Accounting for the Presence of Molecular Clusters in Modeling and Interpreting Nucleation and Growth

The effect of molecular cluster formation on the estimation of kinetic parameters for primary nucleation and growth in different systems has been studied using computationally generated data and three sets of experimental data in the literature. It is shown that the formation of molecular clusters decreases the concentration of monomers and hence the thermodynamic driving force for crystallization, which consequently affects the crystallization kinetics. For a system exhibiting a strong tendency to form molecular clusters, accounting for cluster formation in a kinetic model is critical to interpret kinetic data accurately, for instance, to estimate the specific surface energy γ from a set of primary nucleation rates. On the contrary, for a system with negligible cluster formation, a consideration of cluster formation does not affect parameter estimation outcomes. Moreover, it is demonstrated that using a growth kinetic model that accounts for cluster formation allows the estimation of γ from typical growth kinetic data (i.e., de-supersaturation profiles of seeded batch crystallization), which is a novel method of estimating γ developed in this work. The applicability of the novel method to different systems is proven by showing that the estimated values of γ are closely comparable to the actual values used for generating the kinetic data or the corresponding estimates reported in the literature.