A Minimal description of morphological hierarchy in two-dimensional aggregates

A dimensionless parameter $\Lambda$ is proposed to describe a hierarchy of morphologies in two-dimensional (2D) aggregates formed due to varying competition between short-range attraction and long-range repul- sion. Structural transitions from finite non-compact to compact to percolated structures are observed in the configurations simulated by molecular dynamics at a constant temperature and density. Configurational randomness across the transition, measured by the two-body excess entropy $S_2$, exhibits data collapse with the average potential energy $\bar{\mathcal{E}}$ of the systems. Independent master curves are presented among $S_2$, the reduced second virial coefficient $B_2^*$ and $\Lambda$, justifying this minimal description. This work lays out a coherent basis for the study of 2D aggregate morphologies relevant to diverse nano- and bio-processes.