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 25–2 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.