92168.pdf

Liquid-gas and liquid-liquid interfaces 83

The Gibbs equation in this form could be applied to a solution of a

non-ionic surfactant. For a solution of an ionic surfactant in the

absence of any other electrolyte, Haydon and co-workers^3 '^151 have

argued that equations (4.20) and (4.21) should be modified to allow

for the fact that both the anions and the cations of the surfactant will

adsorb at the solution surface in order to maintain local electrical

neutrality (even though not all of these ions are surface-active in the

amphiphilic sense). For a solution of a 1:1 ionic surfactant a factor of

2 is required to allow for this simultaneous adsorption of cations and

anions, and equation (4.21) must be modified to

p _i _ @_ ^4,ZZJ j_ it -y)\

2RT dcB

In the presence of excess inert electrolyte, however, an electrical

shielding effect will operate and equation (4.21) will apply.

Experimental verification of the Gibbs equation

The general form of the Gibbs equation (dy = —2 F/d/i,,) is
fundamental to all adsorption processes. However, experimental
verification of the equation derived for simple systems is of interest in
view of the postulation which was made concerning the location of
the boundary surface.
McBain and Swain^152 succeeded in verifying the validity of the
Gibbs equation by means of a very direct and ingenious experiment.
Surface layers of about 0.1 mm thickness were shaved off solutions of
surface-active materials, such as phenol and hydrocinnamic acid,
contained in a long rectangular trough, by means of a rapidly moving
microtome blade. The material collected was analysed and experi-
mental surface excess concentrations were calculated. These compared
well with the corresponding surface excess concentrations calculated
from surface tension data.
Surface concentrations have also been successfully measured^47 by
labelling the solute with a ^-emitting radioactive isotope (e.g.

(^3) H, (^14) C, (^35) S or (^45) Ca) and measuring the radiation picked up by a
Geiger counter placed immediately above the surface of the solution.
As /8-rays are rapidly attenuated in the solution, the measured
radiation corresponds to the surface region plus only a thin layer of
bulk region. Direct measurement of surface concentrations is