Crystallizations, Solid-State Phase Transformations and Dissolution Behavior Explained by Dispersive Kinetic Models Based on a Maxwell−Boltzmann Distribution of Activation Energies: Theory, Applications, and Practical Limitations

Abstract

The potential applications of dispersive kinetic models range from solid-state conversions to gas-phase chemical physics and to microbiology. Here, the derivation and application of two such models, for use in solid-state applications, is presented. The models are based on the concept of a Maxwell-Boltzmann distribution of activation energies. The ability of the models to fit/explain an assortment of asymmetric, sigmoidal conversion-versus-time transients presented in the recent literature, as well as to provide physicochemical interpretations of the kinetics via the two fit parameters, alpha and beta, makes them a powerful tool for understanding nucleation/denucleation rate-limited processes that are involved in many phase transformations, dissolutions and crystallizations.

Kinetics and Thermodynamics of Efficient Chiral Symmetry Breaking in Nearly Racemic Mixtures of Conglomerate Crystals

“…That recycling effect, whereby the system renewals are enhanced by the continuous crystal grinding, is consistent with the observation of dispersive kinetics 8,31,32 that will be discussed later. The mechanisms involved in the process (refer to Scheme 1) include crystal nucleation, growth and/or OR, and denucleation (dissolution) of each enantiomeric crystal as well as the solution phase racemization of the two enantiomers.…”

“…55 That finding lends support to a nucleation rate-limited mechanism (e.g. ref 8). Interestingly, Uwaha and Katsuno 28 recently reported the use of an extended BeckerÀ D€ oring-type model to show that OR "is not the essential mechanism" and that "the direct crystallization of small chiral clusters and grinding are essential to the chirality conversion that leads to a homochiral state".…”

“…Since the author 0 s model for denucleation (dissolution) rate-limited kinetics, 8 which is complementary to eq 2, also did not model any of the transients presented in this work adequately (fits not shown), it is not discussed here further.…”

“…ref 6) and for the development of manufacturingscale processes for certain (e.g., pharmaceutical) compounds. 7 However, due to the current ambiguity in the literature regarding the underlying mechanisms relevant to such conversions, this work draws on recent advances in dispersive kinetics theory 8 to lend clarity to those mechanisms.…”

“…For comparison, the broken line fit of the (2) data set was obtained using eq 1 (JMAEK model): R 2 = 0.9870, k = (1.5 ( 0.9) Â 10 À8 au, n = 4.64 ( 0. 15. In recent years, the author has developed his own approach for treating dispersive kinetics, 8 relying on the assumption of an underlying MaxwellÀBoltzmann-like (M-B-like) distribution of activation energies (that fundamental assumption is investigated in a paper that is currently in preparation). The a priori definition of the general functional form of that underlying activation energy distribution was necessitated by his desire to circumvent the use of unitless (thus physically/mechanistically ambiguous e.g.53 ) parameters 52 in those models.…”