In the present study, the effect of calcination temperature on the structure and performance of mesoporous CaO/TiO 2 -ZrO 2 catalyst fabricated by sol-gel method used in the esterification reaction was assessed. Then, CaO/TiO 2 catalyst was also synthesized via the same method to evaluate the effect of zirconia cations on its properties and activity. The samples were characterized by X-ray Diffraction (XRD), Fourier transmittance infra-red (FT-IR), Brunauer-Emmett-Teller (BET)-BarrettJoyner-Halenda (BJH), scanning electron microscope (SEM) and transmission electron microscopy (TEM) analyses. Moreover, Hammett indicator method was utilized to assess the acidity and basicity of the samples. It was found that zirconium was clearly incorporated in CaO/TiO 2 lattice and transformed that from amorphous phase to crystalline structure. In addition, the basicity and acidity of CaO/TiO 2 was clearly increased by zirconia loading. Evaluation of the samples' activity presented that CaO/TiO 2 catalyst exhibit no activity in the esterification reaction, while all CaO/TiO 2 -ZrO 2 catalysts showed high ability to convert oleic acid to its ester. Moreover, the catalyst calcined at 400 °C showed the highest activity in the esterification reaction with desirable properties such as high crystallinity, acidity, basicity and surface area along with well-distribution of particle size and pore size. The best catalyst converted around 90% of oleic acid to ester at optimized conditions of 150 °C, 12:1 molar ratio of methanol/oleic acid, 3 wt% of catalyst for 4 h of reaction time. Moreover, the sample was successfully used for five runs without significant reduction in activity that makes it a suitable choice as a catalyst for industrial applications.

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.