On mean coordination and structural heterogeneity in model amorphous solids

We propose a simple route to analytically evaluate the average coordination of model disordered solids with maximally homogeneous distribution of the particles in space. The model yields the average number of contacts (z) as a function of volume fraction (phi) of a hard-sphere connected system and recovers the critical jamming point of hard spheres (z=6 at phi=0.64). Numerical simulations of Lennard-Jones glasses with a varying attraction range are used to investigate the volume fraction dependence of the average coordination in the presence of attraction. It is observed that upon decreasing phi below 0.6, structural heterogeneity is reflected in values of the coordination number which are higher than those predicted by the model for a statistically homogeneous distribution of particles in space due to the attraction-induced local aggregation. Thus the model can be usefully employed as a quantitative reference to assess the degree of structural heterogeneity in glasses in terms of a directly accessible structural parameter such as the mean number of contacts.