92168.pdf

188 Charged interfaces

electrokinetic potentials (rarely in excess of 75 mV) compared with

thermodynamic potentials (which can be several hundred millivolts).

A refinement of the Stern model has been proposed by Grahame^89 ,

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,