Solvation and electrostatic model for specific electrolyte adsorption

A solvation and electrostatic model has been developed for estimating electrolyte adsorption from physical and chemical properties of the system, consistent with the triple-layer model. The model is calibrated on experimental surface titration data for ten oxides and hydroxides in ten electrolytes over a range of ionic strengths from 0.001 M-2.9 M (Sahai and Sverjensky, 1997a). The model assumes the presence of a single type of surface site, >SOH. It is proposed that for a 1:1 electrolyte of the type M+L−, the logarithms of the adsorption constants (Ks,M+and Ks,L−) representing the equilibria >SO− + Maq+ = >SO− − M+and>SOH2+ + Laq− = >SOH2+ − L− contain contributions from an ion-intrinsic component and a solvation component. According to Born solvation theory, log Ks,M+ and log Ks, L− can be linearly correlated with inverse dielectric constant of the k-th mineral (1ϵk) resulting in the equations log Ks,M+ = − δωM+2.303RT1ϵk + log Kii,M+″and log Ks,L− = − δωL−2.303RT1ϵk + log Kii,L+″ The ion-intrinsic part (log Kii″) is a linear function of the inverse electrostatic radius (1re,j) of the j-th aqueous ion, where, in general, j = M+ or L−. The interfacial solvation coefficient (Δ, Ωj) associated with the solvation component is linearly related to the inverse effective radius (1Re,j) of the adsorbed ion and to the charge (Zj) on the ion. The model is consistent with surface protonation constants (Ks,1and Ks,2) calculated from experimental points of zero charge and values of ΔpK predicted from the Pauling bond-strength per unit bond-length (sr>S−OH) of the bulk mineral (Sahai and Sverjensky, 1997a), site-densities (Ns) from isotopic-exchange data, and outer-layer capacitance (C2) equal to 0.2 F m−2. As a first approximation, we also find an empirical trend between capacitance (C1) of the inner-layer and 1(re,ML·ωML) where re,ML is the electrostatic radius and ωML is the solvation coefficient of the aqueous electrolyte. Taken together, these correlations enable the calculation of surface protonation and electrolyte adsorption at equilibrium from the properties of the mineral/ solution system.