INVITED ARTICLE Accessible volume in quenched-annealed mixtures of hard spheres: a geometric decomposition

Model systems in which fluid particles move in a disordered matrix of immobile obstacles have been found to be a reasonable representation of a colloidal fluid confined in a disordered porous medium. For systems consisting of hard-sphere particles, the obstacle matrix partitions the space available to the fluid particles into voids of finite volume (“traps”) and a percolating void that extends over the entire volume. This geometric distinction plays a key role for the dynamic properties of the confined fluid: while its particles are not able to escape from traps, in the percolating void they can propagate infinitely far. We present a geometric method, based on a Delaunay decomposition, to identify the two different kinds of voids in an arbitrary matrix configuration of finite size under periodic boundary conditions. We subsequently apply a rastering technique, which enables us to statistically characterise the structure of the voids. We investigate the specific case of a quenched-annealed mixture of identical hard spheres, for which, among others, we accurately determine the matrix packing fraction at which the percolation transition of the voids takes place.