Depending on the type of dopant, the glass transition temperature can vary by nearly 300 K. A common crossover is found for all viscosity curves around ~2200–2500 K, which we attribute to a change of the transport mechanism in the melt from being dominated by intrinsic defects at high temperature to dopant-induced defects at low temperatures.

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.