title: Activation energy distributions predicted by dispersive kinetic models for nucleation and denucleation: anomalous diffusion resulting from quantization.
abstract: The activation energy distributions underpinning the two complementary dispersive kinetic models described by the author in a recent work (Skrdla, P. J. J. Phys. Chem. A 2009, 113, 9329) are derived and investigated. In the case of nucleation rate-limited conversions, which exhibit "acceleratory" sigmoidal transients (a kind of S-shaped stretched exponential conversion profile), an activation energy distribution visually similar to the Maxwell-Boltzmann (M-B) distribution is recovered, consistent with the original derivation of that model. In the case of predominantly "deceleratory" conversions, the activation energy distribution is skewed from normal in the opposite direction. While the "M-B-like" activation energy distribution supports the empirical observation of a rate enhancement as a function of the conversion time in nucleation rate-limited processes, the complementary distribution, with its pronounced low-energy tail, reflects a slow-down in the specific rate as the conversion progresses, consistent with experimentally observed denucleation rate-limited conversions. Activation energy distributions were also plotted for real-world data (Qu, H.; Louhi-Kultanen, M.; Kallas, J. Cryst. Growth Des. 2007, 7, 724), depicting the impact of various additives on the nucleation rate-limited kinetics of the solvent-mediated phase transformation of the crystalline drug carbamazepine. Last, by coupling the author's dispersive kinetic description of the time-dependent activation energy for nucleation to the classical description of the critical nucleus energy provided by the Kelvin equation, an accelerated hopping mechanism for the diffusion of monomers to the growing embryo surface was observed. That hopping mechanism was rationalized by modifying the Einstein-Smoluchowski (E-S) equation to allow it to describe the "supra-brownian" molecular motion thought to lie at the heart of nucleation kinetics.
authors: peter_skrdla@merck.com
authors: Peter J
authors: PJ
authors: Skrdla