The understanding and control of colloidal nanocrystal syntheses are essential for discovery and optimization of desired properties and therefore play a key role in the applications of these materials. Typical one variable at a time (OVAT) methods limit the ability of researchers to achieve such goals by providing one-dimensional insight into a complex, multidimensional experimental domain, wasting precious resources in the process. Design of experiments (DoE) in conjunction with response surface methodology (RSM) offers an accelerated route for multivariate investigation and optimization of nanocrystal syntheses. The method enables systematic analysis and multidimensional modeling of the independent and dependent effects that any number of factors have on chosen responses, resulting in easy optimization of a large synthetic space in a fraction of the experiments. Herein, we will outline the general steps to follow when utilizing DoE and RSM for screening and optimization of nanocrystal syntheses, as well as the background needed to appropriately design an investigation and understand the results.
Copper selenides are an important family of materials with applications in catalysis, plasmonics, photovoltaics, and thermoelectrics. Despite being a binary material system, the Cu–Se phase diagram is complex and contains multiple crystal structures in addition to several metastable structures that are not found on the thermodynamic phase diagram. Consequently, the ability to synthetically navigate this complex phase space poses a significant challenge. We demonstrate that data-driven learning can successfully map this phase space in a minimal number of experiments. We combine soft chemistry (chimie douce) synthetic methods with multivariate analyses via classification techniques to enable predictive phase determination. A surrogate model was constructed with experimental data derived from a design matrix of four experimental variables: C–Se bond strength of the selenium precursor, time, temperature, and solvent composition. The reactions in the surrogate model resulted in 11 distinct phase combinations of copper selenide. These data were used to train a classification model that predicts the phase with 95.7% accuracy. The resulting decision tree enabled conclusions to be drawn about how the experimental variables affect the phase and provided prescriptive synthetic conditions for specific phase isolation. This guided the accelerated phase targeting in a minimum number of experiments of klockmannite CuSe, which could not be isolated in any of the reactions used to construct the surrogate model. The reaction conditions that the model predicted to synthesize klockmannite CuSe were experimentally validated, highlighting the utility of this approach.
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