Page 223 - Introduction to Colloid and Surface Chemistry

212 Colloid stability
sols, especially in relation to added electrolyte, is treated in terms of
the energy changes which take place when particles approach one
another. The theory involves estimations of the energy due to the
overlap of electric double layers (usually repulsion) and the London-
van der Waals energy (usually attraction) in terms of interparticle
distance, and their summation to give the total interaction energy in
terms of interparticle distance. Colloid stability is then interpreted in
terms of the nature of the interaction energy-distance curve (see
Figures 8.2-8.4). Theoretical calculations have been made for the
interactions (a) between two parallel charged plates of infinite area
and thickness, and (b) between two charged spheres. The calculations
for the interaction between flat plates are relevant to the stability of
thin soap films, and have been related with a reasonable measure of
success to experimental studies in this field 98 (see Chapter 10). The
calculations for the interaction between spheres are relevant to the
stability of dispersions and will be outlined. In fact, the conclusions
arising from both theoretical treatments are broadly similar.

Double-layer interaction energies

The calculation of the interaction energy, V R, which results from the
overlapping of the diffuse parts of the electric double layers around
two spherical particles (as described by Gouy-Chapman theory) is
complex. No exact analytical expression can be given and recourse
must be had to numerical solutions or to various approximations.
If it is assumed that ion adsorption equilibrium is maintained as
two charged particles approach each other and their double layers
overlap, two well-defined situations can be recognised. If the surface
charge is the result of the adsorption of potential-determining ions,
the surface potential remains constant and the surface charge density
adjusts accordingly; but if the surface charge is the result of
ionisation, the surface charge density remains constant and the
surface potential adjusts accordingly (see page 180). At large
interparticle separations the difference between constant potential
99
and constant charge interactions will be minimal. Overbeek has
considered this problem and concluded that the rate of double-layer
overlap in a typical Brownian motion encounter between particles is
too fast for adsorption equilibrium to be maintained and that the true
situation will, in general, lie somewhere between constant potential
and constant charge.