wheredis the film thickness. The factor of 2 arises because a film has two
surfaces.
Some results are given in Figure 10.35. It is seen thatEGgoes through
a maximum at increasing surfactant concentration, and that the maximum is
higher for a thinner film. At very highcvalues,EGtends to go to zero. This
is becausedc/dGthen becomes very large or, in other words, at very highc
(above the CMC) the original value ofPcan be fully restored. A similar
trend is predicted by Eq. (10.22): at fairly long time scales and a highcvalue,
ESDtends to go to zero. In practice, this is rarely observed. The reason must
be that most surfactant preparations are mixtures. Some components are
present at low concentrations and these can still substantially contribute to
the modulus. The broken line in Figure 10.35 gives an example of a relation
for a surfactant mixture.
Surface dilatational properties tend to differ considerably between
amphiphiles andpolymers, partly because the surface equation of state is
different. From Eqs. (10.22) and (10.23) it follows that if (a)tis short ordis
thin and (b) dc/dGis small (which is true ifGis small),ESD&dP/d lnG.
Figure 10.36 givesPversus lnG, and the slopes of the curves will thus
roughly giveESD. It is seen that SDS will give a substantial modulus at far
smallerGvalues (in mg?m^2 ) than the proteins do. This is a general trend.
Another difference may be even more important. Polymers can change
their conformation in an interface and thereby the interfacial tension. IfAis
increased, causing a decrease inP, polymer molecules in the surface may
expand and thereby increase the value ofPagain, without any additional
adsorption occurring. Looking again at Figure 10.36, we see very different
curves forb-casein and lysozyme, although these proteins do not differ
greatly in molar mass or in hydrophobicity. However, the former can readily
unfold on adsorption, and the latter is a compact protein. Thusb-casein
would give a higherPvalue for the same value ofG. The determination of
curves like those of Figure 10.36 demands quite some time, at least several
minutes, whereas the conformational changes of the casein after adsorption
will be finished within 10 s (see Section 10.4). This implies that at much
shorter time scales, theP/Gcurve may be quite different forb-casein and be
more like that of lysozyme.
This all means that the application of the theory, as given in this
section, to polymers is questionable, primarily because of the conforma-
tional changes mentioned, and possibly also because of coupling with
surface shear effects. Interpretation of results onESDof adsorbed proteins is
still a matter of debate. The moduli are often highly nonlinear, greatly
decreasing with increasingDA.
Surface dilatational properties are essential in several phenomena of
practical importance, because these determine what g will be at fast
singke
(singke)
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