Determination of critical supersaturation from microdroplet evaporation experiments

In this work, we identified a single critical supersaturation, the level of supersaturation above which nucleation will occur instantaneously, for each of a range of compounds: the amino acids glycine and L-histidine, the pharmaceutical paracetamol, the inorganic compound silicotungstic acid (STA), and the protein hen egg white lysozyme (HEWL). Using an evaporation-based microdroplet crystallization platform, we measured the time required to visually detect the first crystal. Crystals were observed to form at increasingly higher levels of supersaturation as the rate of evaporation was increased or as the initial solute concentration was reduced. Through extrapolation of all data of each compound to a nucleation time of zero, we identified a single point of high concentration, the critical supersaturation, which we found to be independent of the rate of solvent evaporation. Using the classical nucleation theory and thermodynamics, we correlated this critical supersaturation with surface tension between the nuclei and the surrounding media, and equilibrium solubility of the solute. This analysis suggests that, at conditions where supersaturation is generated very slowly, all compounds behave in a similar way such that the rate of nucleation at critical supersaturation is a constant fraction of the diffusion-limited rate of nucleation.