solid provides the stress needed to arrest the surface. Something similar
must happen for some adsorbates at afluid interface. Probably, a polymeric
surface layer cannot be considered as an infinitely thin layer, and it may be
that a stress can develop in the layer, i.e., in a direction normal to the
surface. The phenomenon is yet insufficiently understood; it is certainly of
importance, for instance for the rate of drainage in foams.
10.9 RECAPITULATION
Surface Tension. The presence of an interface between two phases
goes along with an excess free energy that is proportional to the interfacial
area. For a clean fluid interface the specific interfacial free energy (in J?m^2 )
equals the surface or interfacial tension (in N?m^1 ). This is a two-
dimensional tension acting in the direction of the interface, which tries to
minimize the interfacial area. The surface tension of a solid cannot be
measured.
Adsorption. Some substances tend to adsorb onto an interface,
thereby lowering the interfacial tension; the amount by which it is lowered is
called the surface pressure. The Gibbs equation gives the relation between
three variables: surface pressure, surface excess (i.e., the excess amount of
surfactant in the interface per unit area), and concentration—or, more
precisely, thermodynamic activity—of the surfactant in solution. This
relation only holds for thermodynamic equilibrium, and the interfacial
tension in the Gibbs equation is thus an equilibrium property. Nevertheless,
also under nonequilibrium conditions, a tension can be measured at a liquid
interface.
The relation between surface excess and surfactant concentration (in
solution) is called the adsorption isotherm, that between surface excess and
lowering of interfacial tension the surface equation of state. Both depend
greatly on the type of surfactant and also on the type of interface (e.g., air–
water or oil–water). A surfactant is said to be more surface active if the
adsorption isotherm is shifted to lower concentrations: in other words, less
surfactant is needed to obtain a given surface excess or a given decrease of
interfacial tension.
Surfactants. Surfactants come in two main types: small
amphiphilic molecules (for short called ‘‘amphiphiles’’) and polymers,
among which are proteins. Small-molecule surfactants readily exchange
between surface and solution, and a dynamic equilibrium is thus established,
in accordance with the presumptions of the Gibbs equation. Most
amphiphiles exhibit a critical micellization concentration (CMC), greatly