S-shaped adsorption isotherms modeled by the Frumkin–Fowler–Guggenheim and Hill–de Boer equations

Abstract

In this study, we used the Frumkin–Fowler–Guggenheim (FFG) and Hill–de Boer (HDB) isotherm models to describe previously published S-shaped isotherms involving water contaminant adsorption, specifically auramine-O and ortho-nitrophenol, onto solid materials. Although the two models differ in their mathematical formulations, they share three key parameters: the monolayer adsorption capacity (qm), the equilibrium constant representing adsorbate−adsorbent interactions, and the equilibrium constant representing adsorbate–adsorbate interactions. Upon comparing the data fitting capabilities of the FFG and HDB models, we found minimal differences. However, substantial discrepancies emerged in the fitted qm values. The FFG model yielded qm values that aligned with the plateaus evident in the auramine-O and ortho-nitrophenol isotherms, whereas the HDB model did not. This inconsistency in the HDB model was also observed when analyzing a hyperbolic tetracycline isotherm. In addition, we delved into the impact of the adsorbate−adsorbent and adsorbate–adsorbate interaction constants on simulated isotherm curves. Our findings revealed that the adsorbate−adsorbent interaction constant influenced the steepness of the simulated curves, while the adsorbate–adsorbate interaction constant determined the nature of isotherm curve generated by the two models (S-shaped or hyperbolic).