Chemistry Reference
In-Depth Information
where
K
K
0
¼
log
10
þ
ð
4
:
22
Þ
2
:
3RT
and n
c
is the number of carbon atoms in the hydrocarbon tail. If it is assumed that
the contribution of the head group
G
mw
is independent of n
c
, then for a homo-
logous series Eq. (4.21) can be abbreviated in the form of Eq. (4.17) where
G
mw
A
¼
3RT
þ
K
0
ð
4
:
23a
Þ
2
:
and
B
¼
G
mh
ð
4
:
23b
Þ
2
:
3RT
It is apparent that such an analysis qualitatively describes the empirical observa-
tions related to the fact that the constant A is relatively invariable for a given
head group and B shows only small changes in different homologous series of
ionic surfactants.
For nonionic surfactants, in the absence of electrical contributions to the aggre-
gation process, the relative importance of the tail and head groups to the system
changes. An empirical relationship between the cmc and the number of oxyethylene
(OE)
y
groups in several nonionic surfactants series has the form
ln
ð
cmc
Þ¼
A
0
þ
B
0
y
ð
4
:
24
Þ
where A
0
and B
0
are constants related to a given hydrophobic group. Examples of
A
0
and B
0
for several commonly encountered hydrophobic groups are given in
Table 4.6. In each case, the results are for one temperature and can be expected
to vary significantly, given the known sensitivity of such systems to changes in T.
In all the cases, not surprisingly, the cmc is found to decrease as the hydrophobicity
of the molecule increases.
TABLE 4.6. Empirical Constants Relating cmc and OE
Content for Various Hydrophobic Groups in Nonionic
Surfactants [(Eq. (4.24)]
Hydrophobic Group
A
B
C
12
H
25
O-
3.60
0.048
C
13
H
27
O-
3.59
0.091
C
18
H
35
O- (oleyl)
3.67
0.015
C
18
H
37
O- (stearyl)
2.97
0.070
C
9
H
19
C
6
H
4
O-
3.49
0.065
