Thermodynamic analyses of critical nuclei and crystallization entropy using size distributions of small clusters of two-dimensional colloidal crystals†

Prenucleation clustering is important for elucidating the elementary processes of nucleation more precisely. Prenucleation clusters of two-dimensional (2D) colloidal crystals of polystyrene particles were observed at the particle level in an aqueous sodium polyacrylate solution. Both redispersing and growing clusters were observed, indicating that clustering processes were reversible. Growing clusters usually showed temporal decreases in the number of particles (hereafter referred to as “dips”) in the clusters, followed by monotonic increases afterwards. Between the maximum number of particles in redispersing clusters and the minimum number of particles in growing clusters at the dips, we determined the range of the number of particles in critical nuclei n_c. We judged n_c using a cluster distribution with a quasi-equilibrium approximation, since the cluster distribution did not change significantly. Assuming the numbers of apparent bonds and dangling bonds around particles, we also estimated the apparent bonding energy and entropy of crystallization thermodynamically.