Remoteness: studying the structure of concentrated particulate systems

The properties of soft matter depend ultimately on structure. When there is any degree of amorphousness in a system, traditional methods of structural characterisation (often based on strong symmetries such as crystallinity) can give only limited information. But quantitatively describing amorphous structures is rather difficult: one is tempted to cry 'blimey! it's a bit of an untidy mess isn't it?' and leave it at that. As an alternative, I will discuss the use of 'remoteness', a measure of empty space, to describe more precisely the structure of concentrated colloidal systems. Demonstrations will be provided via simple Monte Carlo simulations. Remoteness calculations show that, for example, something intriguing happens to empty space during crystallisation of hard spheres. Furthermore, remoteness can be used to demonstrate the non-monotonic behaviour (with interaction energy) of 'sticky' colloidal glasses, where in experiments 're-entrant' crystallisation is observed beyond the usual repulsive hard sphere glass transition.