Chemistry Reference
In-Depth Information
carry with it the need to make a somewhat arbitrary decision as to the exact value to
be reported. The chosen value may depend on the way in which the data are plotted
and lines are extrapolated, the characteristics of the measurements, the specific
techniques (and care) used in the procedure, the accuracy of experimental controls,
and the judgment of the investigator. Light scattering measurements, for example,
can be used to determine the cmc and yield a value related to the weight-average
molecular weight, the size of the micelle, and even some shape factor. An older
technique such as dye solubilization, on the other hand, will produce a number-
average value that will always be smaller than the corresponding weight average
for a polydisperse system. In addition, procedures such as the use of dyes introduce
foreign materials that may actually alter the thermodynamics of the system through
molecular interactions with the surfactant, so that even the choice of dye may influ-
ence the results. Even time-honored techniques that measure some physical charac-
teristic of the solution such as surface tension and conductivity will often produce
results differing in numerical value, if not order of magnitude.
It is obvious, therefore, that any discussion of cmc data must be tempered with
the knowledge that the reported values must not be taken to be absolute; rather, they
reflect certain variable factors inherent in the procedures employed for their deter-
mination. The variations found for nominally the same material under supposedly
identical conditions in the literature should be accepted as minor ''noise'' that does
not significantly affect the overall picture of the system. With those caveats in mind,
our attention now turns to some of the trends that have been identified over the
years that relate surfactant critical micelle concentrations to molecular structures.
4.5.3. The Hydrophobic Group
The length of the chain of a hydrocarbon surfactant has been shown to be a major
factor determining its cmc. It is known that the cmc decreases logarithmically as the
number of carbons in the chain of a homologous series n
c
increases. For straight-
chain hydrocarbon surfactants of 16 carbon atoms or less bound to a single terminal
head group, the cmc is usually reduced by approximately one-half with the addition
of each -CH
2
- group. For nonionic surfactants, the effect can be much larger, with
a decrease by a factor of 10 following the addition of two carbons to the chain. The
insertion of a phenyl and other linking group, the branching of the alkyl group, and
the presence of a polar substituent groups on the hydrophobic chain can produce
different effects on the cmc, as discussed below. For now we confine the subject
to simple alkyl hydrophobic groups.
Mathematically, the relationship between the hydrocarbon chain length and cmc
can be expressed by the so-called Klevens constant as
log
10
ð
cmc
Þ¼
A
Bn
c
ð
4
:
17
Þ
where A and B are constants specific to the homologous series under constant con-
ditions of temperature, pressure, and other parameters. Values of A and B for a wide
variety of surfactant types have been determined, and some are listed in Table 4.5.
