Quantification and application of uncertainty in the formation of nanoparticles
Date
2023
Authors
Long, Danny, author
Bangerth, Wolfgang, advisor
Shipman, Patrick, committee member
Liu, Jiangguo, committee member
Finke, Richard, committee member
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Abstract
Nanoparticles are essential across many scientific applications, but their properties are size-dependent. Despite the usefulness of producing monodisperse particle size distributions, it still remains a challenge to fully understand – and hence be able to control – nanoparticle formation reactions due to limitations in what can be observed experimentally. This thesis transfers mathematical, statistical, and computational techniques to this area of nanoparticle chemistry to substantially bolster the sophistication of the quantitative analysis used to better understand nanoparticle systems. First, more efficient software is developed to simulate the reactions. Then, parameter estimation is performed in a robust manner through Bayesian inference, where I demonstrate the ability to parameterize nonlinear ordinary differential equations in such a way that I can fit the observed data and quantify the uncertainty in the parameter estimates. From Bayesian inference, I build three additional analysis frameworks. (1) Model selection through a Bayesian framework; (2) optimizing the yield of the nanoparticle-forming reactions while accounting for uncertainty; and (3) optimizing future measurements to collect data providing the most new information. The culmination of this thesis provides a quantitative framework to analyze arbitrary nanoparticle systems to complement and fill in the gaps of the current experimental techniques.
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Subject
experimental design
optimization
uncertainty quantification
nanoparticles
Bayesian inversion
population balance modeling