Reply to “A Comparison of the Stochastic and Deterministic Approaches in a Nucleation–Growth Type Model of Nanoparticle Formation”

Reply to “A Comparison of the Stochastic and Deterministic Approaches in a Nucleation–Growth Type Model of Nanoparticle Formation”
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回复“成核过程中随机方法和确定性方法的比较”纳米粒子形成的生长类型模型

DOI:
10.1021/acs.chemmater.1c01690
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发表时间:
2021
影响因子:
8.6
通讯作者:
Martin, James D.
Martin, James D.
中科院分区:
材料科学2区
文献类型:
--
作者:
Martin, James D.

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在最近的一篇评论中,我解决了Finke-Watzky(F-W)模型的挑战,该模型旨在描述纳米颗粒的成核和生长。[1]在那篇评论中,我注意到类似的挑战也适用于相关的萨博和伦特模型(SL)。[2] Finke、Watzky和Whitehead(FWW)同时发表了对这一评论的回应。[3]在前面的评论中,Szabó和Lente(SL)提供了一个额外的回应。[4]我最初评论的目的是强调:(1)在描述颗粒生长时,必须包括维数或颗粒尺寸;(2)为了描述成核和生长的连续过程,必须使用串行而不是并行的数学函数。因此,通常不可能从反应物随时间转化为产物的单一平均测量中提取独立成核和生长过程的细节。SL解释了我的评论,强调需要认识到成核和生长是独立的,系列过程1作为对井的挑战-已知的现实是,大量的随机过程通常可以用确定性模型来描述。在此,如本答复的第二节所述,关键是要区分随机过程和确定性过程之间的关系与不同过程的去卷积,例如成核和生长,它们可能在时间上分开,也可能不分开。应该注意的是,我在前面的评论中使用的M-KJMA模型,5,6也是随机过程的确定性模型。(进一步说明:我从未主张M-KJMA模型是描述纳米颗粒生长的首选模型。在我最初的评论中,我特别指出,这种“分析绝不是
In a recent comment, I addressed challenges with the Finke− Watzky (F− W) model purported to describe nanoparticle nucleation and growth. 1 In that comment I noted similar challenges applied to the related Szabó and Lente’s model (SL). 2 A response to that comment was simultaneously published by Finke, Watzky, and Whitehead (FWW). 3 And in the preceding comment, Szabó and Lente (SL) provide an additional response. 4 The purpose of my initial comment was to highlight that (1) the dimensionality or particle size must be included in any description of particle growth and (2) to describe the consecutive processes of nucleation and growth it is necessary to use serial, and not parallel, mathematical functions. As such, it generally is not possible to extract details of the independent nucleation and growth processes from a single average measurement of the transformation of reactant to product with time.SL interpreted my comment highlighting the need to recognize that nucleation and growth are independent, serial processes 1 as a challenge to the well-known reality that a large number of stochastic processes generally can be described by a deterministic model. Herein, as described in Section II of this reply, it is critical to differentiate the relationship between stochastic and deterministic processes from the deconvolution of distinct processes, such as nucleation and growth, which may, or may not be separated in time. It should be noted that the M-KJMA model, 5, 6 used in my prior comment is also a deterministic model of stochastic processes.(A further note of clarification: I have never advocated that the M-KJMA model is a preferred model to describe nanoparticle growth. In my initial comment I specifically stated that this “analysis in no way
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