AOT

ARTICLE pubs.acs.org/JPCA

Spectrometric Study of AOT-Hydrolysis Reaction in Water/AOT/ Isooctane Microemulsions Using Phenolphthalein as a Chemical Probe Shiyan Mao,† Zhiyun Chen,‡ Dashuang Fan,† Xueqin An,‡ and Weiguo Shen*,†,‡ † ‡

Department of Chemistry, Lanzhou University, Lanzhou, Gansu 730000, China School of Chemistry and Molecular Engineering, East China University of Science and Technology, Shanghai 200237, China

bS Supporting Information ABSTRACT: The kinetics of the alkaline hydrolysis of sodium bis(2-ethylhexyl)sulfosuccinate (AOT) in water/AOT/isooctane microemulsions has been studied by monitoring the absorbance change of the phenolphthalein in the system with time. The apparent first-order rate constant kobs has been obtained and found to be dependent on both the molar ratio of water to AOT ω and the temperature. The dependences of kobs on ω have been analyzed by a pseudophase model which gives the true rate constants ki of the AOT-hydrolysis reaction on the interface and the partition coefficients Kwi for the distribution of OH
between aqueous and interface pseudophases at various temperatures; the latter is almost independent of the temperature and ω. The temperature dependences of the reaction rate constants kobs and ki have been analyzed to obtain enthalpy ΔH6¼, entropy ΔS6¼, and energy Ea of activation, which indicate that the distribution of OH
between aqueous and interface pseudophases increases ΔS6¼ but makes no contribution to Ea and ΔH6¼. The influence of the overall concentration of AOT in the system on the rate constant has been examined and found to be negligible. It contradicts with what was reported by García-Río et al.1 but confirms that the first-order reaction of the AOT-hydrolysis takes place on the surfactant interface. The study of the influence of AOThydrolysis on the kinetics of the alkaline fading of crystal violet or phenolphthalein in the water/AOT/isooctane microemulsions suggests that corrections for the AOT-hydrolysis in these reactions are required.

1. INTRODUCTION The water-in-oil microemulsions are macroscopically homogeneous and thermodynamically stable systems of water nanodroplets dispersed into apolar solvents in the presence of adequate surfactants.2 Sodium bis(2-ethylhexyl)sulfosuccinate (AOT) is one of the few ionic surfactants that forms microemulsions without addition of any cosurfactants due to its double-tailed nature.3 Microemulsions consisting of AOT, water, and oil have been widely investigated as a model system, since it is very well characterized and stable over a wide range of concentrations and temperatures.4
6 It is well-known that the droplets of AOTbased microemulsions can be considered as the microreactors that provide a special medium for various types of chemical reactions, such as synthesis of nanocrystals7 and nanoparticles,8 polymerization,9 Diels
Alder reaction,10 electron-transfer reactions,11 and biological reactions,12 etc. The kinetics of some reactions such as the alkaline fading of phenolphthalein (PN)13 and crystal violet (CV)14
17 as well as lipase-catalyzed hydrolysis18,19 were studied in the AOT-based microemulsions. Being a diester, AOT may undergo hydrolysis in basic media,20,21 causing undesired consumption of OH
, and thus interfere with the kinetic study of the reactions mentioned above. However, AOT-hydrolysis was usually neglected in the studies of such reactions, while only a few papers took this into account. Mukherjee et al.21 determined the activation parameters and the rate constants for the alkaline hydrolysis of AOT in aqueous r 2011 American Chemical Society

and aquo-dioxane media. The reaction of AOT-hydrolysis in a microemulsion system most likely takes place on the AOT interface and is possibly more significant than that in aqueous solutions. Leis et al.15 observed that the occurrence of AOT-hydrolysis in the AOT-based microemulsions resulted in a reduction in the OH
concentration indicated by the recovery of absorbance of CV, but AOT-hydrolysis was found to be so slow that it could be negligible in studying the alkaline fading of CV in the water pools of the AOT-based microemulsions. A quantitative study of AOThydrolysis in the AOT-based microemulsions was reported by García-Río et al.1 When they studied the kinetics of the alkaline hydrolysis of nitroprusside [Fe(CN)5NO]2
to form [Fe(CN)5NO2]4
in the AOT-based microemulsions, they found that the absorbance at 415 nm increased early and then started to decrease after a period of time. This decrease was used to analyze the influence of AOT-hydrolysis. They assumed that the aquation of [Fe(CN)5NO2]4
to form [Fe(CN)5(OH2)]3
was negligible because of the small equilibrium constant, which allowed them to attribute the reduction of [Fe(CN)5NO2]4
only to AOT-hydrolysis. They found that the rate constant of AOT-hydrolysis linearly increased with the concentration of AOT and kept constant when the molar ratio of water to AOT Received: June 24, 2011 Revised: December 13, 2011 Published: December 14, 2011 158

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Figure 1. Structures of the colored quinonoid form L2
of phenolphthalein (a), the colorless carbinol form LOH3
of phenolphthalein (b), and AOT (c).

ω changed, which is somewhat surprising for such an interface reaction. They determined the second-order rate constant of AOT-hydrolysis to be 4.4  10
4 L mol
1 s
1 and suggested that AOT-hydrolysis must be considered in the case where a significant amount of OH
was present in the AOT-based microemulsions. However, after calculation of the equilibrium between [Fe(CN)5NO2]4
and [Fe(CN)5(OH2)]3
, we have found that the ratio of equilibrium concentrations of [Fe(CN)5(OH2)]3
to [Fe(CN)5NO2]4
is as large as about 0.34 under their experimental conditions. It indicates that the contribution of the aquation process must be taken into account when the kinetics of AOT-hydrolysis is studied by using sodium nitroprusside as a chemical probe. Therefore, reexaminations of the kinetics of AOT-hydrolysis in the AOT-based microemulsions and its effects on the kinetics of alkaline hydrolysis reactions are highly required. UV
vis spectroscopy has been widely used in the kinetic studies in solutions. However, when it is used in the study of AOT-hydrolysis, an appropriate indicator must be used because no UV
vis absorbance could be observed for either the reactants or the products of AOT-hydrolysis. PN has a sensitive spectroscopy response to the concentration of OH
. The kinetic behavior of the alkaline fading of PN in alkaline aqueous media was studied by monitoring the absorbance of the reaction system.22 It was found that the reaction was reversible and the rate constants and the equilibrium constants were small.22 This has limited the application of PN as an indicator to study the chemical reactions in aqueous solutions. Recently, we investigated the alkaline fading of PN in the AOT-based microemulsions by the spectroscopy method13 and observed that the absorbance of the quinonoid form of PN L2
at 553 nm and pH > 12 decreased initially with time after OH
was added but increased after passing a minimum as long as the reaction time was long enough, which indicated the occurrence of AOT-hydrolysis. We used the absorbance data before the minimum point to obtain the values of the equilibrium constant and the forward rate constant for the alkaline fading of PN with the AOT-hydrolysis being neglected in the AOT-based microemulsions. These parameters were found to be significantly larger than that in aqueous solutions, suggesting that PN is a proper indicator for the quantitative study of the AOT-hydrolysis kinetics in the AOT-based microemulsions. In this paper we investigate the kinetics of the alkaline hydrolysis of AOT in the water/AOT/isooctane microemulsions with the UV
vis spectroscopy method using PN as an indicator at pH ≈ 13.3. We obtain the apparent first-order rate constant kobs from the absorbance measurements and calculate the true rate constant ki on the interface for AOT-hydrolysis through a pseudophase model. The values of kobs are used to correct the previously reported kinetic parameters, including the pseudofirst-order rate constants of the alkaline fading of CV and the rate constants and the equilibrium constants of the alkaline fading of PN in the AOT-based microemulsions.13,23

2. EXPERIMENTAL SECTION 2.1. Materials. AOT (g98%) was purchased from Aldrich Chemical Co. and was dried over P2O5 in a desiccator for 2 weeks. Isooctane (g99%), potassium hydrogen phthalate (g99.9%), and ethanol (g99.7%) were supplied by Tianjin Second Chemical Co. Phenolphthalein (analytic grade) and sodium hydroxide (g96%) were supplied by Tianjin Jingda Fine Chemical Co. and Tianjin Chemical Reagent Co., respectively. All reagents except AOT were used as received. Twice distilled water was used for preparations of the samples. 2.2. Kinetic Measurements. An aqueous solution with a concentration of sodium hydroxide (NaOH) being slightly larger than 0.2 mol L
1 was prepared, the concentration of which was then titrated with potassium hydrogen phthalate and adjusted with water to an accurate required value. A water/PN/ethanol solution with the concentrations of PN and ethanol being 0.013 mol L
1 and 70% in volume, respectively, was prepared, a small amount of which was added into an appropriate amount of the above NaOH aqueous solution to form a PN/ethanol/NaOH aqueous solution (1) with the concentrations of NaOH and PN being 0.2 mol L
1 (corresponding to pH = 13.3) and 2.02  10
4 mol L
1, respectively. Solution 1 was allowed to equilibrate for at least 8 h. A pink color was developed, indicating that the red-pink L2
and the colorless carbinol form of PN LOH3
coexisted with the latter dominating at pH = 13.3. The structures of L2
and LOH3
are shown in Figures 1a and 1b. An AOT/ isooctane solution (2) with the accurately known composition was prepared and together with solution 1 set at the required constant temperature for about 20 min. All the amounts of the chemicals were accurately weighed during the preparations of the above solutions except for the small amount of water/PN/ethanol solution, which was added with a microsyringe into the NaOH aqueous solution. Appropriate amounts of solutions 1 and 2 and isooctane were mixed to form the microemulsions with desired ω and overall concentration of AOT ([AOT]). This microemulsion contained about 0.1% of ethanol in volume fraction, which most likely resided on the interface as a cosurfactant. However, it was estimated to be only about 0.5% in mass fraction of the surfactant; thus, the effect of the small amount of ethanol on the structure of microemulsion droplets was ignored. This microemulsion system was set in a thermostat with the required constant temperature and stirred before it was transferred into an optical cell and was sealed by a Teflon stop for kinetic measurements. Kinetic measurements and spectral studies were carried out in an Agilent 8453E UV spectrophotometer. The optical cell filled with the sample was loaded in a thermostatted multiple-cell holder, which was able to keep the temperature constant within (0.1 K in the sample cell. The change of absorbance (A) in the microemulsion reaction system with time was monitored at 553 nm in its reaction process after the optical cell was loaded into the cell 159

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rates corresponding to eqs 1 and 2 may be expressed by d½AOT d½OH
 ¼ ¼
kobs ½OH
 dt dt

ð3Þ

dx ¼ k
1 ða
xÞ
k2 x½OH
 dt ¼ ðk2 ½OH
 þ k
1 Þðxe
xÞ

ð4Þ




where t, a, x, and [OH ] are the reaction time, the overall concentration of all species of PN at initial time, the overall concentration of L2
at any time t, and the concentration of OH
referred to the water volume at any time t, respectively; kobs is the apparent first-order rate constant for eq 1; k2 and k
1 are the second-order rate constant and the first-order rate constant for the forward and reverse reactions of eq 2, respectively; and xe is the equilibrium value of x. 3.2. Data Analysis. The equilibrium constant K of the alkaline fading reaction of PN can be expressed as

Figure 2. Absorption spectra of L2
at different time intervals for the alkaline hydrolysis of AOT in water/AOT/isooctane microemulsions with ω = 14 and [AOT] = 0.4 mol L
1 at 298.2 K.

K ¼

hold. In principle, the AOT-hydrolysis reaction starts immediately after mixing solutions 1 and 2. However, as we will explain later, when to start recording the absorbance is not so important. Absorbance was automatically recorded every 15 or 30 s for 10
40 min, depending on the particular experimental condition. The uncertainty in the measurement of A was about (0.003. The change of the spectrum of L2
with time was also monitored during the reaction, and no shift of the absorbance peak was observed in the reaction process shown in Figure 2 as an example.

3.1. Phenomenon and Mechanism. The absorbance of PN in the alkaline water/AOT/isooctane microemulsions after equilibrium should be constant if no additional reactions take place to change the concentration of OH
, but all measurements revealed significant changes of absorbance with time. This behavior may be attributed to the fact that the surfactant AOT used to form the microemulsions undergoes the alkaline hydrolysis which results in OH
uptake.13 The consumption of OH
during AOT-hydrolysis shifted the equilibrium from LOH3
toward L2
, causing an increase in absorbance. This mechanism may be described by the following two equations kobs

slow

ð5Þ

where [LOH3
]e and [L2
]e are the overall equilibrium concentrations of LOH3
and L2
, respectively, and [L2
]e = xe. It was reported in our previous work13 that the values of the rate constant (k2[OH
] + k
1) of the alkaline fading of PN were at least 8 times larger than that of AOT-hydrolysis in water/AOT/ isooctane microemulsions; thus, the reaction described by eq 2 is approximately in the quasi-equilibrium when the two reactions described by eqs 1 and 2 compete with each other. Therefore, it allows us to replace xe by x and rearrange eq 5 to obtain
 .
 a 1 x¼ 1 þ ð6Þ K½OH
 K½OH


3. RESULTS AND DISCUSSION

AOT þ OH
f hydrolyzed products

½LOH3
e a
xe ¼ ½L2
e ½OH
 xe ½OH


When K[OH
] . 1, eq 6 becomes a x¼ K½OH
 dx a d½OH
 ¼
dt dt K½OH
2

ð7Þ ð8Þ

Substituting eq 3 into eq 8 yields dx akobs ¼ dt K½OH


ð1Þ

ð9Þ

Combining eq 7 with eq 9 gives k2

L2
þ OH
a LOH3
k
1

fast

dx ¼ kobs x dt

ð2Þ

ð10Þ

Using the Lambert
Beer law and integrating eq 10 yield

An AOT molecule has two tails, and each of them includes an ester group (see Figure 1c). The two ester groups in an AOT molecule are so close that the reactions of the two OH
ions with the same AOT molecule unlikely occur due to the steric hindrances and the electrostatic repulsions. Thus we assume that only one ester group of AOT molecule participates in the reaction and the AOT-hydrolysis may be treated as a first-order or a pseudo-first-order reaction in both aqueous solutions and microemulsions described by eq 1. It has been well confirmed by the results obtained from Mukherjee et al.21 and Fletcher et al.24 and will be examined in the latter part of this paper. Reaction

ln A ¼ kobs t þ constant

ð11Þ

The plot of ln A versus t should give a straight line with a slope being kobs when K[OH
] . 1. Thus, the time to start the record of absorbance can be flexible as long as enough absorbance data are taken in the initial linear reaction time scale. Relative errors caused by replacing xe by x are estimated to be less than 4%. In our pervious work13 we reported the values of K for various ω and the initial concentration of OH
referred to the water volume ([OH
]0), which are listed in column 5 of Table 1. 160

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Table 1. Values of k2 and K for the Alkaline Fading of PN in Water/AOT/Isooctane Microemulsions with [AOT] = 0.3 mol L
1 and Various ω and [OH
]0 at 298.2 K

a

ω

[OH
]0/mol L
1

102k2/L mol
1 s
1

K/L mol
1

8

0.301

a

4.15 ( 0.46

b

5.71 ( 0.16

a

10 12

0.240 0.200

a

4.85 ( 0.57 a 4.93 ( 0.27

b

6.45 ( 0.15 b 6.65 ( 0.08

a

14

0.172

a

4.68 ( 0.40

b

6.12 ( 0.11

a

189 ( 11

c

16

0.150

a

4.04 ( 0.48

b

5.28 ( 0.18

a

157 ( 13

c

18

0.134

a

3.66 ( 0.86

b

5.02 ( 0.31

a

140 ( 23

c

122 ( 10

440 ( 54

c

264 ( 21 a 331 ( 12

881 ( 91 1044 ( 58 c

c

552 ( 39 428 ( 46 432 ( 90

Data from ref 13. b Data from fitting eq 24. c Data from calculating with eq 25.

Taking these values of K and [OH
]0 = 0.2 mol L
1, the errors introduced from neglecting 1/(K[OH
]) in the denominator of eq 6 were estimated to be less than 4%. As will be discussed later, after correction for the effect of AOT-hydrolysis, the values of K become much larger than the uncorrected ones (see column 6 of Table 1); thus, in fact the above estimated error will be reduced significantly. The validities of quasi-equilibrium and K[OH
] . 1 were confirmed by the plots of ln A versus t for various ω, temperatures, and [AOT] in an initial period of reaction, which gave good straight lines with linear correlation coefficients larger than 0.993. The values of kobs can be obtained by the linear leastsquares fits of eq 11. Measurements of A at various t were repeated at least three times, and the average values of kobs were reported in this paper. The uncertainties in determination of kobs were estimated to be less than 5% of the values. As an example, Figure 3 shows a very good linear relationship between ln A and t for the microemulsion system with ω = 18 and [AOT] = 0.4 mol L
1 at 298.2 K. 3.3. Influence of ω. The effect of ω on kobs was investigated by changing the value of ω from 8 to 18 at various temperatures and the fixed AOT concentration of 0.4 mol L
1. It was found that the microemulsion reaction systems with ω less than 8 were unstable, and some precipitations were observed at the bottom of the sample cells; therefore, the investigation for the system with lower ω was restrained. The determined values of kobs are listed in Table 2, which decrease gradually with increasing ω. It is in contradiction with what was reported by García-Río et al.1 for the same reaction in the water/AOT/isooctane microemulsion system. They found that kobs was independent of ω, which might have resulted from the disaccord between the experimental design and the complicated equilibriums in the alkaline hydrolysis of nitroprusside, including the neglect of the aquation of [Fe(CN)5NO2]4
. Dependence of kobs on ω can be quantitatively explained by applying a pseudophase model.5,25,26 Microemulsions have a peculiar molecular heterogeneity caused by the amphiphilic nature of the surfactant that resides in an interface between water and the nonpolar solvent.5 Three different compartments are available for the localizations of the reactants other than the surfactant: (a) the internal aqueous core or water pool, (b) the micelle interface formed by a monolayer of surfactant molecules with their polar headgroups oriented toward the water pool, and (c) the external organic phase.27 The study of the reaction between CV and the sulfite ion has shown irrefutable evidence of the existence of three well-differentiated compartments in the AOT-based microemulsions, even at very low water contents.28,29 In the AOT alkaline hydrolysis system, AOT only resides in the interface. A part of OH
ions are present in the aqueous

Figure 3. Plot of ln A vs t for the alkaline hydrolysis of AOT in water/ AOT/isooctane microemulsions with ω = 18 and [AOT] = 0.4 mol L
1 at 298.2 K. The points represent experimental results; the line represents the result of the fit of eq 11.

Table 2. Values of kobs/s
1 for the Alkaline Hydrolysis of AOT in Water/AOT/Isooctane Microemulsions with [AOT] = 0.4 mol L
1 and Various ω at Various Temperatures ω

293.2 K

8 6.00  10


4

10 4.95  10


4

12 4.27  10


4

14 3.71  10


4

296.2 K
4

8.26  10


4

6.89  10


4

5.73  10


4

5.16  10


4

298.2 K
4

9.55  10


4

7.85  10


4

6.84  10


4

5.91  10


4


4

301.2 K

303.2 K


3

1.52  10
3


3

1.27  10
3


4

1.09  10
3


4

9.47  10
4

1.29  10 1.10  10 9.02  10 8.21  10


4

16 3.27  10 4.46  10 5.21  10 7.13  10 8.22  10
4
4
4
4
4 18 2.91  10 4.04  10 4.64  10 6.31  10 7.46  10
4

pseudophase, while the rest of them enter into the interface to react with AOT molecules. Thus, the global reaction rate is exactly the rate on the AOT interface r ¼ kobs ½OH
 ¼ ki ½OH
i

ð12Þ

where [OH
]i is the concentration of OH
on the interface and ki is the true rate constant of the AOT-hydrolysis on the interface. The reaction mechanism is shown in Figure 4. The partition coefficient Kwi of OH
between the aqueous and the interface pseudophases can be defined as5 Kwi ¼ 161

½OH
i ω ½OH
w

ð13Þ

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Table 3. Values of Kwi and ki for the Alkaline Hydrolysis of AOT in Water/AOT/Isooctane Microemulsions with [AOT] = 0.4 mol L
1 at Various Temperatures 293.2 K Kwi

296.2 K

298.2 K

301.2 K

303.2 K

1.43 ( 0.17 1.49 ( 0.31 1.41 ( 0.24 1.55 ( 0.43 1.38 ( 0.25

103 ki /s
1 3.93 ( 0.01 5.40 ( 0.02 6.25 ( 0.02 8.52 ( 0.07 9.99 ( 0.04

Figure 4. Model for the alkaline hydrolysis of AOT on the interface in water/AOT/isooctane microemulsions.

Figure 6. Plots of kobs vs Kwi/(Kwi+ω) for the alkaline hydrolysis of AOT in water/AOT/isooctane microemulsions with [AOT] = 0.4 mol L
1 at various temperatures. The points represent experimental results: (9) 293.2 K, (0) 296.2 K, (b) 298.2 K, (O) 301.2 K, (2) 303.2 K. The solid lines represent the results of the fits of eq 14. Figure 5. Plots of 1/kobs vs ω for the alkaline hydrolysis of AOT in water/AOT/isooctane microemulsions with [AOT] = 0.4 mol L
1 at various temperatures. The points represent experimental results: (9) 293.2 K, (0) 296.2 K, (b) 298.2 K, (O) 301.2 K, (2) 303.2 K. The solid lines represent the results of the fits of eq 15.

3.4. Influence of Temperature. As it is shown in Table 3, values of Kwi at various temperatures are almost constant within their estimated uncertainties in the temperature range we studied, and the average of the values is (1.45 ( 0.28). Substitution of this average value of Kwi into eq 14 and plotting kobs versus Kwi/(Kwi + ω) for each temperature yielded straight lines passing through the origin (see Figure 6). The least-squares fits gave the values of ki for five temperatures, which are listed in Table 3. It can be seen from Tables 2 and 3 that the values of kobs and ki increase with temperature. In a narrow range of temperature, the microemulsion properties have been assumed to remain unchanged. According to the Arrhenius law and transition state theory, the temperature dependences of the rate constants k (kobs or ki) may be used to obtain the values of enthalpy ΔH6¼, entropy ΔS6¼, and energy Ea of activation through the following expressions

where [OH
]w is the concentration of OH
in the water phase. All the concentrations are referred to the water volume. Considering that the total concentration of OH
at any time t should be the sum of the concentrations in the two pseudophases, i.e., [OH
] = [OH
]i + [OH
]w, from eqs 12 and 13 we can obtain kobs ¼

ki Kwi Kwi þ ω

ð14Þ

which may be rearranged as 1 kobs

¼

ω 1 þ ki Kwi ki

Ea þ constant RT

ð16Þ



 k kB ΔS 6¼ ΔH 6¼
¼ ln þ T h R RT

ð17Þ

ln k ¼


ð15Þ

Good linear relations of 1/kobs versus ω for various temperatures are shown in Figure 5, evidencing the validity of eq 15 and the pseudophase model described above. The linear least-squares fits gave the slopes and the intercepts of the solid lines in Figure 5. Values of Kwi at various temperatures were calculated by Kwi = intercept/slope and are listed in Table 3 together with their estimated uncertainties. The uncertainties in determination of Kwi were as large as 19% of the values, which may be attributed to the strong correlations between the slopes and the intercepts in the fits.

ln

where kB, h, T, and R are the Boltzmann constant, the Planck constant, the absolute temperature, and the molar gas constant, respectively. Plots of ln(k/T) and ln k versus 1/T for kobs or ki resulted good straight lines (see Figure 7 and Figure S-1 in the Supporting Information). Least-squares fits gave the values of Ea, ΔH6¼, and ΔS6¼ for both kobs and ki. Values related to kobs at various ω are 162

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listed in Table 4. Values related to ki are (68.5 ( 1.2) kJ mol
1, (66.1 ( 1.5) kJ mol
1, and (
65.3 ( 2.0) J K
1 mol
1, respectively. Values of Ea, ΔH6¼, and ΔS6¼ related to kobs show no significant dependence of ω within their uncertainties, with the average values of (68.8 ( 1.5) kJ mol
1 for Ea, (66.3 ( 1.5) kJ mol
1 for ΔH6¼, and (
83.9 ( 3.7) J K
1 mol
1 for ΔS6¼, respectively. Values of Ea and ΔH6¼ are almost the same as that related to ki, indicating that the contributions to Ea and ΔH6¼ from the distribution of OH
between the water pool and the AOT interface are negligible. Values of ΔS6¼ related to ki and kobs are all negative, which support the assumption of a stabilized activation complex.21 The value of ΔS6¼ related to ki is significantly larger than the average value of that related to kobs. The difference is as large as (18.6 ( 4.2) J K
1 mol
1, which evidences that the distribution of OH
between the water pool and the AOT interface has made a significant positive contribution to the ΔS6¼ of the interface reaction. 3.5. Influence of AOT Concentration. A study was carried out to examine the influence of AOT concentration on the rate of AOT-hydrolysis. It was found that the values of kobs kept almost constant as the AOT concentration varied from 0.2 to 0.8 mol L
1 at ω = 14 and 298.2 K (see Figure S-2 in the Supporting Information). According to eq 14, the values of ki were calculated by ki ¼

ðKwi þ ωÞkobs Kwi

Supporting Information). The change of the AOT concentration with fixed ω is equivalent to the change of the concentration of the microemulsion droplets; thus, the rate constants kobs and ki are also almost independent of the number of the microemulsion droplets in the system. This independence indicates that the AOThydrolysis on the interface is a real first-order reaction. Our results contradict what was reported by García-Río et al.1 who found that the pseudo-first-order rate constant of the AOThydrolysis reaction was linearly dependent on [AOT] in the AOTbased microemulsions. It might have resulted from the disaccord between the experimental design and the complicated equilibriums in the alkaline hydrolysis of nitroprusside, including the neglect of the aquation of [Fe(CN)5NO2]4
. However, the independence is not surprising because the reactant AOT is taken as a solvent and reacts with the dilute solute OH
in an interface layer; thus, the mole fraction of AOT may be conveniently chosen as the variable of concentration and is reasonably regarded as a unit in an ideal dilute solution. It is different from the same reaction that takes place in the aqueous solution21 where the two reactants AOT and OH
with the dilute concentrations react through collisions. Therefore, both the concentrations of reactants AOT and OH
determine the reaction rate, showing the character of the second-order reaction. 3.6. Influence of the AOT Hydrolysis on the Alkaline Fading of CV. As the alkaline fading of CV takes place in the AOT-based microemulsions, AOT-hydrolysis consumes OH
and results in a competition with the reaction of the alkaline fading of CV in the AOT-based microemulsions. In this section we will analyze the influence of AOT-hydrolysis on the kinetics of the alkaline fading of CV in the water/AOT/isooctane microemulsions. The study of the alkaline fading of CV was reported previously15,16 where the overall initial concentration of OH
was 5  10
3 mol L
1, and the concentration of CV was much less than that of OH
. Therefore, the consumption of OH
by the alkaline fading of CV was negligible as compared to that by AOT-hydrolysis. Thus, the change of the concentration of OH
may be attributed only to AOT-hydrolysis, and then the integral kinetic equation may be expressed as

ð18Þ

with the experimental values of kobs at various ω and the value of Kwi being 1.45. It resulted that the values of ki were also independent of [AOT] in the microemulsions (see Figure S-2 in the

½OH
 ¼ ½OH
0 expð
kobs tÞ

ð19Þ

The reaction rate of the alkaline fading of CV may be written as r ¼


d½CV
¼ kCV 2 ½CV½OH  dt


¼ kCV 2 ½CV½OH 0 expð
kobs tÞ

Figure 7. Plots of ln(kobs/T) or ln(ki/T) vs 1/T for the alkaline hydrolysis of AOT in water/AOT/isooctane microemulsions with [AOT] = 0.4 mol L
1 and various ω. The points represent experimental results: for ln(kobs/T) (9) ω = 8, (0) ω = 10, (b) ω = 12, (O) ω = 14, (1) ω = 16, (3) ω = 18; for ln(ki/T) (Δ). The solid lines represent the results of the fits of eq 17.

ð20Þ

where [CV] and kCV 2 are the concentrations of CV at any time t and the second-order rate constant of the reaction, respectively. Combining the integral form of eq 20 with the Lambert
Beer law, the change of the absorbance of CV in the microby emulsions with time is related to the rate constant kCV 1

Table 4. Values of Ea, ΔH6¼, and ΔS6¼ Related to kobs for the Alkaline Hydrolysis of AOT in Water/AOT/Isooctane Microemulsions with Various ω ω
1

8

10

12

14

16

18

Ea/kJ mol

68.0 ( 1.2

69.6 ( 2.1

68.4 ( 0.9

69.5 ( 1.9

68.3 ( 1.2

ΔH6¼/kJ mol
1

65.5 ( 1.2

67.2 ( 2.1

66.0 ( 0.9

66.7 ( 1.9

65.8 ( 1.2

66.3 ( 1.6


82.7 ( 3.0


80.5 ( 4.8


84.1 ( 2.2


82.8 ( 4.6


86.8 ( 3.2


86.2 ( 4.1

ΔS6¼/J K
1 mol
1

163

68.7 ( 1.6

dx.doi.org/10.1021/jp2059744 |J. Phys. Chem. A 2012, 116, 158–165

The Journal of Physical Chemistry A

ARTICLE 0

Table 5. Values of kCV and kCV 1 1 for the Alkaline Fading of CV in Water/AOT/Isooctane Microemulsions with [AOT] = 0.4 mol L
1 and Various ω at 298.2 K ω 0
1 10 kCV 1 /s 4 CV
1 10 k1 / s

4

8

10

18

7.29

7.06

4.58

9.32

8.64

5.54

Figure 8. Plots of ln A vs exp(
kobst)
1 and t for the reaction of the alkaline fading of CV in water/AOT/isooctane microemulsions with ω = 10 and [AOT] = 0.4 mol L
1 at 298.2 K. (a) ln A vs exp(
kobst)
1; (b) ln A vs t. The points represent experimental results; the lines represent the results of the fits of eqs 21 and 22, respectively.

the expression kCV ln A ¼ 1 ðexpð
kobs tÞ
1Þ þ ln A0 kobs

Figure 9. Plot of A vs t for the reaction of the alkaline fading of PN in water/AOT/isooctane microemulsions with ω = 14 and [AOT] = 0.3 mol L
1 at 298.2 K. The points represent experimental results; the line represents the result of the fit of eq 24.

ð21Þ


where kCV = kCV 1 2 [OH ]0 is “actual” pseudo-first-order rate constant of the alkaline fading of CV under the competition of AOT-hydrolysis and A0 and A are the absorbance of the system at the initial time and any time t, respectively. When AOT-hydrolysis is negligible, i.e., kobs approaches zero, then eq 21 returns the expression of the simplex alkaline fading of CV

CV

ln A ¼
k1 0 t þ ln A0

3.7. Influence of the AOT Hydrolysis on the Alkaline Fading of PN. AOT-hydrolysis was assumed to be negligible

within a certain period of time to obtain the rate constants and equilibrium constants of the alkaline fading of PN in the water/ AOT/isooctane microemulsions in our previous work.13 In this section we will calculate the “actual” rate constant and the “actual” equilibrium constant under the competition of AOT-hydrolysis. The equilibrium constant K of the alkaline fading of PN in microemulsions is expressed as

ð22Þ

0

with kCV = kCV 1 1 . If eq 22 is used to fit the experimental results for the reaction of the alkaline fading of CV with the significant competition of AOT-hydrolysis, then an apparent 0 is obtained which is possibly different from constant kCV 1 the “actual” value of kCV 1 . The difference indicates the significance of the influence of AOT-hydrolysis. Equations 21 and 22 were used to analyze the previously measured absorbance data23 at various reaction times with the values of kobs listed in Table 2 for the alkaline fading of CV in the AOTbased microemulsions. As a demonstration, Figure 8 shows the plots of ln A versus exp(
kobst)
1 and t respectively for the alkaline fading of CV in the AOT-based microemulsions with ω = 10 and [AOT] = 0.4 mol L
1 at 298.2 K. It can be seen clearly that the linearity in Figure 8a (linear correlation coefficient = 0.997) is significantly better than that in Figure 8b (linear correlation coefficient = 0.989), and the standard deviations for the fits of eqs 21 and 22 are 5.78  10
3 and 1.16  10
2, respectively, which evidence that the influence of AOT-hydrolysis on the alkaline fading of CV needs to be0 taken into account. and kCV The least-squares fits gave the values of kCV 1 1 , which are CV are significantly larger than listed in Table 5. The values of k 1 0 that of kCV 1 .

K ¼

a
xe k2
¼ xe ½OH  k
1

ð23Þ

Substituting eqs 19 and 23 into eq 4, integrating from the overall concentration x0 (= a) of PN being all in the colored form L2
at the initial time to the overall concentration x of L2
at any time, and then combining with the Lambert
Beer law yield
 k2 A0 ½OH
0 ðexpð
kobs tÞ
1Þ A ¼ Ae þ ðA0
Ae Þ exp ðA0
Ae Þkobs ð24Þ where A0 is the absorbance of PN being all in the colored form L2
and Ae and A are the absorbances of L2
at equilibrium and at any time t, respectively. Substituting eqs 19 into 23 and combining with the Lambert
Beer law give K ¼

A0
Ae Ae ð½OH 0 expð
kobs tÞÞ


ð25Þ

Our previous experimental results13 were fitted through eq 24 with the values of kobs listed in Table 2 to obtain the optimal 164

dx.doi.org/10.1021/jp2059744 |J. Phys. Chem. A 2012, 116, 158–165

The Journal of Physical Chemistry A values of Ae, (A0
Ae), and k2 with the standard deviations of the fits being better than 0.001, which is less than the uncertainty in measurement of A. The values of K calculated by eq 25 together with k2 are listed in Table 1, which are significantly larger than those without the corrections for the effect of AOT-hydrolysis reported previously.13 As a demonstration, Figure 9 shows the plot of A versus t for the alkaline fading of PN in the AOT-based microemulsions with ω = 14 and [AOT] = 0.3 mol L
1 at 298.2 K, where the solid line represents the result of fitting eq 24. Above kinetic analysis for the alkaline fading of CV and PN suggest that AOT-hydrolysis should be taken into account.

ARTICLE

’ REFERENCES (1) García-Río, L.; Herv
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4. CONCLUSIONS We have studied the kinetics of the alkaline hydrolysis of AOT in the water/AOT/isooctane microemulsions by monitoring the absorbance changes of PN with time in the system. The apparent first-order rate constants kobs were obtained and found to be dependent on both ω and the temperature. The influences of ω on kobs have been interpreted by a pseudophase model, which assumes that OH
ions are distributed between the aqueous and interface pseudophases and the reaction takes place only on the interface. Based on this model, the values of the “true” rate constant ki and the partition coefficient Kwi for various temperatures were obtained and the latter was found to be almost independent of the temperature and ω. The investigations of the temperature dependence of the rate constants gave the values of enthalpy ΔH6¼, entropy ΔS6¼, and energy Ea of activation for both kobs and ki, which indicate that the distribution of OH
between the aqueous and interface pseudophases increase ΔS6¼ of the interface reaction, while provide no contributions to Ea and ΔH6¼. The influence of the concentration of AOT in the system on the rate constant has been examined and found to be negligible. It contradicts with what was reported by García-Río et al.1 but confirms the first-order reaction of AOT-hydrolysis taking place on the surfactant interface. Corrections for the influences of AOT-hydrolysis on the kinetics of the alkaline fading of CV and PN in the water/ AOT/isooctane microemulsions gave the corrected reaction constants of the alkaline fading of CV and PN. It suggests that AOT-hydrolysis should be taken into account in the kinetic studies of the reactions involving OH
in the water/AOT/oil microemulsion systems when the reaction time is long enough. ’ ASSOCIATED CONTENT

bS

Supporting Information. Plots of ln kobs or ln ki vs 1/T (Figure S-1); plots of kobs and ki vs AOT concentration (Figure S-2). This material is available free of charge via the Internet at http:// pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*Phone +86-21-64250804; fax +86-21-64252510; e-mail shenwg@ lzu.edu.cn.

’ ACKNOWLEDGMENT This work is supported by the National Natural Science Foundation of China (Projects 20973061, 21073063, and 21173080), the Chinese Ministry of Education (Key Project 105074), and Committee of Science and Technology of Shanghai (Projects 0652 nm010 and 08jc1408100). 165

dx.doi.org/10.1021/jp2059744 |J. Phys. Chem. A 2012, 116, 158–165