of the dividing plane, the same curve holds in this case for the concentration
of the water, but at a different vertical scale.) In 10.5b, thereisadsorption,
and the adsorbed amount per unit area, i.e., the surface excess, is
represented by the hatched area under the curve. Notice that in case a
some adsorbate is present at the interface, but there is no excess, as there is
in case b. In Figure 10.5c,negative adsorptionis depicted: the solute stays
away from the interface. According to Eq. (10.2), the surface tension must
then increase with increasing concentration, for instance as in Figure 10.4,
curve for NaCl. In case a,gis not altered, and in case bgis decreased.
Surfactant Concentration. The parameter a needs some
elaboration. In a very dilute system,amay equal the concentration of the
adsorbate (if expressed in the same units), but that is not always true, as
discussed in Section 2.2. Even if it is true, it concerns the concentrationin the
solution, not in the total system. This means that the concentration
adsorbed, which equalsGtimes the specific surface area of the adsorbent,
has to be subtracted from the total concentration.
In Figure 10.6a, examples are given of the relation betweengand log
concentration for some surfactants. Assuming for the moment that the
activity of the solute equals its concentration, the slopes of these curves
would be proportional to the surface excessG. The steeper the slope, the
higherG, implying thatGincreases with increasing surfactant concentration.
This is illustrated by the correspondingadsorption isothermsgiven in Figure
10.6b. It is seen that for a considerable range inc, the slope, and therebyG,
is almost constant; this is further discussed in Section 10.2.3. It is also seen
that the curves in Figure 10.6a show asharp breakand that forcbeyond the
break,gis virtually constant. The latter seems to imply thatGthen is
virtually zero. This is clearly impossible: it would mean that with increasing
concentration of surfactant its adsorption sharply drops. The explanation is
that above the break the thermodynamic activity of the surfactantaremains
virtually constant. The break roughly occurs at thecritical micellization
concentration (CMC), above which next to all additional surfactant
molecules go into micelles; for some systems, the curve stops at the
solubility limit of the surfactant, for instance for Na-stearate (C18) in Figure
10.6. Micellization and the CMC are further discussed in Section 10.3.1.
Figure 10.6 relates to Na soaps of varying chain length, and it is seen
that the longer the chain, the lower the CMC. This means that soaps with a
longer chain length are—other things being equal—more surface active: less
is needed to result in a certainG. The concept ofsurface activityis often
loosely used as referring to the lowering ofg: the component giving the
lowestgthen would be the most surface active one. This is, however, an
ambiguous criterion, because different surfactants give different values for