Page 195 - Introduction to Colloid and Surface Chemistry

184 Charged interfaces

er n
N
kT

where cr m is the surface charge density corresponding to a monolayer
of counter-ions, W A is Avogadro's constant and V m is the molar
volume of the solvent. The adsorption energy is divided between
electrical (ze<f> d) and van der Waals (0) terms.
Treating the Stern layer as a molecular condenser of thickness 5
and with a permittivity e',

=
^b ~F(to ~~ to) (7.16)
where OT O is the charge density at the particle surface.
For overall electrical neutrality throughout the whole of the double
layer,
cr 0 + o-! 4- a 2 = 0 (7.17)

where cr 2 is the surface charge density of the diffuse part of the double
layer and is given by equation (7.8) with the sign reversed and with <^ 0
replaced by i^ d.
Substituting from equations (7.16), (7.15) and (7.8) into equation
(7.17) gives a complete expression for the Stern model of the double
layer:
c' ,, , \. v™
— (to- to)+—TT
8 , N,
kT

f* = 0 (7.18)

This expression contains a number of unknown quantities;
however, as indicated below, some information can be derived about
these from other sources.

Permittivity of the Stern layer

The total capacity C of the double layer has been determined from
electrocapillary measurements for mercury-aqueous electrolyte inter-
89
faces , and from potentiometric titration measurements for silver