Ahn Byeongho, Bosetti Luca, Mazzotti Marco
Institute of Energy and Process Engineering, ETH Zurich, 8092 Zurich, Switzerland.
Cryst Growth Des. 2022 Jun 1;22(6):3625-3636. doi: 10.1021/acs.cgd.1c01314. Epub 2022 May 9.
A nucleation rate model for describing the kinetics of secondary nucleation caused by interparticle energies (SNIPEs) is derived theoretically, verified numerically, and validated experimentally. The theoretical derivation reveals that the SNIPE mechanism can be viewed as enhanced primary nucleation, i.e., primary nucleation with a lower thermodynamic energy barrier (for nucleation) and a smaller critical nucleus size, both caused by the interparticle interactions and the associated energy between the surface of a seed crystal and a molecular cluster in solution, as shown in part I of this series. In the case of a sufficiently agitated suspension, the model depends on four parameters: two reflecting primary nucleation kinetics and the other two accounting for the intensity and effective spatial range of the interparticle interactions. As a numerical verification of the model, we show that the nucleation kinetics described by the SNIPE rate model is in quantitative agreement with those given by the kinetic rate equation model developed in part II of this series. A sensitivity analysis of the SNIPE rate model is conducted to present the effect of key model parameters on the nucleation kinetics. Moreover, the SNIPE rate model is validated by fitting the model to the time-resolved data of secondary nucleation experiments as well as to two other, well-known secondary nucleation rate models. Importantly, all of the estimated parameter values for the SNIPE model were consistent with the theoretical estimates, while some of the estimated parameter values for one of the well-known secondary nucleation models deviated from the corresponding theoretical values significantly.
本文从理论上推导了一种用于描述由颗粒间能量引起的二次成核动力学（SNIPEs）的成核速率模型，进行了数值验证，并通过实验进行了验证。理论推导表明，SNIPE机制可视为增强的一次成核，即由于颗粒间相互作用以及籽晶表面与溶液中分子簇之间的相关能量，导致具有较低热力学能垒（用于成核）和较小临界核尺寸的一次成核，如本系列第一部分所示。在充分搅拌的悬浮液情况下，该模型取决于四个参数：两个反映一次成核动力学，另外两个考虑颗粒间相互作用的强度和有效空间范围。作为对该模型的数值验证，我们表明SNIPE速率模型描述的成核动力学与本系列第二部分中开发的动力学速率方程模型给出的动力学在定量上一致。对SNIPE速率模型进行了敏感性分析，以呈现关键模型参数对成核动力学的影响。此外，通过将该模型拟合到二次成核实验的时间分辨数据以及另外两个著名的二次成核速率模型，对SNIPE速率模型进行了验证。重要的是，SNIPE模型的所有估计参数值与理论估计一致，而其中一个著名的二次成核模型的一些估计参数值与相应的理论值有显著偏差。
