Particle Size Distributions via Mechanism-Enabled Population Balance Modeling
Particle Size Distributions via Mechanism-Enabled Population Balance Modeling
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DOI：
10.1021/acs.jpcc.9b11239
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发表时间：
2020-02-27
影响因子：
3.7
通讯作者：
Finke, Richard G.
中科院分区：
文献类型：
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作者：
Handwerk, Derek R.;Shipman, Patrick D.;Finke, Richard G.
基于机制的人群平衡建模（ME-PBM）最近被定义为实验建立的使用（即基于调音的，故意简约和基于伪椭圆的步骤）机制作为人口平衡模型的更严格的输入。 ME-PBM解决了三个长期追求的目标：基于机制的预测和控制粒度分布（PSD），通过各种机制拟合PSD来测试哪些机制被驳斥与支持的机制，然后还提取了最强烈支持的机制的速率常数从埋在PSD中的动力学信息的财富。 PBModeling开发了一种完整的普通微分方程（ODE）方法，该方法是Smoluchowski 1918年方法的复活，这是一种少量使用但功能强大的方法，进而允许拟合包含信息的PSD，包括其形状。全部详细介绍了12种不同的颗粒形式，伪元素的步骤机制，该方法在基于调谐的方法中测试了PSD和动力学数据的ME-PBM分析，用于原型IR（0）纳米粒子形成系统。 ME-PBM分析导致发现了一种新的粒子形成机制，该机制是1步的，但要点的钥匙，是经典的Finke-Watzky两步机制A-> b，随后是自体催化的表面生长，然后a + b-> 2b。具体而言，ME-PBM分析得出了A-> B（速率常数K（1）），A + B-> C（速率常数K（2））和A + C的新的三步粒子形成机理。 - > 1.5c（速率常数k（3）），其中a代表单体纳米颗粒前体B表示“小”纳米颗粒，而C表示“较大”生长的纳米颗粒。提供了关键结论的列表，包括粒子形成的范式变化，即（i）成核不需要“瞬时”或“爆发”才能实现狭窄的PSD，如经典1950年代的lamer模型所述；（II）代替成核可以可以正如1997年首次显示的那样，通常是连续的成核由于较小的颗粒比较大的颗粒生长快（K（2）> k（3）），从而使较小的颗粒赶上了更慢的较大粒子的颗粒。 > k（3）进行了讨论，以及其他结论，当前研究的含义，需要的含义以及目前的贡献的目标是通过提供ME-PBM的第一个报告。迄今为止，我们工作的全部细节，以便其他希望在自然界中使用自己的粒子形成中的Me-PBM的人，同时适合自己的PSD并测试自己的机械假设，可以很容易地这样做。
Mechanism-enabled population balance modeling (ME-PBM) was recently defined as the use of experimentally established (i.e., disproof-based, deliberately minimalistic, and pseudo-elementary step-based) mechanisms as more rigorous input for population balance models. ME-PBM addresses three long-sought goals: mechanism-based prediction and control of particle size distributions (PSDs), fitting PSDs by various mechanisms to test which mechanisms are refuted versus supported, and then also extracting rate constants for the most strongly supported mechanism from the wealth of kinetics information buried within the PSD. A full ordinary differential equation (ODE) approach is developed to the PBModeling that is a resurrection of Smoluchowski's 1918 approach, a little used, but powerful approach that in turn allows fitting of the information-laden PSD including its shape. The full details are reported of the 12 different particle-formation, pseudo-elementary step mechanisms tested in a disproof-based approach to the ME-PBM analysis of the PSDs and kinetics data for a prototype Ir(0)(n) nanoparticle-formation system. The ME-PBM analysis led to the discovery of a new particle formation mechanism that is a 1-step, but key, expansion of the classic Finke-Watzky two-step mechanism of nucleation, A -> B, followed by autocatalytic surface growth, A + B -> 2B. Specifically, the ME-PBM analysis yielded the new three-step particle-formation mechanism of 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" growing nanoparticles. A list of key conclusions is provided including the paradigm shifts for particle formation that (i) nucleation needs not be "instantaneous" or "burst" "to achieve narrow PSDs as postulated by the classical 1950s LaMer model; that (ii) instead nucleation can be and often is continuous, as first shown in 1997, yet still leads to narrow PSDs; and critically that (iii) narrow PSDs can and do result in spite of continuous nucleation because smaller particles grow faster than larger ones (k(2) > k(3)), thereby allowing the smaller particles to catch up to the more slowly growing larger particles. Surface-ligand capping and other possible reasons that k(2) > k(3) are presented and discussed, as are additional conclusions, implications of the present studies, caveats, and needed additional studies. The goal of the present contribution is to follow up our first report of ME-PBM by providing the full details of our work to date so that others who wish to use ME-PBM in their own particle formations across nature, while fitting their own PSDs and testing their own mechanistic hypotheses, can readily do so.