Computational intelligence for empirical modelling and optimization of methylene blue adsorption phenomena utilizing an activated carbon-supported [Co(NH3)6]Cl3 complex

The study focuses on the efficiency of hexaamminecobalt (III) chloride (HACo, [Co(NH3)₆]Cl₃) immobilized on activated carbon for removing methylene blue (MB) from water solutions. The primary objective of this study was to assess the sorption performance of HACo immobilized on activated carbon in removing MB from water solutions. Additionally, predictive models were developed to optimize the MB removal percentage. Lastly, the study aimed to determine the optimal conditions for achieving maximum MB removal. Samples were characterized using scanning electron microscopy. Batch sorption experiments were conducted to analyze the impact of MB concentration, adsorbent mass, pH, temperature, and contact time. Predictive models were built using multiple linear regression and neural network techniques, specifically artificial neural networks (ANN) and hybrid ANN–particle swarm optimization (ANN-PSO). The PSO-ANN model with a single hidden layer of eight neurons trained using the Levenberg–Marquardt algorithm demonstrated high accuracy in predicting MB removal percentage, with mean absolute percentage error (MAPE) = 0.083788, root mean square error (RMSE) = 0.11441, and R² = 0.99693. The MB adsorption process followed a mono-layer with one energy model and a pseudo-first-order kinetic model. Optimization using the genetic algorithm revealed that the maximum MB removal percentage of 99.56% is achievable at an MB concentration of 9.36 mg/L, adsorbent mass of 15.72 mg, and temperature of 311.2 K. The study confirms the effectiveness of HACo immobilized on activated carbon for MB removal. The PSO-ANN predictive model proved superior in accuracy compared to empirical models. Optimization results provide the optimal conditions for maximizing MB removal, offering valuable insights for practical applications.