Model based process optimization for nanoparticle precipitation

Abstract

This study introduces a derivative-based optimization framework for the controlled synthesis of nanoparticles, with a focus on achieving target particle size distributions via dynamic manipulation of reactant inflow during precipitation. The underlying model couples a population balance equation (PBE), which accounts for nucleation and growth phenomena, with a preceding first-order reduction reaction, and is formulated using the exact method of moments (eMoM). A discretizethen-optimize approach is employed to efficiently compute parameter sensitivities, enabling effective optimization of the time-dependent inflow profile. The objective is to minimize the variance in particle size while ensuring a prescribed mean diameter. Numerical case studies explore the role of process constraints and regularization strategies in control performance. The results demonstrate that optimized, time-varying inflow profiles significantly outperform constant-rate strategies in terms of product uniformity and quality. This framework offers a systematic and computationally tractable approach to optimizing transient operating conditions in nanoparticle synthesis, with strong potential for industrial application.