Title:

Direct computation of the packing entropy of granular materials

Granular materials are the second most manipulated material in industry after water and their properties are of great importance for the pharmaceutical, food, mechanosynthesis and semiconductor industries. Up to 60% of the capacity of some industrial plants is used to process them. This thesis describes computer simulations that aim to evaluate the number of distinct packings of a granular material or, more generally, the socalled ‘granular entropy’. Monte Carlo simulations are used to probe the energy landscape of jammed systems of disks interacting via a repulsive, finiterange potential. In these simulations we make use of a softsphere model with a hard core that approaches the hardsphere model as the width of the soft shell is decreased. To compute the packing entropy, we use and develop Monte Carlo techniques to determine the volumes of the basins of attraction of the potential energy minima at different system sizes. Such Monte Carlo simulations require energy minimisation after every trial move to make sure that all accepted moves keep the system within the same basin of attraction. Hence efficient energy minimisation is a point of paramount significance in this work. A first objective was to find a suitable minimisation algorithm. We report a study of the basins of attraction for potential energy minima defined by different minimisation algorithms for an atomic system. The findings indicate that whereas some minimisation algorithms produce compact basins, others produce basins with complex boundaries or basins consisting of disconnected parts. For the remainder of our work, the FIRE algorithm was chosen because it produces compact basins at a reasonable computational cost. Once the minimisation algorithm is chosen a numerical approach is used to compute the number of ways in which N particles can pack into a given volume V . This technique extends the existing methods in such a way that it can be applied to much larger systems than before (over 100 particles instead of 16). Many of the caveats of previous methods are addressed. Using this novel approach, the system size dependence of the number of distinct packings of a system of polydisperse soft disks is studied. Our simulations enable us to validate a more than 20 years old conjecture due to Edwards. The distribution of jamming densities produced by different protocols has been studied. We found that the distribution of jamming volumes that are generated by starting from different initial densities cannot be characterised by an Edwards’style compactivity although it is possible to construct an ensemble where compactivity is well defined.
