Geoscience Reference
In-Depth Information
Fig. 5.5 Distribution of electrical charges and potentials in a double layer according to a Gouy-
Chapman model and b Stern model, where w
0
and w
d
are surface and Stern potentials,
respectively, and d is the thickness of the Stern layer
The Gouy-Chapman model assumes (1) the exchangeable cations exist as point
charges, (2) colloid surfaces are planar and infinite in extent, and (3) surface
charge is distributed uniformly over the entire colloid surface. Even though this
assumption does not correspond to the subsurface environment, it works well for
the clay colloid component of the subsurface, a fact that may be explained by
mutual cancelation of other interferences. Stern (
1924
) and Grahame (
1947
)
refined the Gouy-Chapman model by recognizing that counter-ions are unlikely to
approach the surface more closely than the ionic radii of the anions and the
hydrated radii of the cations.
The Gouy-Chapman model assumes that the charge is spread uniformly over
the surface, with the overall charge allocation in solution consisting of a non-
uniform distribution of point charges. The solvent is treated as a continuous
medium influencing the double layer only through its dielectric constant, which is
assumed independent of its position in the double layer. Moreover, it is assumed
that ions and surfaces are involved only in electrostatic interactions. The derivation
