J Phys Chem A. 2011 Jun 23;115(24):6413-25. doi: 10.1021/jp111767c. Epub 2011 Jun 1.
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.
本文推导并研究了作者在最近的一项工作（Skrdla, P. J. J. Phys. Chem. A 2009, 113, 9329）中描述的两个互补弥散动力学模型所依据的激活能分布。在成核速率受限转化的情况下，其表现出“加速”的 S 型指数瞬变（一种 S 形拉伸指数转换轮廓），恢复了与该模型原始推导一致的类似于麦克斯韦-玻尔兹曼（M-B）分布的激活能分布。在主要为“减速”转化的情况下，激活能分布从正态分布向相反方向偏斜。虽然“M-B 样”激活能分布支持在成核速率受限过程中作为转化率函数的速率增强的经验观察，但互补分布，其明显的低能尾部，反映了随着转化率的增加，比速率的减慢，与实验观察到的脱核速率受限转化一致。还为实际数据（Qu, H.; Louhi-Kultanen, M.; Kallas, J. Cryst. Growth Des. 2007, 7, 724）绘制了激活能分布，描绘了各种添加剂对溶剂介导的晶态药物卡马西平相转变的成核速率受限动力学的影响。最后，作者通过将弥散动力学描述的随时间变化的成核激活能与 Kelvin 方程提供的经典临界核能量描述相结合，观察到单体向生长胚胎表面扩散的加速跳跃机制。通过修改爱因斯坦-斯莫卢霍夫斯基（E-S）方程来允许其描述被认为是成核动力学核心的“超布朗”分子运动，从而合理化了该跳跃机制。
