Influence of the Micellar Electric Field on Electron-Transfer Processes

7986

Langmuir 2000, 16, 7986-7990

Influence of the Micellar Electric Field on Electron-Transfer Processes (II): A Study of the Ru(NH3)5pz2+ + Co(C2O4)33- Reaction in SDS Micellar Solution Containing NaCl R. de la Vega, P. Lo´pez-Cornejo, P. Pe´rez-Tejeda, A. Sańchez, R. Prado, M. Lo´pez, and F. Sańchez* Facultad de Quı´mica, Departamento de Quı´mica Fı´sica, Universidad de Sevilla, Calle Professor Garcıá Gonza´ lez s/n, 41012 Sevilla, Spain Received March 16, 2000. In Final Form: June 20, 2000

Micellar effects on the oxidation reaction of [Ru(NH3)5pz]2+ with [Co(C2O4)3]3- in the presence of different NaCl concentrations were studied. Experimental results are discussed by using an approach based on the transition-state theory. It is shown that this approach used here is better than others based on the pseudophase model, which can also be used, because the former is able to give a clear meaning to the parameters of the model. Changes in the observed reactivity are explained by a change in the degree of association of the reactant to the micelles, which depends on the surface potential of the micelles. This potential determines the strength of binding of one of the reactants ([Ru(NH3)5pz]2+) to the micellar surface.

Introduction

K

Sw + T {\} Sm

The pseudophase model1-6 or other models derived from it, such as the ion-exchange model,2,7-10 have been frequently and successfully applied to the interpretation of kinetic effects in micellar systems. These models describe the effect of micelles on reaction kinetics by fitting the experimental data to some equations containing several parameters, whose meanings are defined in the model. Thus, as is well-known, the pseudophase model for a first-order reaction (or for a second-order reaction if only one reactant is partitioned between the bulk and micellar pseudophases) results in the following equation:

kobs )

kw + kmK[T] 1 + K[T]

(1)

with kw being the rate constant of the process in the bulk (aqueous pseudophase), km being the rate constant at the micellar pseudophase, and K being the equilibrium constant for the binding of the reactant, S, to the micelles. This equilibrium is * To whom correspondence should be addressed. Tel: +34954557175. Fax: +34-954557174. E-mail: [email protected]. (1) Menger, F. M.; Portnoy, C. E. J. Am. Chem. Soc. 1967, 89, 4698. (2) Bunton, C. A. J. Mol. Liq. 1997, 72, 231. (3) Bunton, C. A.; Romsted, L. S.; Sepulveda, L. J. Phys. Chem. 1980, 84, 2611. (4) Gonsalves, M.; Probst, S.; Rezende, M. C.; Nome, F.; Zucco, C.; Zanette, D. J. Phys. Chem. 1985, 89, 1127. (5) Ortega, F.; Rodenas, E. J. Phys. Chem. 1986, 90, 2408. (6) Marin, M. A. B.; Nome, F.; Zanette, D.; Zucco, C.; Romsted, L. S. J. Phys. Chem. 1995, 99, 10879. (7) Romsted, L. S. In Micellization, Solubilzation and Microemulsions; Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 2. (8) Martinek, K.; Yatsimirski, A. K.; Levashov, A.; Berezin, I. In Micellization, Solubilization and Microemulsions; Mittal, K. L., Ed.; Plenum Press: New York, 1977; Vol. 2. (9) Quina, F. H.; Chaimovich, H. J. Phys. Chem. 1979, 83, 1844. (10) Romsted, L. S. In Surfactants in Solutions; Mittal, K. L., Lindman, B., Eds.; Plenum Press: New York, 1984; Vol. 2, p 1015.

(2)

So, K is given by

K)

[Sm] [Sw][T]

(3)

with T being the micellized surfactant concentration. In the context of the model, it is explicitly assumed that km, K, and kw are surfactant-concentration-independent parameters. However, this assumption is not valid, strictly speaking, when the range of surfactant concentration explored in the study is big enough. This circumstance is the consequence of the change of size (aggregation number),11,12 shape,13 and, mainly, surface potential14,15 of the micelles as the concentration of the surfactant changes. As shown by some of the present authors,16 the changes in the model can be formally taken into account by introducing into eq 1 new parameters that describe the possible variations of kw, km, and K with the surfactant concentration. In this way, an equation of the form

kobs )

kw + s[T] + t[T]2 1 + K[T]

(4)

results. This equation permits fitting kinetic data corresponding to variations of the concentration range for T of ca. 2 orders of magnitude. A major drawback of eq 4 is the fact that, although this fitting shows the change of some (11) Manohar, C.; Kelkar, V. K. Langmuir 1992, 8, 18. (12) Rodenas, E.; Perez-Bendito, E. An.Quim. 1993, 89, 674. (13) Oh, S. G.; Huibers, P. D. T.; Shah, D. O. In Dynamic Properties Of Interfaces and Association Structures; Pillai, V., Shah, D. O., Eds.; AOCS Press: Champaign, IL, 1996, Chapter 5, p 140. (14) Bell, G. M.; Dunning, A. J. Trans. Faraday Soc.. 1970, 66, 500. (15) (a) Grand, D.; Hautecloque, S. J. Phys. Chem. 1990, 94, 837. (b) Hautecloque, S.; Grand, D.; Bernas, A. J. Phys. Chem. 1985, 89, 2705. (16) Lo´pez-Cornejo, P.; Jimeńez, R.; Moya´, M. L.; Sańchez, F.; Burgess, J. Langmuir 1996, 12, 4981.

10.1021/la000406p CCC: $19.00 © 2000 American Chemical Society Published on Web 09/16/2000

Ru(NH3)5pz2+ + Co(C2O4)33- Reaction

Langmuir, Vol. 16, No. 21, 2000 7987

Table 1. Rate Constants for the Reaction of Ru(NH3)5pz2+ + Co(ox)33- in SDS Micellar Systemsa 103[SDS]/mol dm-3

kobs/s-1

103[SDS]/mol dm-3

kobs/s-1

5.4 5.5 5.6 5.8 6.0 7.0 7.5 8.0 8.5 9.0 9.5 10.0 12.5 15.0

2.2 2.0 1.9 1.8 1.4 1.0 0.95 0.81 0.73 0.64 0.59 0.56 0.40 0.35

17.5 20.0 30.0 41.0 45.0 48.0 55.0 70.0 90.0 100 120 150 200

0.32 0.28 0.22 0.20 0.23 0.24 0.25 0.27 0.28 0.33 0.42 0.46 0.58

a

Table 4. Rate Constants for the Reaction of Ru(NH3)5pz2+ + Co(ox)33- in SDS Micellar Systems in the Presence of NaCla 103[SDS]/mol dm-3

kobs/s-1

103[SDS]/mol dm-3

kobs/s-1

6.0 7.0 8.0 8.5 9.0 12.0 14.0

1.59 1.56 1.52 1.49 1.47 1.37 1.29

20.0 50.0 70.0 100 150 200

1.17 0.57 0.45 0.35 0.27 0.22

a

[NaCl] ) 0.5 mol dm-3.

Data taken from ref 16.


kobs/s-1

103[SDS]/mol dm-3

kobs/s-1

6.0 7.0 8.0 8.5 9.0 12.0 14.0

0.98 0.91 0.77 0.75 0.69 0.52 0.46

20.0 50.0 70.0 100 150 200

0.29 0.13 0.11 0.11 0.10 0.13

a



kobs/s-1

103[SDS]/mol dm-3

kobs/s-1

6.0 7.0 8.0 8.5 9.0 12.0 14.0

1.67 1.60 1.46 1.45 1.40 1.27 1.13

20.0 50.0 70.0 100 150 200

0.89 0.36 0.25 0.20 0.18 0.20

a


of the parameters (kw, km, and K), it is not able to establish what is (are) the parameter(s) which change when the surfactant concentration is varied. To answer this question, the present work was undertaken. We selected a quite simple kinetic system wellknown to us,16 the oxidation of [Ru(NH3)5pz]2+ with [Co(C2O4)3]3- (pz, pyrazine; C2O42-, oxalate anion). This process was studied in SDS (sodium dodecyl sulfate) solutions containing NaCl at concentrations of 0, 0.1, 0.3, and 0.5 mol dm-3. Changes in the concentration of this salt were introduced in order to produce changes in the characteristics of the micelles and, in particular, in their surface potential, which is the main parameter whose influence we want to explore here. Experimental Section Kinetics. Experimental details concerning reactants and kinetics have been described elsewhere.16 In the present work, the concentrations of the reactants were [Ru(NH3)5pz]2+) 8 × 10-5 mol dm-3 (as perchlorate salt) and [Co(C2O4)3]3- ) 2 × 10-3 mol dm-3 (as sodium salt). The concentrations of the surfactant corresponding to the different NaCl concentrations are given in Tables 1-4. In these tables, the pseudo-first-order rate constants, kobs, measured at different surfactant concentrations also appear. Surface Potential Measurements. As is known, there is a difference of potential, Ψ, between the surface of a highly charged

Figure 1. Plot of the absorbance of the PADA ligand at 460 nm vs the pH of the medium. The points are experimental data, and the line is the best fit obtained by using a sigmoidal equation. coloidal particle and the bulk of the solution. Bearing this in mind, Hartley and Roe17 showed that the hydrogen ion concentration near the surface would be exp(-Fψ/RT) times that of the hydrogen ion concentration in bulk. Therefore, one can write the equation

(Ka)s ) Ka e-Fψ/RT

(5)

where (Ka)s and Ka are the “apparent” acid dissociation constants of the acid group located close to the surface of a micelle and within the bulk, respectively. Equation 5 can be rewritten as

(pKa)s ) pKa +

ψ 59.2

(6)

with ψ being expressed in mV. In this work, surface-potential values of SDS micelles were calculated in the presence of different NaCl and surfactant concentrations from pH titrations of the 2-[p-(dimethylamino)phenylazo]pyridine, PADA, which show a spectral shift when the pH of the medium is changed. This ligand presents a maximum absorption at λ ) 460 nm and λ ) 550 nm in basic and acidic media, respectively. Therefore, the pKa of PADA in the presence and absence of SDS and NaCl was obtained by measuring the absorbance of PADA solutions at 460 nm and different pH values. The trends observed in the plot of the absorbances vs pH in each medium were fitted to a sigmoidal curve (Figure 1 is representative). The second derivative of the equation obtained from the fits gave the pKa value required for each micellar and salt concentration. The pH values were fixed using a universal buffer of boric acid, citric acid, and sodium phosphate. The concentrations used were in the range of [H3BO3] ) 0.08-0.3 mol dm-3, [C6H8O7‚ H2O] ) 0.02-0.05 mol dm-3, and [Na3PO4‚12H2O] ) 0.06-0.01 mol dm-3. These concentration values correspond to the amount of species added to the solution. In any case, some data were (17) Hartley, G. S.; Roe, J. W. Trans. Faraday Soc. 1940, 36, 107.

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Langmuir, Vol. 16, No. 21, 2000

de la Vega et al.

Table 5. Surface Potential (ψ) Values at Different NaCl and SDS Concentrations [NaCl]/mol dm-3 0

0.1

0.3

[SDS]/mol dm-3

-Ψ/mV

pKa

0.025 0.040 0.050 0.060 0.070 0.090 0.100 0.150 0.200 0.050 0.070 0.100 0.150 0.200 0.100 0.150 0.200

178.0a 172.0a 169.0a 165.0a 162.0a 159.0a 157.0a 150.0a 145.0a 80.5 76.4 71.6 64.5 59.2 34.3 27.8 22.5

5.94 5.87 5.79 5.67 5.58 5.23 5.12 5.03

a Data obtained from ref 23. The pK value of PADA in aqueous a solution is 4.58 for [NaCl] ) 0.1 mol dm-3 and 4.65 for [NaCl] ) 0.3 mol dm-3.

Figure 2. Plot of the rate constants of the reaction [Ru(NH3)5pz]2+ + [Co(C2O4)3]3- in SDS micellar systems vs a micellized surfactant concentration at [NaCl] ) 0 mol dm-3. The points are experimental data, and the line is the best fit obtained by using eq 10 (k0 ) 1.33 s-1 K ) 1611 mol-1 dm3) and a critical micellar concentration value of 5 × 10-3 mol dm-3 taken from ref 16. obtained by using sodium hydrogen phosphate buffers, but no difference was observed in the absorbance value. Surface-potential values obtained are collected in Table 5. All the experiments (kinetic and surface-potential measurements) were carried out at 298.2 ( 0.1 K.

Discussion The variations of kobs with the surfactant concentration appear in Figures 2-5. These figures have a common segment that decreases. However, in Figures 2 and 3, after a minimum, the rate constant increases again as the surfactant concentration increases. Figure 4 shows that above a given surfactant concentration ([SDS] ∼ 0.1 mol dm-3), the rate constant changes very little. Finally, at the higher NaCl concentration, the plot of kobs vs [SDS] always decreases (Figure 5). To interpret these facts, we will consider (see below) that the behavior described above arises from changes in the surface potential of the micelles. In this regard, a good starting point is to think in terms of the transition-state theory, which has been shown to be applicable to reactions

Figure 3. Plot of the rate constants of the reaction [Ru(NH3)5pz]2+ + [Co(C2O4)3]3- in SDS micellar systems vs a micellized surfactant concentration at [NaCl] ) 0.1 mol dm-3. The points are experimental data, and the line is the best fit obtained by using eq 10 (k0 ) 2.98 s-1 K ) 435 mol-1 dm3) and a critical micellar concentration value of 1.5 × 10-3 mol dm-3 taken from ref 18.

Figure 4. Plot of the rate constants of the reaction [Ru(NH3)5pz]2+ + [Co(C2O4)3]3- in SDS micellar systems vs micellized surfactant concentration at [NaCl] ) 0.3 mol dm-3. The points are experimental data, and the line is the best fit obtained by using eq 10 (k0 ) 2.69 s-1 K ) 130 mol-1 dm3) and a critical micellar concentration value of 8 × 10-4 mol dm-3 taken from ref 18.

in micellar systems.16,19-22 According to this theory, the rate constant for a given reaction

A + B f products

(7)

is given by the equation

kobs ) k0

γAγB γ*

(8)

In this equation γA, γB, and γ* are the activity coefficients of the reactants and of the activated complex, respectively, and k0 is the rate constant of the process in the reference state. In micellar solutions, it is convenient to take as (18) van Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physico-Chemical Properties of Selected Anionic, Cationic and Nonionic Surfactants; Elsevier: Amsterdam, 1993. (19) Bunton, C. A.; Robinson, L. J. Am. Chem. Soc. 1968, 90, 5972. (20) Hall, D. G. J. Phys. Chem. 1987, 91, 4287. (21) Ise, N.; Okubo, T.; Shigern, K. Acc. Chem. Res. 1982, 15, 171. (22) Muriel-Delgado, F.; Jimeńez, R.; Go´mez-Herrera, C.; Sańchez, F. Langmuir 1999, 15, 4344.

Ru(NH3)5pz2+ + Co(C2O4)33- Reaction

Langmuir, Vol. 16, No. 21, 2000 7989

Figure 5. Plot of the rate constants of the reaction [Ru(NH3)5pz]2+ + [Co(C2O4)3]3- in SDS micellar systems vs micellized surfactant concentration at [NaCl] ) 0.5 mol dm-3. The points are experimental data, and the line is the best fit obtained by using eq 10 (k0 ) 2.03 s-1 K ) 45 mol-1 dm3) and a critical micellar concentration value of 5 × 10-4 mol dm-3 taken from ref 18.

such the solute in the aqueous pseudophase in contact with the micelles (which, of course, contains the monomers of the surfactant at the critical micellar concentration) instead of the habitual reference state (solute at infinite dilution). In this way, it is easily shown21,22 that

γi )

1 1 + Ki[T]

i ) A, B, *

in the micellar surface potential must be taken into account. Thus, the magnitude of K obviously corresponds to the free energy changes of the process described in eq 2. Without any loss of generality, this free-energy change can be written as the sum of two contributions: (1) a potential independent contribution, ∆Gnel (nonelectrostatic or intrisic), and (2) a potential dependent contribution, ∆Gel (electrostatic),

∆G ) ∆Gnel + ∆Gel

(9)

with Ki being the equilibrium constant defined in eq 3 for solute i (A, B, *). Notice that with the reference state used, k0 in eq 8 is identical to kw in eq 1. Before applying eqs 8 and 9 to the present case, some comments are in order. This is because, in the study presented here, one of the reactants [Co(C2O4)33-] and the transition state bear a negative charge. Thus, it can be assumed that, on the average, both will remain far from the micelles, that is, in the aqueous pseudophase. In other words, they will stay at the reference state, and thus, by definition, γi (i ) Co(C2O4)33- and *) will be unity. According to this, in the present case, a combination of eqs 8 and 9 gives

1 kobs ) k0 1 + K[T]

Figure 6. Plot of ln(kobs[SDS]) vs the surface potential of the micellar system at [NaCl] ) 0 mol dm-3. The points are experimental data, and the line is the best fit obtained by using eq 15.

(10)

with K being the binding constant (eqs 2 and 3) of the ruthenium complex to the micelles and [T], the SDS concentration used. It is also obvious that eq 10 is equivalent to eq 1 with km ) 0. Notice that, according to eq 10, changes in kobs arise from changes in [SDS], as the pseudophase model says, as well as from changes of K. These changes can be related to the changes of the surface potential of the micelles. Before showing that, it is interesting to consider Figures 2-5. In these figures, the curves correspond to a fit of the experimental data by considering K to be a true constant, that is, independent of the potential. As can be seen, the first part of the curves in Figures 2-4 and the whole curve in Figure 5 go through the experimental points. So at the lower range of surfactant concentrations in the cases of Figures 2-4 and in the complete range of [SDS] when [NaCl] ) 0.5 mol dm-3, when the surface potential of the micelles is a constant,23 the data are well-fitted to eq 10, because in this range, K is a true constant. However, for higher [SDS], the changes

(11)

The latter contribution can be expressed as

∆Gel ) zRuRFψ

(12)

where R is a parameter which takes into account the location of the ruthenium complex (R gives the fraction of the surface potential influencing K) whose charge is zRu. F is the Faraday constant, and Ψ, the surface potential of the micelles. If K0 is defined as

K0 ) e-∆Gnel/RT

(13)

K ) K0 e-∆Gel/RT ) Ko e-zRuRFψ/RT

(14)

it is obvious that

Introducing this equation into eq 10, and considering that KRu[SDS] . 1 (see ref 24), the results are

k0 zRuRFψ ln(kobs[SDS]) ) ln + K0 RT

(15)

According to eq 15, a plot of ln(kobs[SDS]) vs Ψ should be linear in the range of surfactant concentrations in which the experimental points deviate from the curve in Figures 2-4. Figures 6-8 give the plots. Their linearity supports our ideas. From the slopes of the plots, the values of parameter R corresponding to the different NaCl concentrations can be obtained. These values are 1.07, 0.83, and 0.72 for [NaCl] ) 0, 0.1, and 0.3 mol dm-3, respectively. These values imply that the average penetration of the (23) Bernas, A.; Grand, D.; Hautecloque, S.; Giannotti, C. J. Phys. Chem. 1986, 90, 6189. (24) This inequality does not neccesarily hold in the complete range of concentrations of SDS, but it clearly holds in the range in which Ψ changes with the concentration of the surfactant.

7990

Langmuir, Vol. 16, No. 21, 2000

Figure 7. Plot of ln(kobs[SDS]) vs the surface potential of the micellar system at [NaCl] ) 0.1 mol dm-3. The points are experimental data, and the line is the best fit obtained by using eq 15.

ruthenium complex at the double layer of the micelles depends on the salt concentration, and this penetration decreases as the concentration of NaCl increases, that is, when the Stern layer of the micelles becomes more compact. In conclusion, we have shown that when the concentration range of the surfactant is high enough, the simple assumptions of a pseudophase model concerning the constancy of the parameters appearing in eq 1 cannot be maintained. In this case, an extended pseudophase equation can be used (as in ref 6) in order to fit the experimental data. However, this extended equation does not give a clear meaning to the parameters, because it describes a change in each or some of the parameters in eq 1. For this reason, in the authors’ opinion, the approach

de la Vega et al.

Figure 8. Plot of ln(kobs[SDS]) vs the surface potential of the micellar system at [NaCl] ) 0.3 mol dm-3. The points are experimental data, and the line is the best fit obtained by using eq 15.

developed in this paper, based on the transition-state theory, is better in the sense that it gives a clear meaning to the parameters of the model. According to this approach, for a process in which only one of the reactants is near the micellar surface (adsorbed), changes in reactivity can be explained by a change in the degree of association of the reactant to the micelles, as in the pseudophase model, but taking into account that this binding is described by a constant which depends on the surface potential of the micelles. Acknowledgment. This work was financed by the D.G.I.C.Y.T. (PB-98-0423), the Consejerıá de Educacioń y Ciencia de la Junta de Andalucıá, and the Universidad de Sevilla by a grant of the Plan Propio de Investigacioń. LA000406P

Influence of the Micellar Electric Field on Electron-Transfer Processes

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