92168.pdf

92 Liquid-gas and liquid-liquid interfaces

The alternative approach is to treat micellisation as a simple phase

separation of surfactant in an associated form, with the unassociated

surfactant concentration remaining practically constant above the

c.m.c.

In the build-up from surfactant monomers to micelles, the

existence, albeit transitorily, of intermediate levels of aggregation is

to be expected. Close examination of experimental evidence suggests

that there may be some smoothness of property change at the c.m.c. ,

but that sub-micelle aggregates exist only in trace amounts,

Energetics of micellisation

Since the equilibrium constant, &K, in equation (4.23) and the
standard free energy change, AG^, for the micellisation of 1 mole of
surfactant are related by

RT

AG° = -- InK (4.24)

m

then, substituting into equation (4.23),

RT ( ex ^\

In — \ + RT\n(c(l-x)] (4.25)

V m )

At the c.m.c. (neglecting pre-c.m.c. association and, therefore,

reverting to the phase separation model), x - 0 and

(c.m.c.) (4.26)

Therefore, *S» =
dF

dT

and

(c.m.c.)