# Kinetic Evidence for Near Irreversible Nonionic Micellar Entrapment ofN-(2′-Methoxyphenyl)phthalimide (1) under the Typical Alkaline Reaction Conditions

Authors: M. Niyaz Khan; Yoke-Leng Sim; Azhar Ariffin
Journal: The Scientific World Journal
 (2014)

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## Abstract

The values of pseudo-first-order rate constants (kobs) for alkaline hydrolysis of 1, obtained at 1.0 mM NaOH and within CmEnT (total concentration of CmEn) range of 3.0–5.0 mM for C12E23 and 10–20 mM for C18E20, fail to obey pseudophase micellar (PM) model. The values of the fraction of near irreversible CmEn micellar trapped 1 molecules (FIT1) vary in the range ~0–0.75 for C12E23 and ~0–0.83 for C18E20 under such conditions. The values of FIT1 become 1.0 at ≥10 mM C12E23 and 50 mM C18E20. Kinetic analysis of the observed data at ≥10 mM C12E23 shows near irreversible micellar entrapment of 1 molecules under such conditions.


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## Body

## 1. Introduction

The 2-state Hartley model of micelle (i.e., hydrophilic  headgroup/palisade/Stern layer, and hydrophobic core) of 1936 is still under extensive use [1]. However, relatively recent studies involving kinetic and spectrometric probes strongly favor the multistate model of micelle [2–6]. The unusual effects of pure C12E23 and mixed CTABr-C12E23 micelles on the acid-base behavior of phenyl salicylate were observed in 1999 [7]. In order to gain a better and clear understanding of this unusual finding, we started studying such effects on the rate of alkaline hydrolysis of esters and imides under variety of reaction kinetic conditions. This includes the use of reaction kinetic probe molecules of different structural features in the presence of pure CmEn (m/n=12/23, 16/20, 18/20, and 16/10) and mixed CmEn-CTABr micelles [8–12]. The unusual and unexpected observations of these studies are as follows. (i) The decrease of hydroxide ions from the neighborhood of micellized reaction kinetic probe molecules with the increase of R (=[CmEn]T/[NaOH] at a constant value of [NaOH]) at a typical value of Rt which represents a typical value of [CmEn]T/[NaOH] above which kobs versus [CmEn]T data fails to obey PM model. (ii) The observed data (kobs versus [CmEn]T) obey PM model at R≤Rt. (iii) The rate of hydrolysis of reaction kinetic probe molecules almost ceased when R≫Rt. (iv) The unusual observation of (iii) could be detected with C12E23, C16E10, and C18E20 but not with C16E20 under approximately similar conditions.Under the typical reaction conditions of earlier studies whereR≫Rt and the rate of reaction which could not be detected within the reaction period of more than ~24 h, the possibility of whether the cessation of the rate of reaction was due to complete or near irreversible micellar binding of one of the reactants of a bimolecular reaction has not been explored. Although the meaning of “near irreversible binding” is a subjective one, we arbitrarily consider the transition of a reversible binding to near irreversible binding if the value of kobs changes from ~10−4 s−1 (under the reversible binding condition) to ~10−8 s−1 (under the near irreversible binding condition). The present work was initiated with an aim to find out if the cessation of the rate of reaction at ≥0.01 M C12E23 was caused by the near irreversible micellar binding of 1. The observed results and their probable explanations are described in this paper.


## 2. Materials and Methods

### 2.1. Materials

Synthesis of1 (Figure 1) has been reported earlier [14], and all the other chemicals used were commercial products of the highest available purity. Stock solutions of 1(5 mM and 10 mM) were prepared in acetonitrile. Throughout the text, the symbol [X]T represents the total concentration of X.Figure 1
Molecular structures of compounds1, 2, 3 and 4.


### 2.2. Kinetic Measurements

The rate of nonionic micellar-mediated alkaline hydrolysis of1 was studied spectrophotometrically at 35°C by monitoring the appearance of hydrolysis product, N-(2′-methoxyphenyl)phthalamate (2) of 1 at 290 nm as a function of reaction time, t. The observed data, absorbance (Aobs) versus t, obeyed
(1)Aobs=δap[10][1-exp⁡(-kobst)]+A0,
where kobs and δap represent pseudo-first-order rate constants for alkaline hydrolysis of 1 and molar absorptivity of reaction mixture, respectively, and [10] is the initial concentration of 1 and A0=Aobs at t=0. The details of the product characterization are described elsewhere [13].


## 2.1. Materials

Synthesis of1 (Figure 1) has been reported earlier [14], and all the other chemicals used were commercial products of the highest available purity. Stock solutions of 1(5 mM and 10 mM) were prepared in acetonitrile. Throughout the text, the symbol [X]T represents the total concentration of X.Figure 1
Molecular structures of compounds1, 2, 3 and 4.


## 2.2. Kinetic Measurements

The rate of nonionic micellar-mediated alkaline hydrolysis of1 was studied spectrophotometrically at 35°C by monitoring the appearance of hydrolysis product, N-(2′-methoxyphenyl)phthalamate (2) of 1 at 290 nm as a function of reaction time, t. The observed data, absorbance (Aobs) versus t, obeyed
(1)Aobs=δap[10][1-exp⁡(-kobst)]+A0,
where kobs and δap represent pseudo-first-order rate constants for alkaline hydrolysis of 1 and molar absorptivity of reaction mixture, respectively, and [10] is the initial concentration of 1 and A0=Aobs at t=0. The details of the product characterization are described elsewhere [13].


## 3. Results

### 3.1. Effects of [C12E23]T  and [C18E20]T on Pseudo-First-Order Rate Constants (kobs) for Hydrolysis of 1 at 1.0 mM NaOH and 35°C

The rate of alkaline hydrolysis of1 was studied within [C12E23]T range of 3–50 mM, but the absorbance of the reaction mixtures within [C12E23]T range of 10–50 mM remained unchanged in the reaction time (t) range of ~15 s–623 h. However, the observed data (Aobs versus t), obtained within [C12E23]T range of 3–5 mM, were found to fit to (1). The least-squares calculated values of kobs, δap, and A0, obtained under such conditions, are shown in Table 1. Similarly, the kinetic runs for the rate of alkaline hydrolysis of1 were carried out within [C18E20]T range of 10–50 mM. But the absorbance of the reaction mixture at 50 mM C18E20 remained unchanged within the t range of ~15 s–~260 h. The calculated values of kobs, δap, and A0 for the kinetic runs carried out within [C18E20]T range of 10–20 mM are shown in Table 2.Table 1
The values ofkobs, δap, and A0 for alkaline hydrolysis of 1 in the presence of C12E23a.
[C12E23]T M
104  kobs s−1
δ
ap M−1cm−1
102A0
Y
obs
b
Y
cald
c
F
IT
1
d
0.003
30.5
±
1.4
e
3012
±
53
e
24.8
±
0.5
e
11.1
3.76
0
0.0034
19.3
±
1.0
2691
±
48
24.8
±
0.5
17.6
4.13
0.13
0.0038
8.31
±
1.89
2280
±
158
26.3
±
1.3
40.9
4.50
0.26
0.0042
2.21
±
0.47
1657
±
129
25.9
±
0.8
154
4.87
0.46
0.005
0.273
±
0.019
770
±
22
23.9
±
0.1
1245
5.61
0.75
0.01
f
0.02
g
0.03
h
0.05
i
[
1
0
]
a
=
0.1 mM, [NaOH] = 1.0 mM, λ=290 nm, T=35°C, and the aqueous reaction mixture contained 2% v/v CH3CN. bYobs=kW/kobs, where kW=kobs (=340×10-4 s−1 [13]) at [micelles] = 0. cCalculated from the relationship: Ycald=ϕ+Ψ  [C12E23] with ϕ=0.982 and Ψ=925 M−1 [13].  dThe values of FIT1 were calculated from  (2) with δapavg=3090 M−1 cm−1. eError limits are standard deviations. fNo change in Aobs until t=600 h, where Aobs=0.246. gNo change in Aobs until t=1083 h, where Aobs=0.261. hNo change in Aobs until t=1085 h, where Aobs=0.271. iNo change in Aobs until t=1102 h, where Aobs=0.286.Table 2
The values ofkobs, δap, and A0 for alkaline hydrolysis of 1 in the presence of C18E20a.
[C18E20]T M
104  kobs s−1
δ
ap M−1 s−1
102A0
Y
obs
b
Y
cald
c
F
IT
1
d
0.01
41.9
±
0.3
e
3233
±
9
e
27.2
±
0.0
e
7.92
7.89
0
0.012
15.7
±
0.5
2637
±
30
28.0
±
0.1
21.1
9.27
0.17
0.014
11.6
±
0.4
2459
±
31
28.6
±
0.2
28.6
10.6
0.23
0.016
7.11
±
0.24
1239
±
15
29.1
±
0.1
46.7
12.0
0.61
0.018
5.89
±
0.38
898
±
19
29.5
±
0.1
56.4
13.4
0.72
0.02
2.17
±
0.22
546
±
26
29.9
±
0.1
153
14.8
0.83
0.05
f
[
1
0
]
a
=
0.1 mM, [NaOH] = 1.0 mM, λ=290 nm, T=35°C, and the aqueous reaction mixture contained 2% v/v CH3CN. Footnotes b and c represent respective footnotes b and c of Table 1 with replacement of [C12E23] by [C18E20] as well as kW=338×10-4 s−1, ϕ=0.998, and Ψ=689 M−1 [13]. dThe values of FIT1 were calculated from (2) with δapavg=3190 M−1 cm−1. eError limits are standard deviations. fSpectrophotometrically undetectable reaction within the reaction period of ~260 h, where Aobs=0.392.


## 3.1. Effects of [C12E23]T  and [C18E20]T on Pseudo-First-Order Rate Constants (kobs) for Hydrolysis of 1 at 1.0 mM NaOH and 35°C

The rate of alkaline hydrolysis of1 was studied within [C12E23]T range of 3–50 mM, but the absorbance of the reaction mixtures within [C12E23]T range of 10–50 mM remained unchanged in the reaction time (t) range of ~15 s–623 h. However, the observed data (Aobs versus t), obtained within [C12E23]T range of 3–5 mM, were found to fit to (1). The least-squares calculated values of kobs, δap, and A0, obtained under such conditions, are shown in Table 1. Similarly, the kinetic runs for the rate of alkaline hydrolysis of1 were carried out within [C18E20]T range of 10–50 mM. But the absorbance of the reaction mixture at 50 mM C18E20 remained unchanged within the t range of ~15 s–~260 h. The calculated values of kobs, δap, and A0 for the kinetic runs carried out within [C18E20]T range of 10–20 mM are shown in Table 2.Table 1
The values ofkobs, δap, and A0 for alkaline hydrolysis of 1 in the presence of C12E23a.
[C12E23]T M
104  kobs s−1
δ
ap M−1cm−1
102A0
Y
obs
b
Y
cald
c
F
IT
1
d
0.003
30.5
±
1.4
e
3012
±
53
e
24.8
±
0.5
e
11.1
3.76
0
0.0034
19.3
±
1.0
2691
±
48
24.8
±
0.5
17.6
4.13
0.13
0.0038
8.31
±
1.89
2280
±
158
26.3
±
1.3
40.9
4.50
0.26
0.0042
2.21
±
0.47
1657
±
129
25.9
±
0.8
154
4.87
0.46
0.005
0.273
±
0.019
770
±
22
23.9
±
0.1
1245
5.61
0.75
0.01
f
0.02
g
0.03
h
0.05
i
[
1
0
]
a
=
0.1 mM, [NaOH] = 1.0 mM, λ=290 nm, T=35°C, and the aqueous reaction mixture contained 2% v/v CH3CN. bYobs=kW/kobs, where kW=kobs (=340×10-4 s−1 [13]) at [micelles] = 0. cCalculated from the relationship: Ycald=ϕ+Ψ  [C12E23] with ϕ=0.982 and Ψ=925 M−1 [13].  dThe values of FIT1 were calculated from  (2) with δapavg=3090 M−1 cm−1. eError limits are standard deviations. fNo change in Aobs until t=600 h, where Aobs=0.246. gNo change in Aobs until t=1083 h, where Aobs=0.261. hNo change in Aobs until t=1085 h, where Aobs=0.271. iNo change in Aobs until t=1102 h, where Aobs=0.286.Table 2
The values ofkobs, δap, and A0 for alkaline hydrolysis of 1 in the presence of C18E20a.
[C18E20]T M
104  kobs s−1
δ
ap M−1 s−1
102A0
Y
obs
b
Y
cald
c
F
IT
1
d
0.01
41.9
±
0.3
e
3233
±
9
e
27.2
±
0.0
e
7.92
7.89
0
0.012
15.7
±
0.5
2637
±
30
28.0
±
0.1
21.1
9.27
0.17
0.014
11.6
±
0.4
2459
±
31
28.6
±
0.2
28.6
10.6
0.23
0.016
7.11
±
0.24
1239
±
15
29.1
±
0.1
46.7
12.0
0.61
0.018
5.89
±
0.38
898
±
19
29.5
±
0.1
56.4
13.4
0.72
0.02
2.17
±
0.22
546
±
26
29.9
±
0.1
153
14.8
0.83
0.05
f
[
1
0
]
a
=
0.1 mM, [NaOH] = 1.0 mM, λ=290 nm, T=35°C, and the aqueous reaction mixture contained 2% v/v CH3CN. Footnotes b and c represent respective footnotes b and c of Table 1 with replacement of [C12E23] by [C18E20] as well as kW=338×10-4 s−1, ϕ=0.998, and Ψ=689 M−1 [13]. dThe values of FIT1 were calculated from (2) with δapavg=3190 M−1 cm−1. eError limits are standard deviations. fSpectrophotometrically undetectable reaction within the reaction period of ~260 h, where Aobs=0.392.


## 4. Discussion

### 4.1. Evidence for the Near Irreversible C12E23 Micellar Binding of 1 under the Typical Reaction Conditions

It can be easily shown from the derivation of (1) that δap=δ2-δ1, where δ2 represents molar absorptivity of 2(Figure 1). The values of δ1 and δ2, at 290 nm, are 2480 and 5570 M−1cm−1 [15], respectively, in aqueous alkaline solvent containing 2% v/v CH3CN. The values of δ1 are independent of [CmEn]T [13]. The values of δap [13] reveal that the values of δ2 are also independent of [CmEn]T within its range of 0.0–3.0 mM for C16E20 and C12E23 as well as 0.0–5.0 mM for C18E20. However, the values of δ2 show a nonlinear increase from 5570 to 8450 M−1cm−1 at 290 nm with the increase in the content of CH3CN from 2 to 80% v/v in mixed H2O-CH3CN solvent [15]. Thus, the decrease in δap with increase in [CmEn]T (Tables 1 and 2) rules out the possibility of CmEn (m/n=16/20, 12/23, and 18/20) micellar binding of 2 in a micellar environment of lower concentration of water compared with water concentration of bulk aqueous phase. These observations show that the effects of [CmEn]T on δ1 and δ2 cannot explain the observed decrease in δap with increase in [CmEn]T at the typical values of [CmEn]T (Tables 1 and 2). Thus, the most plausible reason for such decrease in δap is due to near irreversible micellar trapping of unreacted  1. Under such circumstances, the observed data (kobs versus [CmEn]T) listed in Tables 1 and 2 cannot be expected to obey pseudophase micellar model (PM).It can be shown that the fraction of near irreversiblyCmEn micellar trapped 1 at t=∞ (FIT1) may be given as
(2)FIT1=1-(δapδapavg),
where δap and δapavg represent apparent molar absorptivity of the reaction mixture at FIT1≠0 and FIT1=0, respectively. The derivation of (2) involves the assumption that the absorbance due to medium microturbidity remains unchanged within the reaction period of t=0 to t=∞. The values of FIT1 were calculated from (2) at different [CmEn]T and these values are summarized in Table 1 for C12E23 and Table 2 for C18E20. It is evident from the calculated values of FIT1 that the value of [CmEn]T/[NaOH] (=R) is nearly 3.6-fold larger for C18E20 than that for C12E23 to result in nearly same value of FIT1, while the value of FIT1 remains zero even at R=170 for C16E20 [13]. The typical value of R (=Rt), at which FIT1=0.13, is 3.4 for C12E23. Similarly, the value of Rt, at which FIT1=0.17, is 12.0 for C18E20. The values of FIT1 and FIT3 are ~0 [13] and 0.60 [11], respectively, at R=170 for C16E20 micelles which reveal that the structural features of imide substrates (1 and 3) (Figure 1) affect the values of FIT1 at a fixed value of R. It is interesting and amazing to note that the difference of only 2 methylene (CH2) groups between C18E20 and C16E20 has so much different effects on FIT1.If micellar entrapment of unreacted1, as shown by FIT1 values in Tables 1 and 2, is indeed an irreversible or near irreversible process, then the values of Aobs at t ≥ 10 half-lives (Reaction time t at ~10 half-lives is equivalent to t∞ because more than 99.9% reaction is progressed during the reaction period of 10 half-lives and therefore, at t∞, Aobs=A∞) should remain essentially unchanged with the increase in t at t=t∞ or at t, where Aobs=A∞. In order to test this conclusion, the kinetic reaction mixtures at 0.01, 0.02, 0.03, and 0.05 M C12E23 were left at 35°C for the reaction period of ~1.10 × 103 h and the values of Aobs, during these reaction periods, remained essentially unchanged (Table 1).It is apparent from Tables1 and 2 that the values of FIT1 increase nonlinearly with the increase of R at a typical value of R (=Rt) and the values of FIT1 appear to become 1 at R≥10 for C12E23 (Table 1) and at R=50 for C18E20 (Table 2). If the reversible and near irreversible  nonionic micellar binding of 1 is a function of R, then the change of inequality from R>Rt to R<Rt, by sudden external addition of known amount of NaOH to the reaction mixture at t>t∞, must cause near irreversible bound 1M molecules to become reversible bound 1M molecules. Consequently, the rate of appearance of product (2) of this reaction mixture would follow (1) and the value of kobs may then be compared with kobs obtained by carrying out another kinetic run by the use of authentic sample of 1 under essentially similar experimental conditions. Such an attempt is described as follows.To 3.0 cm3 of the reaction mixture containing 0.1 mM 1, 1.0 mM NaOH, and 10 mM C12E23 (i.e., R=10), 0.02 cm3 of 1.0 M NaOH was added at t=432 h. The absorbance change of the resulting reaction mixture was quickly monitored spectrophotometrically at 290 nm as a function of reaction time (t). The observed data (Aobs versus t) were found to fit to (1) and the least-squares calculated values of kinetic parameters kobs, δap, and A0 are summarized in Table 3. Similar kinetic runs were carried out at different t (≥600 h) and [C12E23]T (=0.02, 0.03, and 0.05 M) and the values of kobs, δap, and A0, obtained under these conditions, are also shown in Table 3.Table 3
Values ofkobs, δap, and A0 calculated from (1) for alkaline hydrolysis of 1 in the presence of C12E23
micellesa.
103 [C12E23]T M
103 [NaOH] M
103  kobs s−1
δ
ap M−1 cm−1
103A0
k
OH
b M−1 s−1
F
IT
1
c
R
d
t
e h
108  k1f s−1
9.9g
7.6
64.2
±
0.8
h
2088
±
25
h
256
±
3
h
8.45
0.68
1.30
432
25
9.9
7.6
66.1
±
1.1
1691
±
32
267
±
3
8.70
0.55
1.30
600
27
10.0i
7.6
67.8
±
0.5
3293
±
25
260
±
3
8.92
1.32
19.8
11.0
44.4
±
0.5
2127
±
19
303
±
2
4.04
0.70
1.82
623
16
19.8
11.0
35.0
±
0.2
1564
±
7
314
±
1
3.18
0.51
1.82
1083
18
20.0i
11.0
51.2
±
0.2
3344
±
13
282
±
1
4.65
1.82
29.5
17.4
69.9
±
0.9
2714
±
45
297
±
5
4.02
0.89
1.70
600
5.5
29.5
17.4
70.3
±
0.3
2271
±
92
310
±
9
4.04
0.74
1.70
1085
7.6
30.0i
17.0
64.8
±
0.3
3325
±
16
331
±
2
3.81
1.76
48.5
30.0
86.3
±
1.5
3302
±
93
291
±
9
2.88
1.08
1.62
622
—
48.5
30.0
88.1
±
1.8
2789
±
89
324
±
9
2.94
0.91
1.62
1102
2.3
48.5i
30.0
78.6
±
2.5
3365
±
129
406
±
13
2.62
1.62
a[10] = 0.1 mM, λ=290 nm, T=35°C, and the aqueous reaction mixture contained 2% v/v CH3CN. bkOH=kobs [NaOH]. cFIT1=δap/δapavg with δapavg=3058 M−1 cm−1. dR = [C12E23]T/[NaOH]. et
is reaction time (t≥t∞) where the kinetic reaction mixture was used for micellar entrapment experiment. fCalculated from the relationship: k1=(1/t)ln⁡(1/FIT1). gValue of [C12E23]T after external addition of [NaOH]. hError limits are standard deviations. iReaction mixture for kinetic run was freshly prepared, where δap=δapavg.A few kinetic runs were carried out using authentic sample of1 freshly prepared at 35°C, 0.1 mM 1, different values of [C12E23]T (ranging from 10 to 50 mM) and [NaOH] (ranging from 4.2 to 30.0 mM). The spectrophotometrically observed data for these kinetic runs followed strictly (1) as evident from the standard deviations associated with the calculated kinetic parameters kobs, δap, and A0 (Table 3). The values of kOH (=kobs/[NaOH]) are >4-fold smaller than kOH (=36 M−1 s−1) [15] obtained under similar kinetic conditions in the absence of micelles. These results may be attributed to merely  nonionic micellar inhibitory effect (the fraction of micellized 1, i.e., 1M, under such conditions, is >90%, where KS=925 M−1 [13]).The values ofkobs, obtained from the reaction mixtures at different [C12E23]T and the reaction time t (ranging from 432 to 1102 h) at which the value of [NaOH] was increased from 1.0 mM to ≥7.6 mM and ≤30.0 mM, are comparable with the corresponding values of kobs, obtained from authentic sample of 1(Table 3). These observations support the proposal of near irreversible entrapment of 1 molecules by C12E23 micelles at R≫Rt. The observed values of Aobs at t≥600 h as well as ≤1102 h and [C12E23]T range of 10–50 mM (Table 1) reveal that the values of FIT1 must be nearly 1. But the calculated values of FIT1 at t≈600 h, as summarized in Table 3, increase from ~0.55 to ~1.0 with the respective increase in [C12E23]T from 10 to 50 mM. Similarly, the values of FIT1 at t range of ≈1083–1102 h, shown in Table 3, increase from 0.51 to 0.91 with the respective increase in [C12E23]T from 20 to 50 mM. These results show that, even at the highest value of [C12E23]T (=50 mM) of the present study, nearly 9% hydrolysis of 1 occurred within the reaction time (t) of 1102 h. Thus, it is apparent that there is not any absolute/complete irreversible micellar entrapment of 1 molecules—a situation encountered with usual shielding effect of the micelles. A qualitative explanation of these observations may be described as below.In view of the earlier reports [8, 11] on the related reaction systems, the rate of hydrolysis of 1 at 1.0 mM NaOH, 35°C, and within [C12E23]T range of 0.01–0.05 M may be expected to follow an irreversible consecutive reaction path:
(3)1M→k12M→k2PAnM+2-MAM,
where PAn and 2-MA represent phthalic anhydride and 2-methoxyaniline, respectively, and subscript M represents micellar pseudophase. The values of k2 (at 35°C) are almost zero and 12 × 10−4 s−1 at 1.0 mM NaOH and 49 mM HCl, respectively [15]. The efficient reactivity of nonionized 2 (i.e., 2H) towards the formation of PAn is primarily due to intramolecular carboxylic group—assisted cleavage of 2H [15]. The respective absence and presence of the formation of PAn in the aqueous cleavage of 3 at 1.0 mM NaOH, [C16E10]T≤30 mM, and at [C16E10]T≥50 mM have been ascribed to the consequence of the effects of [C16E10]T on the pH of micellar environment of nonionized 4(Figure 1) [11]. Spectrophotometric evidence revealed the fact that the increase in [C12E23]T at R≫Rt with a constant value of [NaOH] caused decrease in pH of micellar environment of micellized ionized phenyl salicylate [7, 9]. In view of this study, at [C12E23]T≥10 mM, the pH of the micellar environment of 2M dropped to a level where there was significant amount of 2H which caused kinetically detectable occurrence of k2—step (see (3)) within [C12E23]T range of 10–30 mM.The respective values ofδ1, δ2, δ2H, and δPAn (with δX representing molar absorptivity of X) at 290 nm are ~2420 [13], 5570–8450, 4545–7490, and 2300–2000 M−1cm−1 [11] within CH3CN content range of 2–80% v/v in mixed aqueous solvent. Close similarity of the values of δ1 and δPAn coupled with significantly higher values of δ2 or δ2H compared with those of δ1 and δPAn reveal that k2>k1. These observations explain the observed constancy of Aobs within reaction time (t) ranging from ~15 s to ≤1102 h at 10–50 mM C12E23 (Table 1). The rough and approximate values of k1 were obtained from the relationship: k1=(1/t)ln⁡(1/FIT1) and such calculated values of k1 at two different t and three [C12E23]T (10, 20, and 30 mM) are shown in Table 3. It is evident from these results that the values of k1 at two different t and at a constant [C12E23]T are comparable within the limits of experimental uncertainties. But the values of k1 decrease almost nonlinearly with the increasing values of [C12E23]T. Thus, the values of k1 became almost zero at 50 mM C12E23 and as a consequence only ~9% conversion of 1 to 2 could occur at t=1102 h (Table 3). The values of k1 decreased from ~26 × 10−8 to 2.3 × 10−8 s−1 with the increase in [C12E23]T from 10 to 50 mM. The values of k1 were found to decrease by ~3-fold, while the values of k2 remained unchanged with the increase of [C16E10]T from 50 to 88 mM in the aqueous cleavage of 3 [11]. Although the calculated values of k1 are not very reliable because they are derived from only either two or one data point(s), these values of k1 appear to be plausible for the reason that the value of k1 at pH ~3.5, in mixed aqueous solvent containing 2% v/v CH3CN, is 67 × 10−8 s−1 [16]. Under such typical conditions, the value of k2 is 120 × 10−5 s−1 and it decreases from 120 × 10−5 to 6.6 × 10−5 s−1 with increase in CH3CN content from 2 to 82% v/v [15].The values ofkobs and k1 show a nonlinear decrease with the increase of [C12E23]T within its range of 1.0 × 10−6–0.05 M (Tables 1 and 3). The value of kM (=rate constant for hydrolysis of 1 in the micellar pseudophase) remained kinetically undetectable under such conditions. The observed data failed to obey the pseudophase micellar (PM) model at >1.4 mM C12E23 because the values of micellar binding constant of 1 (KS) increase significantly (~103-fold) with the increase in [C12E23]T from 1.4 to 50 mM at 1.0 mM NaOH (Tables 1 and 3). Similar but not identical observations have been obtained in CTABr-(cetyltrimethylammonium bromide-) mediated pH-independent hydrolysis of N-(2-hydroxyphenyl)phthalimide [17]. The scenario exhibited by these observations supports the multicompartmental model of micelle [2, 18, 19] and it may best be represented by Scheme 1, where n11M molecules are in equilibrium with n1W molecules and equilibrium or micellar binding constant KS1 at R≤2 and [NaOH] = 1.0 mM. Similarly, n21M, n31M, n41M, and n51M molecules are in equilibrium with n1W molecules and equilibrium constants KS2, KS3, KS4, and KS5 at respective R=10, 20, 30, and 50 and a constant 1.0 mM NaOH.Scheme 1


## 4.1. Evidence for the Near Irreversible C12E23 Micellar Binding of 1 under the Typical Reaction Conditions

It can be easily shown from the derivation of (1) that δap=δ2-δ1, where δ2 represents molar absorptivity of 2(Figure 1). The values of δ1 and δ2, at 290 nm, are 2480 and 5570 M−1cm−1 [15], respectively, in aqueous alkaline solvent containing 2% v/v CH3CN. The values of δ1 are independent of [CmEn]T [13]. The values of δap [13] reveal that the values of δ2 are also independent of [CmEn]T within its range of 0.0–3.0 mM for C16E20 and C12E23 as well as 0.0–5.0 mM for C18E20. However, the values of δ2 show a nonlinear increase from 5570 to 8450 M−1cm−1 at 290 nm with the increase in the content of CH3CN from 2 to 80% v/v in mixed H2O-CH3CN solvent [15]. Thus, the decrease in δap with increase in [CmEn]T (Tables 1 and 2) rules out the possibility of CmEn (m/n=16/20, 12/23, and 18/20) micellar binding of 2 in a micellar environment of lower concentration of water compared with water concentration of bulk aqueous phase. These observations show that the effects of [CmEn]T on δ1 and δ2 cannot explain the observed decrease in δap with increase in [CmEn]T at the typical values of [CmEn]T (Tables 1 and 2). Thus, the most plausible reason for such decrease in δap is due to near irreversible micellar trapping of unreacted  1. Under such circumstances, the observed data (kobs versus [CmEn]T) listed in Tables 1 and 2 cannot be expected to obey pseudophase micellar model (PM).It can be shown that the fraction of near irreversiblyCmEn micellar trapped 1 at t=∞ (FIT1) may be given as
(2)FIT1=1-(δapδapavg),
where δap and δapavg represent apparent molar absorptivity of the reaction mixture at FIT1≠0 and FIT1=0, respectively. The derivation of (2) involves the assumption that the absorbance due to medium microturbidity remains unchanged within the reaction period of t=0 to t=∞. The values of FIT1 were calculated from (2) at different [CmEn]T and these values are summarized in Table 1 for C12E23 and Table 2 for C18E20. It is evident from the calculated values of FIT1 that the value of [CmEn]T/[NaOH] (=R) is nearly 3.6-fold larger for C18E20 than that for C12E23 to result in nearly same value of FIT1, while the value of FIT1 remains zero even at R=170 for C16E20 [13]. The typical value of R (=Rt), at which FIT1=0.13, is 3.4 for C12E23. Similarly, the value of Rt, at which FIT1=0.17, is 12.0 for C18E20. The values of FIT1 and FIT3 are ~0 [13] and 0.60 [11], respectively, at R=170 for C16E20 micelles which reveal that the structural features of imide substrates (1 and 3) (Figure 1) affect the values of FIT1 at a fixed value of R. It is interesting and amazing to note that the difference of only 2 methylene (CH2) groups between C18E20 and C16E20 has so much different effects on FIT1.If micellar entrapment of unreacted1, as shown by FIT1 values in Tables 1 and 2, is indeed an irreversible or near irreversible process, then the values of Aobs at t ≥ 10 half-lives (Reaction time t at ~10 half-lives is equivalent to t∞ because more than 99.9% reaction is progressed during the reaction period of 10 half-lives and therefore, at t∞, Aobs=A∞) should remain essentially unchanged with the increase in t at t=t∞ or at t, where Aobs=A∞. In order to test this conclusion, the kinetic reaction mixtures at 0.01, 0.02, 0.03, and 0.05 M C12E23 were left at 35°C for the reaction period of ~1.10 × 103 h and the values of Aobs, during these reaction periods, remained essentially unchanged (Table 1).It is apparent from Tables1 and 2 that the values of FIT1 increase nonlinearly with the increase of R at a typical value of R (=Rt) and the values of FIT1 appear to become 1 at R≥10 for C12E23 (Table 1) and at R=50 for C18E20 (Table 2). If the reversible and near irreversible  nonionic micellar binding of 1 is a function of R, then the change of inequality from R>Rt to R<Rt, by sudden external addition of known amount of NaOH to the reaction mixture at t>t∞, must cause near irreversible bound 1M molecules to become reversible bound 1M molecules. Consequently, the rate of appearance of product (2) of this reaction mixture would follow (1) and the value of kobs may then be compared with kobs obtained by carrying out another kinetic run by the use of authentic sample of 1 under essentially similar experimental conditions. Such an attempt is described as follows.To 3.0 cm3 of the reaction mixture containing 0.1 mM 1, 1.0 mM NaOH, and 10 mM C12E23 (i.e., R=10), 0.02 cm3 of 1.0 M NaOH was added at t=432 h. The absorbance change of the resulting reaction mixture was quickly monitored spectrophotometrically at 290 nm as a function of reaction time (t). The observed data (Aobs versus t) were found to fit to (1) and the least-squares calculated values of kinetic parameters kobs, δap, and A0 are summarized in Table 3. Similar kinetic runs were carried out at different t (≥600 h) and [C12E23]T (=0.02, 0.03, and 0.05 M) and the values of kobs, δap, and A0, obtained under these conditions, are also shown in Table 3.Table 3
Values ofkobs, δap, and A0 calculated from (1) for alkaline hydrolysis of 1 in the presence of C12E23
micellesa.
103 [C12E23]T M
103 [NaOH] M
103  kobs s−1
δ
ap M−1 cm−1
103A0
k
OH
b M−1 s−1
F
IT
1
c
R
d
t
e h
108  k1f s−1
9.9g
7.6
64.2
±
0.8
h
2088
±
25
h
256
±
3
h
8.45
0.68
1.30
432
25
9.9
7.6
66.1
±
1.1
1691
±
32
267
±
3
8.70
0.55
1.30
600
27
10.0i
7.6
67.8
±
0.5
3293
±
25
260
±
3
8.92
1.32
19.8
11.0
44.4
±
0.5
2127
±
19
303
±
2
4.04
0.70
1.82
623
16
19.8
11.0
35.0
±
0.2
1564
±
7
314
±
1
3.18
0.51
1.82
1083
18
20.0i
11.0
51.2
±
0.2
3344
±
13
282
±
1
4.65
1.82
29.5
17.4
69.9
±
0.9
2714
±
45
297
±
5
4.02
0.89
1.70
600
5.5
29.5
17.4
70.3
±
0.3
2271
±
92
310
±
9
4.04
0.74
1.70
1085
7.6
30.0i
17.0
64.8
±
0.3
3325
±
16
331
±
2
3.81
1.76
48.5
30.0
86.3
±
1.5
3302
±
93
291
±
9
2.88
1.08
1.62
622
—
48.5
30.0
88.1
±
1.8
2789
±
89
324
±
9
2.94
0.91
1.62
1102
2.3
48.5i
30.0
78.6
±
2.5
3365
±
129
406
±
13
2.62
1.62
a[10] = 0.1 mM, λ=290 nm, T=35°C, and the aqueous reaction mixture contained 2% v/v CH3CN. bkOH=kobs [NaOH]. cFIT1=δap/δapavg with δapavg=3058 M−1 cm−1. dR = [C12E23]T/[NaOH]. et
is reaction time (t≥t∞) where the kinetic reaction mixture was used for micellar entrapment experiment. fCalculated from the relationship: k1=(1/t)ln⁡(1/FIT1). gValue of [C12E23]T after external addition of [NaOH]. hError limits are standard deviations. iReaction mixture for kinetic run was freshly prepared, where δap=δapavg.A few kinetic runs were carried out using authentic sample of1 freshly prepared at 35°C, 0.1 mM 1, different values of [C12E23]T (ranging from 10 to 50 mM) and [NaOH] (ranging from 4.2 to 30.0 mM). The spectrophotometrically observed data for these kinetic runs followed strictly (1) as evident from the standard deviations associated with the calculated kinetic parameters kobs, δap, and A0 (Table 3). The values of kOH (=kobs/[NaOH]) are >4-fold smaller than kOH (=36 M−1 s−1) [15] obtained under similar kinetic conditions in the absence of micelles. These results may be attributed to merely  nonionic micellar inhibitory effect (the fraction of micellized 1, i.e., 1M, under such conditions, is >90%, where KS=925 M−1 [13]).The values ofkobs, obtained from the reaction mixtures at different [C12E23]T and the reaction time t (ranging from 432 to 1102 h) at which the value of [NaOH] was increased from 1.0 mM to ≥7.6 mM and ≤30.0 mM, are comparable with the corresponding values of kobs, obtained from authentic sample of 1(Table 3). These observations support the proposal of near irreversible entrapment of 1 molecules by C12E23 micelles at R≫Rt. The observed values of Aobs at t≥600 h as well as ≤1102 h and [C12E23]T range of 10–50 mM (Table 1) reveal that the values of FIT1 must be nearly 1. But the calculated values of FIT1 at t≈600 h, as summarized in Table 3, increase from ~0.55 to ~1.0 with the respective increase in [C12E23]T from 10 to 50 mM. Similarly, the values of FIT1 at t range of ≈1083–1102 h, shown in Table 3, increase from 0.51 to 0.91 with the respective increase in [C12E23]T from 20 to 50 mM. These results show that, even at the highest value of [C12E23]T (=50 mM) of the present study, nearly 9% hydrolysis of 1 occurred within the reaction time (t) of 1102 h. Thus, it is apparent that there is not any absolute/complete irreversible micellar entrapment of 1 molecules—a situation encountered with usual shielding effect of the micelles. A qualitative explanation of these observations may be described as below.In view of the earlier reports [8, 11] on the related reaction systems, the rate of hydrolysis of 1 at 1.0 mM NaOH, 35°C, and within [C12E23]T range of 0.01–0.05 M may be expected to follow an irreversible consecutive reaction path:
(3)1M→k12M→k2PAnM+2-MAM,
where PAn and 2-MA represent phthalic anhydride and 2-methoxyaniline, respectively, and subscript M represents micellar pseudophase. The values of k2 (at 35°C) are almost zero and 12 × 10−4 s−1 at 1.0 mM NaOH and 49 mM HCl, respectively [15]. The efficient reactivity of nonionized 2 (i.e., 2H) towards the formation of PAn is primarily due to intramolecular carboxylic group—assisted cleavage of 2H [15]. The respective absence and presence of the formation of PAn in the aqueous cleavage of 3 at 1.0 mM NaOH, [C16E10]T≤30 mM, and at [C16E10]T≥50 mM have been ascribed to the consequence of the effects of [C16E10]T on the pH of micellar environment of nonionized 4(Figure 1) [11]. Spectrophotometric evidence revealed the fact that the increase in [C12E23]T at R≫Rt with a constant value of [NaOH] caused decrease in pH of micellar environment of micellized ionized phenyl salicylate [7, 9]. In view of this study, at [C12E23]T≥10 mM, the pH of the micellar environment of 2M dropped to a level where there was significant amount of 2H which caused kinetically detectable occurrence of k2—step (see (3)) within [C12E23]T range of 10–30 mM.The respective values ofδ1, δ2, δ2H, and δPAn (with δX representing molar absorptivity of X) at 290 nm are ~2420 [13], 5570–8450, 4545–7490, and 2300–2000 M−1cm−1 [11] within CH3CN content range of 2–80% v/v in mixed aqueous solvent. Close similarity of the values of δ1 and δPAn coupled with significantly higher values of δ2 or δ2H compared with those of δ1 and δPAn reveal that k2>k1. These observations explain the observed constancy of Aobs within reaction time (t) ranging from ~15 s to ≤1102 h at 10–50 mM C12E23 (Table 1). The rough and approximate values of k1 were obtained from the relationship: k1=(1/t)ln⁡(1/FIT1) and such calculated values of k1 at two different t and three [C12E23]T (10, 20, and 30 mM) are shown in Table 3. It is evident from these results that the values of k1 at two different t and at a constant [C12E23]T are comparable within the limits of experimental uncertainties. But the values of k1 decrease almost nonlinearly with the increasing values of [C12E23]T. Thus, the values of k1 became almost zero at 50 mM C12E23 and as a consequence only ~9% conversion of 1 to 2 could occur at t=1102 h (Table 3). The values of k1 decreased from ~26 × 10−8 to 2.3 × 10−8 s−1 with the increase in [C12E23]T from 10 to 50 mM. The values of k1 were found to decrease by ~3-fold, while the values of k2 remained unchanged with the increase of [C16E10]T from 50 to 88 mM in the aqueous cleavage of 3 [11]. Although the calculated values of k1 are not very reliable because they are derived from only either two or one data point(s), these values of k1 appear to be plausible for the reason that the value of k1 at pH ~3.5, in mixed aqueous solvent containing 2% v/v CH3CN, is 67 × 10−8 s−1 [16]. Under such typical conditions, the value of k2 is 120 × 10−5 s−1 and it decreases from 120 × 10−5 to 6.6 × 10−5 s−1 with increase in CH3CN content from 2 to 82% v/v [15].The values ofkobs and k1 show a nonlinear decrease with the increase of [C12E23]T within its range of 1.0 × 10−6–0.05 M (Tables 1 and 3). The value of kM (=rate constant for hydrolysis of 1 in the micellar pseudophase) remained kinetically undetectable under such conditions. The observed data failed to obey the pseudophase micellar (PM) model at >1.4 mM C12E23 because the values of micellar binding constant of 1 (KS) increase significantly (~103-fold) with the increase in [C12E23]T from 1.4 to 50 mM at 1.0 mM NaOH (Tables 1 and 3). Similar but not identical observations have been obtained in CTABr-(cetyltrimethylammonium bromide-) mediated pH-independent hydrolysis of N-(2-hydroxyphenyl)phthalimide [17]. The scenario exhibited by these observations supports the multicompartmental model of micelle [2, 18, 19] and it may best be represented by Scheme 1, where n11M molecules are in equilibrium with n1W molecules and equilibrium or micellar binding constant KS1 at R≤2 and [NaOH] = 1.0 mM. Similarly, n21M, n31M, n41M, and n51M molecules are in equilibrium with n1W molecules and equilibrium constants KS2, KS3, KS4, and KS5 at respective R=10, 20, 30, and 50 and a constant 1.0 mM NaOH.Scheme 1


## 5. Conclusions

The new and notable aspects of the present paper are the experimentally determined pseudo-first-order rate constants(k1≡kobs) of the order of 10−7–10−8 s−1 for the hydrolysis of 1 within the R range of 10–50, where R = [C12E23]T/[NaOH], with a constant value of [NaOH] (= 1.0 mM). These values of k1 are >105-fold smaller than kobs at R≤1.4, where pseudophase micellar (PM) reveals that kM≈0 and KS=925 M−1 [13]. The kinetic data of this paper show that the half-lives of alkaline hydrolysis of 1 at 1.0 mM NaOH and 35°C vary in the order 24 s, 6 min, 7 h, 31, 47, 122, and 349 days at R=0.2,3.4,5.0,10,20,30, and 50, respectively. Such quantitative information may be useful for designing nonionic micelles as the carrier of drug molecules containing imide functionality. These kinetic data also provide quantitative but indirect evidence for the multistate model of micelle suggested, to the best of our knowledge, in only a few reports [2–6, 18, 19].



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*Source: 592691-2014-01-16.xml*