Searching for optimum adsorption curve for metal sorption on soils: comparison of various isotherm models fitted by different error functions

Abstract

Studies comparing numerous sorption curve models and different error functions are lacking completely for soil-metal adsorption systems. We aimed to fill this gap by studying several isotherm models and error functions on soil-metal systems with different sorption curve types. The combination of fifteen sorption curve models and seven error functions were studied for Cd, Cu, Pb, and Zn in competitive systems in four soils with different geochemical properties. Statistical calculations were carried out to compare the results of the minimizing procedures and the fit of the sorption curve models. Although different sorption models and error functions may provide some variation in fitting the models to the experimental data, these differences are mostly not significant statistically. Several sorption models showed very good performances (Brouers-Sotolongo, Sips, Hill, Langmuir-Freundlich) for varying sorption curve types in the studied soil-metal systems, and further models can be suggested for certain sorption curve types. The ERRSQ error function exhibited the lowest error distribution between the experimental data and predicted sorption curves for almost each studied cases. Consequently, their combined use could be suggested for the study of metal sorption in the studied soils. Besides testing more than one sorption isotherm model and error function combination, evaluating the shape of the sorption curve and excluding non-adsorption processes could be advised for reliable data evaluation in soil-metal sorption system.

Exploring Modified Rice Straw Biochar as a Sustainable Solution for Simultaneous Cr(VI) and Pb(II) Removal from Wastewater: Characterization, Mechanism Insights, and Application Feasibility

“…The Fritz–Schlunder isotherm model, also known as the four-parameter model, is employed to analyze experimental data over a broad range and improve the adsorption process through empirical equations. 13 By utilizing nonlinear regression analysis, the parameters of this model can be determined. Equaiton 10 represents the Fritz–Schlunder isotherm model.…”

Removal of fluoride ions from aqueous solutions on unmodified and iron-modified hydrogels

“…Figure 7 shows the concentration of the solute in the adsorbent (qe) as a function of the remaining concentration of fluoride ions in solution (Ce) at different initial concentrations of fluoride ions. The behavior and shape of the curve allow identification of the type of isotherm [75]; in this case, the isotherms are type L, where the relationship between the concentration of fluoride remaining in the solution and that adsorbed in the hydrogel decreases as the solute concentration increases [76].…”

Isothermal adsorption models: mini-focused observations

“…So, this multilayer adsorption model describes how various adsorbate to adsorbent ratio is gained with changing of concentration leading to surface heterogeneity. In this model even in competitive state between different adsorbates, concave curve may represent an adsorption situation with an appropriate correlate coefficient[15, 18,21].Multisystem action of adsorbate (like ion or organic molecule) into homogeneous adsorbent as a macromolecule reflecting non-competition binding phenomenon is known as Hill isothermal model[22].…”