Crystals form from liquid phase by the aggregation and attachment of basic building blocks. While recent advance shows such building blocks may include multi-ion complexes, molecular clusters, and fully crystallized nanoparticles, the classical theory based upon the monomeric chemical species still finds enormous success in predicting and interpreting crystal formation various systems from engineering, biominerals, to mineralization in geological settings. For nucleation, the classical model assumes random collisions of monomers leading to the formation of condensed clusters, which proceed to growth if the particle size r is greater than a critical value rc, or revert to the constituent building blocks if r fails to reach rc. For growth, the classical view postulates that elemental particles attach at kinks to advance steps, and the step rate will be determined by the net flux attaching at and detaching from the kinks. Overall the classical model predicates that crystallization systems are controlled by the difference between surface energy increase arising from the newly formed solid and chemical potential decrease in solution due to the loss of solute components. Despite the widely accepted success, growing evidence suggests that the classical model is incomplete or inappropriate in a plethora of cases where the theoretical predictions digress from experimental results. I will provide an overview of the classical model followed by two case studies pinpointing some of the discrepancies between theory and observations. In the first case, it is shown that the classical model correctly predicts the linear relation between step kinetics and the deviation of supersaturation index from the equilibrium value, but fails to account for the effects of solution chemistry and surface charge on the growth kinetics. In the second case, experimentally determined nucleation kinetics corroborates nicely with the energetics of critical nucleus formation, but yield a positive correlation between surface energy and nucleation rate in doing so and contradict the theoretical prediction. These results on the one hand attest to the power of the classical theory but on the other hand point to the need to revise the existing model.

Validity and limitations of the classical crystallization model

256th National Meeting (2018)

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