Source-normalized error analysis method for accurate prediction of adsorption isotherm: application to Cu(II) adsorption on PVA-blended alginate beads

In the present work, alginate-blended polybeads (ALPVA) were synthesized and were employed for Cu(II) adsorption from the water sample. The parameters for efficient adsorption of Cu(II) on ALPVA beads were optimized by batch adsorption studies. The ALPVA beads were characterized using FESEM, EDAX, and BET surface area analysis. The adsorption isotherm studies are essential in determining the final distribution of adsorbate on the adsorbent, which in turn can help in elucidating the mechanism of adsorption. The experimental data of Cu(II) adsorption were analyzed using modified Langmuir, Freundlich, Temkin, Sips, and modified Langmuir–Freundlich isotherm models. The conventional methods for finding the best fitting isotherm are based on the calculation of regression coefficient values. However, for nonlinear adsorption isotherm models, regression coefficient values can be misleading. To overcome errors caused due to regression analysis, error analysis on Cu(II) adsorption data was performed. Five different errors, namely the sum of the squares of errors, the average relative error, the hybrid fractional error function, the Marquardt's percent standard deviation, and the sum of the absolute errors, were calculated. The best adsorption isotherm was predicted by normalizing five error functions and finding the sum of normalized error (SNE). The Sips isotherm model was found to be the best fitting model with the minimum SNE value for Cu(II) adsorption on ALPVA beads. SNE values indicated the sum of the square error, and hybrid error functions provided the best overall results.