Adsorption isotherm modeling of carbendazim and flumetsulam onto homoionic-montmorillonite clays: comparison of linear and nonlinear models

This study deals with the adsorption of two pesticides, carbendazim and flumetsulam, from aqueous solutions onto four homoionic-montmorillonite clays (Ag$^{+}$, Zn$^{2+}$, Cu$^{2+}$, and H$^{+})$. Equilibrium adsorption isotherm data were analyzed using Freundlich, Dubinin-Radushkevich, and Temkin isotherms. Linear and nonlinear fitting methods were compared to determine the best-fitting isotherms for the experimental data. Three error analysis methods were used to evaluate the data for each method: the coefficient of determination (R$^{2})$, sum of squared errors (SSE), and chi-square test ($\chi^{2})$. Equilibrium adsorption isotherms exhibited that the carbendazim adsorption mainly involved cation exchange with homoionic-montmorillonite adsorbents. However, for flumetsulam, the main mechanisms were possibly the cation bridging by Ag$^{+}$, Zn$^{2+}$, and Cu$^{2+}$ cations and the surface complexation reactions of the adsorption on homoionic-montmorillonite (H$^{+})$ adsorbent. The modeling results showed that the nonlinear Freundlich model could fit the data better than the Dubinin-Radushkevich or Temkin models, with relatively higher R$^{2}$ and smaller SSE and $\chi ^{2}$ values. Thus, the nonlinear method is a better way to obtain the isotherm parameters.