Mechanism-Enabled Population Balance Modeling of Particle Formation en Route to Particle Average Size and Size Distribution Understanding and Control
Mechanism-Enabled Population Balance Modeling of Particle Formation en Route to Particle Average Size and Size Distribution Understanding and Control
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DOI：
10.1021/jacs.9b06364
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发表时间：
2019-10-09
影响因子：
15
通讯作者：
Finke, Richard G.
中科院分区：
文献类型：
--
作者：
Handwerk, Derek R.;Shipman, Patrick D.;Finke, Richard G.
报道了机理使能的粒子数平衡模型（ME-PBM）的概念，并将其应用于Ir（0）（n）纳米粒子的生成反应。ME-PBM在本文中被定义为使用现在可用的、实验建立的、基于反证的、故意最小化的颗粒形成机制作为更严格的群体平衡模型的所需输入，关键地包括实验建立的成核机制。ME-PBM实现了长期追求的目标，即将这种现有的实验最小机制与颗粒尺寸和尺寸分布的理解和合理控制联系起来。12 pseudoelementary步骤，粒子形成机制被认为是使ME-PBM的方法也广泛disproof为基础的。复活的Smoluchowski的1918年全常微分方程（ODE）的PBM方法是另一个，我们的方法，这反过来，允许无偏拟合的信息负载的粒径分布（PSD），包括其形状的关键方面。结果为“逆问题”提供了一种解决方案，其中PSD告知人们正确的颗粒形成机制：已经发现了一种新的、故意最小化的3步颗粒形成机制，其是现在广泛使用的Finke-Watzky（FW）2步机制的单附加步骤扩展，新的3步机制是：A -> B（速率常数k（1）），A + B -> C（速率常数k（2）），和A + C -> 1.5C（速率常数k（3）），其中A表示单体纳米颗粒前体，B表示“小”纳米颗粒，和C表示“较大”纳米颗粒。结果强烈支持三个范式转变的成核和颗粒的生长，最关键的范式转变是，“突发”成核假设在LaMer的20世纪50年代的颗粒形成模型是不需要产生狭窄的，近单分散的PSD。相反，尽管连续成核，仍然可以并且确实实现窄的PSD，因为较小的颗粒比较大的颗粒生长得更快，k（2）> k（3），从而允许较小的颗粒在尺寸上赶上生长更慢的较大颗粒。
The concept of Mechanism-Enabled Population Balance Modeling (ME-PBM) is reported, illustrated by its application to a prototype Ir(0)(n) nanoparticle formation reaction. ME-PBM is defined herein as the use of now available, experimentally established, disproof-based, deliberately minimalistic mechanisms of particle formation as the required input for more rigorous Population Balance models, critically including an experimentally established nucleation mechanism. ME-PBM achieves the long-sought goal of connecting such now available experimental minimum mechanisms to the understanding and rational control of particles size and size distributions. Twelve pseudoelementary step, particle-formation mechanisms are considered so that the approach to the ME-PBM is also extensively disproof-based. Resurrection of Smoluchowski's 1918 full Ordinary Differential Equation (ODE) approach to the PBM is another, critical aspect of our approach which, in turn, allows unbiased fitting of the information-laden particle-size distribution (PSD) including its shape. The results provide one solution to the "inverse problem" in which the PSD informs one as to the correct particle formation mechanism: A new, deliberately minimalistic 3-step particle-formation mechanism has been uncovered that is a single-additional-step expansion of the now broadly used Finke-Watzky (FW) 2-step mechanism, the new 3-step mechanism being: A -> B (rate constant k(1)), A + B -> C (rate constant k(2)), and A + C -> 1.5C (rate constant k(3)), where A represents the monomeric nanoparticle precursor, B represents "small" nanoparticles, and C represents "larger" nanoparticles. The results strongly support three paradigm shifts for nucleation and growth of particles, the most critical paradigm shift being that the "burst" nucleation assumption in LaMer's 1950s model of particle formation is not required to produce narrow, near-monodisperse PSDs. Instead, narrow PSDs can be and are achieved despite continuous nucleation because smaller particles grow faster than larger ones, k(2) > k(3), thereby allowing the smaller particles to catch up in size to the more slowly growing larger particles.