Quantification of the heterogeneity of particle packings

The microstructure of coagulated colloidal particles, for which the interparticle potential is described by the Derjaguin-Landau-Verweg-Overbeek theory, is strongly influenced by the particles' surface potential. Depending on its value, the resulting microstructures are either more "homogeneous" or more "heterogeneous," at equal volume fractions. An adequate quantification of a structure's degree of heterogeneity (DOH), however, does not yet exist. In this work, methods to quantify and thus classify the DOH of microstructures are investigated and compared. Three methods are evaluated using particle packings generated by Brownian dynamics simulations: (1) the pore size distribution, (2) the density-fluctuation method, and (3) the Voronoi volume distribution. Each method provides a scalar measure, either via a parameter in a fit function or an integral, which correlates with the heterogeneity of the microstructure and which thus allows to quantitatively capture the DOH of a granular material. An analysis of the differences in the density fluctuations between two structures additionally allows for a detailed determination of the length scale on which differences in heterogeneity are most pronounced.