Conductometric, Surface Tension, and Kinetic Studies in Mixed SDS

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Conductometric, Surface Tension, and Kinetic Studies in Mixed SDS-Tween 20 and SDS-SB3-12 Micellar Solutions Marıá Munõz, Amalia Rodrı´guez, Marıá del Mar Graciani, and Marıá Luisa Moya´* Departamento de Quı´mica Fı´sica, Universidad de Sevilla, C/Profesor Garcıá Gonza´ lez s/n, 41012 Sevilla, Spain Received July 13, 2004. In Final Form: September 8, 2004 Micellization in sodium dodecyl sulfate (SDS)-N-dodecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate and SDS-polyoxyethylenesorbitan monolaurate binary surfactant solutions was studied by means of conductivity and surface tension measurements. These studies showed that two types of micellar aggregates are present in the mixed micellar solutions. Two reactions were investigated in these micellar media, the oxidation of 1-methoxy-4-(methylthio)benzene by IO4- and the spontaneous hydrolysis of phenyl chloroformate. Information on the distribution of reagents in the micellar reaction media was obtained through conductivity and spectroscopic measurements. Discussion of the kinetic data showed that the redox reaction takes place mainly in the aqueous phase of the mixed solutions, whereas hydrolysis occurs in the aqueous as well as in the micellar pseudophase. Variations in the observed rate constants of the two processes studied are gradual within the whole surfactant concentration range investigated, revealing little information about the mixed micellar medium.

Introduction Surfactant mixtures are commonly utilized in many surfactant formulations and practical applications because mixtures often behave synergistically and provide more favorable, or desirable, properties than the constituent single surfactants.1 Similar to the behavior of individual surfactants on micellization, mixed systems undergo abrupt changes in physicochemical properties that can be monitored conveniently using suitable experimental methods. The mixture of two different surfactants can be characterized by the presence of two kinds of micelles, each essentially containing a pure surfactant or mixed micelles formed by both surfactants. In the latter case, at a fixed surfactant ratio, the composition of the mixed micelles can be determined, as well as its dependence on the total concentration. The formation of mixed micelles is accompanied by structural changes as compared to pure surfactant micelles. Changes in the aggregation number, size, shape, and degree of ionization (for ionic surfactants) occur.2 At first, all these structural and thermodynamic changes could be evidenced through variations in the reaction rates of appropriate micelle-modified processes taking place in mixed micelle solutions, when the surfactant ratio as well as the [surfactant] changes. However, despite thermodynamic and structural aspects of mixed micellar systems having been under close scrutiny for many years, studies on the effects of mixed micelles on reaction rates are relatively few.3 In this work conduc* To whom all correspondence should be directed. E-mail: [email protected]. (1) (a) Holland, P. M.; Rubingh, D. N. In Mixed Surfactants Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501; American Chemical Society: Washington, DC, 1992; p 1. (b) Rosen, M. J. In Phenomena in Mixed Surfactant Systems; Scamehorn, J. F., Ed., ACS Symposium Series 311; American Chemical Society: Washington, DC, 1986; p 144. (c) Hill, R. M. In Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Surfactant Science Series 46, Marcel Dekker: New York, 1993; Chapter 11. (d) Rosen, M. J. J. Am. Oil Chem. 1989, 66, 1840. (2) Milioto, S. Encyclopedia of Surface and Colloid Science; Marcel Dekker: New York, 2002; p 683.

tometric, surface tension, and kinetic measurements were carried out in mixed anionic-zwitterionic and anionicnonionic micellar solutions. The anionic surfactant was sodium dodecyl sulfate, SDS, the zwitterionic surfactant was N-dodecyl-N,N-dimethyl-3-ammonio-1-propanesulfonate, SB3-12, and the nonionic surfactant was polyoxyethylenesorbitan monolaurate, Tween 20. The interfacial and micellization behavior of the SDS-Tween 20 binary mixtures were previously studied by Ghosh and Moulik at 294.2 K;4 however, new and interesting information about this system was obtained in this work at 298.2 K. With regard to the SDS-SB3-12 binary mixture, to our knowledge no previous information has been provided about this binary system in the literature. It is also interesting to note that studies on mixed micellar systems with the presence of zwitterionic surfactants are relatively few.5 The reactions investigated were the oxidation of 1-methoxy-4-(methylthio)benzene, ArSMe, by IO4- and the spontaneous hydrolysis of phenyl chloroformate. All experiments were carried out at 298.2 K. Experimental Section Materials. ArSME, phenyl chloroformate, and sodium periodate were obtained from Aldrich. SB3-12 and Tween 20 were from Fluka and used as received. Reichardt’s dye, ET(30), and SDS were also obtained from Aldrich. Water was obtained form (3) (a) Blasko´, A.; Bunton, C. A.; Toledo, E. A.; Holland, P. M.; Nome, F. J. Chem. Soc., Perkin Trans. 2 1995, 2367 and references therein. (b) Davis, D. M.; Foggo, S. J. Chem. Soc., Perkin Trans. 2 1998, 247. (c) Khan, M. N. J. Chem. Soc., Perkin Trans. 2 1990, 435. (d) Khan, M. N.; Arifin, Z.; Yusoff, M. N.; Ismail, E. J. Colloid Interface Sci. 1999, 220, 474. (e) Lee, B. S.; Nome, F. Langmuir 2000, 16, 10136. (f) Khan, M. N.; Ismail, E. J. Colloid Interface Sci. 2001, 240, 636. (g) Munõz, M.; Rodrı´guez, A.; Graciani, M. M.; Moya´, M. L. Int. J. Chem. Kinet. 2002, 34, 443. (h) Fernańdez, G.; Rodrı´guez, G.; Graciani, M. M.; Munõz, M.; Moya´, M. L. Int. J. Chem. Kinet. 2003, 35, 45. (4) Ghosh, S.; Moulik, S. P. J. Colloid Interface Sci. 1998, 208, 357. (5) (a) Iwasaki, T.; Ogawa, M.; Esumi, K.; Meguro, K. Langmuir 1991, 7, 30. (b) Shiloach, A.; Blankschtein, D. Langmuir 1997, 13, 3968 and references therein. (c) Li, F.; Li, G.-Z.; Chen, J.-B. Colloids Surf., A 1998, 145, 167. (d) Lee, B. S.; Nome, F. Langmuir 2000, 16, 10131. (e) Peyre´, V. Langmuir 2002, 18, 1014.

10.1021/la048247n CCC: $27.50 © 2004 American Chemical Society Published on Web 10/20/2004

SDS-Tween 20 and SDS-SB3-12 Micellar Solutions

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a Millipore Milli-Q water system, its conductivity being less than 10-6 S cm-1. Conductivity Measurements. Conductivity was measured with a Crison microCM 2201 conductimeter connected to a water flow thermostat maintained at 298.2 ( 0.1 K. The conductivity cell was calibrated with KCl solutions of the appropriate concentration range. ET Values. Spectra of the assay solutions containing the ET(30) dye were recorded in a Unicam UV-2 spectrophotometer at 298.2 K. These spectra were recorded against a blank consisting of an aqueous micellar solution of a concentration identical to that of the assay solution. Five spectra were recorded for each assay solution. The ET(30) value obtained for SDS was 57.5, in good agreement with that in the literature.6 Surface Tension Measurements. The air/solution interfacial tensions were measured with a du Nouÿ tensiometer (KSV 703, Finland). The tensiometer was connected to a water flow thermostat maintained at 298.2 ( 0.1 K. Prior to each measurement the ring was heated briefly until glowing by holding it above a Bunsen burner. The vessel was cleaned by using chromic sulfuric acid, boiled in distilled water, and then flamed with a Bunsen burner before use. The precision in the measurements was (1 mN m-1. Equilibrium Binding Constants. The equilibrium binding constants of ArSMe to the micellar aggregates can be written as

Km )

[ArSMem] [ArSMew][surfactantm]

(1)

where the subscripts w and m denote the aqueous and micellar pseudophases, respectively, and [surfactantm] is the micellized surfactant concentration. Assuming that Beer’s law is obeyed, one can write7

Km )

A - Aw 1 Am - A [surfactantm]

(2)

where A is the observed absorbance and Aw and Am are the absorbances in water and of fully bound organic substrate, respectively. In the case of ArSMe, Am could not be measured directly because of the relatively low binding of this organic substrate to micellar aggregates, as indicated previously by Bunton et al.8a-c To estimate Km without the measurement of Am the following equation was considered:9

A ) Aw +

Am - Aw 1/(Km[surfactantm]) + 1

(3)

The experimentally accessible terms of eq 3 are A, Aw, and [surfactantm]. This equation was used to estimate the equilibrium binding constants of ArSMe by registering the changes in absorbance at 260 and 265 nm and by fitting these data using eq 3. From the fittings of the absorbance data, at the two different wavelengths, the same Km value was obtained, within experimental errors. The spectra were recorded in a Unicam UV-2 spectrophotometer at 298.2 ( 0.1 K against a blank consisting of an aqueous micellar solution of concentration identical to that of the assay solution. In this way, the absorbance data were corrected from the possible contribution of the surfactant absorbance. Kinetics. Rates of the reaction ArSMe + IO4- were studied under the presence of an excess of periodate ion at 260 nm. The rate measurements were performed by using a Unicam Helios-γ spectrophotometer. In all cases the sulfide concentration was (6) Zachariasse, K. A.; Phuc, N. V.; Kozankiewicz, B. J. Phys. Chem. 1981, 85, 2676. (7) Sepu´lveda, L. J. Colloid Interface Sci. 1974, 46, 372. (8) (a) Bacaloglu, R.; Blasko, A.; Bunton, C. A.; Foroudian, H. J. J. Phys. Org. Chem. 1992, 5, 171. (b) Blasko´, A.; Bunton, C. A.; Wright, S. J. Phys. Chem. 1993, 97, 5435. (c) Blasko´, A.; Bunton, C. A.; Foroudian, H. J. J. Colloid Interface Sci. 1995, 175, 122. (d) Rodrı´guez, A.; Munõz, M.; Graciani, M. M.; Fernańdez, G.; Moya´, M. L. New J. Chem. 2001, 25, 1084. (9) (a) Novaki, L. P.; El Seoud, O. Phys. Chem. Chem. Phys. 1999, 1, 1957. (b) Novaki, L. P.; El Seoud, O. Langmuir 2000, 16, 35.

Figure 1. Dependence of the specific conductivity, κ in µS cm-1, on surfactant concentration for mixed SDS-SB3-12 micellar solutions. T ) 298.2 K. 1.5 × 10-5 mol dm-3 and the periodate concentration was 2 × 10-3 mol dm-3. The low solubility of ArSMe in water made it necessary to prepare its solutions in acetonitrile. The percentage of acetonitrile in the reaction mixture was 1 vol %. We found experimentally that the presence of this small amount of acetonitrile does not affect the critical micelle concentration (cmc) of the micellar solutions used as reaction media. The temperature for the kinetic runs was maintained at 298.2 ( 0.1 K by using a water-jacketed cell compartment. Each rate constant was repeated at least twice. Rate constants were reproducible within a precision of better than 5%. The second-order rate constant for the reaction in water was 1.51 dm3 mol-1 s-1, in good agreement with the literature value 1.55 dm3 mol-1 s-1.7 The kinetic data obtained in SDS micellar solutions are also in good agreement with those in a previous work.8b Hydrolysis of phenyl chloroformate was recorded spectrophotometrically at 270 nm (appearance of phenol) with Unicam UV-2 and Unicam Helios-R spectrophotometers. The substrate was added to the reaction solutions in 1-cm cuvettes as relatively concentrated solutions in acetonitrile, so the final reaction mixtures contained 1 vol % of acetonitrile and the final substrate concentration was 10-4 mol dm-3. Phenyl chloroformate reacts readily with hydroxide ions. The reaction of this substrate with basic impurities was suppressed by the addition of 1.5 × 10-3 mol dm-3 HBr to the reaction medium. It was found that the presence of an HBr concentration within the range 10-3-10-2 mol dm-3 does not affect the rate constant. The value of the rate constant in water was 14.1 × 10-3 s-1 at 298.2 K, in agreement with previous results.10 The temperature for the kinetic runs was maintained at 298.2 ( 0.1 K by using a water-jacketed cell compartment. Each rate constant was repeated at least twice. Rate constants were reproducible within a precision of better than 4%.

Results and Discussion Micellization in the binary surfactant solutions was studied through conductivity measurements. Figure 1 shows the plots of conductivity against the surfactant concentration for pure SDS and mixed SDS-SB3-12 surfactant solutions. In all cases, a break in the conductivity against concentration plots, characteristic of micelle formation, was observed. For mixed SDS-Tween 20 binary solutions two breaks in the conductivity against surfactant concentration were found for the compositions 3:1 and 1:1 (see Figure 2). The mixed SDS-Tween 20 (1:3) solution (10) (a) Al Loedan, H.; Bunton, C. A.; Mhala, M. M. J. Am. Chem. Soc. 1982, 104, 6654. (b) Brinchi, L.; Di Profio, P.; Germani, R.; Savelli, G.; Bunton, C. A. Eur. J. Org. Chem. 2001, 1115. (c) Munõz, M.; Rodrı´guez, A.; Graciani, M. M.; Moya´, M. L. Int. J. Chem. Kinet. 2002, 34, 445.

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Mun˜ oz et al. Table 1. cmc and Micellar Ionization Degree, r, Values for Various Mixed SDS-Tween 20 and SDS-SB3-12 Binary Solutionsa 103 × cmc, M XSDS

first break

second break

R

SDS-SB3-12

Figure 2. Dependence of the specific conductivity, κ in µS cm-1, on surfactant concentration for mixed SDS-Tween 20 (1:1) micellar solutions. T ) 298.2 K.

Figure 3. Dependence of surface tension on log [surfactant] for mixed SDS-Tween 20 (1:1) micellar solutions. T ) 298.2 K.

could not be studied because the conductivity corresponding to the dilute solutions was too low. The presence of these two breaks seems to indicate the formation of two different kinds of mixed micelles. To investigate this point further, the cmc’s of the pure and mixed micellar solutions were also determined by surface tension measurements. The cmc’s obtained through surface tension measurements for pure SDS, SB3-12, and Tween 20 aqueous solutions were in agreement with literature values (8 × 10-3, 2.1 × 10-3, and 5 × 10-5 mol dm-3, respectively).11 For the mixed SDS-Tween 20 micelles with compositions 3:1, 1:1, and 1:3 the plots of surface tension, γ, against the logarithm of surfactant concentration show two breaks (see Figure 3). The existence of two breaks in the surface tension against log [surfactant] plots has also been found for mixed micellar solutions by other authors,12 thus indicating the formation of two different types of micellar aggregates. For the compositions 3:1 and 1:1, the breaks found through the surface tension measurements coincide (11) (a) Frescura, V.; Marconi, D. M. O.; Zanette, D.; Nome, F.; Blasco, A.; Bunton, C. A. J. Phys. Chem. 1995, 99, 11494. (b) Van Os, N. M.; Haak, J. R.; Rupert, L. A. Phisicochemical Properties of Selected Anionic, Cationic and Nonionic Surfactants; Elsevier: New York, 1993. (12) (a) Abe, M.; Tsubaki, N.; Ogino, K. J. Colloid Interface Sci. 1985, 107, 503. (b) Ogino, K.; Tsubaki, N.; Abe, M. J. Colloid Interface Sci. 1985, 107, 509.

1.00 0.75 (3:1) 0.50 (1:1) 0.25 (1:3) 0.00

8.15 (8.0) (2.00) (2.00) (2.00) (2.10)

1.00 0.75 (3:1) 0.50 (1:1) 0.33 (1:3) 0.00

SDS-Tween 20 8.15 (8.0) 1.7 × 10-1 (1.66 × 10-1) 1.20 (1.07) 8.2 × 10-2 (7.99 × 10-2) 6.5 (6.36 × 10-1) (5.01 × 10-2) (3.78 × 10-1) (5.01 × 10-2)

6.20 (6.0) 4.16 (4.1) 3.32 (3.1)

0.32 0.49 0.57 0.80

0.32 0.67 0.83

a T ) 298.2 K. Values in parentheses were obtained through surface tension measurements, and values without parenthesis were obtained through conductivity measurements.

with those found by means of the conductivity measurements. The first break, at low surfactant concentration, would correspond to mixed micelles with a high ionization micellar degree, shown by the slight change in slopes from one linear region to the other in the conductivity versus [surfactant] plots (see Figure 2). The second break, at higher surfactant concentrations than the previous one, would show the existence of another type of mixed micelles. Taking the cmc values corresponding to the pure surfactants into account, these being 5 × 10-5 mol dm-3 for Tween 20 and 8 × 10-3 mol dm-3 for SDS, respectively, one would expect the mixed micelles formed at low surfactant concentrations to be richer in Tween 20 than those formed at higher [surfactant]. The incorporation of nonionic surfactant molecules into an ionic micelle results in a decrease of the repulsion between the ionic headgroups in the micelles, and, therefore, the attachment of counterions decreases, thus increasing the micellar ionization degree. Therefore, one would expect a higher R value for the mixed micelles formed at the first break than that corresponding to the second break. For the mixed SDSTween 20 (1:3) solutions, the first break observed in the surface tension versus log [surfactant] plots corresponds to the pure Tween 20 micelles (cmc ) 5 × 10-5 mol dm-3), and the second break corresponds to the mixed micelles. With regard to the SDS-SB3-12 binary systems, the dependence of the surface tension on the logarithm of the surfactant concentration shows two breaks. At low [surfactant] the first break corresponds to the formation of pure SB3-12 micelles (cmc ) 2.1 × 10-3 mol dm-3) in all the compositions studied. The second break corresponds to the formation of mixed micelles, and it coincides with that observed in the conductivity measurements. Because SB3-12 micelles are neutral, the first break observed in the surface tension measurements cannot be observed in the conductivity measurements. Table 1 summarizes the cmc values obtained through conductivity and surface tension measurements. The micellar ionization degree could be estimated for the mixed micelles present in mixed SDS-SB3-12 micellar solutions and for the mixed micelles formed at the first break in mixed SDS-Tween 20 (3:1) and (1:1) micellar solutions. These R values are also listed in Table 1. At this point, the estimation of the cmc and R values through conductivity measurements deserves some comments. The cmc values can be determined by fitting the data points above and below the break to two equations of the form κ ) A[surfactant] + B and solving the two equations simul-


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for the other solutions. This gives reliability to the cmc and R values listed in Table 1. The mixing of surfactants forming mixed micelles can be both ideal and nonideal. The formation may be represented by the relation16 n

1

)

cmcobs

Xi 1

∑ i)1 f

i

cmci

(6)

where cmci and cmcobs are the cmc’s of the ith component and the mixture, respectively. Xi is the mole fraction of the component i in the solution, and f is its activity coefficient in the mixed micelle. In the ideal situation, fi ) 1 and eq 7, the Clint equation, is obtained.17

1 Figure 4. Specific conductivity, κ in µS cm-1, of mixed SDSSB3-12 (1:3) micellar solutions as a function of surfactant concentration. (b) Experimental points. The continuous line is the fitting curve of these points. The discontinuous line corresponds to the Gaussian, and the arrow denotes the cmc.

taneously to obtain the point of intersection (Williams’ method).13 Least-squares analysis is employed. This was the method used to estimate the cmc corresponding to the first and second breaks in the conductivity versus surfactant concentration plots. The micellar ionization degree, R, of the aggregates present in the different solutions can be calculated from the relation of the slopes of the linear plots above and below the cmc. The Williams method allows one to calculate a reliable value for the cmc, and also for R, when conductivity shows an abrupt change in going from the premicellar surfactant concentration range to the postmicellar surfactant concentration range. One can see in Figure 1 that this is the case for pure SDS and for the mixed 3:1 system. However, when the amount of SB3-12 present in the mixture increases, the change in conductivity for the mixed 1:1 and 1:3 solutions is less abrupt and the uncertainties in the evaluation of the cmc and R values by using the Williams method increase. This is also found for the mixed SDS-Tween 20 micellar solutions. For these media, Phillips’ method14 was used, together with the Williams method, for the estimation of the cmc. Phillips defined the cmc as the concentration corresponding to the maximum change in a gradient in a solution property versus concentration (φ - ct) curve

(d3φ/dct3)ct ) cmc ) 0

(4)

φ ) a[S] + b[M]

(5)

where

a and b being constants of proportionality and [S] and [M] concentrations of the monomeric surfactant and of the micelles, respectively. Pillips’ method was applied as proposed by Mosquera et al.15 This consists of an integration by the Runge-Kutta method and a least-squares Levenberg-Maquardt fitting. Figure 4 shows the application of the Phillips method to the SDS-SB3-12 (1:3) mixed system. The cmc values estimated by the two methods are in agreement. The same result was obtained (13) Williams, R. J.; Phillips, J. N.; Mysels, K. J. Trans. Faraday Soc. 1955, 51, 728. (14) Phillips, J. N. Trans. Faraday Soc. 1955, 51, 561. (15) Mosquera, V.; Garcıá, M.; Varela, N. M. In Handbook of Surfaces and Interfaces of Materials; Nalwa, H. S., Ed.; Academic Press: New York, 2001; Vol. 3, p 405 and references therein.

cmcobs

)

Xi

∑i cmc

(7)

i

Equation 7 can be used to predict the cmc in the binary surfactant solutions studied if they behave ideally. The cmc values listed in Table 1 do not fit eq 7, which indicates a deviation from the ideal behavior, thus showing mutual interactions of the surfactants in the micelles. Knowledge of experimental cmc values of individual surfactants, the cmc of binary mixtures, and the mole fractions of the surfactants in binary solutions allows one to obtain information about the interactions of surfactant molecules in mixed micelles.16-20 This can be done for the first break found in mixed SDS-Tween 20 (3:1) and (1:1) solutions but not for the rest of the mixed micellar solutions studied. For these solutions, the mole fractions of the surfactants in the binary system are not known because pure or mixed micelles are formed previously. Ghosh and Moulik4 obtained thermodynamic information about the mixed SDS-Tween 20 (3:1) and (1:1) micelles, the cmc values given by these authors coinciding with the first break found in this work, taking into account the difference in temperature. They conclude that the synergism is substantial, the overall nonideality arising from the interaction of the SDS (SO42-) headgroup with those of Tween 20. Despite not being able to obtain thermodynamic information on the other mixed micelles, data in Table 1 indicate a nonideal behavior. The interactions responsible for this behavior could be the attraction between the negatively charged headgroups of SDS molecules and the positively charged ammonium group of SB3-12 molecules but also possibly the repulsion between the SDS headgroup and the sulfonate group of the sulfobetaine surfactant molecules. The possibility of the structural changes accompanying the formation of two different types of micellar aggregates in the mixed micellar solutions studied, to be shown through changes in the rate of a reaction taking place in them, was worth investigating. With this in mind, the oxidation of ArSMe by IO4- was studied in various mixed (16) (a) Puvvada, S.; Blankschtein, D. J. Phys. Chem. 1992, 96, 5567. (b) Puvvada, S.; Blankschtein, D. J. Phys. Chem. 1992, 96, 5579. (c) Puvvada, S.; Blankschtein, D. In Mixed Surfactant Systems; Holland, P. M., Rubingh, D. N., Eds.; ACS Symposium Series 501; American Chemical Society: Washington, DC, 1992; p 96. (d) Moulik, S. P. Curr. Sci. 1996, 71, 368. (17) Clint, J. H. J. Chem. Soc., Faraday Trans. 1975, 71, 1327. (18) Rubingh, D. N. In Solution Chemistry of Surfactants; Mittal, K. L., Ed.; Plenum: New York, 1979; Vol. 1, p 337. (19) Sarmoria, C.; Puvvada, S.; Blankschtein, D. Langmuir 1992, 8, 2690. (20) (a) Motomura, K.; Yamanaka, M.; Aratono, M. Colloid Polym. Sci. 1982, 262, 948. (b) Motomuta, K.; Aratono, M.; Ogino, K.; Abe, M. Mixed Surfactant Systems; Ogino, K., Abe, M., Eds.; Dekker: New York, 1993; p 99.

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Mun˜ oz et al. Table 2. Equilibrium Binding Constants for the ArSMe Molecules Obtained through Spectroscopic Measurements (See the Text)a

a

Figure 5. Dependence of the observed rate constant, kobs in s-1, for the reaction ArSMe + IO4- on surfactant concentration in mixed SDS-SB3-12 micellar solutions. T ) 298.2 K.

Figure 6. Dependence of the observed rate constant, kobs in s-1, for the reaction ArSMe + IO4- on surfactant concentration in mixed SDS-Tween 20 micellar solutions. T ) 298.2 K.

SDS-Tween 20 and SDS-SB3-12 micellar solutions. The mechanism of this reaction is well-known,21 and it has been shown that large kinetic micellar effects, not connected to concentration effects, are operative in this process.8 Besides, spectroscopic measurements can be used to obtain information about the binding of ArSMe molecules to the micellar aggregates present in the reaction media. Figures 5 and 6 show the dependence of the observed rate constant for this reaction on surfactant concentration in mixed micellar solutions. An increase in surfactant concentration results in a decrease in the observed rate constant value, kobs, showing a tendency toward limiting values at high [surfactant], where the substrate should be extensively micellar bound. The variations in kobs are gradual within the whole range of total surfactant concentration studied for all the mixed micellar solutions. For [surfactant] below the cmc corresponding to the first break kobs remains unchanged and only for [surfactant] above this cmc kobs begins to decrease. However, no discontinuities in kobs values are observed in the vicinity of the cmc corresponding to the second break. To obtain more information on the reaction studied, the distribution of the two reagents in the mixed micellar reaction media was investigated. The distribution of the (21) Ruff, F.; Kucsman, A. J. Chem. Soc., Perkin Trans. 2 1985, 683.

surfactant

Km, mol-1 dm3

SDS SDS-SB3-12 (1:1) SB3-12 SDS-Tween 20 (3:1) SDS-Tween 20 (1:1) Tween 20

183 ( 8 141 ( 11 117 ( 9 207 ( 12 243 ( 12 280 ( 11

T ) 298.2 K.

ArSMe molecules between the aqueous and micellar pseudophases was studied by means of spectroscopic measurements, using the method described in the experimental section. Table 2 shows the values of the equilibrium binding constants obtained. First, some comments about the Km values corresponding to pure micellar solutions will be made. The Km value for SDS agrees quite well with that given by Bunton et al.8a The equilibrium binding constant obtained for SB3-12 micelles seemed too small as compared to those for SB3-14 and SB3-16 micelles, these being 300 and 320 mol-1 dm3, respectively.8d To check this result, the Km value for SB314 micellar solutions was measured again, the result being in agreement with the previous one. A lower Km value in SB3-12 than in SB3-14 or SB3-16 micellar solutions could be explained by considering that the interfacial region of SB3-12 micelles is more polar than those of SB3-14 or SB3-16 micelles, as the ET parameter values show (see below), ET being the Reichardt parameter used as a polarity indicator. The Km values listed in Table 2 for the studied mixed micellar solutions deserve some comments. Equation 1 and, therefore, eq 3 are valid when only one type of micellar aggregate is present in the solution. However, in the mixed micellar solutions studied two different aggregates are formed and two different equilibrium binding constants, Km1 and Km2, should be considered. In the case of mixed SDS-Tween 20 micelles with compositions 3:1 and 1:1 the absorbance was registered within the range from 2.5 × 10-4 to 200 × 10-4 M in the former and from 1 × 10-4 to 600 × 10-4 M in the latter. For mixed SDS-SB3-12 (1:1) micelles the surfactant concentration range studied was from 3 × 10-3 to 100 × 10-3 M. In all cases dependence of absorbance on the [surfactant] was gradual, not showing discontinuities in the vicinity of the surfactant concentrations corresponding to the second breaks as shown in Figure 7 for the mixed SDS-Tween 20 (3:1) micellar solutions. With the idea of obtaining a kind of average equilibrium binding constant eq 3 was used to fit the absorbance data. To do the calculations the two cmc values listed in Table 1 for each of the mixed micellar systems were used and the absorbance values considered were those corresponding to the [surfactant] higher than the cmc. The two Km values estimated for each of the mixed micellar solutions do not differ much. For instance, 136 and 148 mol-1 dm3 were obtained for mixed SDS-SB3-12 (1:1) micellar solutions. Table 2 shows the average of the two values obtained which will give information about the mean affinity of the ArSMe molecules for the two types of micellar aggregates present in the solution. In relation to the distribution of periodate anions between the aqueous and the micellar pseudophases, one would expect the IO4- anions to remain preferentially in the aqueous phase of SDS and mixed SDS-Tween 20 and SDS-SB3-12 micellar solutions because the surface of the aggregates is negatively charged. In Tween 20 micellar solutions IO4- anions will be localized in the aqueous as


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Figure 7. Dependence of the absorbance of ArSMe at 265 nm on surfactant concentration in mixed SDS-Tween 20 (3:1) micellar solutions. T ) 298.2 K.

well as in the micellar pseudophases, these anions not showing preference for any of them. In the case of SB3-12 micelles, radioactive tracer self-diffusion and fluorescence quenching data22-24 have shown that anions bind more strongly than cations to the sulfobetaine surfactants. The binding appears to be essentially of an electrostatic nature because the charge density due to the cationic ammonium centers is higher than that at the anionic sulfonate center,22,23 although ion specificity cannot be neglected. The incorporation of periodate anions into the SB3-12 micelles can be described by25

KIO4- )

[IO4-m] [IO4-w]([SB3-12m] - [IO4-m])

(8)

In this equation all concentrations are expressed as moles per liter of total solution volume, and w and m refer to the aqueous and micellar pseudophases. This equation was shown to fit conductivity data well for added salts in sulfobetaine micelles and has permitted the estimation of KX values for several anions.26,27 Figure 8 shows the variation of the conductivity of an aqueous 5 × 10-3 mol dm-3 NaIO4 solution when different concentrations of SB312 are added to the medium at 298.2 K. To fit the conductivity data shown in Figure 8, ion-ion and ionmicelle interactions were neglected as well as excluded from volume effects (which became important for [SB312] > 0.1 M). The conductivity of the aqueous sodium periodate solutions in the presence of SB3-12 can be expressed as27

κ)

qFR[SB3-12m] 9.11 × 104F

+ 10-3[IO4-w]ΛIO4- + 10-3[Na+ w]ΛNa+ (9)

(22) Kamenka, N.; Chevalier, Y.; Zana, R. Langmuir 1995, 11, 3351. (23) Kamenka, N.; Chorro, M.; Chevalier, Y.; Levy, H.; Zana, R. Langmuir 1995, 11, 4234. (24) Baptista, M. S.; Politi, M. J. Phys. Chem. 1990, 95, 5936. (25) Bunton, C. A.; Gan, L. H.; Moffatt, J. R.; Romsted, L. S.; Savelli, G. J. Phys. Chem. 1986, 85, 4118. (26) (a) Chorro, N.; Kamenka, K.; Faucompre´, B.; Partyka, S.; Lindeimer, N.; Zana, R. Colloids Surf., A 1990, 110, 249. (b) Rodrı´guez, A.; Graciani, M. M.; Guinda, A.; Munõz, M.; Moya´, M. L. Langmuir 2000, 16, 3182. (27) Di Profio, P.; Germani, R.; Savelli, G.; Cerichelli, B.; Chiarini, G.; Mancini, G.; Bunton, C. A.; Gillitt, N. D. Langmuir 1998, 14, 2662.

Figure 8. Plot of the variation of the specific conductivity, κ in µS cm-1, against the SB3-12 concentration added to an aqueous sodium periodate solution with [NaIO4] ) 5 × 10-3 mol dm-3 at 298.2 K.

Here, F is the Faraday constant (esu mol-1), q is the elementary charge (4.8 × 1010 esu), and R is the fractional charge of the micelle equal to [IO4-m] - [Na+m]/[SB3-12m]. F is the friction coefficient given by the Stokes approximation F ) 6πηRh, η being the macroscopic viscosity of the dilute sodium periodate solution, which can be approximated to that of water (0.89 cP at 298.2 K) and Rh being the micellar hydrodynamic radius equal to 26 Å28 for SB3-12 micelles. [IO4-w] ) [IO4-T] - [IO4-m], and [Na+w] ) [Na+T] - [Na+m]. Λ is the equivalent conductance at infinite dilution. The numerical factors in eq 9 are introduced to express the specific conductance in the CGS system. The first term on the right-hand side of eq 9 takes into account that, despite SB3-12 micelles being neutral, in the presence of a salt a fraction of the ions binds to the micelles and, because the anion binding is stronger than that of the cations, the resulting micelles are negatively charged. Therefore, this term accounts for the micelle contribution. The solid line in Figure 8 was fitted to the experimental conductivity data by including the binding of Na+ ions with KNa+ ) 1.5 mol-1 dm3 (refs 22, 23, and 27) and by considering KIO4- ) 30 mol-1 dm3. In a previous work8d a value of KIO4- ) 27 mol-1 dm3 was found in SB314 micelles. Taking the KIO4- value into account, one can conclude that the periodate ions will be distributed between the aqueous and the micellar pseudophases, the presence of these anions increasing in the micellar pseudophase upon increasing [SB3-12]. On the basis of the distribution of the reagents between the aqueous and the micellar pseudophases in the different pure and mixed micellar solutions, one would expect that in some of them the reaction took place only in the aqueous phase. To investigate this point, the pseudophase model will be taken into account. This model considers that chemical reactivity depends on the amounts of the different components of the micellar solution but not on the sizes or shapes of the aggregates. On the basis of the pseudophase model one can write29

-

d[ArSMeT] ) kobs[ArSMeT] ) dt w k2 [ArSMew][IO4-w] + k2m1[ArSMem1][IO4-]m1 + k2m2[ArSMem2][IO4-]m2 (10)

In this equation, square brackets indicate concentrations expressed in moles per liter of solution volume. The

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Mun˜ oz et al.

subscripts T, w, m1, and m2 refer to the total, the aqueous, and the two different micellar pseudophases which could be present in the mixed micellar solutions, respectively. k2w, k2m1, and k2m2 are the second-order rate constants, in dm3 s-1 mol-1, for the reaction in the aqueous and micellar pseudophases. The observed rate constant of the reaction depends on the solution concentration of ArSMe and periodate ions. However, the rate of the reaction within the micellar pseudophases depends on the concentration of the periodate ions within the micelles in moles per liter of the reaction volume, [IO4-]mi, and not on its solution concentration, [IO4mi-].29 The relationship between the interfacial and the solution concentrations of periodate ions is [IO4-]mi ) [IO4mi-]/(Vmi[surfactantmi]), Vmi being the molar reaction volume in units of dm3 mol-1 and [surfactantmi] being the micellized surfactant concentration, related to the number of the i micellar aggregates present in the reaction medium. Taking this into account, the observed first-order rate constant for the oxidation of ArSMe by periodate ions can be expressed as kobs ) k2w[IO4-w] + (k2m1/Vm1)[IO4-m1]Km1 + (k2m2/Vm2)[IO4-m2]Km2 1 + Km1[surfactantm1] + Km2[surfactantm2]

(11) In this equation k2m1/Vm1 ) k2m1 (s-1) and k2m2/Vm2 ) k2m2 (s-1) are the second-order rate constants in the micellar pseudophases written with the concentrations as a molar ratio, [IO4-mi]/[surfactantmi]. Km1 and Km2 are the equilibrium binding constants of the organic substrate molecules to the micellar aggregates present in the reaction medium. If eq 11 is written as a function of the pseudofirst-order rate constants, it reads

kobs ) kw + km1Km1[surfactantm1] + km2Km2[surfactantm2] 1 + Km1[surfactantm1] + Km2[surfactantm2] (12) where kw, km1, and km2 are the pseudo-first-order rate constants in the aqueous and micellar pseudophases. These rate constants are composite and depend on periodate ions concentrations in the aqueous and micellar pseudophases. Because [NaIO4] ) 0.002 M is present in the reaction medium, the influence of the presence of this reagent on the cmc of the mixed micellar solutions used as reaction media was investigated. In the case of pure SDS solutions, and by means of conductivity measurements, the cmc obtained in the presence of 0.002 M NaIO4 was 7.5 × 10-3 mol dm-3. For pure aqueous Tween 20 and SB3-12 solutions the cmc obtained was similar to that in the absence of sodium periodate. For the mixtures, the cmc values change little. For instance, in the case of mixed SDS-SB3-12 (1:1) the cmc values found were 2 × 10-3 and 3.93 × 10-3 mol dm-3 for the first and the second breaks, respectively. In the case that only one type of micellar aggregate is present in the reaction medium, as in the case of pure micellar solutions, eq 12 can be written as

kobs )

kw + kmKm[surfactantm] 1 + Km[surfactantm]

(13)

This equation predicts a straight line for the plot of 1/kobs against [surfactantm] if the process occurs mainly in the

Figure 9. Plots of the dependence of 1/kobs on the micellized surfactant concentration for the reaction ArSMe + IO4- in some pure and mixed micellar solutions (see the text). T ) 298.2 K.

aqueous pseudophase. Figure 9 shows that the plot of 1/kobs against [surfactantm] is linear for the reaction ArSMe + IO4- in SDS for [SDS] up to 0.09 M, but for more concentrated SDS solutions the plot curves. This deviation is clearly shown in the work of Bunton et al.8c who studied the reaction at surfactant concentrations up to 0.25 M, thus pointing out that there is significant reaction in the micellar pseudophase. The second-order rate constant estimated by Bunton et al. was k2m ) 0.6 mol-1 dm3 s-1.8c From the slope of the linear part of the plot, and considering the experimental kw value, an equilibrium binding constant of 164 mol-1 dm3 was obtained. In the case of Tween 20 micellar solutions, in the absence of charge effects, the periodate ions concentration in the Stern layer (the reaction site) will be the same as that in the aqueous phase. For Tween 20 micellar solutions eq 13 is adequate to rationalize the kinetic data, as was shown in ref 8d, with km ) 2.7 × 10-4 s-1 (k2m ) 0.13 mol-1 dm3 s-1) and Km ) 287 mol-1 dm3. In this work the surfactant concentration range studied was wider than in ref 8d. The plots 1/kobs versus [surfactantm] for SDS-Tween (1:1) and SDS-SB3-12 (1:1) mixed micellar solutions are shown in Figure 9. The micellized surfactant concentration was calculated by considering the cmc corresponding to the first break as well as that corresponding to the second break. In both cases a linear relation was found. The same result was obtained for mixed SDS-Tween 20 (3:1) micellar solutions. If the reaction would take place in the aqueous phase eq 12 could be written as

Km1 Km2 1 1 ) + [surfactantm1] + [surfactantm2] kobs kw kw kw (14) The effect of the presence of the micellar aggregates on the reaction is to incorporate the organic substrate into the micelles. The amount of ArSMe incorporated will be proportional to the micelles concentration, which in turn will be proportional to the total surfactant concentration, independent of one or more micellar aggregates being (28) Chevalier, Y.; Kamenka, N.; Chorro, M.; Zana, R. Langmuir 1996, 12, 3225. (29) Bunton, C. A.; Yao, J.; Romsted, L. S. Curr. Opin. Colloid Interface Sci. 1996, 65, 125.


Langmuir, Vol. 20, No. 25, 2004 10865 Table 3. ET Parameter for Pure and Mixed Micellar Solutions (See the Text)a surfactant

A

ET, kcal mol-1 57.5 a

Figure 10. Dependence of the observed rate constant, kobs in s-1, for the reaction ArSMe + IO4- on surfactant concentration in SB3-12 micellar solutions at 298.2 K. The solid line is the fitting of the experimental kinetic data by using a simplified form of eq 11. Scheme 1

present. This would explain the linear relation found between 1/kobs and [surfactantmi], shown in Figure 9, and it allows one to conclude that the reaction occurs mainly in the aqueous phase. With regard to SB3-12 micellar solutions and considering that periodate ions are distributed between the aqueous and the micellar pseudophases, a simplified form of eq 11, considering only one type of micellar aggregate, was used to rationalize the kinetic data in the sulfobetaine micellar solution. [IO4-w] and [IO4-m] were calculated from eq 8 with KIO4- ) 30 mol-1 dm3. Figure 10 shows the fitting of the kinetic data obtained in SB3-12 micellar solutions by using a simplified form of eq 11. From the fitting one obtains Km ) 102 ( 8 mol-1 dm3 and k2m ) k2m/Vm ) (3.3 ( 0.4) × 10-3 s-1. The equilibrium binding constant is in agreement with that in Table 2, within experimental errors, and the k2m value obtained is close to three times larger than those obtained for SB3-14 and SB3-16 in ref 8d,c, respectively. To rationalize the kinetic micellar effects observed the mechanism of the process will be considered. As is known, the reaction studied follows the mechanism shown in Scheme 1, with the transition state more polar than the initial state. The sulfide suffers an electrophilic attack by the periodate anion, which results in a positive polarization of the sulfur atom and in an increase of the negative charge in the periodate moiety. A decrease in the polarity of the medium would make these two processes more difficult and, in fact, the reaction is strongly inhibited by a decrease in the polarity of the reaction medium.6,8d For instance, a decrease in the dielectric constant from 78.5 (pure water) to 50 (some water-organic mixtures) results in a slowing down of the reaction close to 100 times,8d a clear demonstration of the strong polarity influence of the reaction medium in the process studied. A parameter frequently used as a polarity index is the Reichardt and Dimroth ET parameter.30 This parameter is equal to the lowest energy transition of the indicator N-phenol betaine, (30) Reichardt, C. Solvent Effects in Organic Chemistry; Verlag Chemie: Weinheim, 1979.

A-B (1:1)

B

55.2

52.4

A-C (3:1) A-C (1:1) 55.5

54.3

C 52.5

T ) 298.2 K. A ) SDS; B ) SB3-12; C ) Tween 20.

ET(30), dissolved in a given solvent, expressed in kcal mol-1. In the case of micellar solutions, NMR studies have shown that the ET(30) molecules are predominantly solubilized in the micellar surface region and, therefore, from this parameter one obtains information about the surroundings of the ET(30) molecules at the micellar surface. We obtained the ET parameter for the pure and mixed micellar solutions used as reaction media, listed in Table 3. The values corresponding to SDS micellar solutions are in good agreement with that given by Zachariasse et al.6 One can see in Table 3 that the polarities of the mixed micellar solutions are between those of the pure micellar solutions; however, taking into account the complexity of the mixed micellar solutions, the ET values for these media have to be considered as an average of the polarity of the interfacial regions of the two types of micellar aggregates present in those solutions. The ET parameter for SB3-14 and SB3-16 is 52;8d therefore, the interfacial region of the SB3-12 micelles seems to be a little more polar than those of tetradecyl and hexadecyl. Because the reaction is strongly sensitive to changes in the polarity of the reaction medium and considering that the reaction site is the interfacial region, one would expect k2m to be somewhat larger in SB3-12 than in SB3-14 or SB3-16 micellar solutions, as was found. This change in polarity could also explain the smaller value of Km obtained in SB3-12 as compared to those in SB3-14 and SB3-16. It should be noted that we have assumed the location of the ArSMe molecules to be similar to that of ET(30) molecules in the above discussion. Comparison between the second-order rate constants in the micellar pseudophase for pure micellar solutions was done in ref 8d. It was shown that the differences in reactivity are mainly due to the polarity of the interfacial region and charge-charge interactions. With regard to the former, the reaction site in sulfobetaine micelles seems to be the less polar. With respect to the latter, oxidation of sulfide to sulfoxide involves a buildup of a positive charge on sulfur in the transition state (Scheme 1) because there is a formal transfer of an electron to the oxidant; therefore, the process should be disfavored by interaction with cationic headgroups and favored by interaction with anionic micellar headgroups. In nonionic micelles, chargecharge interactions are not operative. In sulfobetaine micelles, the interfacial electrical potential is about 30 mV;28a therefore, charge-charge interactions retard the reaction as compared to nonionic micelles. As a result, the reaction rate follows the trend k2m(SDS) > k2m(Tween 20) > k2m(SB3-12), the process being slower in micellar solutions than in water because of a lower polarity of the micellar pseudophase with respect to the aqueous phase. Kinetic data in mixed micelles show that in SDS-Tween 20 and SDS-SB3-12 mixed micellar solutions, the reaction occurs mainly in the aqueous phase, as a result of the repulsive electrostatic interactions between the periodate anions and the negatively charged mixed micelles. From the above kinetic results it is clear that the formation of the second type of micellar aggregates in the mixed micellar solutions studied when [surfactant] increases is not shown through changes in the observed rate constant of the reaction ArSMe + IO4-. This could be due to the fact that in the mixed micellar media the process

10866


Figure 11. Dependence of the observed rate constant on surfactant concentration for the spontaneous hydrolysis of phenyl chloroformate in mixed SDS-SB3-12 (3:1) and SDSTween 20 (1:1) micellar solutions. T ) 298.2 K. Scheme 2

takes place mainly in the aqueous phase. For this reason the authors decided to investigate a process which occurs in the micellar pseudophase and whose mechanism was well-known. The spontaneous hydrolysis of phenyl chloroformate was investigated in the mixed SDS-Tween (1:1) and SDS-SB3-12 (3:1) micellar solutions. Phenyl chloroformate is scarcely soluble in water, and in the presence of micellar aggregates the contribution of the reaction taking place in the micellar pseudophase increases upon increasing the surfactant concentration,10 the reaction site being the Stern region. The process, a true first-order reaction, follows an addition-elimination mechanism (see Scheme 2), with the addition step being rate determining, which leads to a polar transition state. The mechanism is the same in water as in micellar solutions.10c Therefore, a decrease in the water content as well as a decrease in the polarity of the medium would result in a slowing of the reaction. The mechanism leads to the development of a negative fractional charge at the oxygen atom of the carbonyl group, and, consequently, charge-charge interactions are expected to influence the reaction rate. In cationic micellar solutions electrostatic interactions between the ionic headgroups and the transition state will be attractive, and in anionic micellar solutions these interactions will be repulsive. In the case of sulfobetaine micellar solutions and considering that a permanent positive dipole is present, these electrostatic interactions will also be attractive. In nonionic micellar solutions charge-charge interactions are not operative. Figure 11 shows the dependence of kobs on surfactant concentration for the spontaneous hydrolysis of phenyl chloroformate in the mixed micellar solutions used as reaction media. One can see that the reaction rate is inhibited by an increase in surfactant concentration, this

Mun˜ oz et al.

decrease being larger at low rather than at high surfactant concentrations. At high enough [surfactant], the reaction rate reaches a plateau. The changes in kobs on [surfactant] are gradual, and no discontinuities are observed, the trend being similar to that found in pure SDS, Tween 20, and SB3-14 and SB3-16 micellar solutions.34c That is, kobs remains unchanged at [surfactant] below the cmc corresponding to the first break (although the kinetic data are not shown) and begins to decrease for [surfactant] above it. The same result was also found for the mixed SDSTween 20 (1:1) micellar solutions and also for the reaction ArSMe + IO4- in mixed micellar solutions (as was shown above). No breaks in the plots of kobs against surfactant concentration are observed in the vicinity of [surfactant] corresponding to the second break. The effect of the presence of the micellar aggregates on the reaction is to incorporate the organic substrate into the micelles, the amount of phenyl chloroformate molecules incorporated being proportional to the total surfactant concentration. This explains that the kinetic data in Figure 11 can be rationalized by using eq 13. The results obtained do not provide relevant information, and, therefore, it has not been included. We can conclude that in the study of the structural characteristics of mixed micellar solutions, it is important to investigate the whole range of surfactant concentrations, from [surfactant] lower than the lowest cmc value corresponding to the pure surfactants to high surfactant concentrations (well above the highest cmc of the pure surfactants). This way, if more than one type of micellar aggregates are formed, it will be detected through the experimental data. The use of more than one technique to draw structural information is also important, as was shown in this work. With regard to the kinetic data, for the two reactions studied the formation of two different kinds of micellar aggregates upon increasing surfactant concentration is not mirrored by changes in the observed rate constant by varying [surfactant]. In the mixed micellar solutions the reaction rate decreases gradually upon increasing [surfactant] in the whole concentration range studied. This could be due to the following reasons. The process ArSMe + IO4- takes place mainly in the aqueous phase of the mixed micellar solutions, and the effect of the presence of the micellar aggregates on the reaction is related to the incorporation of the ArSMe molecules into the micelles present in the reaction medium. The extent of this incorporation into one or two micellar aggregates is proportional to the total surfactant concentration, and, therefore, gradual changes in the observed rate constant are found, the plot of 1/kobs against [surfactant] being a straight line. The spontaneous hydrolysis of phenyl chloroformate occurs in the aqueous as well as in the micellar pseudophases of the mixed micellar solutions. The contribution of the reaction occurring in the two micellar pseudophases is proportional to the incorporation of the phenyl chloroformate molecules into the micelles. Micellar concentration effects are not operative and, hence, the differences in the reaction rate in the two micellar pseudophases will arise from the micellar medium effects. However, this process is not particularly sensitive to changes in the characteristics of the reaction medium (polarity, ionic strength, etc.) and, because kobs changes gradually upon increasing [surfactantT], this would mean that the reaction rate is similar, or at least not too different, when it takes place in the two micellar pseudophases present in the reaction medium. As a consequence, kinetic micellar effects reveal little information about the mixed micellar medium.


Acknowledgment. This work was financed by the DGCYT (Grant BQU2002-00691) and Consejerıá de Educacioń y Ciencia de la Junta de Andalucıá (FQM-274). The authors want to thank Profesor Victor Mosquera, from

Langmuir, Vol. 20, No. 25, 2004 10867

the University of Santiago de Compostela, Spain, for helping us in the application of the Phillips method for obtaining the cmc values. LA048247N

Conductometric, Surface Tension, and Kinetic Studies in Mixed SDS

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