A mathematical model for crystal growth by aggregation of precursor metastable nanoparticles
A mathematical model for crystal growth by aggregation of precursor metastable nanoparticles
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DOI：
10.1021/jp0537299
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发表时间：
2005-12-22
影响因子：
3.3
通讯作者：
Tsapatsis, M
中科院分区：
文献类型：
--
作者：
Drews, TO;Katsoulakis, MA;Tsapatsis, M
建立了一个数学模型来描述聚集晶体的生长，包括定向聚集，从进化的预先存在的纳米颗粒组成和结构不同于最终的晶体聚集。该模型的基本假设是基于早期发表的报告[Buyanov和Krivoruchko， Kinet]中介绍的思想。Katal. 1976, 17, 666-675]描述了低溶解度金属氢氧化物（如氧化铁）的定向聚集生长。假设初生颗粒可以被描述为A、B和C伪种，它们具有以下性质：(1)新鲜的初生颗粒（胶体稳定的惰性纳米颗粒，记为A），(2)成熟的初生颗粒（部分转化的纳米颗粒，在生长晶体的最佳发育阶段，记为B），(3)成核的初生颗粒（记为C-1）。原生粒子A -> B -> C-1的演化被视为两个一级连续反应。晶体生长通过晶体聚集（C-i + C-j -> - C-ij）是用斯摩鲁乔夫斯基方程描述的。该模型的新元素是通过在晶体（C-i）中添加初级颗粒(B)来包含额外的晶体生长机制：（B + Ci -> Ci+l）。使用两个不同但不变的核（K不等于K'）。结果表明，当K′= 0时，晶体尺寸呈阶梯状分布。在K′/K值范围内（如K′/K = 10(3)），可得到多峰CSD。与不包括初级粒子(B)中间阶段的模型的预测相比，表明了明显的差异。尽管它很简单，但该模型能够捕捉到从赤铁矿晶体生长实验中获得的CSD演化的定性特征，赤铁矿是一个被认为经历定向聚集的系统。
A mathematical model is developed to describe aggregative crystal growth, including oriented aggregation, from evolving pre-existing primary nanoparticles with composition and structure that are different from that of the final crystalline aggregate. The basic assumptions of the model are based on the ideas introduced in an earlier published report [Buyanov and Krivoruchko, Kinet. Katal. 1976, 17, 666-675] to describe the growth of low-solubility metal hydroxides (e.g., iron oxides) by oriented aggregation. It is assumed that primary particles can be described as pseudo-species A, B, and C, which have the following properties: (1) fresh primary particles (colloidally stable inert nanoparticles, denoted as A), (2) mature primary particles (partially transformed nanoparticles at an optimum stage of development for attachment to a growing crystal, denoted as B), and (3) nucleated primary particles (denoted as C-1). The evolution of primary particles, A -> B -> C-1 is treated as two first-order consecutive reactions. Crystal growth via crystal-crystal aggregation (C-i + C-j -> C-ij) is described using the Smoluchowski equation. The new element of this model is the inclusion of an additional crystal growth mechanism via the addition of primary particles (B) to crystals (C-i): (B + Ci -> Ci+l). Two distinct, but constant, kernels (K not equal K') are used. It is shown that, when K' = 0, a steplike crystal size distribution (CSD) is obtained. Within a range of K'/K values (e.g., K'/K = 10(3)), CSD with multiple peaks are obtained. Comparison with predictions of models that do not include the intermediate stage of primary particles (B) indicates pronounced differences. Despite its simplicity, the model is able to capture the qualitative features of CSD evolution that have been obtained from crystal growth experiments in hematite, which is a system that is believed to undergo oriented aggregation.