Edge free energy of a 2D colloidal crystal estimated from the size distribution of small clusters†

Direct observation of elementary processes during solidification is challenging in many material systems. Such difficulties hinder accurate estimation of critical nucleation size and nucleation rate. However, in colloidal systems, the large particle size and slow particle dynamics enable direct observation of elementary processes such as nucleation. We observed the formation of two-dimensional colloidal clusters by optical microscopy and applied machine learning to small clusters to determine the cluster size distribution. We estimated the edge free energy for two-dimensional islands. Brownian dynamics simulations were also performed, which obtained similar results. The edge free energy estimated from the simulations has the same magnitude as expected from a bond-counting model. Thus, we suggest that the interaction energy between particles in an experimental system can be estimated from the observed edge energy.