Homogeneous Organic Crystal Nucleation Rates in Solution from the Perspective of Chemical Reaction Kinetics

Abstract

It is demonstrated for 11 different combinations of organic solutes and solvents that the supersaturation dependence of homogeneous organic crystal nucleation rates from solution can be predicted from the solubility, bar a single empirical rate constant, when it is assumed that nucleation takes place in reversible aggregates of solvated solutes formed in supersaturated solutions. Reversible solute aggregation represents natural solute density fluctuations that take place in any solute/solvent system. For thermodynamically ideal solutions, the steady state size distribution, and thus the population of reversible aggregates in supersaturated solution, can be predicted quantitatively from the overall solute concentration by a simple mathematical expression. Supersaturation creates an excess of reversible aggregates with sizes exceeding that of the largest aggregate in saturated solution. It is shown that the number of these excess aggregates is proportional to experimental homogeneous nucleation rates, suggesting a rate equation for homogeneous nucleation that has only one empirical parameter, namely, a rate constant specific to the solute/solvent combination. This rate constant can be determined from standard nucleation rate data. The system-specificity of homogeneous nucleation rates thus appears to be encoded solely in a rate constant for the transformation of the large excess aggregates into crystal nuclei. The driving force for triggering nucleation events in these aggregates is likely the extremely high local supersaturation, which provides the conditions for spatiotemporally aligned bond-breaking (e.g., de-solvation) and bond-forming (e.g., solute–solute bonding) events that create stable crystal nuclei. The possible influence of heterogeneous nucleation by solid impurities is considered.