Properties of the glass transition as a mixture of jamming and random organization
Final Report Abstract
In many particulate systems a dramatic slowdown of the dynamics can be observed upon an increase of the packing fraction or a decrease of the temperature. On the timescale of experiments or simulations the system might become effectively nonergodic, i.e., it does not explore all possible states. The transition from an ergodic state to an effectively on-ergodic state usually is referred to as dynamical glass transition. In our project, we considered a system of soft spheres that interact according to shortranged repulsive interaction. We studied how the system explored the energy landscape and specifically determined whether a ground state, i.e., a state without overlaps can be reached or not. In our approach we employ a protocol that is composed of minimization towards a local minimum as known from studies on athermal jamming and steps where energy barriers can be crossed. We find a transition packing fraction above which the system can no longer reach the ground states and therefore is effectively non-ergodic. Interestingly, for small but non-zero probabilities to cross energy barriers (corresponding to small but non-zero temperatures) this transition packing fraction does not depend on the probability and is much smaller than the transition density of athermal jamming. To be specific, for random initial configurations, we find that the transition from an ergodic to a non-ergodic system, i.e., the glass transition, takes place at a packing fraction of 0.55±0.01. Note that for other initial configurations or small systems the transition packing fraction shifts to larger values. We analyzed the critical behavior of the glass transition, which has turned out to be the same as for a random organization or a directed percolation transition. Our interpretation of the glass transition as a function of density and at small temperatures is as follows: While at small densities rearrangements can occur locally and the subsequent relaxation usually is fast, above the glass transition density rearrangements might affect the whole system and might occur on a timescale that is (directed) percolated in time. To strengthen our interpretation, we have also studied the percolation in space as well as the relaxation of a system after an enforced rearrangement event. Furthermore, we are able to relate the probability of barrier crossing to the density and thus predict that the glass transition line as a function of temperature is not only given by a mapping onto hard spheres with an effective diameter but that an additional shift of the transition packing fraction has to be consider ed. Finally, we have studied the glass transition of a bidisperse system in 2D, of ellipsoidal particles in 3D, as well as of active particles. In conclusions, in our project we employed a new approach to study the glass transition as a function of density. We were able to analyze the critical behavior and can make a prediction on how the transition density depends on temperature. Unfortunately, the possibility to study the glass transition in full non-equilibrium turned out to be a reason to dismiss our approach for many fellow scientists. I hope that one day it will be accepted that glasses can occur far away from equilibrium and until then I want to point out that the quasi-equilibrium exploration of the glass transition is possible as well within our approach.
