Geoscience Reference
In-Depth Information
is for a flat surface, infinite in size. The double-layer theory applies equally well to
rounded or spherical surfaces (Overbeek
1952
). The model of Stern (
1924
)
assumes that the region near the surface consists of a layer of ions known as the
Stern layer and a diffuse ion layer. A schematic representation illustrating the
fundamental differences between the Gouy-Chapman and Stern models is pre-
sented in Fig.
5.5
.
The surface charge is balanced by the charge in solution, which is distributed
between the Stern layer at a distance d from the surface and a diffuse layer having
an ionic Boltzmann-type distribution. The total charge r is therefore due to the
charge in the two layers:
r ¼
ð
r
1
þ
r
2
Þ;
ð
5
:
10
Þ
where r
1
is the Stern layer, and r
2
is the diffuse layer charge.
A development of the DDL theory also considers the interactions between the
two flat layers of the Gouy-Chapman model. The double-layer charge is affected
only slightly when the distance between the two plates is large. Grahame (
1947
)
suggests that specifically adsorbable anions may be adsorbed into the Stern layer
when they lose their hydration water, whereas the hydrated cations are attracted
only electrostatically to the surface. Bolt (
1955
) added the effects of ion size,
dielectric saturation, polarization energy, and coulombic interactions of the ions,
as well as short-range repulsion of ions into the Gouy-Chapman model. Note that
the simple Gouy-Chapman model gives fairly reliable results for colloids with a
constant charge density not exceeding 0.2-0.3 C/m
2
.
The Gouy-Chapman model provides an invaluable answer to a number of
processes occurring in the subsurface system, by explaining the exchange capacity
concept for the range of surface charge densities normally encountered in clays
(Bolt et al.
1991
). In general, double-layer theory explains the processes occurring
in the contaminant-subsurface system when the pollutants have a charge opposite
to that of the surface. By studying molecular dynamics simulations of the electrical
double layer on smectite surfaces contacting concentrated mixed electrolyte (Na-
CaCl
2
) solutions, Bourg and Sposito (
2011
) defined three ion adsorption planes: 0,
b, and d with different qualifications. The locations of b- and d-planes are inde-
pendent of ionic strength or ion type, and ''indifferent electrolyte'' ions can occupy
all three planes.
CEC and selectivity are among the most important processes that control the
fate of charged (ionic) contaminants in the subsurface. These processes involve the
cationic concentration in solution and the cation dimensions, as well as the con-
figuration of exchange sites on the interface. The Gapon relation approaches the
process as an exchange of equivalents of electric charges, where the solute con-
centration is measured in terms of activity and the adsorption on an equivalent
basis.
Negatively charged surfaces having the same exchange properties do not nec-
essarily interact in the same manner with different cations having the same
