A single parameter description of aggregate morphologies in two-dimensions

A morphological hierarchy of two-dimensional aggregates has been studied using molecular dynamics. Particulate aggregates resulting from the competition between short-range attraction and long-range repulsion show a transition from non-compact to compact to percolated `gel' structures as the competition varies at a constant temperature and density. A three-dimensional (3D) parameter space controlling the competition is mapped to a single dimensionless parameter $\Lambda$. A unique relation found between the reduced second virial coefficient $B_2^*$, computed for a large set of points in the 3D parameter space, and $\Lambda$ provides strong support for the proposed description. The observed morphologies were further quantified using an entropic measure $S_2$ of positional information. A simple scaling relation between $S_2$ and $\Lambda$ shows the promise of describing the static structures of aggregates in terms of geometry alone.