2
126 J . Org. Chem., Vol. 66, No. 6, 2001
Blagoeva et al.
-
pH ) pH + log{[AcO ] + cmc + R([D] - cmc)} -
0
0
T
log[AcOH]0 (6)
We obtain R ) 0.48 ( 0.01 and cmc ) (0.0004 ( 0.0002)
M using least-squares nonlinear regression fit of the data
for 0.02 M buffer. The corresponding â value of 0.52 is
1
8
in the range of published values for CTAOAc. The cmc
-
-
-
18
values of CTAX (X ) AcO , Cl , and Br ) in pure water
-
3
are in the range of 1-1.5 × 10 M, but the cmc values
of CTACl in the presence of 0.1 and 0.01 M buffers are
-
4
-4
in the range of 2 × 10 to 6 × 10 M, whatever the
buffer concentration.19
If the R value of 0.48, obtained in 0.02 M buffer, is
applied to the pH data in 0.2 M buffer, the calculated
pH of a 0.1 M solution of CTAOAc is only 0.17 pH units
higher than that of the pure aqueous buffer. The experi-
mental increase is, however, 0.30 pH units and would
correspond to R ) 0.8, which value is highly unlikely.
Most likely, this additional pH increase arises, in contrast
to an earlier assumption,20 from an intake of acetic acid
in the micelles from the buffer, since the concentration
of the acid in the concentrated buffer is very large (0.1
F igu r e 3. Dependence of pH values of acetate buffers 50%
base on the concentration of CTAOAc and CTACl. Open
symbols, 0.02 M buffer; closed symbols, 0.2 M buffer; circles,
CTAOAc; squares, CTACl.
surfactant concentration, before applying eq 2 to the rate
data for calculating k .
M
pH Ch an ges with Su r factan t Con cen tr ation . When
the surfactant counterion is identical to that of the buffer
-
base (CTAOAc in acetate buffer), the [AcO ]
w
/[AcOH]
w
M).
AcOH
buffer ratio changes as a result of the dissociation of the
The association constant, KS
, for incorporation of
surfactant.1
a,14
The pH changes of acetate buffers with
acetic acid in cetyltrimethylammonium micelles can be
-1
increasing surfactant concentrations are shown in Figure
estimated as 1.7 M from the linear solvation free energy
relationship proposed by Quina et al.21 With this value
we calculate that up to 14.5% of the acetic acid of the
buffer is incorporated at the maximum concentration of
3
0
. In the case of 0.02 M buffer, the pH increases up to
.8 pH units with the addition of 0.1 M surfactant, while
in the more concentrated (0.2 M) buffer, where the
amount of acetate ions released by the surfactant is less
significant as compared to the buffer acetate ions, the
pH changes only by 0.3 pH units.
-
2
CTAOAc ([AcOH]M ) 1.45 × 10 M for [CTAOAc] ) 0.1
M). Accordingly, eq 6 is transformed in eq 7 in which the
In CTACl and CTABr the pH values decrease with
addition of surfactant as a result of opposite changes in
-
pH ) pH + log{[AcO ] + cmc + R([D] - cmc)} -
0
0
T
the buffer ratio.1
5,16
-
[AcOH]0
w
[AcO ] decreases since chloride and
log
(7)
bromide surfactant counterions exchange for acetate ions
from the buffer. The observed decreases of pH are in
these cases not larger than 0.2 pH units.
{
AcOH
}
1
+ KS ([D] - cmc)
T
concentration term for the acetic acid in the water phase
is calculated by means of KS
acetate buffer from eq 7 is now 0.48 ( 0.02, in agreement
with that found from 0.02 M buffer22 in which the
micellar inclusion of acetic acid can be neglected ([AcO-
r, Degr ee of Micelle Dissocia tion , in CTAOAc
Bu ffer ed Solu tion s. These pH data (Figure 3) allow for
the calculation of the degree of CTAOAc dissociation.
Micelle dissociation is characterized by the parameter R,
while â represents the fraction of counterions bound to
AcOH
. The value of R in 0.2 M
-
3
-1
1
a
H]
M
) 1.5 × 10 M only for [CTAOAc] ) 10 M).
the micelle :
Ra te-Su r fa cta n t P r ofiles. The dependences of the
rate constants for ring closure of E3 and E2 in 0.02 and
AcO-]
[
w
0
.2 M acetate buffers on the concentration of CTACl are
R ) (1 - â) )
(4)
(
[D] - cmc)
shown in Figure 1. The maxima in the rate profiles are
consistent with second-order micelle-mediated ion-
molecule reactions.1 The experimental first-order rate
constants, kobs, increase with increasing [CTACl] and
then decrease. The largest accelerations in 0.02 M buffer
T
a
of acetic acid13,17 and
a
When it is assumed that the pK
the concentration of acetic acid in the water phase of the
diluted buffer remain unchanged (eq 5 with [AcOH]
AcOH] , index 0 indicating initial concentrations of
w
)
w
for E3 and E2 (expressed as kmax/k ) are 10 and 4,
[
0
respectively. In 0.2 M buffer, the rate constants are
surprisingly smaller (vide infra), but the decrease at high
surfactant concentrations due to dilution of the reagents
in the micellar phase is very small.
buffer species), R is calculated from the pH change via
eq 6, pH
0
being the value in the absence of surfactant.
-
pH ) pH + log[AcO ] - log[AcOH]
(5)
0
w
w
(
18) Gallion, L.; Hamidi, M.; Lelievre, J .; Gaboriaud, R. J . Chim.
(
15) Ouarti, N.; Marques, A.; Blagoeva, I.; Ruasse, M.-F. Langmuir
000, 16, 2157.
16) (a) Quina, F. H.; Politi, M. J .; Cuccovia, I. M.; Baumgarten, E.;
Martins-Franchetti, S. M.; Chaimovich, H. J . Phys. Chem. 1980, 84,
61. (b) Romsted, L. S. J . Phys. Chem. 1985, 89, 5107, 5113.
17) pK in the micellar phase is about the same as that in bulk
Phys. 1997, 94, 707.
(19) Unpublished measurements by tensiometry and spectrofluo-
rometry.
(20) Toullec, J .; Couderc, S. Langmuir 1997, 13, 1918.
(21) Quina, F. H.; Alonso, E. O.; Farah, J . P. S. J . Phys. Chem. 1995,
99, 11708.
2
(
3
(
a
water. (El Seoud, O. A. Adv. Colloid Interface Sci. 1989, 30, 1. Berthold,
A.; Saliba, C. Analusis 1985, 13, 437.)
(22) Soldi, V.; Keiper, J .; Romsted, L. S.; Cuccovia, I. M.; Chaimov-
ich, H. Langmuir 2000, 16, 59.