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

Abstract

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.

Keywords:

• Modeling
• regression analysis
• kinetic models
• adsorption
• environmental pollutants
• flow analysis
• glyphosate
• phosphate
• mercury
• paraquat

Authors contribution

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Carlos Martin Infante C, Erico Aparecido Oliveira Pereira, Fernando H. do Nascimento and Samara Tessinari Leites. Jorge Cesar Masini wrote the first draft of the manuscript and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

All data generated or analyzed during this study are available from the corresponding author on reasonable request.

Additional information

Funding

This work was funded by National Council for Scientific and Technological Development (CNPq) (Grant No. 306674/2021-1). F.H.N. acknowledges a post-doc fellowship from coordination for the Improvement of Higher Education Personnel (CAPES) for a post-doc fellowship (Contract 88882.315696/2019-01). EAOP acknowledges CNPq for an MSc fellowship (Grant 134790/2016-2). STL acknowledges CNPq for a Ph.D. fellowship (Grant 141106/2016-6).