Modelling and Optimisation of the Sol-Gel Conditions for Synthesis of Semi-Hexagonal Titania-Based Nano-Catalyst for Esterification Reaction

Design and fabrication of a catalyst with the highest activity can be achieved by optimising the synthesis conditions. In this study, the sol-gel synthesis conditions of citric acid concentration, gelling temperature, complex time, and calcination temperature were studied for the preparation of a novel semi-hexagonal calcium/titania-zirconia nano-catalyst used in the esterification reaction. After synthesis of around 24 samples at various conditions, their activity was tested in the esterification reaction and the results were analysed by multi-layer perceptron (MLP) and support vector machine (SVM) models. Both models predicted the actual data with high coefficients of determination, and indicated that the calcination temperature has the most influence on the activity of the prepared semi-hexagonal calcium/titania-zirconia nano-catalyst for the esterification reaction. Moreover, the genetic algorithm (GA) was utilised for optimising the preparation conditions based on the SVM model, due to its higher generalisation capability for prediction. The prepared nano-catalysts under the optimum conditions of 1.42 acid ratio, gelling temperature of 72 °C, complex time of 2.65 h, and calcination temperature of 487 °C showed good crystalline structure and metal–metal and metal–oxygen cation bonding. Finally, the fabricated catalyst had a high surface area (276.5 m2/g) with 3.5 nm pore diameter and almost uniform particle size (80–110 nm) distribution, leading to a high conversion of 97.6% in the esterification reaction, with good catalytic stability up to five times.