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Robust Optimization in Nanoparticle Technology: A Proof of Principle by Quantum Dot Growth in a Residence Time Reactor

Jana Dienstbier (jana.jd.dienstbier***at***fau.de)
Kevin-Martin Aigner (kevin-martin.aigner***at***fau.de)
Jan Rolfes (jan.rolfes***at***fau.de)
Wolfgang Peukert (wolfgang.peukert***at***fau.de)
Doris Segets (doris.segets***at***uni-due.de)
Lukas Pflug (lukas.pflug***at***fau.de)
Frauke Liers (frauke.liers***at***fau.de)

Abstract: Knowledge-based determination of the best-possible experimental setups for nanoparticle design is highly challenging. Additionally, such processes are accompanied by noticeable uncertainties. Therefore, protection against these uncertainties is needed. Robust optimization helps determining such best possible processes. The latter guarantees quality requirements regardless of how the uncertainties, e.g. with regard to variations in raw materials, heat and mass transport characteristics, material properties and (growth) rates, manifest within predefined ranges. To approach this huge task, in this paper we exemplarily model a particle synthesis process with seeded growth by population balance equations and study different growth kinetics. We determine the mean residence time maximizing the product mass subject to a guaranteed yield. Additionally, we hedge against uncertain growth rates and derive an algorithmically tractable reformulation for the robustified problem. We evaluate our approach for seeded growth synthesis of zinc oxide quantum dots and demonstrate computationally that a guaranteed yield is met for all growth rates within previously defined regions. The protection against uncertainties only reduces the maximum amount of product that can be obtained by a negligible margin.

Keywords: particle design, robust optimization, process optimization, reformulation

Category 1: Applications -- Science and Engineering (Chemical Engineering )

Category 2: Robust Optimization

Citation: unpublished: Friedrich-Alexander Universität Erlangen-Nürnberg, 91058 Erlangen, 02/2021

Download: [PDF]

Entry Submitted: 02/23/2021
Entry Accepted: 02/23/2021
Entry Last Modified: 07/21/2021

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