Versatility of the Langmuir Equation Is Rooted in Its Theoretical and Empirical Nature.

The Langmuir equation has been widely used in studying adsorption of chemical species to surfaces. The versatility is firmly rooted in its dual theoretical and empirical nature, depending on the system of interest. While initially developed for gaseous adsorption, it has been commonly used in liquid systems. In the past, we have used the Langmuir equation to study sorption of phosphate (P) on soils, antibiotics on biochars, and arsenic on magnetite nanoparticles. For amorphous and heterogeneous sorbents such as soils and biochars, we considered the Langmuir model as an empirical fitting equation. For well-crystalized and homogeneous sorbents such as magnetite nanoparticles, the Langmuir equation has physical meaning and can be used to infer adsorption mechanisms. More specifically, we used a modified Langmuir equation to estimate zero-sorption equilibrium concentration of P in soils that is an index of P release potential. We also fitted lincomycin sorption isotherms on manure-derived biochars to estimate maximum sorption capacity. Indeed, for these heterogeneous sorbents, the Langmuir equation was used empirically to assess the release and sequestration potential of targeted species. For arsenic adsorption on magnetite nanoparticles, the Langmuir equation was employed to understand the thermodynamics of adsorption reaction, which was then corroborated with microscopic and spectroscopic investigations to identify reaction mechanisms. Therefore, the Langmuir equation is a powerful tool for both theoretical and empirical applications in soil and environmental chemistry.