Fig. 2. Cluster size distributions and size fluctuations.
(A) Still frames from movies S1 to S3, showing precursors to film formation, and the emergence of nanometer-scale clusters as the temperature is increased from 40° to 50°C in a pH 3.7 solution (1 mM AlCl3 + 0.2 mM HCl). (B) Image sequence from movie S3 (50°C), showing fluctuations in cluster size over time. Highlighted region 1 shows a cluster appearing and growing, while region 2 shows a cluster changing shape and disappearing. (C) Cluster population distributions, measured at 40°, 45°, and 50°C. Color bands show ±1 SD from the mean. (D) Calculated cluster energy landscapes obtained by applying Eq. 1 to the population distributions in (A). Lines show attempts to fit the energy landscape using the classical capillarity approximation. (E) Trajectories of ensemble-average size for initially monodisperse ensembles of clusters (heavy lines, outlined in black), along with size trajectories for selected individual clusters from those ensembles. Ensembles were extracted from the 50°C dataset. Ensembles were prepared with initial sizes near 3.0 nm2 (yellow), 2.0 nm2 (cyan), or 1.0 nm2 (purple). Although individual clusters may either grow or shrink, the average behavior shows a clear tendency to shrink.