Estimating reaction parameters in mechanism‐enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach. Issue 1 (21st October 2021)

• Record Type: Journal Article
• Authors: Long, Danny K.; Bangerth, Wolfgang; Handwerk, Derek R.; Whitehead, Christopher B.; Shipman, Patrick D.; Finke, Richard G.
• Is Part Of: Journal of computational chemistry. Volume 43:Issue 1(2022)
• Page Start: 43
• Page End: 56
• Publication Date: 2021-10-21
• Subjects: Bayesian inversion -- kinetics and mechanism -- nanoparticles -- nucleation and growth -- particle size distribution -- population balance modeling; Chemistry -- Data processing -- Periodicals; 542.85
• DOI: 10.1002/jcc.26770
• Languages: English
• ISSNs: 0192-8651

Abstract

Abstract: In order to quantitatively predict nano‐ as well as other particle‐size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism‐enabled population balance models (ME‐PBM) of nanoparticle growth. The Bayesian approach addresses the question of "how well do we know our parameters, along with their uncertainties?." The results reveal that Bayesian inversion statistical analysis on an example, prototype Ir 0 n nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. The paper can also be seen as a tutorial with the additional goal of achieving a "Gold Standard" Bayesian inversion ME‐PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems. Abstract : Nanoparticles are widely used in catalysis and optical applications, among many others, but it has been difficult to predict and, in particular, control their size distribution because quantitative models for their growth were missing. Herein, we use a Bayesian framework to estimate reaction parameters and their uncertainties in a class of mechanism‐enabled population‐based models. We then show that with these estimates, we can accurately predict nanoparticle size distributions.