Page 215 - Introduction to Colloid and Surface Chemistry

204 Charged interfaces

conductivity in the mobile part of the double layer can be calculated
(and is allowed for in the treatments of relaxation which are outlined
in the next section). Experimental surface conductivities (which are
not very reliable) tend to be higher than those calculated for the
mobile part of the double layer, and the possibility of surface
conductance inside the shear plane, especially if the particle surface is
porous, has been suggested to account for this discrepancy 901188 .
There is, therefore, some uncertainty regarding the influence of
surface conductance on electrophoretic behaviour; however, it is
unlikely to be important when the electrolyte concentration is greater
3
than c. 0.01 mol dm~ .

Relaxation

The ions in the mobile part of the double layer show a net movement
in a direction opposite to that of the particle under the influence of
the applied electric field. This creates a local movement of liquid
which opposes the motion of the particle, and is known as electro-
phoretic retardation. It is allowed for in the Henry equation.
The movement of the particle relative to the mobile part of the
double layer results in the double layer being distorted, because a
finite time (relaxation time) is required for the original symmetry to
be restored by diffusion and conduction. The resulting asymmetric
mobile part of the double layer exerts an additional retarding force
on the particle, known as the relaxation effect, and this is not
accounted for in the Henry equation. Relaxation can be safely
neglected when KU is either small (< c. 0.1) or large (> c. 300), but it
is significant for intermediate values of KU especially at high potentials
and when the counter-ions are of high charge number and/or have
low mobilities.
190
Wiersema, Loeb and Overbeek have derived equations which
allow for retardation, relaxation and for surface conductance in the
mobile part of the double layer, and have solved them numerically by
computer. The main assumptions upon which this treatment is based
are:

1. The particle is a rigid, non-conducting sphere with its charge
uniformly distributed over the surface.
2. The electrophoretic behaviour of the particle is not influenced by
other particles in the dispersion.