Effects of [NaBr] on the rate of intramolecular general base-assisted hydrolysis of N -(2a?2-hydroxyphenyl)phthalimide in the presence of cationic micelles: Kinetic evidence for the probable micellar structural transition

Article abstract of DOI:10.1021/jp102109q

Pseudofirst-order rate constants for aqueous cleavage of N-(2a?2-hydroxyphenyl)phthalimide (1), obtained at 0.001 M NaOH, 2??10^-4 M 1, 2% v/v CH₃CN, and 30 ?°C, show a nonmonotonic decrease with the increase in the total concentration of cetyltrimethylammonium bromide ([CTABr]_T) within its range a?￥9??10^-5-a?? 0.17 M. Similar observations have been obtained in the presence of the constant concentration of NaBr at a??0.02 M. The values of k_obs become independent of [CTABr]_T at a?￥0.04 M CTABr and within a [NaBr] range of 0.0-0.005 M. These observations, in view of the pseudophase (PP) model of the micelle, reveal the presence of presumably spherical micelles at a??3??10^-4 M CTABr in the presence of a constant concentration of NaBr within its range of 0.0-0.01 M. The average value of the CTABr micellar binding constant (K_S) of ionized 1 (i.e., 1^-), under these conditions, is (1.88 ?± 0.62)??10 ³ M^-1. The increase in [CTABr]_T at a?￥4??10^-4 M causes a micellar structural transition from most likely spherical to cylindrical, which is evident from the increase in K _S values from 3.46??10³ to 11.4??10³ M^-1 with the increase in [CTABr]_T from 4??10 ^-4 to a??1??10^-3 M in the absence of NaBr. The values of k_obs at different [NaBr] and at a constant [CTABr] _T follow a kinetic relationship derived from an empirical equation coupled with a PP model of micelle. This relationship gives the value of a kinetic parameter, F_X/S, which represents the fraction of micellized S^- (S^- = 1^-) transferred to the aqueous phase by the limiting concentration of X^- (X^- = Br^-) through ion exchange X^-/S^-. The value of F_Br/1 is 0.65 ?± 0.12. ? 2010 American Chemical Society.

Full text of DOI:10.1021/jp102109q

J. Phys. Chem. B 2010, 114, 8089–8099
8089
Effects of [NaBr] on the Rate of Intramolecular General Base-Assisted Hydrolysis of
N-(2′-Hydroxyphenyl)phthalimide in the Presence of Cationic Micelles: Kinetic Evidence for
the Probable Micellar Structural Transition
M. Niyaz Khan* and M. Haswaneezal Rizan Azri
Department of Chemistry, Faculty of Science, UniVersity of Malaya, 50603 Kuala Lumpur, Malaysia
ReceiVed: March 8, 2010; ReVised Manuscript ReceiVed: May 11, 2010
Pseudofirst-order rate constants for aqueous cleavage of N-(2′-hydroxyphenyl)phthalimide (1), obtained at 0.001
M NaOH, 2 × 10-4 M 1, 2% v/v CH3CN, and 30 °C, show a nonmonotonic decrease with the increase in the total
concentration of cetyltrimethylammonium bromide ([CTABr]T) within its range g9 × 10-5-e 0.17 M. Similar
observations have been obtained in the presence of the constant concentration of NaBr at e0.02 M. The values of
kobs become independent of [CTABr]T at g0.04 M CTABr and within a [NaBr] range of 0.0-0.005 M. These
observations, in view of the pseudophase (PP) model of the micelle, reveal the presence of presumably spherical
micelles at e3 × 10-4 M CTABr in the presence of a constant concentration of NaBr within its range of 0.0-0.01
M. The average value of the CTABr micellar binding constant (KS) of ionized 1 (i.e., 1-), under these conditions,
is (1.88 ( 0.62) × 103 M-1. The increase in [CTABr]T at g4 × 10-4 M causes a micellar structural transition
from most likely spherical to cylindrical, which is evident from the increase in KS values from 3.46 × 103 to
11.4 × 103 M-1 with the increase in [CTABr]T from 4 × 10-4 to ∼1 × 10-3 M in the absence of NaBr. The
values of kobs at different [NaBr] and at a constant [CTABr]T follow a kinetic relationship derived from an empirical
equation coupled with a PP model of micelle. This relationship gives the value of a kinetic parameter, FX/S, which
represents the fraction of micellized S- (S- ) 1-) transferred to the aqueous phase by the limiting concentration
of X- (X- ) Br-) through ion exchange X-/S-. The value of FBr/1 is 0.65 ( 0.12.
Introduction
KX/S is an empirical constant whose magnitude is the measure
of the ability of a counterion X to expel another counterion S
from the ionic micellar surface to the aqueous phase, gives the
observed data (kobs vs [MX]) fit as good as the PIE model in
terms of residual errors (REs). The validity of eq 1 has been
studied since 1997 through micellar-mediated reaction rate
studies under a variety of reaction conditions.9 The micellar
affinity of solubilizates depends upon several factors including
the structural features of solubilizates. Ionized phenyl salicylate
(PS-) is almost similar to ionized N-(2′-hydroxyphenyl)phthal-
imide (1-) in terms of delocalization of their negative charges
and perhaps reaction mechanisms of their pH-independent
hydrolysis, but they are significantly different in terms of their
structural features. In the continuation of our work on testing
the validity of eq 1, the effects of [NaBr] on the rate of
intramolecular general base (IGB)-assisted hydrolysis of 1 have
been described in the present manuscript.
A normal micelle is a highly dynamic molecular aggregate
formed from amphipathic monomers. Structural features of
micelles at the molecular level are not yet fully understood.
Normal micellar-mediated reactions may be considered as the
appropriate yet crude models for membrane-mediated and
perhaps other biological aggregate-mediated reactions. The
kinetic data on the rate of a reaction in the presence of micelles
provide insight about the mechanism(s) by which micelles exert
their effects on the reaction rate. Such an insight led to the
discovery of the occurrence of ion exchange between counter-
ions at the ionic micellar surface and consequently led to the
formulation of a pseudophase ion exchange (PIE) micellar model
for the bimolecular reactions where one of the reactants carries
a charge similar to the charge of counterions of the normal
micelles.1 The use of the PIE model has been extended to such
reactions in the presence of reversed micelles,2 microemulsions,3
mixed micelles,4 and vesicles.5 Although the PIE model1,6 and
its various extensions as well as the PIE model coupled with
an empirical equation7 explain a large amount of kinetic data
in an apparent satisfactory sense, its inherent weakness has
become more apparent in recent years.7a,8
An alternative model that is based upon a pseudophase (PP)
micellar model coupled with an empirical equation (eq 1),7d
0
K ) K / 1 + K [MX]
(1)
(
)
S
S
X/S
Experimental Section
where KS and KS0 represent ionic micellar binding constants of
Reagent grade chemicals such as cetyltrimethylammonium
bromide (CTABr) and sodium bromide were commercial
products of the highest available purity. N-(2′-Hydroxyphe-
nyl)phthalimide (1) was synthesized as described elsewhere.10
ion S in the presence and absence of MX, respectively, and
* To whom correspondence should be addressed. E-mail:
niyaz@um.edu.my.
10.1021/jp102109q  2010 American Chemical Society
Published on Web 05/28/2010

8090 J. Phys. Chem. B, Vol. 114, No. 24, 2010
Khan and Azri
TABLE 1: Values of kobs and Percent REs for the Cleavage of 1 in the Presence of CTABr at 0.001 M NaOH and [NaBr] ) 0a
[CTABr]T (M) 103 kobs (s-1) REd (%) 103 kobs (s-1) REd (%) 10-3 KS (M-1) 10-3 KS (M-1) 10-3 KS (M-1) 10-3 KS (M-1) 10-3 KS (M-1
)
b
c
e
h
9 × 10-5
9 × 10-5
1 × 10-4
1.5 × 10-4
2 × 10-4
3 × 10-4
4 × 10-4
5 × 10-4
6 × 10-4
7 × 10-4
8 × 10-4
1 × 10-3
2 × 10-3
5 × 10-3
0.01
90.0 ( 0.01f
85.3 ( 0.8
83.9 ( 0.8
83.6 ( 1.0
73.0 ( 0.5
62.1 ( 0.9
48.5 ( 0.5
34.9 ( 0.2
25.1 ( 0.9
21.7 ( 0.5
18.3 ( 0.1
14.7 ( 0.1
11.3 ( 0.1
9.54 ( 0.06
2
-8
-6
10
11
16
1.86g
3.13
2.97
1.69
2.35
2.50
3.32
4.95
7.29
8.01
9.52
2.41h
4.07
3.68
1.89
2.54
2.62
3.43
5.08
7.45
8.16
9.67
77.6 ( 2.0f
-9
2.74i
2.75j
3.69k
72.9 ( 0.5
58.4 ( 0.5
43.7 ( 0.5
32.8 ( 1.0
26.3 ( 0.3
20.5 ( 0.2
16.8 ( 0.2
13.5 ( 0.1
8.86 ( 0.03
7.58 ( 0.07
7.92 ( 0.04
7.79 ( 0.08
7.33 ( 0.07
16
17
8
-5
-15
-32
-46
-53
-40
11
1.61
2.35
3.51
4.85
5.97
7.97
1.62
2.37
3.54
4.91
6.07
8.17
1.80
2.53
3.71
5.10
6.26
8.38
11
-6
-30
-34
-44
-51
-13
31
10.1
10.5
10.7
11.7
11.1
7.99
11.9
11.1
8.09
12.9
27.1
66.8
13.6
34.3
-ve
13.9
34.6
-ve
40
63
61
0.10
0.17
7.39 ( 0.05
7.23 ( 0.05
70
71
a [10] ) 2 × 10-4 M, 30 °C, λ ) 300 nm, and the aqueous reaction mixture in each kinetic run contains 2% acetonitrile. b Total
c
avg
avg
concentration of CTABr. δapp ) 2815 ( 338 M-1 cm-1, and 102 A∞ ) 87.9 ( 5.8. d RE ) 100 × (kobs - kcalcd)/kobs, where kcalcd
represents nonlinear least-squares calculated rate constants using eq 3 and parameters listed in Table 5. δapp ) 3099 ( 142 M-1 cm-1, and
e
avg
102 A∞ ) 86.9 ( 3.0. f Error limits are standard deviations. g The values of KS were calculated from eq 5 with 103 kW ) 98.0 s-1, 103 kM
)
avg
7.31 s-1, and 105 CMC ) 3.8 M. h The values of KS were calculated from eq 5 with 103 kW ) 98.0 s-1, 103 kM ) 7.31 s-1, and 105 CMC )
5.0 M. i The values of KS were calculated from eq 5 with 103 kW ) 90.5 s-1, 103 kM ) 7.33 s-1, and 105 CMC ) 3.3 M. j The values of KS
were calculated from eq 5 with 103 kW ) 90.5 s-1, 103 kM ) 7.65 s-1, and 105 CMC ) 3.3 M. k The values of KS were calculated from eq 5
with 103 kW ) 90.5 s-1, 103 kM ) 7.65 s-1, and 105 CMC ) 5.0 M.
Glassed-distilled water was used throughout, and the stock
solution of 1 was prepared in acetonitrile.
(Aob) as a function of reaction time (t) at 300 nm using a double
beam UV-2102/310/PC UV-vis-NIR spectrophotometer equipped
with a thermostatted cell holder. The constant temperature (30 °C)
of the cell holder was maintained by using a thermostatted
circulating water bath. All of the kinetic runs were carried out for
the reaction period of more than seven half-lives. The observed
data (Aobs vs t) fit well to eq 2
Kinetic Measurements. In a typical kinetic run, the reaction
mixture (4.9 mL) containing all of the reaction ingredients except
1 was temperature equilibrated at 30 °C for about 5-10 min. The
reaction was then initiated by adding 0.1 mL of 0.01 M 1 (in
acetonitrile) to the temperature-equilibrated reaction mixture (4.9
mL). Nearly 2.5 mL of the reaction mixture was quickly transferred
to a 3 mL quartz cuvette, which was kept in the thermostatted cell
holder of the UV-visible spectrophotometer. The progress of the
reaction was monitored by recording the decrease in absorbance
Aobs ) δapp R exp -k t + A
(2)
[
]
(
)
0
obs
∞
where δapp is an apparent molar extinction coefficient of the reaction
TABLE 2: Values of kobs and Percent REs for the Cleavage of 1 in the Presence of CTABr at 0.001 M NaOH and a Constant
[NaBr]a
[NaBr] )
0.003 Mb
103 kobs (s-1
0.005 Mc
0.02 Md
103 kobs (s-1
e
[CTABr]T (M)
)
REf (%)
103 kobs (s-1
)
REf (%)
)
REf (%)
1 × 10-4
1.3 × 10-4
1.6 × 10-4
2 × 10-4
3 × 10-4
4 × 10-4
5 × 10-4
6 × 10-4
7 × 10-4
1 × 10-3
2 × 10-3
3 × 10-3
5 × 10-3
7 × 10-3
0.01
82.8 ( 0.8g
81.4 ( 0.8
72.4 ( 0.9
74.1 ( 0.9
55.3 ( 0.3
47.5 ( 0.4
36.1 ( 0.3
28.3 ( 0.6
21.9 ( 1.0
15.0 ( 0.3
-8
2
0
13
7
71.8 ( 1.1g
75.2 ( 0.9
70.5 ( 1.2
71.1 ( 0.7
63.7 ( 2.0
50.6 ( 0.7
-12
0
1
9
16
8
68.1 ( 1.1g
68.3 ( 0.7
59.5 ( 0.8
65.9 ( 0.6
52.4 ( 0.4
41.1 ( 0.3
38.4 ( 0.2
34.9 ( 0.5
25.3 ( 0.1
-5
1
-7
17
10
8
-2
-15
-33
-52
-44
-6
-3
-4
-17
31.4 ( 0.6
27.0 ( 0.3
15.4 ( 0.2
11.5 ( 0.2
9.49 ( 0.14
9.13 ( 0.13
9.37 ( 0.35
7.68 ( 0.49
7.34 ( 0.03
-16
-22
-70
-40
-29
3
21
19
44
8.86 ( 0.03
13.0 ( 0.2
-17
-16
-4
8.68 ( 0.06
7.87 ( 0.06
7.76 ( 0.09
7.00 ( 0.04
8.00 ( 0.21
8.29 ( 0.03
2
6
16
29
42
45
9.13 ( 0.13
9.38 ( 0.16
8.32 ( 0.10
-2
0.04
0.10
0.17
8.30 ( 0.46
7.86 ( 0.16
32
30
8.04 ( 0.12
56
b
avg
a [10] ) 2 × 10-4 M, 30 °C, λ ) 300 nm, and the aqueous reaction mixture in each kinetic run contains 2% acetonitrile. δapp ) 3120 (
289 M-1 cm-1, and 102 A∞ ) 88.5 ( 4.1. δapp ) 3283 ( 471 M-1 cm-1, and 102 A∞ ) 91.3 ( 4.5. δapp ) 3274 ( 374 M-1 cm-1
,
avg
c
avg
avg
d
avg
and 102 A∞ ) 91.1 ( 3.7. e Total concentration of CTABr. f RE ) 100 × (kobs - kcalcd)/kobs, where kcalcd represents nonlinear least-squares
avg
calculated rate constants using eq 3 and parameters listed in Table 5. g Error limits are standard deviations.

Hydrolysis of N-(2′-Hydroxyphenyl)phthalimide
J. Phys. Chem. B, Vol. 114, No. 24, 2010 8091
TABLE 3: Values of kobs and Percent REs for the Cleavage
of 1 in the Presence of CTABr at 0.001 M NaOH and a
Constant [NaBr]a
TABLE 4: Values of kobs, δapp, and A∞ for the Cleavage of 1
in the Presence of NaBr at 0.001 M NaOHa
[NaBr] (M)
103 kobs (s-1
)
δapp (M-1 cm-1
)
102 A∞
[NaBr] )
0.01
0.10
0.50
1.0
1.5
2.0
87.2 ( 0.8b
77.0 ( 3.0
77.0 ( 1.1
71.2 ( 0.7
59.5 ( 0.6
53.0 ( 0.5
2407 ( 16b
2397 ( 69
2632 ( 25
2649 ( 17
2866 ( 15
2782 ( 13
97.1 ( 0.1b
99.3 ( 0.3
104 ( 0.2
102 ( 0.1
102 ( 0.1
103 ( 0.1
0.3 Mb
0.5 Mc
d
[CTABr]T (M) 103 kobs (s-1
)
REe (%) 103 kobs (s-1
)
REe (%)
2 × 10-5
72.2 ( 0.7f
73.9 ( 0.7
69.5 ( 1.0
64.8 ( 0.2
65.1 ( 1.1
62.5 ( 0.8
53.8 ( 0.7
56.4 ( 0.8
54.5 ( 1.0
58.6 ( 1.0
51.0 ( 0.8
46.3 ( 0.9
52.2 ( 1.0
41.2 ( 0.9
39.6 ( 1.0
33.4 ( 0.4
30.4 ( 0.4
24.0 ( 0.3
21.2 ( 0.2
10.4 ( 0.4
g
-4
-9
-4
-10
-8
-12
-20
-6
-3
9
0
-5
17
8
13
9
13
4 × 10-5
6 × 10-5
8 × 10-5
9 × 10-5
1 × 10-4
2 × 10-4
3 × 10-4
4 × 10-4
5 × 10-4
6 × 10-4
7 × 10-4
1 × 10-3
1.5 × 10-3
2 × 10-3
3 × 10-3
5 × 10-3
7 × 10-3
0.01
76.4 ( 0.6f
74.6 ( 0.8
79.2 ( 0.9
69.3 ( 0.8
56.0 ( 1.2
54.7 ( 1.7
59.0 ( 0.6
62.7 ( 0.4
53.6 ( 1.2
51.3 ( 0.7
48.7 ( 0.5
-1
-1
5
-7
-22
-15
1
11
1
2
a [10] ) 2 × 10-4 M, 30 °C, λ ) 300 nm, and the aqueous
reaction mixture in each kinetic run contains 2% acetonitrile. b Error
limits are standard deviations.
Rheological Measurements. Samples (with a total volume
of each sample of 25 mL) were prepared by mixing a constant
amount of NaOH (1 mM), 1 (0.2 mM), and CTABr. Different
concentrations of CTABr were maintained at 0.02, 0.3, 5, and
100 mM. The rheological measurements were carried out using
the Brookfield R/S+ rheometer, while the temperature was
controlled at 35 °C by an external temperature controller.
However, because of the air-conditioned room, the sample
temperature varied from 34.3 to 33.4 °C. A coaxial double gap
cylinder (CC-DG) was used with the required volume of sample
for every run as 16 mL. A new sample was used for every repeat
measurement. By fixing the shear rate (γ) range at 0.5-15.0
s-1 for 2400 s and 1-1000 s-1 for 1000 s, the dependent shear
stress (τ) and shear viscosity (η) were recorded after each 80
and 10 s, respectively.
9
34.8 ( 0.4
31.8 ( 0.5
23.3 ( 0.9
21.0 ( 0.5
17.2 ( 0.2
11.2 ( 0.2
g
4
11
1
1
-8
-33
-2
-9
-90
0.04
0.10
0.17
g
g
a [10] ) 2 × 10-4 M, 30 °C, λ ) 300 nm, and the aqueous
reaction mixture in each kinetic run contains 2% acetonitrile.
b δapp ) 3337 ( 510 M-1 cm-1, and 102 A∞ ) 94.2 ( 6.4.
avg
avg
avg
avg
c δapp ) 3113 ( 304 M-1 cm-1, and 102 A∞ ) 96.6 ( 4.3.
d Total concentration of CTABr. e RE ) 100 × (kobs - kcalcd)/kobs
,
Results
where kcalcd represents nonlinear least-squares calculated rate
constants using eq 3 using parameters listed in Table 5. f Error
limits are standard deviations. g The reaction mixture became gelly,
and consequently, the rate of reaction could not be studied.
Kinetic Data. A series of kinetic runs were carried out within
the total concentration of CTABr ([CTABr]T) range of 0.0-e
0.17 M at 30 °C in aqueous solvent containing 2% v/v MeCN,
2 × 10-4 M 1, 0.001 M NaOH, and a constant [NaBr]. The
values of kobs, obtained under such conditions and within a
[NaBr] range of 0.0-0.5 M, are shown in Tables 1-3, Figure
1, and Table I in the Supporting Information. A few kinetic
runs were also carried out within a [NaBr] range if 0.01-2.0
M at 30 °C, 0.001 M NaOH, and [CTABr]T ) 0.0, and the
values of kobs, δapp, and A∞ for these kinetic runs are summarized
in Table 4. The calculated values of δapp and A∞ turned out to
be almost independent of [CTABr]T, and the average values of
δapp ()δappavg) and A∞ ()A∞avg) are shown in Tables 1-3 and
Table I in the Supporting Information.
mixture at 300 nm, [R0] is the initial concentration of reactant 1,
and A∞ ) Aobs at t ) ∞. The pseudofirst-order rate constant (kobs),
app, and A∞ were considered as three unknown kinetic parameters
δ
in the data analysis. The details of the data analysis are the same
as described elsewhere.6a
Product Identification. An UV spectral study was carried
out to identify N-(2-hydroxyphenyl)phthalamate ion (2-) as the
immediate stable mild alkaline hydrolysis product of 1. The
details of such a study are described elsewhere.10
Rheological Data. The rheological behavior of CTABr/1 was
examined at 33.9 ( 0.5 °C under steady shear. The micellar
solutions contained a constant concentration of additives, that
is, 1 (0.2 mM), NaOH (1 mM), and CTABr (g0.02 and e100
mM). The semilog plots of shear viscosity (η) versus shear rate
(γ) at different values of [CTABr] ()0.02, 0.3, 5, and 100 mM)
are shown in Figure 2 where all of the plots represent shear
thinning except the one at 0.02 mM CTABr, which exhibits
Newtonian fluid behavior. The shear thinning behavior of the
plots is indicative of the presence of rodlike/wormlike
micelles.11-15 The values of η at γ ) 1.0 s-1 (i.e., η1.0γ) were
obtained by the interpolation of the plots of Figure 2, which is
carried out by the empirical relationship: η ) η0e-Rγ (where η0
and R are empirical constants) using the observed data points
at lower values of γ (e10 s-1). The calculated values of η1.0γ
at different [CTABr] are shown graphically in Figure 3. The
nonlinear plot of Figure 3 is indicative of the micellar structural
transition from spherical to rodlike to entangled wormlike.16
Figure 1. Plots showing the dependence of kobs upon [CTABr]T for
hydrolysis of 1- at 0.001 (9), 0.01 (2), and 0.10 M (b) NaBr. The
solid lines are drawn through the calculated rate constants (kcalcd
)
obtained from eq 3 with parameters (CMC, kW, kM, and KS) listed in
Table 5.

8092 J. Phys. Chem. B, Vol. 114, No. 24, 2010
Khan and Azri
TABLE 5: Nonlinear Least-Squares Calculated Values of
kM and KS Using Eq 3
[NaBr] 105 CMCa
103 kW
103 kM
(s-1
10-2 KS
(M-1
b
(M)
(M)
(s-1
98.0 ( 2.2b,c 1.98 ( 1.47c 40.7 ( 5.8c
)
)
)
0.0
0.0
7.25
8.50
(5.0)d
8.90
(9.3)
10.3
(8.0)
5.5
(5.0)
5.1
(6.3)
3.8
90.5 ( 0.8
90.5 ( 0.8
91.7 ( 2.8
91.7 ( 2.8
88.2 ( 1.7
88.2 ( 1.7
91.0 ( 2.3
91.0 ( 2.3
87.3 ( 1.4
87.3 ( 1.4
88.9 ( 1.2e
88.9 ( 1.2
77.0 ( 3.0
77.0 ( 3.0
78.9 ( 0.8
77.0 ( 1.1
2.73 ( 3.24
2.08 ( 3.60
2.90 ( 2.43
3.00 ( 2.44
4.46 ( 1.99
3.93 ( 2.25
3.35 ( 2.59
3.22 ( 2.60
3.79 ( 2.57
4.11 ( 2.6
5.28 ( 1.91
5.14 ( 1.92
8.06 ( 1.57
8.42 ( 1.77
13.6 ( 3.1
19.2 ( 3.2
42.1 ( 7.1
36.6 ( 6.4
41.0 ( 5.3
41.9 ( 5.5
40.1 ( 4.6
35.3 ( 4.4
30.1 ( 3.8
29.4 ( 3.7
28.4 ( 3.4
30.0 ( 3.8
24.3 ( 2.3
23.6 ( 2.2
11.9 ( 1.0
12.6 ( 1.2
12.2 ( 1.9
13.8 ( 2.7
0.001
0.003
0.005
0.01
0.02
0.1
(3.0)
∼0
(2.0)
∼0
Figure 3. Plot showing the dependence of shear viscosity η at shear
rate γ ) 1.0 s-1 (η1.0γ) upon [CTABr]T at constant [1] ) 2.0 × 10-4
M and [NaOH] ) 0.001 M.
0.3
0.5
∼0
a The values of CMC were obtained by an iterative method as
mentioned in the text. b The value of kW represents the average
value of three or more than three kobs values obtained within the
[CTABr]T range 0 to <CMC in the absence and at a constant value
of [NaBr]. c Error limits are standard deviations. d Parenthesized
values of CMC were obtained by a graphical technique. e The value
of kW ) kobs at [CTABr]T ) 0.
SCHEME 1
Discussion
form of 1 (i.e., 1-) under the experimental conditions of the
present study.
The values of molar extinction coefficient (δ) of nonionized
-1
-
1 (δ1) and ionized 1 (δ1 ) at 300 nm are 2680 and 7530 M
The rate of hydrolysis of 1 was found to be pH-independent
within the pH range of 9.60-10.10, and the respective values
of the pseudofirst-order rate constant (k0 ) kw[H2O]) for pH-
independent hydrolysis of 1 and the second-order rate constant
(kOH) for the reaction of HO- with 1- are 0.10 s-1 and 3.0 M-1
s-1 at 35 °C.10 The brief reaction scheme for alkaline hydrolysis
of 1 is shown in Scheme 1. The reaction mechanism of pH-
independent hydrolysis of 1 involves IGB assistance where the
ionized phenolic group of 1 acts as an IGB-assisted rate-
enhancing group as shown by the transition state TS1. The
possible occurrence of kinetically indistinguishable alternative
reaction mechanism involving intramolecular general acid (IGA)
assistance through transition state TS2 has been ruled out as
cm-1, respectively.10 The initial absorbance (i.e., A0 ) Aobs at t
described elsewhere.10 The reported values of k0 ()0.10 s-1
)
and kOH ()3.0 M-1 s-1) show that k0 + kOH[HO-] ≈ k0 at
8 × 10-4 M NaOH.
Figure 2. Semilogarithmic plots showing the dependence of shear
viscosity (η) upon shear rate (γ) at constant [1] ) 2.0 × 10-4 and
[NaOH] ) 0.001 M and at different [CTABr]T ) 0.1 M (b), 5.0 × 10-3
M (O), and 3.0 × 10-4 M (9). Inset: The plot showing the dependence
of η vs γ at 2.0 × 10-5 M CTABr (×).
The values of kobs decreased ∼10-fold with the increase
in [CTABr]T from CMC (critical micelle concentration) to
∼5.0 × 10-3 M, while an increase in [CTABr]T from
5.0 × 10-3 to 0.10 M caused only ∼1.3-fold decrease in kobs
at [NaBr] ) 0.0 (Table 1). The values of kobs remained almost
unchanged with the change in [CTABr]T from 0.10 to 0.17
) 0) values of the reaction mixtures for entire kinetic runs were
found to be unchanged with the change in [CTABr]T from 0.0
to e0.17 at 0.001 M NaOH and different values of [NaBr].
These observations show the presence of almost a 100% ionized

Hydrolysis of N-(2′-Hydroxyphenyl)phthalimide
J. Phys. Chem. B, Vol. 114, No. 24, 2010 8093
SCHEME 2
minimum, the values of kobs showed the systematic, large,
increasing negative and positive deviations from kcalcd as
represented by RE {) 100 × (kobs - kcalcd)/kobs} values within
the respective [CTABr]T range ∼6.0 × 10-4 to ∼10.0 × 10-4
M and ∼50.0 × 10-4-0.17 M (Table 1). Similar observations
could be seen within a [NaBr] range of 0.0-0.010 M (Tables
1 and 2 and Table I in the Supporting Information). The
observed data fit to eq 3 at g0.02 M CTABr seems satisfactory
as evident from RE values summarized in Table 3 and Table I
in the Supporting Information.
The calculated values of kM are associated with very large
standard deviations, which imply that the kM values are not
reliable. The values of kobs are almost unchanged with the change
in [CTABr]T from ∼0.04 to 0.17 M at [NaBr] ranging from
0.0 to 0.005 M (Tables 1 and 2 and Table I in the Supporting
Information). Thus, these values of kobs should be equal to kM.
However, these values of kobs (7.2 × 10-3-8.3 × 10-3 s-1) are
significantly different from kM values at different [NaBr] except
at 0.10 M NaBr (Table 5). Hence, it is apparent that the data fit
to eq 3 at [NaBr] e 0.02 M and >0.10 M may not be considered
as reliable, although the data fit at [NaBr] g 0.02 M looks
apparently satisfactory in terms of RE values (Table 3 and Table
I in the Supporting Information). The observed data at [NaBr]
) 0 and within [CTABr]T range 9.0 × 10-5-2.0 × 10-3 M were
also treated with eq 3, and the least-squares calculated respective
values of kM and KS are (- 14.7 ( 7.9) × 10-3 s-1 and 2740 (
500 M-1 with 105 CMC ) 7.0 M and 103 kW ) 98.0 s-1. The
negative calculated value of kM with a standard deviation of
>50% reveals the unreliability of the calculated values of both
kM and KS.
M, which could be ascribed to almost complete (∼100%)
micellar binding of 1 under such conditions. Nearly 13-fold
decrease in kobs with an increase in [CTABr]T from CMC to
0.17 M cannot be attributed to merely a salt effect on kobs in
the aqueous phase because only a 1.18-fold decrease in kobs
has been observed with the increase in [NaBr] from 0.01 to
0.5 M at [CTABr]T ) 0.0 (Table 5).
The inhibitory effect of CTABr micelles on the rate of
hydrolysis of 1- at 0.001 M NaOH may be explained in terms
of the PP model of micelle as shown in Scheme 2, where Dn
represents CTABr micelles, subscripts W and M represent the
water/aqueous phase and micellar PP, respectively, KS is the
CTABr micellar binding constant of 1-, and kW and kM represent
pseudofirst-order rate constants for the reaction of H2O with
1- in the water phase and micellar PP, respectively. The
observed rate law, rate ) kobs [1-]T (where [1-]T ) [1-W] +
[1-M]), and Scheme 2 give eq 3
kW + k K D
n
[
]
M
S
kobs
)
(3)
1 + K D
[
]
n
S
An attempt was made to calculate the values of KS from eq
4, which is the rearranged form of eq 3 with kM ) 0. In eq 4,
Yobs ) kW/kobs and R ) 1 - KS CMC. However, the observed
values of kobs
where [Dn] ) [CTABr]T - CMC. The values of CMC, under
the present experimental conditions, were determined by both
an iterative technique17 and a graphical technique.18 However,
values obtained from the graphical technique are not very
reliable because the intersection points of the two linear lines,
above and below CMC, are not well-defined due to low slopes
of the lines below CMC. However, the values of CMC at
e0.005 M NaBr (Table 5) appear to be reasonable wthin the
domain of the reported values of CMC of CTABr + NaX as
6 × 10-5-9 × 10-5 M (at NaX ) 0.2 mM NaPS)19,20 and
23 × 10-5 M (at NaX ) 0.2 mM Na3, where 3- represents
anionic phthalimide).21 The value of CMC of CTASAL (where
Yobs ) R + KS[CTABr]T
(4)
(Tables 1 and 2 and Table I in the Supporting Information),
obtained at [CTABr]T e 0.002 M, did not give a satisfactory
fit to eq 4 as evident from RE values shown in Tables II-IV in
the Supporting Information. The values of RE show a regular
decease with the increase in [CTABr]T within its range
∼1.0 × 10-4 to ∼3.0 × 10-4 M. However, the increase in
[CTABr]T within its range ∼4.0 × 10-4 to ∼1.0 × 10-3
M
reveals a regular increase in RE values (Tables II-IV in the
Supporting Information). These results show that the values of
kM * 0 or alternatively the values of kMKS[Dn] are not negligible
as compared with kW under such conditions. The least-squares
calculated values of R and KS are summarized in Table 6.
However, the values of kobs at e3.0 × 10-4 M CTABr revealed
a satisfactory fit (in terms of RE values) of the observed data
to eq 4 (Tables II-IV in the Supporting Information). The least-
squares calculated values of R and KS, under such conditions,
are also shown in Table 6. The calculated values of CMC {)
(1 - R)/KS}, as shown in Table 6, may be compared with CMC
values obtained in the presence of 2.0 × 10-4 M ionized PS.20
The calculated values of KS are associated with large standard
deviations because of the low number of observations and low
values of Yobs (Tables II-IV in the Supporting Information).
The average value of KS {) 1.88 ( 0.62) × 103 M-1} predicts
SAL represents monoanionic salicylic acid) is 15 × 10-5 M.22
The values of kW at different concentrations of NaBr are the
average values of kobs obtained within the [CTABr]T range
0-<CMC, and these kW values are summarized in Table 5.
The values of kobs at different total concentrations of CTABr
ranging from >CMC value to 0.17 M at [NaBr] ) 0 were used
to calculate kM and KS from eq 3 using the nonlinear least-
squares method. These calculated values of kM and KS at
different [NaBr] ranging from 0.0 to 0.5 M are summarized in
Table 5. Although the nonlinear least-squares method converged
the least-squares (∑di2 where di ) kobs i - kcalcd i with kobs i and
kcalcd i representing, respectively, observed and least-squares
calculated rate constants at the i-th value of [Dn]) values to the
that the value of kM should be e0.02 s-1 at e3.0 × 10-4
M
CTABr if kW + kMKS[Dn] ≈ kW at kW/(kW + kMKS[Dn]) g
0.90 where [CTABr]T e 3.0 × 10-4 M, kM e 0.02 s-1, 103
kW ) 92.1 s-1, and 105 CMC ) 3 M.

8094 J. Phys. Chem. B, Vol. 114, No. 24, 2010
Khan and Azri
NDc
TABLE 6: Effects of [NaBr] on Least-Squares Calculated Values of r and KS Using Eq 4
[NaBr] (M)
102 R
10-2 KS (M-1
)
105 CMCa (M)
[CTABr]T rangeb (M)
0.0
0.0
0.0
0.0
80.1 ( 28.4d
91.9 ( 4.2
47.0 ( 30.5
93.6 ( 14.5
54.7 ( 22.2
85.6 ( 10.6
48.8 ( 18.4
78.9 ( 9.0
61.1 ( 24.8
113 ( 5
44.8 ( 3.8d
21.3 ( 2.4
51.9 ( 3.6
19.2 ( 6.7
47.9 ( 2.9
23.7 ( 6.6
44.4 ( 2.4
27.5 ( 4.7
38.8 ( 3.2
9.3 ( 2.8
35.6 ( 1.3
13.1 ( 4.0
25.0 ( 1.1
17.7 ( 4.3
7.1 ( 0.6
6.0 ( 0.6
4.3 ( 0.5
(4.4)
3.8
(10.2)
3.3
(9.5)
6.1
(11.5)
7.7
9 × 10-5-2 × 10-3
9 × 10-5-3 × 10-4
1 × 10-4-2 × 10-3
1 × 10-4-3 × 10-4
1 × 10-4-2 × 10-3
1 × 10-4-3 × 10-4
1 × 10-4-2 × 10-3
1 × 10-4-3 × 10-4
1 × 10-4-2 × 10-3
1 × 10-4-3 × 10-4
8 × 10-5-2 × 10-3
8 × 10-5-3 × 10-4
2 × 10-5-1 × 10-3
2 × 10-5-3 × 10-4
2 × 10-5-1 × 10-3
6 × 10-5-2 × 10-3
2 × 10-5-1 × 10-3
13
6
10
3
11
5
11
5
11
5
12
6
15
10
20
12
15
0.001
0.001
0.003
0.003
0.005
0.005
0.01
0.01
0.02
0.02
0.1
(10.0)
∼0e
62.2 ( 9.2
102 ( 7
(10.6)
∼0e
86.0 ( 4.5
95.4 ( 6.0
109 ( 2
108 ( 5
117 ( 4
(5.6)
2.6
∼0e
0.3
0.5
∼0e
∼0e
a The value of CMC was calculated from the relationship: CMC ) (1 - R)/KS, where the parenthesized values were obtained with less
reliable values of R and KS as mentioned in the text. b The [CTABr]T range used in the calculation of R and KS. c ND represents the total
number of data points. d Error limits are standard deviations. e The calculated values of CMC were slightly negative.
The observed data, summarized in Tables 1 and 2 and Table
I in the Supporting Information, reveal that the values of kobs
are almost independent of [CTABr] at g0.01 M CTABr within
a [NaBr] range of 0.0-0.005 M. If we assume that the inequality
kW , kMKS[Dn] is valid at kW/(kW + kMKS[Dn]) e 0.1, then the
value of KS should be g11.1 × 103 M-1 with [CTABr]T ) 0.01
M, 103 kM ) 7.68 s-1, 103 kW ) 92.1 s-1, and 105 CMC ) 3
M. Thus, the observed data at e3.0 × 10-4 M CTABr where
KS ≈ 1.88 × 103 M-1 and at g0.01 M CTABr where KS g
11.1 × 103 M-1 show that the value of KS changes significantly
with the change in [CTABr]T at a [NaBr] range of 0.0-0.005
M.
Physical studies of different kinds revealed the fact that the
structure of CTABr micelles changed from spherical to cylindri-
cal with the increase in [CTABr]T.23 The presence of inert salts
such as NaBr appeared to accelerate such micellar structural
transition,24 which could sometimes be seen even with the naked
eye due to a drastic increase in the viscosity of the micellar
mixture. The reaction mixture containing 2.0 × 10-4 M phthal-
imide, 0.02 M NaOH, 0.04 M CTABr, and 0.4 M NaBr became
very viscous at ambient temperature (∼27 °C) and the increase
in [NaBr] beyond 0.4 M (i.e., at 0.6 and 0.7 M NaBr) caused
precipitation into the reaction mixture at ∼27 °C, which
disappeared at 35 °C. Such characteristic observations could
not be observed at 0.01 M CTABr.21
In the present study, the reaction mixtures containing
2.0 × 10-4 M 1, 1.0 × 10-3 M NaOH, g0.10 M CTABr, and
g0.3 M NaBr formed a gel, and consequently, the rate of
reaction could not be studied under such typical reaction
conditions. Such gelly reaction mixtures could not be observed
at e0.04 M CTABr and e0.5 M NaBr. An aqueous mixture of
the cationic surfactant such as CTABr and sodium salicylate
(SS) forms the so-called viscoelastic system,25-31 and this system
has been shown to consist of long threadlike micelles (1000-2000
Å in length), which have been called a liVing polymer
system.32-34 The essential feature of SS, which is believed to
be the source for viscoelasticity of the cationic surfactant-SS
systems, is the presence of carboxylate ion and o-OH groups
in salicylate ion. Thus, the presence of the o-OH group in 1
may enhance the CTABr micellar structural transition from
spherical to threadlike at 2.0 × 10-4 M 1, although the o-OH
group of 1 exists as o-O- in the presence of 0.001 M NaOH.
However, such micellar structural transitions have been found
to be generally insensitive to the rates of the micellar-mediated
reactions.
The satisfactory observed data fit to eq 4 at [CTABr]T e
3.0 × 10-4 reveals that either kM ≈ 0 or alternatively kW
.
kMKS[Dn], while kM values (≈7.68 × 10-3 s-1) remain un-
changed within the [CTABr]T range g9 × 10-5-e0.17 M.
These observations appear to be unusual for the reason that in
a related but not exactly similar CTABr micellar-mediated
reaction system involving similar IGB-assisted hydrolysis of
ionized phenyl salicylate (PS-), the values of both kM and KS
were found to be unchanged with the change in [CTABr]T
from 1.0 × 10-4 to 0.12 at 0.01 M NaOH, 2.0 × 10-4 M PS,
and 37 °C.20
Probable Reason for the Presence of a Significant Change
in KS with the Change in [CTABr]T at g4.0 × 10-4
M
CTABr and e0.005 M NaBr. Almost all of the reports on
micellar-mediated rate studies reveal the presence of either one
of the following possibilities in terms of Scheme 2: (i) The
significance of both kW and kM steps, (ii) the kM step is
insignificant as compared with the kW step, and (iii) the kW step
is insignificant as compared with the kM step within the entire
range of the concentration of micelles attained in the studies.
In typical reaction conditions where kW ≈ kM, the rate of reaction
turns out to be independent of [Dn] even though KS * 0. There
are only a few reports where contrary to the PP model of micelle
and other related micellar kinetic models, observations such as
a double rate maxima35 and the complete absence of reaction
in the micellar PP36 have been obtained in respective low and
high concentrations of micelle-forming surfactants. These reports
describe some conceivable reasons for these rather unusual
observations. To the best of our literature search, there are only
a few reports that have appeared rather recently where the failure
of the observed kinetic data fit to the usual PP model of micelle
has been attributed to the change in micellar structure from
spherical to cylindrical with the increasing concentration of
cationic surfactants.37 The present manuscript reveals a signifi-
cant increase in KS with the increase in [CTABr]T within its
range 3.0 × 10-4-0.17 M at a [NaBr] range of 0.0-0.005 M.
These observations cannot be explained in terms of any existing
kinetic model for micellar-mediated reactions because one of

Hydrolysis of N-(2′-Hydroxyphenyl)phthalimide
J. Phys. Chem. B, Vol. 114, No. 24, 2010 8095
the basic assumptions of these models requires that the values
of kM and KS should be independent of [CTABr]T.
Rheometric measurements were carried out at 0.02, 0.3, 5,
and 100 mM CTABr under the reaction conditions of the
observed kinetic data of Table 1. In view of the calculated values
of KS (Tables 1 and 6) and the observed data fit to eq 3, there
should be no micelles at 0.02 mM CTABr (CMC > 0.02 mM),
sample solutions should contain mixed spherical and rodlike
micelles at 0.3 mM CTABr, while rodlike/wormlike micelles
of presumably different lengths are expected to exist at 5 and
100 mM CTABr. The values of η1.0γ are <1.7, 345, 585, and
832 mPa.s at 0.02, 0.3, 5, and 100 mM CTABr, respectively.
Similarly, the zero-shear rate viscosity (η0) of viscoelastic
aqueous solutions of cetyltrimethylammonium tosylate (CTAT)
at 35 °C increases rapidly with a CTAT concentration up to
2-3 wt % CTAT, and then, it remains constant upon increasing
CTAT concentrations.16 However, the values of η0 of viscoelas-
tic aqueous solutions of CTABr increase nonlinearly with an
increasing concentration of CTABr within its range of 0.1-0.4
at 0.5 M KBr and 0.35-0.6 at 0.25 M KBr at 35 °C.40 Perhaps,
it may be noteworthy that the aqueous solution of CTABr
containing 15 mM CTABr, 0.2 mM PS, 30 mM NaOH, and
0.1 M piperidine exhibited like Newtonian fluid with apparent
shear viscosity not different from water within the shear rate
There are a few factors that are believed to be responsible
for micellar transition from spherical to cylindrical.6a However,
perhaps the most important factors may be described as an
increase in headgroup-counterion association and consequently
dehydration at the ionic micellar surface.38 Thus, the micellar
growth is accompanied by an increase in the counterion
association (i.e., ꢀ) and a decrease in the interfacial water
content. In view of these reported observations, the increase in
the KS value from ∼1.88 × 103 M-1 at e3.0 × 10-4 M CTABr
to ∼11.4 × 103 M-1 at g0.01 M CTABr may be attributed to
the presence of the respective spherical and cylindrical micelles
at e3.0 × 10-4 M and g0.001 M CTABr in both the absence
and the presence of e0.01 M NaBr. The values of kM may not
be expected to be sensitive to the micellar growth because
pseudofirst-order rate constants for pH-independent hydrolysis
of 1- are weakly sensitive to the ionic strength (Table 4) and
polarity of the reaction medium.39 The values of kobs, obtained
at 0.001 M NaOH, decreased by only 20, 31, 41, 50, and 60%
with the decrease in the water content from 100 to 30% v/v in
mixed H2O-X solvents with X ) 2-propanol, 1,4-dioxan,
1-propanol, ethanol, and acetonitrile, respectively.39
range of 1-1000 s-1
.
As discussed earlier in the text, the value of kM should be
e0.02 s-1 at 3.0 × 10-4 M CTABr and the experimentally
observed value of kM is (7.56 ( 0.41) × 10-3 s-1 ()the average
values kobs obtained at [CTABr]T g 0.01 M and [NaBr] e 0.005
M). Because the rate of hydrolysis of 1 at 0.001 M NaOH
involves 1- and H2O as the reactants, the value of kM may not
be significantly affected by the CTABr micellar growth. Thus,
Although it is widely believed that the micellar growth due
to an increasing concentration of counterions is accompanied
by micellar structural changes from spherical to cylindrical,6a
quantitative data on such information are rarely available. The
micellar structural transition, exhibited by CTABr and CTASAL
(cetyltrimethylammonium salicylate) as a function of their
concentrations, may be expressed as follows:22
it may not be unreasonable to assume that the value of kM
)
7.56 × 10-3 s-1 is independent of the micellar structural
transition from spherical to cylindrical. In view of this assump-
tion, the values of KS were calculated from eq 5, which is the
rearrangement form of eq 3.
CTABr:0 mM monomer8 0.8 mM spherical micelle8
270 mM cylindrical micelle8 720 mM f LC
kw - kobs
KS )
(5)
k
- kM D
)[ ]
n
(
obs
CTASAL:0 mM monomer8 0.15 mM cylindrical micelle8
720 mM f LC
The calculated values of KS are summarized in Table 1 for the
typical duplicate set of observations at [NaBr] ) 0, with slightly
different values of CMC (obtained from the observed data with
eq 4 at e3.0 × 10-4 M CTABr as well as from the graphical
technique) and constant kM. It is evident from these results that
the values of KS are almost independent of [CTABr]T within
its range 9.0 × 10-5-3.0 × 10-4 M as predicted by the observed
data treatment with eq 4. Similarly, KS values are also
independent of [CTABr]T at g0.001 M CTABr, while there is
a nonlinear increase in KS values with the increase in [CTABr]T
within its rather narrow range of ∼3.0 × 10-4 to ∼10.0 × 10-4
M (Table 1).
It is perhaps noteworthy that the statistical reliability of kW
- kobs seems to decrease as [Dn] f 0. However, (kW - kobs) f
0 as [Dn] f 0 and, consequently, the values of KS, calculated
under such conditions, would be unreliable. Similarly, under
the typical reaction conditions where kobs f kM, the factor (kobs
- kM) f 0 and consequently KS f ∞. Thus, the calculated
values of KS, under such conditions, become also unreliable.
Thus, it is evident that the data treatment with eq 5 suffers from
the disadvantages of being very sensitive to errors (associated
with the observed data, kobs versus [Dn]) when (i) kobs values
are nearly equal to kW (i.e., when [Dn] f 0) and (ii) kobs values
are nearly equal to kM (i.e., at the saturation region of the plot
of kobs vs [Dn]).
However, the recent studies show the CTABr micellar transition
from spherical to cylindrical at 100 mM.38
The kinetic data (specially RE values) shown in Tables 1
and 2 and Tables I-IV in the Supporting Information reveal
that the approximate values of [CTABr]T (≈ 3.0 × 10-4 M) at
which presumably cylindrical micelles begin to form remain
essentially unchanged with the change in [NaBr] from 0.0 to
∼0.02 M. SS has been shown to be surface active,22,41 while
sodium bromide does not appear to be surface active under a
typical surfactant concentration range. In view of the results
described in this paper, the micellar growth is not essentially
affected by the presence of NaBr at e0.02 M NaBr. However,
the region of spherical micelles appears to be totally wiped out
at g0.1 M NaBr.
Analysis of the Observed Data, kobs vs [NaBr], Obtained
at a Constant [CTABr]T. Because CTABr micellar growth is
strongly and weakly sensitive to the respective [CTABr] and
[NaBr] and cylindrical micelles appeared to exist at >4.0 × 10-4
M CTABr in the absence and presence of NaBr (Tables 1, 2,
and 6), it was thought that the observed data, kobs versus [NaBr],
at a constant [CTABr]T (>4.0 × 10-4 M) should fit to the
following empirical equation42

8096 J. Phys. Chem. B, Vol. 114, No. 24, 2010
Khan and Azri
TABLE 7: Values of kobs and Percent REs for the Cleavage of 1 at Different [NaBr] in the Presence of 0.001 M NaOH and a
Constant [CTABr]T
[CTABr]T (M) )
1.0 × 10-4
103 kobs (s-1
77.6 ( 2.0
2.0 × 10-4
3.0 × 10-4
4.0 × 10-4
b
[NaBr] (M)
)
103 kobs (s-1
)
103 kobs (s-1
)
103 kob (s-1
)
REa (%)
RE (%)
0.0
0.0
73.0 ( 0.5
72.9 ( 0.5
70.8 ( 0.4
74.1 ( 0.9
71.1 ( 0.7
71.1 ( 0.5
59.5 ( 0.8
55.2 ( 0.8
60.4 ( 0.2
56.0 ( 1.2
53.8 ( 0.7
62.1 ( 0.9
58.4 ( 0.5
57.0 ( 0.5
55.3 ( 0.3
63.7 ( 2.0
61.1 ( 0.5
65.9 ( 0.6
56.1 ( 0.7
59.4 ( 0.7
54.7 ( 1.7
56.4 ( 0.8
0.001
0.003
0.005
0.010
0.020
0.10
0.10
0.30
0.50
76.2 ( 0.8
82.8 ( 0.8
71.8 ( 1.1
75.0 ( 1.0
85.7 ( 1.3
68.3 ( 1.1
67.1 ( 0.8
69.3 ( 0.8
62.5 ( 0.8
44.0 ( 0.4
47.5 ( 0.4
50.6 ( 0.7
50.7 ( 0.5
52.4 ( 0.4
58.4 ( 1.4
54.1 ( 1.0
59.0 ( 0.6
54.5 ( 01
-2.8
0.1
3.2
-1.0
-1.8
4.1
-3.6
4.0
-4.2
-0.1
4.2
8.1
4.7
3.4
5.3
-2.2
4.4
-4.7
a RE ) 100 × (kobs - kcalcd)/kobs, where kcalcd represents nonlinear least-squares calculated rate constants using eq 6 and parameters listed in
Table 10. b RE ) 100 × (kobs - kcalcd)/kobs, where kcalcd represents rate constants calculated from eq 6, where an arbitrarily assigned value of KX/
S of 50 M-1 was used along with θ and k0 values listed in Table 10.
TABLE 8: Values of kobs and Percent REs for the Cleavage of 1 at Different [NaBr] in the Presence of 0.001 M NaOH and a
Constant [CTABr]T
[CTABr]T (M) )
5.0 × 10-4
6.0 × 10-4
7.0 × 10-4
1.0 × 10-3
[NaBr] (M)
103 kobs (s-1
)
REa (%)
103 kobs (s-1
)
REa (%)
103 kobs (s-1
)
REa (%)
103 kobs (s-1
)
REa (%)
0.001
0.003
0.005
0.010
0.020
0.10
34.7 ( 0.4
36.1 ( 0.3
0.5
1.0
25.8 ( 0.2
28.3 ( 0.6
31.4 ( 0.6
33.3 ( 0.2
38.4 ( 0.2
50.5 ( 0.4
53.6 ( 1.2
51.0 ( 0.8
-3.9
-2.1
2.5
-2.4
-0.8
3.2
20.0 ( 0.2
21.9 ( 1.0
27.0 ( 0.3
28.7 ( 0.3
34.9 ( 0.5
49.0 ( 0.4
51.3 ( 0.7
46.3 ( 0.9
-11.5
-11.4
2.61
-4.5
0.3
6.7
3.7
-8.6
14.4 ( 0.1
15.0 ( 0.3
15.4 ( 0.2
19.4 ( 0.2
25.3 ( 0.1
43.3 ( 3.5
48.7 ( 0.5
52.2 ( 1.0
-2.8
-8.0
-13.6
-5.2
0.4
4.8
-2.2
0
40.1 ( 0.6
41.1 ( 0.3
55.1 ( 0.4
62.7 ( 0.4
58.6 ( 1.0
2.1
-4.6
1.2
4.5
-4.7
0.30
0.50
2.2
-4.3
a RE ) 100 × (kobs - kcalcd)/kobs, where kcalcd represents nonlinear least-squares calculated rate constants using eq 6 and parameters listed in
Table 10.
k0 + θKX/S[NaBr]
1 + KX/S[NaBr]
TABLE 9: Values of kobs and Percent REs for the Cleavage
of 1 at Different [NaBr] in the Presence of 0.001 M NaOH
and a Constant [CTABr]T
kobs
)
(6)
[CTABr]T (M) )
where k0 ) kobs at [NaBr] ) 0 and θ as well as KX/S are empirical
constants. The values of θ and KX/S are expected to remain
constant as long as the micellar structure remains unchanged
with the change in [NaBr]. The values of k0 at 0.001 M NaOH
and different [CTABr]T were obtained experimentally by
carrying out the kinetic runs at [NaBr] ) 0. The observed data,
shown in Tables 7-9, Figure 4, and Table V in the Supporting
Information, were treated with eq 6, and the nonlinear least-
squares technique was used to calculate θ and KX/S from eq 6.
These calculated values of θ and KX/S at different [CTABr]T
are summarized in Table 10. The extent of the reliability of the
observed data fit to eq 6 is evident from the RE values
summarized in Tables 7-9 and Table V in the Supporting
Information and from the standard deviations associated with
the calculated parameters, θ and KX/S (Table 10).
1.0 × 10-2
0.10
103 kobs
(s-1
0.17
[NaBr]
(M)
103 kobs
REa
(%)
REb
(%)
103 kobs
(s-1
)
)
(s-1
)
0.001
0.003
0.005
0.010
0.020
0.10
7.28 ( 0.05 -9.5 6.87 ( 0.08 -9.8 7.22 ( 0.06
7.76 ( 0.09 -3.9 8.00 ( 0.21
7.68 ( 0.49 -6.3
5.5 8.29 ( 0.03
8.04 ( 0.12
10.2 7.24 ( 0.09
6.9 7.86 ( 0.16
7.92 ( 0.08 -6.1 7.38 ( 0.08
8.32 ( 0.10 -6.5 8.30 ( 0.46
12.7 ( 0.1
17.2 ( 0.2
21.2 ( 0.2
4.7 8.45 ( 0.01 -1.1 8.33 ( 0.09
0.30
0.50
-2.3
0.5
a RE ) 100 × (kobs - kcalcd)/kobs, where kcalcd represents nonlinear
least-squares calculated rate constants using eq 6 and parameters
listed in Table 10. b RE ) 100 × (kobs - kcalcd)/kobs, where kcalcd was
calculated from the relationship: kobs ) k0′ + θ KX/S[NaBr] with
least-squares calculated values of k0′ and θ KX/S as (7.53 (
0.32) × 10-3 s-1 and (10.2 ( 7.1) × 10-3 M-1 s-1, respectively.
Perhaps, it is noteworthy that although the data fit to eq 6 is
satisfactory in view of the RE values, the calculated values of
θ and KX/S at [CTABr]T e 7.0 × 10-4 M may not be considered
as reliable for the reason that the maximum changes in kobs with
the change in [NaBr] from 0.0 to 0.5 M are rather low (Tables
7 and 8). The values of ratio kobs (at 0.5 M NaBr)/kobs (at 0.0 M
KX/S on the RE values at 4.0 × 10-4 M CTABr, the values of
kcalcd were obtained from eq 6 with an arbitrary assigned value
of 50 M-1 for KX/S while keeping the same θ value
()57.0 × 10-3 s-1). These calculated values of rate constants
(kcalcd) gave RE values as shown in Table 7. Although the value
of KX/S is reduced from 132 to 50 M-1, most of the RE values
are also below or close to 5%.
NaBr) are 1.2, 1.7, 2.0, and 2.2 at 4.0 × 10-4, 5.0 × 10-4
,
6.0 × 10-4, and 7.0 × 10-4 M CTABr, respectively. The least
reliable values of θ and KX/S are at 4.0 × 10-4 M CTABr. To
find the effect of significant variation in the magnitude of only

Hydrolysis of N-(2′-Hydroxyphenyl)phthalimide
J. Phys. Chem. B, Vol. 114, No. 24, 2010 8097
1- under the experimental conditions of the present study. The
ion exchange Br-/HO- remained kinetically insignificant be-
cause the rate of hydrolysis of 1- under the present experimental
conditions involved 1- and H2O as the reactants and the
concentration of nonionized 1 remained almost zero as measured
UV spectrophotometrically. Similarly, the ion exchange HO-/
1- may be considered to be kinetically insignificant as compared
with Br-/1-, at least for two reasons: (i) the difference in
hydrophobicity or hydrophilicity between HO- and Br- is
significantly large and (ii) the values of [Br-]/[HO-] vary from
1.4 to 510. However, ion exchange processes Br-/HO- and
HO-/1- might indirectly affect the ion exchange Br-/1- by
reducing the effective concentration of NaBr required for it.42,43
However, such effects might be significant only at very low
values of [NaBr].43
The effects of the concentration of inert salts (MX) on
kinetically21,44 and spectrophotometrically45 determined values
of KS (where KS represents the cationic micellar binding constant
of S-sanionic PS and phthalimide) have been explained
quantitatively in terms of eq 1. It can be easily shown that eqs
1 and 3 would produce a kinetic equation similar to eq 6 where
Figure 4. Plots showing the dependence of kobs upon [NaBr] for
hydrolysis of 1- at 0.002 (9), 0.003 (2), 0.005 (b), and 0.007 M (×)
CTABr. The solid lines are drawn through the calculated rate constants
(kcalcd) obtained from eq 6 with parameters (k0, θ, and KX/S) listed in
Table 10.
It is evident from eq 6 that (i) if k0 > θ, then the values of
kobs should decrease with the increase in [NaBr]; (ii) if k0 ≈ θ,
then the values of kobs should be independent of [NaBr]; and
(iii) k0 < θ, then the values of kobs should increase with the
increase in [NaBr]. The values kobs show a mild decrease with
the increase in [NaBr] at 1.0 × 10-4 and 2.0 × 10-4 M CTABr,
while the values of kobs appear to be independent of [NaBr] at
3.0 × 10-4 M CTABr. As discussed earlier in the text, CTABr
micelles are presumably spherical and kW . kMKS[Dn] under
such conditions. Thus, the decrease in kobs with increasing
[NaBr] at 1.0 × 10-4 and 2.0 × 10-4 M CTABr is due to mild
negative NaBr salt effect (Tables 4 and 5).
The values of kobs increase nonlinearly with the increase in
[NaBr] at a constant [CTABr]T within its range 4.0 × 10-4-0.01
M CTABr (Tables 7-9, Figure 2, and Table V in the Supporting
Information). These observations cannot be explained in terms
of the ionic strength effect for the reason that the effect of
[NaBr] on kobs is weakly negative in nature (Table 4). The most
obvious cause for the increase in kobs with the increase in [NaBr]
at a constant [CTABr]T is the transfer of micellized ionized 1
(1M-) to the aqueous phase through ion exchange Br-/1-.
Although the possible ion exchange processes in the present
reaction system are Br-/HO-, Br-/1-, and HO-/1-, the kineti-
cally most effective ion exchange process among these is Br-/
kW + kMKS0 D
[
]
n
k0 )
(7)
1 + KS0 D
[
]
n
with kW ) kobs at [Dn] ) [MX] ) 0,
MX
θ ) FX/SkW
(8)
with kWMX ) kobs at a typical value of [MX] and [Dn] ) 0, and
KX/S ) KX/S/ 1 + K 0 D
(9)
(
)
]
n
[
S
In eq 8, FX/S represents the fraction of micellized ion S-
transferred to water phase by the limiting concentration of ion
X- (the limiting concentration of ion X- is the total concentra-
tion of ion X-, [X-]T, at which the expulsion of ion S- from
cationic micellar PP to the water phase due to ion exchange
X-/S- ceased almost completely; hence, an increase in [X-]T
beyond its limiting value has no effect on such ion exchange).
The value of θ in eq 6 is expected to remain independent of
TABLE 10: Values of Empirical Constants at Different [CTABr]T, Calculated from Eq 6 for the Alkaline Hydrolysis of 1 in
the Presence of CTABr Micelles
a
0
b
c
c,d
[CTABr]T (M) 103 k0 (s-1
)
10-3KS (M-1
)
103 θ (s-1
)
KX/S (M-1
)
102 FX/S (M-1
)
KX/S b (M-1
)
KX/S (M-1
)
KX/S
4.0 × 10-4
4.0 × 10-4
5.0 × 10-4
6.0 × 10-4
7.0 × 10-4
1.0 × 10-3
2.0 × 10-3
3.0 × 10-3
5.0 × 10-3
7.0 × 10-3
1.0 × 10-2
43.7
43.7
33.9
25.7
21.1
14.1
3.46e
3.46
4.90
6.44
8.05
11.4
11.4
11.4
11.4
11.4
11.4
57.0 ( 1.2f
57.0 ( 1.2
63.8 ( 2.1
54.5 ( 1.1
51.7 ( 2.2
56.6 ( 1.7
47.3 ( 1.6
43.0 ( 3.4
48.8 ( 6.7
30.4 ( 2.2
36.7 ( 6.6
132 ( 5f
75 ( 1f
49.1 ( 14.2f
315 (292)
119 (111)
117 (109)
50g
21.9 ( 6.1
41.3 ( 6.5
40.7 ( 11.7
17.6 ( 2.6
7.46 ( 0.94
5.74 ( 1.69
2.32 ( 0.70
4.93 ( 1.27
1.68 ( 0.63
84 ( 3
71 ( 2
68 ( 3
74 ( 3
60 ( 3
56 ( 3
66 ( 10
42 ( 3
52 ( 13
16.2 ( 4.3
29.2 ( 4.8
30.2 ( 8.3
14.7 ( 2.8
8.23 ( 1.4
5.38 ( 0.79
2.09 ( 0.68
3.57 ( 0.70
1.40 ( 0.64
75.6 (70.2)
201 (188)
270 (254)
218 (208)
178 (173)
202
135
398
193
55.9 (51.9)
142 (133)
200 (188)
182 (174)
196 (191)
189
121
288
161
8.86
8.70
7.58
7.80
7.92
MX
MX
a Total concentration of CTABr. b These parameters were calculated from eq 6 with replacement of θ by FX/SkW with the values of kW
(MX ) NaBr) listed in Table 5 as kW. c The values of KX/S were calculated from eq 9 where [Dn] ) [CTABr]T - CMC with CMC ) 0 and for
parenthesized values 105 CMC ) 5.0 M. d The values of KX/S, obtained under the footnote b, were used to calculate KX/S e The average value
.
of KS obtained for a duplicate set of kinetic runs at [NaBr] ) 0 and 105 CMC ) 3.8 and 3.3 M as summarized in Table 1. f Error limits are
standard deviations. g This is an arbitrary assigned value of KX/S as described in the text.

8098 J. Phys. Chem. B, Vol. 114, No. 24, 2010
Khan and Azri
[NaBr] only if the kW value is independent of [NaBr]. However,
it is evident from Tables 4 and 5 that the values of kW decrease
by ∼18% with the increase in [NaBr] from 0.0 to 0.5 M.
However, the satisfactory observed data fit to eq 6, in terms of
RE values (Tables 7-9, Figure 2, and Table V in the Supporting
Information), shows that such a rather weak negative sodium
bromide salt effect on kW is kinetically insignificant. Despite
Conclusions
The values of pseudofirst-order rate constants (kobs) for
CTABr micellar-mediated hydrolysis of 1, under the typical
reaction conditions where the reactants are 1- and H2O, revealed
the presence of the most likely spherical micelles at e3 × 10-4
M CTABr. Under such conditions, the PP model of micelle gave
the value of CTABr micellar binding constant (KS) of 1- as
(1.88 ( 0.62) × 103 M-1 at a constant value of [NaBr] ranging
from 0.0 to 0.01 M. The presence of [NaBr] at g0.1 M has
almost completely wiped out the presence of spherical micelles
within the [CTABr]T range g6 × 10-4 to e0.17 M. The values
of kobs showed a micellar structural transition from presumably
spherical (e3 × 10-4 M CTABr) to cylindrical (at ∼4 × 10-4
to ∼5 × 10-4 M CTABr). This micellar structural transition is
supported by the increase in KS value from 3.46 × 103 to
11.4 × 103 M-1 with the increase in [CTABr]T from 4 × 10-4
to ∼1 × 10-3 M at [NaBr] ) 0. These observations are also
supported by the rheological measurements that gave η1.0γ as
<1.7, 345, 585, and 832 mPa s at the respective 0.02, 0.3, 5,
and 100 mM CTABr in the absence of NaBr.
The CTABr micellar structural transition with the increasing
values of [CTABr]T appears to be caused by the presence of
2 × 10-4 M 1-/2- because such a micellar structural transition
could not be detected kinetically under similar experimental
conditions in terms of solvent, [CTABr]T range, [NaOH],
temperature, and 2 × 10-4 M PS- (ionized PS) or 3- (anionic
phthalimide). A look at the molecular structures of 1-, 3-, and
PS- reveals that the presence of the o-O- group, hydrophobicity,
and peculiarity of the structural network of these additives are
the probable factors for micellar structural transition observed
with only 1-. It is perhaps noteworthy that the values of CMC2
(specific [CTABr]T at which the micellar structural transition
from spherical to cylindrical takes place) is ∼0.4 to ∼0.5 mM
in the presence of 0.2 mM 1- (as additive). The value of CMC2
(∼0.4 to ∼0.5 mM) is several fold smaller and only ∼3-fold
larger than the reported CMC2 for the respective CTABr (CMC2
) 100-270 mM)22,37 and CTASAL (CMC2 ) 0.15 mM)22 in
the absence of an additive. Because salicylate ion (SAL) is well-
known to be surface active and a viscoelastic agent,22,41 there
is a strong possibility of 1- and 2- acting as viscoelastic agents.
In view of one of the reviewers, these results show very
clearly that CTABr in the reaction conditions undergoes the
sphere to rod transition. Aromatic compounds, especially anions,
bind very strongly to CTA+, and there is considerable uncer-
tainty regarding structures of the associated particles, which can
complicate fits to data. It is too easy to fit micellar inhibitions
of reactions involving ions, especially when they have an
aromatic group attached and bind strongly to any counterionic
solute. The combination of kinetics and rheology gives very
clear evidence for a major change in colloidal structure, which
is known to occur very readily with CTABr. The usual PP
treatments typically have problems when there are large changes
in micellar structure, and it then becomes very difficult to apply
the classical equations, if only because they involve approxima-
tions that can be ignored only in well-behaved systems. The
results given here are good examples of where, and why, the
generally accepted treatment fails.
this conclusion, the observed data were also used to calculate
MX
FX/S and KX/S from eq 6 with the replacement of θ by FX/SkW
,
MX
where kW (MX ) NaBr) and k0 were considered as known
parameters. The nonlinear least-squares calculated values of FX/S
and KX/S are summarized in Table 10. The values of RE (not
shown) are not appreciably different from the corresponding
RE values obtained by the use of eq 6 with θ and KX/S as
unknown parameters.
The calculated values of FX/S appear to be independent of
[CTABr]T within its range of 4 × 10-4-1 × 10-2 M (Table 10).
In view of the conclusion described earlier into the text, it may
not be unreasonable to assume that the micellar solution should
contain a significant fraction of spherical micelles at ∼4 × 10-4
M CTABr (where 10-3 KS ) 3.46 ( 0.12 M-1) because the
kinetically detectable presence of presumed cylindrical micelles
is nearly 0% at e3 × 10-4 M CTABr (where 10-3 KS ) 1.88
( 0.62 M-1). Thus, the calculated values of FX/S at different
[CTABr]T show that the micellar growth has essentially no effect
on the FX/S value. The average value of FX/S ()0.65 ( 0.12)
reveals that the limiting concentration of NaBr could cause only
nearly 65% expulsion of 1- from the micellar PP to the aqueous
phase. The value of FX/S of 0.65 is significantly smaller than
FX/S of 1.0 where X ) Br- and S ) ionized phthalimide (3-).21
The structural features of 1- and 3- reveal that the hydropho-
bicity of 1- is apparently larger than that of 3-, and conse-
quently, ions 1-, as compared with ions 3-, are expected to
penetrate deeper into the CTABr micelles. These observations
support the proposal that the value of FX/S is the measure of
the penetration of ion X into the micellar PP relative to that of
ion S in an ion exchange X-/S-.6a
The values of KX/S at different [CTABr]T were calculated from
0
eq 9 with the values of KS listed in Table 10. The values of
CMC, obtained from R values for the duplicate set of kinetic
runs at [NaBr] ) 0, are 3.3 × 10-5 and 3.8 × 10-5 M, while a
graphical technique gave CMC as 5.0 × 10-5 M (Table 6). To
find out the effects of moderate variations of CMC values on
the values of KX/S, the calculation of KX/S from eq 9 was carried
out at CMC ) 0 and 5.0 × 10-5 M. The calculated values of
KX/S, as shown in Table 10, reveal ∼7, 7, 6, 6, 4, and 3%
decrease in the values of KX/S with the increase in CMC from
0.0 to 5.0 × 10-5 M at 4 × 10-4, 5 × 10-4, 6 × 10-4, 7 × 10-4,
1 × 10-3, and 2 × 10-3 M CTABr, respectively. These reduc-
tions in KX/S values are significantly smaller than the percent
standard deviations associated with the average values of
KX/S ) 224 ( 80 M-1 when θ and KX/S were calculated from
eq 6 and KX/S ) 185 ( 50 M-1 when FX/S and KX/S were
calculated from eq 6 as described into the text. The values of
KX/S at 4 × 10-4 and 5 × 10-4 M CTABr were not included in
the calculation of the average values of KX/S because the values
of KX/S, obtained under such conditions, are less reliable as
discussed into the text. Perhaps, it is noteworthy that the values
of KX/S are independent of [CTABr]T within its range
6 × 10-4-1 × 10-2 M. Although the average values of KX/S
()224 and 185 M-1) are associated with large standard
deviations, the normalized KX/Sn ()FX/SKX/S) values are 146 and
120 M-1 (where FX/S ) 0.65), which may be compared with a
Acknowledgment. We thank the University of Malaya (UM)
for financial assistance through research grant RG022/09AFR,
the Ministry of Science, Technology and Innovation for Science
Fund (Project No. 14-02-03-4014), and the Centre of Ionic
Liquids, UM, for allowing us to carry out the rheological study.
We also thank Dr. Sim Yoke Leng for the help in the preparation
n
KX/S value of 101 M-1 with X ) Br- and S ) 3-.21

Hydrolysis of N-(2′-Hydroxyphenyl)phthalimide
J. Phys. Chem. B, Vol. 114, No. 24, 2010 8099
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Supporting Information Available: Tables 1-4. This
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