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

The values of pseudo-first-order rate constants (k obs) 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 (F IT1) vary in the range ~0–0.75 for C12E23 and ~0–0.83 for C18E20 under such conditions. The values of F IT1 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.


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][3][4][5][6]. The unusual effects of pure C 12 E 23 and mixed CTABr-C 12 E 23 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 C E ( / = 12/23, 16/20, 18/20, and 16/10) and mixed C E -CTABr micelles [8][9][10][11][12]. The unusual and unexpected observations of these studies are as follows. Under the typical reaction conditions of earlier studies where ≫ 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 obs 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 C 12 E 23 was caused by the near irreversible micellar binding of 1. The observed results and their probable explanations are described in this paper.

Materials and Methods
2.1. Materials. Synthesis of 1 ( Figure 1) has been reported earlier [14], and all the other chemicals used were commercial 2 The Scientific World Journal  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.

Kinetic
Measurements. The rate of nonionic micellarmediated alkaline hydrolysis of 1 was studied spectrophotometrically at 35 ∘ C by monitoring the appearance of hydrolysis product, -(2 -methoxyphenyl)phthalamate (2) of 1 at 290 nm as a function of reaction time, . The observed data, absorbance ( obs ) versus , obeyed where obs and ap represent pseudo-first-order rate constants for alkaline hydrolysis of 1 and molar absorptivity of reaction mixture, respectively, and [1 0 ] is the initial concentration of 1 and 0 = obs at = 0. The details of the product characterization are described elsewhere [13].  Table 1. Similarly, the kinetic runs for the rate of alkaline hydrolysis of 1 were carried out within [C 18 E 20 ] T range of 10-50 mM. But the absorbance of the reaction mixture at 50 mM C 18 E 20 remained unchanged within the range of ∼15 s-∼260 h. The calculated values of obs , ap , and 0 for the kinetic runs carried out within [C 18 E 20 ] T range of 10-20 mM are shown in Table 2.

Evidence for the Near Irreversible C 12 E 23 Micellar Binding of 1 under the Typical Reaction Conditions.
It can be easily shown from the derivation of (1) that ap = 2 − 1 , where 2 represents molar absorptivity of 2 ( Figure 1). The values of 1 and 2 , at 290 nm, are 2480 and 5570 M −1 cm −1 [15], respectively, in aqueous alkaline solvent containing 2% v/v CH 3 CN. The values of 1 are independent of [C E ] T [13]. The values of ap [13] reveal that the values of 2 are also independent of [C E ] T within its range of 0.0-3.0 mM for C 16 E 20 and C 12 E 23 as well as 0.0-5.0 mM for C 18 E 20 . However, the values of 2 show a nonlinear increase from 5570 to 8450 M −1 cm −1 at 290 nm with the increase in the content of CH 3 CN from 2 to 80% v/v in mixed H 2 O-CH 3 CN solvent [15]. Thus, the decrease in ap with increase   (Tables 1 and  2). Thus, the most plausible reason for such decrease in ap is due to near irreversible micellar trapping of unreacted 1. Under such circumstances, the observed data ( obs versus Tables 1 and 2 cannot be expected to obey pseudophase micellar model (PM).
It can be shown that the fraction of near irreversibly C E micellar trapped 1 at = ∞ ( IT1 ) may be given as where ap and ap avg represent apparent molar absorptivity of the reaction mixture at IT1 ̸ = 0 and IT1 = 0, respectively. The derivation of (2) involves the assumption that the absorbance due to medium microturbidity remains unchanged within the reaction period of = 0 to = ∞. The values of IT1 were calculated from (2) at different [C E ] T and these values are summarized in Table 1 for C 12 E 23 and Table 2 for C 18 E 20 . It is evident from the calculated values of IT1 that the value of [C E ] T /[NaOH] (= ) is nearly 3.6-fold larger for C 18 E 20 than that for C 12 E 23 to result in nearly same value of IT1 , while the value of IT1 remains zero even at = 170 for C 16 E 20 [13]. The typical value of (= ), at which IT1 = 0.13, is 3.4 for C 12 E 23 . Similarly, the value of , at which IT1 = 0.17, is 12.0 for C 18 E 20 . The values of IT1 and IT3 are ∼0 [13] and 0.60 [11], respectively, at = 170 for C 16 E 20 micelles which reveal that the structural features of imide substrates (1 and 3) (Figure 1) affect the values of IT1 at a fixed value of . It is interesting and amazing to note that the difference of only 2 methylene (CH 2 ) groups between C 18 E 20 and C 16 E 20 has so much different effects on IT1 .
If micellar entrapment of unreacted 1, as shown by IT1 values in Tables 1 and 2, is indeed an irreversible or near irreversible process, then the values of obs at ≥ 10 halflives (Reaction time at ∼10 half-lives is equivalent to ∞ because more than 99.9% reaction is progressed during the reaction period of 10 half-lives and therefore, at ∞ , obs = ∞ ) should remain essentially unchanged with the increase in at = ∞ or at , where obs = ∞ . In order to test this conclusion, the kinetic reaction mixtures at 0.01, 0.02, 0.03, and 0.05 M C 12 E 23 were left at 35 ∘ C for the reaction period of ∼1.10 × 10 3 h and the values of obs , during these reaction periods, remained essentially unchanged (Table 1).
It is apparent from Tables 1 and 2 that the values of IT1 increase nonlinearly with the increase of at a typical value of (= ) and the values of IT1 appear to become 1 at ≥ 10 for C 12 E 23 (Table 1) and at = 50 for C 18 E 20 ( Table 2). If the reversible and near irreversible nonionic micellar binding of 1 is a function of , then the change of inequality from > to < , by sudden external addition of known amount of NaOH to the reaction mixture at > ∞ , must cause near irreversible bound 1 M molecules to become reversible bound 1 M molecules. Consequently, the rate of appearance of product (2) of this reaction mixture would follow (1) and the value of obs may then be compared with obs 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 cm 3 of the reaction mixture containing 0.1 mM 1, 1.0 mM NaOH, and 10 mM C 12 E 23 (i.e., = 10), 0.02 cm 3 of 1.0 M NaOH was added at = 432 h. The absorbance change of the resulting reaction mixture was quickly monitored spectrophotometrically at 290 nm as a function of reaction time ( ). The observed data ( obs versus ) were found to fit to (1) and the least-squares calculated values of kinetic parameters obs , ap , and 0 are summarized in Table 3. Similar kinetic runs were carried out at different (≥600 h) and [C 12 E 23 ] T (=0.02, 0.03, and 0.05 M) and the values of obs , ap , and 0 , obtained under these conditions, are also shown in Table 3.
A few kinetic runs were carried out using authentic sample of 1 freshly prepared at 35 ∘ C, 0.1 mM 1, different values of [C 12 E 23 ] 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 obs , ap , and 0 (  [13]). The values of obs , obtained from the reaction mixtures at different [C 12 E 23 ] T and the reaction time (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 obs , obtained from authentic sample of 1 (Table 3). These observations support the proposal of near irreversible entrapment of 1 molecules by C 12 E 23 micelles at ≫ . The observed values of obs at ≥ 600 h as well as ≤1102 h and [C 12 E 23 ] T range of 10-50 mM (Table 1) reveal that the values of IT1 must be nearly 1. But the calculated values of IT1 at ≈ 600 h, as summarized in Table 3, increase from ∼0.55 to ∼1.0 with the respective increase in [C 12 E 23 ] T from 10 to 50 mM. Similarly, the values of IT1 at range of ≈1083-1102 h, shown in Table 3, increase from 0.51 to 0.91 with the respective increase in [C 12 E 23 ] T from 20 to 50 mM. These results show that, even at the highest value of [C 12 E 23 ] T (=50 mM) of the present study, nearly 9% hydrolysis of 1 occurred within the reaction time ( ) 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 [C 12 E 23 ] T range of 0.01-0.05 M may be expected to follow an irreversible consecutive reaction path: where PAn and 2-MA represent phthalic anhydride and 2-methoxyaniline, respectively, and subscript M represents micellar pseudophase. The values of 2 (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].  Figure 1) [11]. Spectrophotometric evidence revealed the fact that the increase in [C 12 E 23 ] T at ≫ 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 [C 12 E 23 ] T ≥ 10 mM, the pH of the micellar environment of 2 M dropped to a level where there was significant amount of 2H which caused kinetically detectable occurrence of 2 -step (see (3)) within [C 12 E 23 ] T range of 10-30 mM.
The respective values of 1 , 2 , 2H , and PAn (with X representing molar absorptivity of X) at 290 nm are ∼2420 [13], 5570-8450, 4545-7490, and 2300-2000 M −1 cm −1 [11] within CH 3 CN content range of 2-80% v/v in mixed aqueous solvent. Close similarity of the values of 1 and PAn coupled The Scientific World Journal 5 with significantly higher values of 2 or 2H compared with those of 1 and PAn reveal that 2 > 1 . These observations explain the observed constancy of obs within reaction time ( ) ranging from ∼15 s to ≤1102 h at 10-50 mM C 12 E 23 ( Table 1). The rough and approximate values of 1 were obtained from the relationship: 1 = (1/ ) ln(1/ IT1 ) and such calculated values of 1 at two different and three [C 12 E 23 ] T (10, 20, and 30 mM) are shown in Table 3. It is evident from these results that the values of 1 at two different and at a constant [C 12 E 23 ] T are comparable within the limits of experimental uncertainties. But the values of 1 decrease almost nonlinearly with the increasing values of [C 12 E 23 ] T . Thus, the values of 1 became almost zero at 50 mM C 12 E 23 and as a consequence only ∼9% conversion of 1 to 2 could occur at = 1102 h ( Table 3). The values of 1 decreased from ∼26 × 10 −8 to 2.3 × 10 −8 s −1 with the increase in [C 12 E 23 ] T from 10 to 50 mM. The values of 1 were found to decrease by ∼3-fold, while the values of 2 remained unchanged with the increase of [C 16 E 10 ] T from 50 to 88 mM in the aqueous cleavage of 3 [11]. Although the calculated values of 1 are not very reliable because they are derived from only either two or one data point(s), these values of 1 appear to be plausible for the reason that the value of 1 at pH ∼3.5, in mixed aqueous solvent containing 2% v/v CH 3 CN, is 67 × 10 −8 s −1 [16]. Under such typical conditions, the value of 2 is 120 × 10 −5 s −1 and it decreases from 120 × 10 −5 to 6.6 × 10 −5 s −1 with increase in CH 3 CN content from 2 to 82% v/v [15].
The values of obs and 1 show a nonlinear decrease with the increase of [C 12 E 23 ] T within its range of 1.0 × 10 −6 -0.05 M (Tables 1 and 3). The value of M (=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 C 12 E 23 because the values of micellar binding constant of 1 ( ) increase significantly (∼10 3 -fold) with the increase in [C 12 E 23 ] 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 pHindependent hydrolysis of -(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 n 1 1 M molecules are in equilibrium with n1 W molecules and equilibrium or micellar binding constant 1 at ≤ 2 and [NaOH] = 1.0 mM. Similarly, n 2 1 M , n 3 1 M , n 4 1 M , and n 5 1 M molecules are in equilibrium with n1 W molecules and equilibrium constants 2 , 3 , 4 , and 5 at respective = 10, 20, 30, and 50 and a constant 1.0 mM NaOH.

Conclusions
The new and notable aspects of the present paper are the experimentally determined pseudo-first-order rate constants where pseudophase micellar (PM) reveals that M ≈ 0 and = 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 = 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].