Chemistry Reference
In-Depth Information
On the other hand, a theoretical assumption may start out as an acceptable or
comfortable explanation of experimental data, but if the ''truth'' of that assumption
cannot be tested or if its shortcomings are not obvious, it may be promoted to the
rank of being an article of faith causing contradictory data to be discarded or rele-
gated to a category of ''bad'' experimental technique. In the absence of a firm basis
for choosing one approach to the theory of micelle formation, or any other theory
for that matter, over others, and in line with the stated goal of keeping things as
simple as possible, the following discussion is limited to a brief summary of the
classical concepts of micelle formation.
4.3.3. Classical Theories of Micelle Formation
In the literature on micelle formation, two primary models have gained general
acceptance as useful (although not necessarily accurate) for understanding the
energetic basis of the process. The two approaches are the mass action model,in
which the micelles and monomeric species are considered to be in a kind of chemi-
cal equilibrium, and the phase separation model, in which the micelles are consi-
dered to constitute a new phase formed in the system at and above the critical
micelle concentration. In each case, classical thermodynamic approaches are used
to describe the overall process of micellization.
In the mass action model, it is assumed that equilibrium exists between the
monomeric surfactant and the micelles. For the case of nonionic (or un-ionized)
surfactants, the monomer-micelle equilibrium can be written
nS
$
S
n
ð
4
:
1
Þ
with a corresponding equilibrium constant, K
m
, given by
K
m
¼
½
S
n
½
S
n
ð
4
:
2
Þ
where brackets indicate molar concentrations and n is the number of monomers in
the micelle or the aggregation number. Theoretically, one must use activities
rather than concentrations in Eq. (4.2); however, the substitution of concentrations
for activities is generally justified by the fact that the cmc occurs at such low con-
centrations that activity coefficients can be assumed to be unity.
It is usually observed that the cmc for a surfactant is relatively sharp and char-
acteristic of a given surfactant. Although the detailed theory of micelle formation
can become quite complex, the sharpness of the cmc can be explained conceptually
in terms of the law of mass action. If C
t
denotes the total concentration of surfactant
in solution, C
m
the fraction of monomer units in the aggregated or micellar state,
and C
s
that of free molecules, Eq. (4.2) may be written
C
m
C
s
K
m
¼
ð
4
:
3
Þ
