The acid-base properties of brides are well described by the surface c
omplexation model, which superposes a thermodynamic description of aci
d-base reactions at the oxide surface with a double-layer model of the
electrostatics at the solid-solution interface. So far, however, this
model has not been extended to include the effects of permanent charg
es such as result, for example, from isomorphic substitution in clays.
Contrary to oxides, solids with permanent charge often exhibit an inc
reasing degree of protonation with decreasing ionic strength at low pH
. They also show an increase in their zero proton condition (ZPC) with
decreasing ionic strength. Here we examine the influence of the pH-in
dependent charge of a solid on its acid-base properties. We consider t
wo simple cases: model 1 in which all the acid-base groups and pH-inde
pendent charges are distributed at the surface of a nonpenetrable soli
d, at the interface with the solution; Model 2 in which the solid is p
orous (i.e., penetrable by water and electrolyte ions), and the pH-ind
ependent charges are distributed inside the bulk of the solid, while t
he acid-base groups are on the surface of the solid. For model 1, the
Gouy-Chapman theory yields the surface potential as a function of surf
ace charge and ionic strength; for model 2, the solution to the Poisso
n-Boltzmann equation applied both inside and outside the solid yields
expressions for the internal and surface potentials as a function of i
nternal charge, surface charge, and ionic strength. When these equatio
ns are used with reasonable physical and chemical parameters for model
s 1 and 2, the resulting acid-base calculations exhibit the same quali
tative behavior as observed experimentally for clays. Models 1 and 2 a
i-e then shown to describe parsimoniously published acid-base titratio
n data for kaolinite and montmorillonite, respectively.