Nonlinear regression for treating adsorption isotherm data to characterize new sorbents: Advantages over linearization demonstrated with simulated and experimental data

This paper demonstrates that determining adsorption capacity and affinity through data fitting of adsorption isotherms by nonlinear regression (NLR) is more accurate than linearized Langmuir equations. Linearization errors and the subjective choice of data points used to apply the linear regression analysis may deviate the fitted adsorption parameters (constants and adsorption capacities) from the expected values. The deviation magnitude increases for heterogeneous sorbents such as environmental particles and molecularly imprinted polymers, which adsorb by more than one sorption mechanism or adsorption sites of diverse chemical natures. For instance, Lineweaver-Burk linearization of isotherms simulated considering the presence of two adsorption sites (distinct adsorption energies) provides excellent linear regression fittings but for only one kind of adsorption site. Contrary, Scatchard and Eadie-Hoffsiee's equations indicate the presence of more than one kind of adsorption site, but if the difference between the adsorption constants is not significant, the choice of points used to perform the computation becomes subjective. On the contrary, NLR analysis considers all the adsorption points (experimental or simulated), providing objective criteria to define if more than one kind of site or retention mechanism rules the adsorbed amounts of analyte. The fitted constants have smaller deviations from the expected values than those obtained by linearization. In addition to the simulated data, the enhanced robustness of the NLR was demonstrated in the determination of the adsorption capacity and adsorption affinity of a humic acid sample towards Cu2+ at different pH.