The difference decreases as the concentration of the surfactant, hence
the value ofG, increases. The plateau values ofGdiffer greatly below and
aboveTc, being, e.g., 6 and 3mmol?m^2 , respectively. Consequently, the
interfacial tensions also differ, being, e.g., 7 and 20 mN?m^1 , respectively.
Making an emulsion at, say, 40 8 C with an excess of glycerol monopalmitate,
and then cooling it to 5 8 C, may thus lead to a considerable reduction ing,
although it will take some time before equilibrium adsorption has been
attained.
Micelle formationis briefly discussed in Section 2.2.5, item 4; see
especially Figure 2.8. Soap micelles typically contain 50 to 100 molecules,
and the radius is roughly 2 nm (about the length of a surfactant molecule).
The core of a micelle contains a little water, at most one molecule per
surfactant molecule. The size and shape of the micelles closely depend on the
molecular configuration of the surfactant. Micelles are dynamic structures.
They are not precisely spherical, and surfactant molecules move in and out.
Characteristic times for these processes are a matter of debate, but they seem
to be of the order of 10ms. Presumably, a micelle can disappear in 10–100 ms
upon dilution.
Ideally, micellization occurs above a sharply defined concentration,
thecritical micellization concentrationor CMC. Surfactant molecules added
above the CMC tend to go into the micelles, as is illustrated in Figure
10.10b. This means that the thermodynamic activity of the surfactant does
not increase above the CMC, and neither do the resultant colligative
properties, such as osmotic pressure. Most ionic surfactants give a sharper
transition from solution to micelles than many nonionic, although even the
former show a transition zone rather than a transition point, as illustrated in
Figure 10.10b. Tweens, for instance, which are mixtures in that aliphatic
chain length and the number of oxyethylene groups are variable, do not
show a clear CMC, although micellelike structures are present at high
concentration. In a solution containing different surfactant molecules,
mixed micelles readily form.
The CMC is smaller for a longer chain length, as measured by the
number of carbon atomsn; see, for instance, Figure 10.6. The CMC tends to
decrease somewhat with increasing temperature (see Figure 10.10a).
For ionic surfactants, theionic strengthhas a large effect. Figure 10.11
shows that with increasing NaCl concentration, the CMC of Na dodecyl
sulfate (SDS) greatly decreases and the surface activity increases. This is
because the negative charge of the head groups is shielded to a greater extent
for a higher ionic strength, so that the mutual repulsion of these groups acts
over a smaller distance. This implies that a denser packing is possible (higher
G), hence a lowergat the same bulk concentration of SDS. Explaining the
phenomenon in other words, the thermodynamic activity of SDS increases
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