Chemistry Reference
In-Depth Information
TABLE 4.5. Klevens Constants [Eq. (4.17)] for Common
Surfactant Classes
Temperature (
C)
Surfactant Class
A
B
Carboxylate soaps (Na
þ
)
20
1.85
0.30
Carboxylate soaps (K
þ
)
25
1.92
0.29
n-Alkyl-1-sulfates (Na
þ
)
45
1.42
0.30
n-Alkyl-2-sulfates(Na
þ
)
55
1.28
0.27
n-Alkyl-1-sulfonates
40
1.59
0.29
p, n-Alkylbenzene sulfonates
55
1.68
0.29
n-Alkylammonium chlorides
25
1.25
0.27
n-Alkyltrimethylammonium bromides
25
1.72
0.30
n-Alkylpyridinium bromides
30
1.72
0.31
It has generally been found that the value of A is approximately constant for a
particular ionic head group, while B is constant and approximately equal to
log
10
2 for all paraffin chain salts having a single ionic head group. The value of
B will change, however, in systems having two head groups, or for nonionic systems.
A number of empirical relationships between cmc and hydrocarbon chain length
consistent with the relationship in Eq. (4.17) have been developed by various
researchers. The fundamental principle on which the derivations are based stems
from the fact that the cmc is related to the free-energy change on micelle formation
through Eqs. (4.13) and (4.14). Rearrangement of Eq. (4.13) yields
G
RT
þ
ln 55
ln
ð
cmc
Þ¼
:
4
ð
4
:
18
Þ
Converting to log
10
gives
G
log
10
ð
cmc
Þ¼
3RT
þ
log
10
55
:
ð
4
:
19
Þ
4
2
:
Because the aggregation process represents a balance of the forces tending to favor
micelle formation and those in opposition, the free-energy term can be divided into
its components as
G
m
¼
G
mh
þ
G
mw
ð
4
:
20
Þ
where the superscripts h and w indicate the hydrophobic forces driving the system
to aggregation and the work required to bring the hydrophilic head groups into
close proximity at the micellar surface, respectively. Data on the solubility of
hydrocarbons in water indicate that the contribution to
G
mh
of each -CH
2
-
group added to the chain is a constant. In addition, the contribution of the terminal
-CH
3
differs only by the addition of a constant K, so that
G
mw
G
mh
log
10
ð
cmc
Þ¼
3RT
þ
n
c
3RT
þ
K
0
ð
4
:
21
Þ
:
:
2
2
