Page 199 - Introduction to Colloid and Surface Chemistry

188 Charged interfaces
electrokinetic potentials (rarely in excess of 75 mV) compared with
thermodynamic potentials (which can be several hundred millivolts).
89
A refinement of the Stern model has been proposed by Grahame ,
who distinguishes between an 'outer Helmholtz plane* to indicate the
closest distance of approach of hydra ted ions (i.e. the same as the
Stern plane) and an 'inner Helmholtz plane' to indicate the centres of
ions, particularly anions, which are dehydrated (at least in the
direction of the surface) on adsorption.
Finally, both the Gouy-Chapman and the Stern treatments of the
double layer assume a uniformly charged surface. The surface
charge, however, is not 'smeared out' but is located at discrete sites
on the surface. When an ion is adsorbed into the inner Helmholtz
plane, it will rearrange neighbouring surface charges and, in doing so,
impose a self-atmosphere potential <j>p on itself (a two-dimensional
analogue of the self-atmosphere potential occurring in the Debye-
Hiickel theory of strong electrolytes). This 'discreteness of charge'
effect can be incorporated into the Stern-Langmuir expression,
which now becomes

N A I *-K\vd r tj/fl/ r v (7 21)
«oKn L kT
The main consequence of including this self-atmosphere term is that
the theory now predicts that, under suitable conditions, i^ d goes
through a maximum as tf/ 0 is increased. The discreteness of charge
effect, therefore, explains, at least qualitatively, the experimental
observations that both zeta potentials (see Figure 7.4) and coagulation
concentrations (see Chapter 8) for sols such as silver halides go
through a maximum as the surface potential is increased 183 .

Ion exchange

Ion exchange involves an electric double layer situation in which two
kinds of counter-ions are present, and can be represented by the
equation

RA + B = RB + A

where R is a charged porous solid. Counter-ions A and B compete for
position in the electric double layer around R, and, in this respect,