The Statistical Error Optimization of Dye Sorption Equilibria for the Precise Prediction of Adsorption Isotherms on Activated Graphene

Abstract

The adsorption equilibrium of methyl blue (MB) at different temperatures was optimized using activated graphene (AG) as an adsorbent. The experimental data were compared using five linear and nonlinear adsorption isotherms, namely, Langmuir, Freundlich, Redlich–Peterson (R-P), Sips, and Toth, to estimate the best fit of the equilibrium data. Five distinct error functions were utilized to conduct nonlinear regression for the adsorption equilibrium: SSE, ARE, HYBRID, MPSD, and EABS. These functions offered a wide range of residuals for comparison. For a more accurate prediction of the isotherm model, two statistical techniques—SNE and CND—were applied. By using these techniques in conjunction, a more objective analysis of the error and deviation between the observed and predicted data was achieved, ultimately leading to improved accuracy in the error analysis. The sorption results demonstrated the highest MB removal of 691.89 mg g−1, which amounted to 98.32% within 120 min. The error analysis findings indicated that the SSE and HYBRID functions produced the smallest error residuals. Based on the “goodness of fit” criterion, the models in this study were ranked as R-P > Toth > Langmuir > Sips > Freundlich. Among these models, the R-P isotherm demonstrated the best fit for the data, exhibiting the lowest variance in residuals. Its CND value ranged between 0.0025 and 0.0048, which further supports its superior fit compared to the other models. The combination of multiple error functions and statistical methods allowed for a comprehensive and objective assessment of the nonlinear regression models. The results highlight the importance of using various techniques to improve the accuracy of error analysis and identify the best-fitting isotherms for adsorption.