Efficient preparation of magnesium–aluminum mixed metal oxide and reaction integration mediated by ball milling technology, and the kinetics study of non-constant temperature reaction systems based on the “MTM” method

In this study, a friendly synthesis route for Mg–Al mixed metal oxide catalysts was successfully developed using the one-pot ball milling method, which was then applied to cyclohexanone self-condensation. This solvent-free solid-phase preparation, driven by mechanical force, rapidly fabricates the mixed metal oxide crystalline phase. Unlike the traditional hydrothermal co-precipitation method, it eliminates the need for solvent separation and recycling, reducing preparation time from hours to just 30 min. Consequently, it is both environmentally friendly and efficient. The structure and performance of the catalyst were analyzed using various techniques. Results indicate that it has a higher active sites density and is effective in cyclohexanone condensation reactions. The mean temperature method (MTM) was also proposed to analyze the temperature fluctuations during the ball milling process, which more accurately reveals the impact of temperature variations on the reaction. The results demonstrate that the ball milling method has a low apparent activation energy (Ea, app = 46.25 kJ/mol), indicating its superiority in catalytic reactions.