Effects of [NaBr] on the Rate of Intramolecular General Base-Assisted

May 28, 2010 - Pseudofirst-order rate constants for aqueous cleavage of N-(2′-hydroxyphenyl)phthalimide (1), obtained at 0.001 M NaOH, 2 × 10−4 M...
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J. Phys. Chem. B 2010, 114, 8089–8099

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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 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 counterions 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

KS ) KS0 / (1 + KX/S[MX])

(1)

where KS and KS0 represent ionic micellar binding constants of ion S in the presence and absence of MX, respectively, and * To whom correspondence [email protected].

should

be

addressed.

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)phthalimide (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.

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Experimental Section Reagent grade chemicals such as cetyltrimethylammonium bromide (CTABr) and sodium bromide were commercial products of the highest available purity. N-(2′-Hydroxyphenyl)phthalimide (1) was synthesized as described elsewhere.10

10.1021/jp102109q  2010 American Chemical Society Published on Web 05/28/2010

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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]Tb (M) 103 kobsc (s-1) REd (%) 103 kobse (s-1) REd (%) 10-3 KS (M-1) 10-3 KS (M-1) 10-3 KSh (M-1) 10-3 KS (M-1) 10-3 KS (M-1) 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 0.10 0.17

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 11 -6 -30 -34 -44 -51 -13 31

7.39 ( 0.05 7.23 ( 0.05

70 71

77.6 ( 2.0f

-9

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 40 63 61

1.86g 3.13 2.97 1.69 2.35 2.50 3.32 4.95 7.29 8.01 9.52 11.7 11.1 7.99

2.41h 4.07 3.68 1.89 2.54 2.62 3.43 5.08 7.45 8.16 9.67 11.9 11.1 8.09

2.74i

2.75j

3.69k

1.61 2.35 3.51 4.85 5.97 7.97 10.1 12.9 27.1 66.8

1.62 2.37 3.54 4.91 6.07 8.17 10.5 13.6 34.3 -ve

1.80 2.53 3.71 5.10 6.26 8.38 10.7 13.9 34.6 -ve

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 concentration of CTABr. c δappavg ) 2815 ( 338 M-1 cm-1, and 102 A∞avg ) 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. e δappavg ) 3099 ( 142 M-1 cm-1, and 102 A∞avg ) 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 ) 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. 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

(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

Aobs ) δapp[R0] exp(-kobst) + A∞

(2)

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 e

3

-1

0.005 Mc f

3

-1

0.02 Md f

[CTABr]T (M)

10 kobs (s )

RE (%)

10 kobs (s )

RE (%)

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 0.04 0.10 0.17

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 8.86 ( 0.03

-8 2 0 13 7 10 -2 -15 -33 -52 -44

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

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

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

8.04 ( 0.12

56

3

-1

10 kobs (s )

REf (%)

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 8 -6 -3 -4 -17

13.0 ( 0.2 9.13 ( 0.13 9.38 ( 0.16 8.32 ( 0.10

-17 -16 -4 -2

8.30 ( 0.46 7.86 ( 0.16

32 30

a [10] ) 2 × 10-4 M, 30 °C, λ ) 300 nm, and the aqueous reaction mixture in each kinetic run contains 2% acetonitrile. b δappavg ) 3120 ( 289 M-1 cm-1, and 102 A∞avg ) 88.5 ( 4.1. c δappavg ) 3283 ( 471 M-1 cm-1, and 102 A∞avg ) 91.3 ( 4.5. d δappavg ) 3274 ( 374 M-1 cm-1, and 102 A∞avg ) 91.1 ( 3.7. e Total concentration of CTABr. f RE ) 100 × (kobs - kcalcd)/kobs, where kcalcd represents nonlinear least-squares calculated rate constants using eq 3 and parameters listed in Table 5. g Error limits are standard deviations.

Hydrolysis of N-(2′-Hydroxyphenyl)phthalimide

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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 [NaBr] ) 0.3 Mb [CTABr]Td (M)

103 kobs (s-1)

0.5 Mc REe (%)

-5

2 × 10 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 0.04 0.10 0.17

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 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 g

4 11 1 1 -8 -33

103 kobs (s-1)

REe (%)

72.2 ( 0.7 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 g

-4 -9 -4 -10 -8 -12 -20 -6 -3 9 0 -5 17 8 13 9 13 -2 -9 -90

f

a [10] ) 2 × 10-4 M, 30 °C, λ ) 300 nm, and the aqueous reaction mixture in each kinetic run contains 2% acetonitrile. b δappavg ) 3337 ( 510 M-1 cm-1, and 102 A∞avg ) 94.2 ( 6.4. c δappavg ) 3113 ( 304 M-1 cm-1, and 102 A∞avg ) 96.6 ( 4.3. d Total concentration of CTABr. e RE ) 100 × (kobs - kcalcd)/kobs, 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.

mixture at 300 nm, [R0] is the initial concentration of reactant 1, and A∞ ) Aobs at t ) ∞. The pseudofirst-order rate constant (kobs), δapp, and A∞ were considered as three unknown kinetic parameters 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

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.

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∞

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

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. Results 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. 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

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TABLE 5: Nonlinear Least-Squares Calculated Values of kM and KS Using Eq 3 [NaBr] (M)

105 CMCa (M)

103 kWb (s-1)

103 kM (s-1)

10-2 KS (M-1)

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 (3.0) ∼0 (2.0) ∼0 ∼0

98.0 ( 2.2b,c 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

1.98 ( 1.47c 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

40.7 ( 5.8c 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

0.0 0.0 0.001 0.003 0.005 0.01 0.02 0.1 0.3 0.5

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 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. 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

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 leastsquares 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 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.

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TABLE 6: Effects of [NaBr] on Least-Squares Calculated Values of r and KS Using Eq 4 [NaBr] (M)

102 R

0.0 0.0 0.0 0.0 0.001 0.001 0.003 0.003 0.005 0.005 0.01 0.01 0.02 0.02 0.1 0.3 0.5

80.1 ( 28.4 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 62.2 ( 9.2 102 ( 7 86.0 ( 4.5 95.4 ( 6.0 109 ( 2 108 ( 5 117 ( 4

10-2 KS (M-1) d

44.8 ( 3.8 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

d

105 CMCa (M) (4.4) 3.8 (10.2) 3.3 (9.5) 6.1 (11.5) 7.7 (10.0) ∼0e (10.6) ∼0e (5.6) 2.6 ∼0e ∼0e ∼0e

[CTABr]T rangeb (M) -5

-3

9 × 10 -2 × 10 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

NDc 13 6 10 3 11 5 11 5 11 5 12 6 15 10 20 12 15

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 cylindrical 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 phthalimide, 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 unchanged 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 significant 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

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the basic assumptions of these models requires that the values of kM and KS should be independent of [CTABr]T. 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., β) 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 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, 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 assumption, the values of KS were calculated from eq 5, which is the rearrangement form of eq 3.

KS )

kw - kobs (kobs - kM) [Dn]

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 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

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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

2.0 × 10-4

-1

3

3.0 × 10-4

-1

3

4.0 × 10-4

-1

3

-1

[NaBr] (M)

10 kobs (s )

10 kobs (s )

10 kobs (s )

10 kob (s )

REa (%)

RE b (%)

0.0 0.0 0.001 0.003 0.005 0.010 0.020 0.10 0.10 0.30 0.50

77.6 ( 2.0

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

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

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

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. b RE ) 100 × (kobs - kcalcd)/kobs, where kcalcd represents rate constants calculated from eq 6, where an arbitrarily assigned value of KX/ -1 was used along with θ and k0 values listed in Table 10. S of 50 M

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 3

-1

-4

6.0 × 10 a

[NaBr] (M)

10 kobs (s )

RE (%)

0.001 0.003 0.005 0.010 0.020 0.10 0.30 0.50

34.7 ( 0.4 36.1 ( 0.3

0.5 1.0

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

-4

-1

7.0 × 10-4

RE (%)

10 kobs (s )

RE (%)

10 kobs (s-1)

REa (%)

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 2.2 -4.3

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

a

3

-1

1.0 × 10-3

10 kobs (s )

3

a

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.

kobs )

k0 + θKX/S[NaBr] 1 + KX/S[NaBr]

(6)

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 leastsquares 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). 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 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

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 [CTABr]T (M) ) 1.0 × 10

-2

0.10

0.17

[NaBr] (M)

103 kobs (s-1)

REa (%)

103 kobs (s-1)

REb (%)

103 kobs (s-1)

0.001 0.003 0.005 0.010 0.020 0.10 0.30 0.50

7.28 ( 0.05 7.76 ( 0.09 7.68 ( 0.49 7.92 ( 0.08 8.32 ( 0.10 12.7 ( 0.1 17.2 ( 0.2 21.2 ( 0.2

-9.5 -3.9 -6.3 -6.1 -6.5 4.7 -2.3 0.5

6.87 ( 0.08 8.00 ( 0.21

-9.8 5.5

7.38 ( 0.08 8.30 ( 0.46 8.45 ( 0.01

10.2 6.9 -1.1

7.22 ( 0.06 8.29 ( 0.03 8.04 ( 0.12 7.24 ( 0.09 7.86 ( 0.16 8.33 ( 0.09

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.

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%.

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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 kinetically most effective ion exchange process among these is Br-/

1- under the experimental conditions of the present study. The ion exchange Br-/HO- remained kinetically insignificant because 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

k0 )

kW + kMKS0[Dn]

(7)

1 + KS0[Dn]

with kW ) kobs at [Dn] ) [MX] ) 0,

θ ) FX/SkWMX

(8)

with kWMX ) kobs at a typical value of [MX] and [Dn] ) 0, and

KX/S ) KX/S / (1 + KS0[Dn])

(9)

In eq 8, FX/S represents the fraction of micellized ion Stransferred to water phase by the limiting concentration of ion X- (the limiting concentration of ion X- is the total concentration 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 [CTABr]Ta (M) -4

4.0 × 10 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

103 k0 (s-1) 43.7 43.7 33.9 25.7 21.1 14.1 8.86 8.70 7.58 7.80 7.92

10-3KS0 (M-1) 3.46 3.46 4.90 6.44 8.05 11.4 11.4 11.4 11.4 11.4 11.4

e

103 θ (s-1)

KX/S (M-1)

102 FX/Sb (M-1)

KX/S b (M-1)

KX/Sc (M-1)

KX/Sc,d

57.0 ( 1.2 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 ( 5 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

75 ( 1

49.1 ( 14.2

315 (292) 119 (111) 75.6 (70.2) 201 (188) 270 (254) 218 (208) 178 (173) 202 135 398 193

117 (109)

f

f

f

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

f

55.9 (51.9) 142 (133) 200 (188) 182 (174) 196 (191) 189 121 288 161

a Total concentration of CTABr. b These parameters were calculated from eq 6 with replacement of θ by FX/SkWMX with the values of kWMX (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.

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[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 this conclusion, the observed data were also used to calculate FX/S and KX/S from eq 6 with the replacement of θ by FX/SkWMX, where kWMX (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 hydrophobicity of 1- is apparently larger than that of 3-, and consequently, 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 eq 9 with the values of KS0 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 reductions 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 KX/Sn value of 101 M-1 with X ) Br- and S ) 3-.21

Khan and Azri 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