Bayesian Optimization of Wet-Impregnated Co-Mo/Al₂O₃ Catalyst for High-Yield Carbon Nanotubes

Carbon nanotubes (CNTs) have become a significant component for various fields because of their outstanding electronic and mechanical properties. To meet the requirement of specific applications, CNTs synthesis with controlled properties is significantly required. Chemical vapor deposition (CVD) using solid supported catalysts is considered an attractive approach for controllability of the nanostructure and large scale production. Since the early 2000s, many researchers have used mono-metallic catalysts to control CNT properties, but it was hard. To overcome these limitations, bi- and tri-metallic catalysts are being studied. However, there are a variety of possible combinations of multi-metallic catalyst systems. In addition, the development of multi-metallic catalysts requires a more complicated optimization than that of mono-metallic catalysts.<br/>In this presentation, we introduce our research efforts to implement Bayesian optimization (BO) in optimizing a bimetallic catalyst for the CVD growth of CNTs. BO, one of a machine learning processes based on Bayes’ theorem that finds the optimum value of a black-box function, could quickly optimize parameters of less than 20 dimensions. BO consists of two main components: surrogate model and acquisition function. The surrogate model is a model that performs probabilistic estimation of the shape of a black-box function based on the investigated input-output values ((x₁, f(x₁), …, (x_n, f(x_n)). The acquisition function is a function that recommends input values for the next experiment based on the probabilistic estimation of the surrogate.<br/>Specifically, we attempted to optimize the wet impregnation of Co-Mo/Al₂O₃ catalyst. Co-Mo is one of the famous bimetallic system because of their ability to synthesize chirality-specific single-walled CNTs. Here, we optimized the experimental variables to maximize the CNT yield. Four input parameters were chosen: total wt% of catalyst, ratio of Co and Mo of catalyst, drying temperature, and calcination temperature. To compare the performance of two types of acquisition functions: Expected improvement (noise-free) and One-shot knowledge gradient (with noise), we parallelly performed two BO processes. As a result, both the acquisition functions successfully optimized the CNT yield with similar performance. The contour plot established by the surrogate model that predicts black-box function show that addition of Mo has negative effect on CNT yield. This study demonstrates the potential of BO in the material synthesis.