The adsorption of one phosphonate, two hydroxyphosphonates, and five aminophosphonates onto the iron (hydr)oxide goethite (␣-FeOOH) has been studied as a function of pH. At phosphonate concentrations significantly lower than the total number of available surface sites, nearly 100% adsorption is observed below pH 8.0. Adsorption decreases to negligible levels as the pH is increased to 12.0. Under the conditions just described, adsorption of nitrilotris(methylenephosphonic acid) as a function of pH is nearly independent of the ionic strength (from 1 mM to 1 M). At phosphonate concentrations close to the total number of available surface sites, adsorption decreases over a broader range in pH and reflects the number of phosphonate groups. At pH 7.2, the maximum extent of adsorption decreases as the number of phosphonate groups increases from one to five. Adsorption is modeled using a 2-pK constant capacitance model that postulates formation of a 1:1 surface complex involving one surface site and one phosphonate functional group. Denoting the fully deprotonated phosphonate ligand as L a؊ , different protonation levels for adsorbed phosphonate species are represented by a series of equilibrium constants of the form n؉1) ] .
For a phosphonate of charge a؊, there are (a ؊ 1) possible surface protonation levels. For a surface protonation level n, log  n,surf values derived from this modeling approach are related to the surface complex charge Z through the following linear relationship: log  n,surf ؍ (11.45 ؉ 7.31 ؒ n) ؊ (2.53 ؊ 0.46 ؒ n) ؒ Z.
Using this approach, adsorption as a function of phosphonate concentration and pH can be fully accounted for.