Robust optimization in nanoparticle technology: A proof of principle by quantum dot growth in a residence time reactor

• Published in: Computers & chemical engineering Vol. 157; p. 107618
• Main Authors: Dienstbier, Jana, Aigner, Kevin-Martin, Rolfes, Jan, Peukert, Wolfgang, Segets, Doris, Pflug, Lukas, Liers, Frauke
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.01.2022
• Subjects: Particle design; Process optimization; Reformulation; Robust optimization; Process optimization; Robust optimization; Particle design; Reformulation
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/j.compchemeng.2021.107618

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 those is needed. Robust optimization helps determining optimal processes. The latter guarantees quality requirements regardless of how uncertainties e.g., in raw materials, particle size distributions (PSD), heat and mass transport characteristics, and (growth) rates, manifest within predefined ranges. To approach this task, 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. This reformulation can be applied if both the objective and the constraint functions are quasiconcave in the uncertainty which is a natural assumption in this context. We also show that the approach extends to higher-dimensional uncertainties if the uncertain parameters do not influence each other. 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 predefined regions. The protection against uncertainties only reduces the maximum amount of product that can be obtained by a negligible margin.