Mechanical production and sonocatalytic application of Cu₂S nanoparticles for degradation of isopropylxanthic acid: Kinetic modeling via white and black box methods

Three kinetic models were used for disclosing the kinetic characteristics of isopropylxanthic acid degradation via sonocatalytic process in the presence of Cu₂S nanoparticles (NPs). The high-energy planetary mechanical ball milling (HEBM)was used for the production of Cu₂S NPs in different milling times of 0.5, 1.5, 3 and 4.5 h. A thorough characterization analysis was performed to investigate some physical and chemical properties of the samples. The main oxidizing species during the sonocatalytic process were determined using organic and inorganic scavengers in different concentrations. In the first step, to calculate the sodium SIPX RE (%), a mathematical kinetic model, which is a type of deterministic white box model, was established based on the reaction mechanism, the scientific assumptions, and the responsible oxidizing species. Secondly, another category of deterministic white box modeling such as an empirical kinetic modeling was developed using nonlinear regression analysis based on the main key factors. The proposed kinetic models were able to closely describe the evolution of k_app with each of the operating parameters. Thirdly, a three layered feed forward back propagation neural network (ANN), as a type of black box modeling, was built to compare the effectiveness of the two groups of the models. Prediction results by ANN declared the high accuracy of this model (R² and MSE values were 0.995 and 4.361, respectively). Finally, analysis of variance (ANOVA)used to compare the ability and the accuracy of the three developed models. ANOVA results showed that there was a significant difference between the predicted values of the deterministic white box models and the black box model. Therefore, under certain operating conditions, the models could not be used instead.