Statistical experimental design, least squares-support vector machine (LS-SVM) and artificial neural network (ANN) methods for modeling the facilitated adsorption of methylene blue dye

Abstract

This study is based on the usage of a composite of zinc sulfide nanoparticles with activated carbon (ZnS-NPs-AC) for the adsorption of methylene blue (MB) from aqueous solutions. The properties of ZnS-NPs-AC were identified by X-ray diffraction (XRD), field emission scanning electron microscopy (FE-SEM), energy dispersive X-ray spectroscopy (EDS) and Fourier transformation infrared spectroscopy (FTIR). Response surface methodology (RSM), an artificial neural network (ANN) and the least squares-support vector machine (LS-SVM) were used for the optimization and/or modeling of pH, ZnS-NPs-AC mass, MB concentration and sonication time to develop respective predictive equations for the simulation of the efficiency of MB adsorption. The obtained results using LS-SVM and ANN exhibit two nonlinear approaches (LS-SVM and ANN models) which show better performances in comparison to central composite design (CCD) for the prediction of MB adsorption. The root mean square error (RMSE) values corresponding to the validation set for MB were 0.00013, 0.00071 and 0.00117, while the respective coefficient of determination (R²) values were 0.9996, 0.9983 and 0.9978 for the LS-SVM, ANN and CCD models, respectively. In the training set, the RMSE values of 0.00011, 0.00065 and 0.00110 and the R² values of 0.9997, 0.9984 and 0.9980 were obtained using the LS-SVM, ANN and multiple linear regression (MLR) models, respectively. The significant factors were optimized using CCD combined with desirability function (DF) and genetic algorithm (GA) approaches. The obtained optimum point was located in the valid region, experimental confirmation tests were conducted and good agreement was found between the predicted and experimental data. The optimum conditions for searching for the optimum point were set as pH 7.0, 0.015 g ZnS-NPs-AC, 20 mg L⁻¹ MB and 3 min sonication, while at this point, the removal percentages were 98.02% and 98.12% by the DF and GA approaches, respectively. The adsorption equilibrium data in all conditions according to the optimum point are represented by the Langmuir model with a maximum monolayer adsorption capacity of 243.90 mg g⁻¹ while, in all situations, the kinetics and rate of MB adsorption follow the pseudo-second-order kinetic model. Moreover, ZnS-NPs-AC was efficiently regenerated using methanol and, over five cycles, the removal percentage did not change significantly.