The Scientific World Journal

Volume 2014 (2014), Article ID 592691, 6 pages

http://dx.doi.org/10.1155/2014/592691

Research Article

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

M. Niyaz Khan, Yoke-Leng Sim, and Azhar Ariffin

Department of Chemistry, Faculty of Science, University of Malaya, 50603 Kuala Lumpur, Malaysia

Received 7 November 2013; Accepted 19 December 2013; Published 16 January 2014

Academic Editors: J. Gebler and S.-P. Ju

Copyright © 2014 M. Niyaz Khan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract.

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

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 and mixed CTABr- 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 (/, 16/20, 18/20, and 16/10) and mixed -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 (/[NaOH] at a constant value of [NaOH]) at a typical value of which represents a typical value of /[NaOH] above which versus data fails to obey PM model. (ii) The observed data ( versus ) obey PM model at . (iii) The rate of hydrolysis of reaction kinetic probe molecules almost ceased when . (iv) The unusual observation of (iii) could be detected with , , and but not with under approximately similar conditions.

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 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 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 of 1 (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 represents the total concentration of .

Figure 1: Molecular structures of compounds 1, 2, 3 and 4.

2.2. Kinetic Measurements

The rate of nonionic micellar-mediated alkaline hydrolysis of 1 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, . The observed data, absorbance versus , obeyed

where and 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 at . 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 for Hydrolysis of 1 at 1.0 mM NaOH and 35°C

The rate of alkaline hydrolysis of 1 was studied within range of 3–50 mM, but the absorbance of the reaction mixtures within range of 10–50 mM remained unchanged in the reaction time () range of ~15 s–623 h. However, the observed data ( versus ), obtained within range of 3–5 mM, were found to fit to (1). The least-squares calculated values of , , and , obtained under such conditions, are shown in Table 1. Similarly, the kinetic runs for the rate of alkaline hydrolysis of 1 were carried out within range of 10–50 mM. But the absorbance of the reaction mixture at 50 mM remained unchanged within the range of ~15 s–~260 h. The calculated values of , , and for the kinetic runs carried out within range of 10–20 mM are shown in Table 2.

Table 1: The values of , , and for alkaline hydrolysis of 1 in the presence of .

[C₁₂E₂₃]T 

M
10⁴   

s⁻¹

M−1 cm⁻¹
10²

0.003

11.1
3.76
0

0.0034

17.6
4.13
0.13

0.0038

40.9
4.50
0.26

0.0042

154
4.87
0.46

0.005

1245
5.61
0.75

0.01
f

0.02
g

0.03
h

0.05
i

 mM, [NaOH] = 1.0 mM,  nm, °C, and the aqueous reaction mixture contained 2% v/v CH₃CN. , where ( s⁻¹ [13]) at [micelles] = 0. cCalculated from the relationship: [C₁₂E₂₃] with and  M⁻¹ [13]. dThe values of were calculated from (2) with  M⁻¹ cm⁻¹. eError limits are standard deviations. fNo change in until  h, where . gNo change in until  h, where . hNo change in until  h, where . iNo change in until  h, where .

Table 2: The values of , , and for alkaline hydrolysis of 1 in the presence of .

[C₁₈E₂₀]T 

M
10⁴   

s⁻¹

M⁻¹ s⁻¹
10²

0.01

7.92
7.89
0

0.012

21.1
9.27
0.17

0.014

28.6
10.6
0.23

0.016

46.7
12.0
0.61

0.018

56.4
13.4
0.72

0.02

153
14.8
0.83

0.05
f

 mM, [NaOH] = 1.0 mM,  nm, °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  s⁻¹, , and  M⁻¹ [13]. dThe values of were calculated from (2) with  M⁻¹ cm⁻¹. eError limits are standard deviations. fSpectrophotometrically undetectable reaction within the reaction period of ~260 h, where .

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 , where represents molar absorptivity of 2 (Figure 1). The values of and , at 290 nm, are 2480 and 5570 M−1 cm⁻¹ [15], respectively, in aqueous alkaline solvent containing 2% v/v CH₃CN. The values of are independent of [13]. The values of [13] reveal that the values of are also independent of within its range of 0.0–3.0 mM for and as well as 0.0–5.0 mM for . However, the values of show a nonlinear increase from 5570 to 8450 M−1 cm⁻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 with increase in (Tables 1 and 2) rules out the possibility of (/, 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 on and cannot explain the observed decrease in with increase in at the typical values of (Tables 1 and 2). Thus, the most plausible reason for such decrease in is due to near irreversible micellar trapping of unreacted  1. Under such circumstances, the observed data ( versus ) listed in Tables 1 and 2 cannot be expected to obey pseudophase micellar model (PM).

It can be shown that the fraction of near irreversibly micellar trapped 1 at () may be given as

where and represent apparent molar absorptivity of the reaction mixture at and , respectively. The derivation of (2) involves the assumption that the absorbance due to medium microturbidity remains unchanged within the reaction period of to . The values of were calculated from (2) at different and these values are summarized in Table 1 for and Table 2 for . It is evident from the calculated values of that the value of /[NaOH] () is nearly 3.6-fold larger for than that for to result in nearly same value of , while the value of remains zero even at for [13]. The typical value of (), at which , is 3.4 for . Similarly, the value of , at which , is 12.0 for . The values of and are ~0 [13] and 0.60 [11], respectively, at for micelles which reveal that the structural features of imide substrates (1 and 3) (Figure 1) affect the values of at a fixed value of . It is interesting and amazing to note that the difference of only 2 methylene (CH₂) groups between and has so much different effects on .

If micellar entrapment of unreacted 1, as shown by values in Tables 1 and 2, is indeed an irreversible or near irreversible process, then the values of at ≥ 10 half-lives (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 , ) should remain essentially unchanged with the increase in at or at , where . In order to test this conclusion, the kinetic reaction mixtures at 0.01, 0.02, 0.03, and 0.05 M were left at 35°C for the reaction period of ~1.10 × 10³ h and the values of , during these reaction periods, remained essentially unchanged (Table 1).

It is apparent from Tables 1 and 2 that the values of increase nonlinearly with the increase of at a typical value of (=) and the values of appear to become 1 at for (Table 1) and at for (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 molecules to become reversible bound molecules. Consequently, the rate of appearance of product (2) of this reaction mixture would follow (1) and the value of may then be compared with 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 (i.e., ), 0.02 cm³ of 1.0 M NaOH was added at  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 ( versus ) were found to fit to (1) and the least-squares calculated values of kinetic parameters , , and are summarized in Table 3. Similar kinetic runs were carried out at different (≥600 h) and (=0.02, 0.03, and 0.05 M) and the values of , , and , obtained under these conditions, are also shown in Table 3.

Table 3: Values of , , and calculated from (1) for alkaline hydrolysis of 1 in the presence of micellesa.

10³ [C₁₂E₂₃]T 

M
10³ [NaOH] 

M
10³   

s⁻¹

M⁻¹ cm⁻¹
10³

M⁻¹ s⁻¹

h
10⁸   

s⁻¹

9.9g
7.6

8.45
0.68
1.30
432
25

9.9
7.6

8.70
0.55
1.30
600
27

10.0i
7.6

8.92

1.32

19.8
11.0

4.04
0.70
1.82
623
16

19.8
11.0

3.18
0.51
1.82
1083
18

20.0i
11.0

4.65

1.82

29.5
17.4

4.02
0.89
1.70
600
5.5

29.5
17.4

4.04
0.74
1.70
1085
7.6

30.0i
17.0

3.81

1.76

48.5
30.0

2.88
1.08
1.62
622
—

48.5
30.0

2.94
0.91
1.62
1102
2.3

48.5i
30.0

2.62

1.62

[1 ₀] = 0.1 mM,  nm, °C, and the aqueous reaction mixture contained 2% v/v CH₃CN. [NaOH]. with  M⁻¹ cm⁻¹. = [C₁₂E₂₃]T/[NaOH]. is reaction time () where the kinetic reaction mixture was used for micellar entrapment experiment. fCalculated from the relationship: . gValue of [C₁₂E₂₃]T after external addition of [NaOH]. hError limits are standard deviations. iReaction mixture for kinetic run was freshly prepared, where .

A few kinetic runs were carried out using authentic sample of 1 freshly prepared at 35°C, 0.1 mM 1, different values of (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 , , and (Table 3). The values of (=/[NaOH]) are >4-fold smaller than (=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., , under such conditions, is >90%, where  M⁻¹ [13]).

The values of , obtained from the reaction mixtures at different 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 , obtained from authentic sample of 1 (Table 3). These observations support the proposal of near irreversible entrapment of 1 molecules by micelles at . The observed values of at  h as well as ≤1102 h and range of 10–50 mM (Table 1) reveal that the values of must be nearly 1. But the calculated values of at  h, as summarized in Table 3, increase from ~0.55 to ~1.0 with the respective increase in from 10 to 50 mM. Similarly, the values of at range of ≈1083–1102 h, shown in Table 3, increase from 0.51 to 0.91 with the respective increase in from 20 to 50 mM. These results show that, even at the highest value of (=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 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 represents micellar pseudophase. The values of (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,  mM, and at  mM have been ascribed to the consequence of the effects of on the pH of micellar environment of nonionized 4 (Figure 1) [11]. Spectrophotometric evidence revealed the fact that the increase in 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  mM, the pH of the micellar environment of dropped to a level where there was significant amount of 2H which caused kinetically detectable occurrence of —step (see (3)) within range of 10–30 mM.

The respective values of , , , and (with representing molar absorptivity of X) at 290 nm are ~2420 [13], 5570–8450, 4545–7490, and 2300–2000 M−1 cm⁻¹ [11] within CH₃CN content range of 2–80% v/v in mixed aqueous solvent. Close similarity of the values of and coupled with significantly higher values of or compared with those of and reveal that . These observations explain the observed constancy of within reaction time () ranging from ~15 s to ≤1102 h at 10–50 mM (Table 1). The rough and approximate values of were obtained from the relationship: and such calculated values of at two different and three (10, 20, and 30 mM) are shown in Table 3. It is evident from these results that the values of at two different and at a constant are comparable within the limits of experimental uncertainties. But the values of decrease almost nonlinearly with the increasing values of . Thus, the values of became almost zero at 50 mM and as a consequence only ~9% conversion of 1 to 2 could occur at  h (Table 3). The values of decreased from ~26 × 10⁻⁸ to 2.3 × 10⁻⁸ s⁻¹ with the increase in from 10 to 50 mM. The values of were found to decrease by ~3-fold, while the values of remained unchanged with the increase of from 50 to 88 mM in the aqueous cleavage of 3 [11]. Although the calculated values of are not very reliable because they are derived from only either two or one data point(s), these values of appear to be plausible for the reason that the value of 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 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 of and show a nonlinear decrease with the increase of within its range of 1.0 × 10⁻⁶–0.05 M (Tables 1 and 3). The value of (=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 because the values of micellar binding constant of 1 () increase significantly (~10³-fold) with the increase in 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 n₁1 M molecules are in equilibrium with n1 W molecules and equilibrium or micellar binding constant at and [NaOH] = 1.0 mM. Similarly, n₂1 M, n₃1 M, n₄1 M, and n₅1 M molecules are in equilibrium with n1 W molecules and equilibrium constants , , , and at respective , 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 of the order of 10⁻⁷–10⁻⁸ s⁻¹ for the hydrolysis of 1 within the range of 10–50, where = /[NaOH], with a constant value of [NaOH] (= 1.0 mM). These values of are >10⁵-fold smaller than at , where pseudophase micellar (PM) reveals that and  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 , 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].

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The authors thank the Ministry of Higher Education (MOHE) and University of Malaya (UM) for financial assistance through research Grants UM.C/HIR/MOHE/SC/07.

References

F. M. Menger, “The structure of micelles,” Accounts of Chemical Research, vol. 12, no. 4, pp. 111–117, 1979.

D. M. Davies, N. D. Gillitt, and P. M. Paradis, “Catalysis and inhibition of the iodide reduction of peracids by surfactants: partitioning of reactants, product and transition state between aqueous and micellar pseudophases,” Journal of the Chemical Society, Perkin Transactions 2, vol. 4, pp. 659–666, 1996.

A. Mishra, R. K. Behera, P. K. Behera, B. K. Mishra, and G. B. Behera, “Cyanines during the 1990s: a review,” Chemical Reviews, vol. 100, no. 6, pp. 1973–2011, 2000.

M. N. Khan and E. Ismail, “An empirical approach to study the occurrence of ion exchange in the alkaline hydrolysis of phthalimide in the presence of cationic micelles and inert salts,” Journal of Molecular Liquids, vol. 136, no. 1-2, pp. 54–63, 2007.

A. Laschewsky, “Polymerized micelles with compartments,” Current Opinion in Colloid and Interface Science, vol. 8, no. 3, pp. 274–281, 2003.

F. Sterpone, C. Pierleoni, G. Briganti, and M. Marchi, “Molecular dynamics study of temperature dehydration of a C₁₂E₆ spherical micelle,” Langmuir, vol. 20, no. 11, pp. 4311–4314, 2004.

M. N. Khan, Z. Arifin, M. R. Yusoff, and E. Ismail, “Effects of nonionic, cationic, and mixed nonionic-cationic surfactants on the acid-base behavior of phenyl salicylate,” Journal of Colloid and Interface Science, vol. 220, no. 2, pp. 474–476, 1999.

M. N. Khan and E. Ismail, “Effects of non-ionic and mixed cationic—non-ionic micelles on the rate of alkaline hydrolysis of phthalimide,” Journal of Physical Organic Chemistry, vol. 15, no. 7, pp. 374–384, 2002.

M. N. Khan, E. Ismail, and M. R. Yusoff, “Effects of pure non-ionic and mixed non-ionic—cationic surfactants on the rates of hydrolysis of phenyl salicylate and phenyl benzoate in alkaline medium,” Journal of Physical Organic Chemistry, vol. 14, no. 10, pp. 669–676, 2001.

M. N. Khan and E. Ismail, “Effects of non-ionic and mixed non-ionic-cationic micelles on the rate of aqueous cleavages of phenyl benzoate and phenyl salicylate in alkaline medium,” Journal of Physical Organic Chemistry, vol. 17, no. 5, pp. 376–386, 2004.

M.-Y. Cheong, A. Ariffin, and M. N. Khan, “Kinetic coupled with UV spectral evidence for near-irreversible nonionic micellar binding of N-benzylphthalimide under the typical reaction conditions—an observation against a major assumption of the pseudophase micellar model,” Journal of Physical Chemistry B, vol. 111, no. 42, pp. 12185–12194, 2007.

M. N. Khan and C. T. Fui, “Unusual effects of pure nonionic and mixed nonionic-cationic micelles on the rate of alkaline hydrolysis of N-hydroxyphthalimide,” Journal of Dispersion Science and Technology, vol. 31, no. 7, pp. 909–917, 2010.

Y.-L. Sim, N. S. M. Yusof, A. Ariffin, and M. N. Khan, “Effects of nonionic micelles on the rate of alkaline hydrolysis of N-(2′-methoxyphenyl)phthalimide (1): kinetic and rheometric evidence for a transition from spherical to rodlike micelles under the typical reaction conditions,” Journal of Colloid and Interface Science, vol. 360, no. 1, pp. 182–188, 2011.

Y.-L. Sim, A. Ariffin, and M. N. Khan, “Efficient rate enhancement due to intramolecular general base (IGB) assistance in the hydrolysis of N-(o-hydroxyphenyl)phthalimide,” The Journal of Organic Chemistry, vol. 72, no. 7, pp. 2392–2401, 2007.

Y.-L. Sim, A. Ariffin, and M. N. Khan, “Intramolecular carboxylic group-assisted cleavage of N-(2-hydroxyphenyl)- phthalamic acid (7) and N-(2-methoxyphenyl)-phthalamic acid (8): absence of intramolecular general acid catalysis due to 2-OH in 7,” International Journal of Chemical Kinetics, vol. 38, no. 12, pp. 746–758, 2006.

Y.-L. Sim, W. H. W. Ahmad, M. Y. Cheong, A. Ariffin, and M. N. Khan, “Kinetics and mechanism of hydrolysis of N-arylphthalimides,” Progress in Reaction Kinetics and Mechanism, vol. 34, no. 4, pp. 347–359, 2009.

M. N. Khan and M. H. R. Azri, “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,” Journal of Physical Chemistry B, vol. 114, no. 24, pp. 8089–8099, 2010.

G. G. Warr, T. N. Zemb, and M. Drifford, “Liquid-liquid phase separation in cationic micellar solutions,” The Journal of Physical Chemistry, vol. 94, no. 7, pp. 3086–3092, 1990.

Y. Geng, L. S. Romsted, and F. Menger, “Specific ion pairing and interfacial hydration as controlling factors in gemini micelle morphology. Chemical trapping studies,” Journal of the American Chemical Society, vol. 128, no. 2, pp. 492–501, 2006.