Having established that the interaction of our mono-divalent, and trivalent cations with the surface is fully reversible, we proceeded to analyze the adsorption isotherms shown in Fig. using a variety of classical adsorption models. Fig. appears to indicate two interaction regimes, one for ion concentrations up to about 0.1 mM and a second regime for higher ion concentrations, as indicated by the dashed lines in Fig. . Attempts to fit a single-or dual-site Langmuir adsorption isotherm model to the data failed, but a dual Kd model 71 of the form qads,i = Kd,i . Cbulk (here, qads,i is the surface coverage in regime i relative to 10 13 cm -2 , the saturation level) resulted in binding constants of 3 to 30 mol -1 and ~300 mol -1 for the low and high concentration regime, respectively, from which we compute adsorption free energies of -13 to -18 and -24 kJ mol -1 at room temperature, respectively (here, we used the 55.5 molarity of liquid water as a standard reference state by which we multiply the binding constants, according to DGi=-RT . ln(55.5 . Kd,i)). The range of binding constants and adsorption free energies in the low concentration regime are the result of using eqn. 1 with only 50% of the total potential to account for just the mobile charges (c.f. Fig. ) as opposed to 100% of the total potential.