Classic adsorption isotherms incorporated in modern surface complexation models: Implications for sorption of actinides

Computer-aided surface complexation models (SCMs) are widely used in describing mineral-water interface reactions such as sorption of actinides onto (hydr)oxides and clays. Most SCMs are built upon balances of surface binding sites. In fact, such models can reproduce only competitive Langmuir isotherms, plus optional electrostatic corrections. Hence, it may be difficult to extend such SCMs to some real-surface phenomena (site heterogeneity, lateral interactions, surface precipitation) described in isotherms other than Langmuir. In this contribution, a new approach to overcome this difficulty is presented which does not use surface site balances, is not restricted only to Langmuir isotherms, and can be implemented within the Gibbs energy minimization solvers of chemical (adsorption) equilibria. It is suggested to define the ideal behavior of a surface species using a linear isotherm only. Conversely, an adsorption isotherm equation of choice can be split into a linear term (involving the standard-state density and the equilibrium constant referenced to infinite dilution) and a non-linear surface activity coefficient term (SACT, involving the site density parameter). A simple method is proposed for deriving a SACT for the monodentate surface binding from the Langmuir isotherm. This method is then applied to obtain SACTs for mono-, bi-, tri- and tetra-dentate binding from the “quasi-chemical approximation” isotherm, as well as a SACT accounting for non-ideal lateral interactions between surface species from the Frumkin isotherm. The new approach is illustrated by modeling UVI adsorption on goethite at ambient conditions using a GEM SCM. It is shown that SACTs are useful at moderate- to high surface coverage, but only when the site density parameter is fixed from independent (crystallographic) data and not adjusted to fit the titration data. Ways to enhance SCMs with BET, Freundlich and other isotherms of interest for retention of actinides and fission products on mineral surfaces are also discussed.

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