often stick out partly in the one, partly in the other phase. This is not
possible at solid interfaces.
At a fluid interface (gas–liquid or liquid–liquid) interfacial tension can
be measured, and adsorption leads to lowering ofg(Figure 10.4). The extent
by whichgis decreased is called thesurface pressure, defined as
P:g 0 g ð 10 : 1 Þ*Pis, likeg, expressed in N?m^1. If the surface containing adsorbate is
confined between barriers, as is illustrated in Figure 10.2b, the surface
pressure appears to become manifest as a force acting on the barrier, which
equalsPtimes the length of the barrier. Nevertheless, the force is not due to
an autonomous pressure but to a difference in the tensile (two-dimensional)
stresses acting on either side of the barrier. A surface tension always ‘‘pulls,’’
never ‘‘pushes.’’
10.2.1 The Gibbs Adsorption Equation
Adsorption occurs because it lowers the free energy of the system.
According to Gibbs, the chemical potential of the adsorbate is at
equilibrium equal in the solution and at the surface. He further postulated
an infinitely thindividing planebetween the two phases and then derived the
equation
dP¼dg¼RTGdlna ð 10 : 2 Þ*where R and T have their normal meanings. G is the surface excess
concentration (in moles per square meter) of the adsorbate, usually
abbreviated to surface excess. a is the thermodynamic activity of the
adsorbatein the solution. Note that it does not matter in what unitsais
expressed, since d lna¼(1/a)da. The equation is valid, and exact, for one
solute at equilibrium. It is especially useful ifgcan be measured, i.e., for
fluid interfaces.
Thesurface excesscan be defined in various ways. Actually, there is no
true dividing plane, but rather an A–W interface that is not sharp, since
molecules have a finite size and moreover exhibit Brownian motion. Hence
the ‘‘interface’’ extends over a layer of some molecular diameters. In the
derivation of Eq. (10.2), the position of the dividing plane has been chosen
so that the surface excess of the solvent is zero. In Figure 10.5 the
concentration of the solute is depicted as a function of the distance from the
dividing plane (z). In Figure 10.5a, there is no adsorption: the two hatched
areas on either side of the dividing plane are equal. (Because of the definition