Physical Systems
In the domain of physical systems, the question of how to pack spheres optimally is familiar from everyday examples such as a greengrocer's stack of oranges. But what if the spheres have a range of sizes, as happens for example in colloidal suspensions? Controversy has surrounded this issue, with proposals that the optimal structure could be disordered. Sollich and co-workers have recently provided a definitive answer, combining mathematical theory (polydisperse phase equilibrium calculations) with specialized numerical simulation techniques. The optimal structures are ordered, i.e. crystalline solids, but depending on the density and the spread of particle sizes the system will fractionate: the particles are effectively sorted out into several solid phases, with each containing only a small range of particle sizes.