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unpublished: Friedrich-Alexander Universität Erlangen-Nürnberg, 91058 Erlangen, 02/2021