Statistical Multiobjective Optimization of Thiospinel CoNi₂S₄ Nanocrystal Synthesis via Design of Experiments

Thiospinels, such as CoNi₂S₄, are showing promise for numerous applications, including as catalysts for the hydrogen evolution reaction, hydrodesulfurization, and oxygen evolution and reduction reactions; however, CoNi₂S₄ has not been synthesized as small, colloidal nanocrystals with high surface-area-to-volume ratios. Traditional optimization methods to control nanocrystal attributes such as size typically rely upon one variable at a time (OVAT) methods that are not only time and labor intensive but also lack the ability to identify higher-order interactions between experimental variables that affect target outcomes. Herein, we demonstrate that a statistical design of experiments (DoE) approach can optimize the synthesis of CoNi₂S₄ nanocrystals, allowing for control over the responses of nanocrystal size, size distribution, and isolated yield. After implementing a 2^5-2 fractional factorial design, the statistical screening of five different experimental variables identified temperature, Co:Ni precursor ratio, Co:thiol ratio, and their higher-order interactions as the most critical factors in influencing the aforementioned responses. Second-order design with a Doehlert matrix yielded polynomial functions used to predict the reaction parameters needed to individually optimize all three responses. A multiobjective optimization, allowing for the simultaneous optimization of size, size distribution, and isolated yield, predicted the synthetic conditions needed to achieve a minimum nanocrystal size of 6.1 nm, a minimum polydispersity (σ/d̅) of 10%, and a maximum isolated yield of 99%, with a desirability of 96%. The resulting model was experimentally verified by performing reactions under the specified conditions. Our work illustrates the advantage of multivariate experimental design as a powerful tool for accelerating control and optimization in nanocrystal syntheses.