Empirical adsorption kinetics: comparing linear and nonlinear regression analysis emphasizing the need for high throughput analysis.

This paper evaluates linear and nonlinear regression analysis to describe the empirical adsorption kinetics using pseudo-first-order (PFO) and pseudo-second-order (PSO) models. These models have been used to characterize the performance of adsorbents for environmental remediation and environmental modeling. Data were simulated using the PFO and PSO models with 1, 2, and 5% noise levels and fitted by nonlinear and linearized PFO and PSO equations. Nonlinear regression analysis provided rate constants and adsorption capacities with better accuracy than linearization. Besides the correlation coefficient, Chi-square and residual plot analysis helped choose the proper model to describe the adsorbent efficiency and validate the results. Both models and the NLR fitting were employed to reevaluate data obtained in our research group, including the adsorption of Hg(II) on thiol-modified vermiculite, glyphosate on soils rich in aluminum and iron oxides, phosphate on Fe(III) polyhydroxy cations modified montmorillonite, and paraquat on soil and vermiculite. While fitting the simulated data indicates an unequivocal and correct kinetic model, fitting the experimental data is not straightforward, suggesting mixed models rule the adsorption and that a large number of data points, especially at the initial steps of adsorption, provided by high throughput analysis, help to improve the kinetic modeling.