Salt, Solvent, and Micellar Effects on the Intervalence Transition within

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Salt, Solvent, and Micellar Effects on the Intervalence Transition within the Binuclear Complex Pentaammineruthenium(III)(µ-cyano)pentacyanoiron(II). An Estimation of Rate Constant from Static (Optical and Electrochemical) Data Pilar Neto-Ponce, Francisco Sa´nchez, Francisco Pe´rez, Antonio Garcı´a-Santana, and Pilar Pe´rez-Tejeda* Departamento de Quı´mica Fı´sica, Facultad de Quı´mica, C/Prof. Garcı´a Gonza´ lez s/n, 41012 Sevilla, Spain Received February 14, 2000. In Final Form: November 28, 2000 A study of the metal-to-metal charge-transfer transition within the binuclear complex pentaammineruthenium(III)(µ-cyano)pentacyanoiron(II), (NH3)5RuIII-NC-FeII(CN)5-, was carried out in salt solutions, water-cosolvent mixtures, and micellar solutions containing sodium dodecyl sulfate and hexadecyltrimethylammonium chloride (CTACl). Using these data, as well as the reaction free energies (obtained from electrochemical measurements), the rate constants, ket, for the forward and reverse electron-transfer processes have been estimated and compared with data for this and related electron-transfer processes existing in the literature for electrolyte and water-cosolvent solutions. The approximations involved in the method of estimating electron-transfer rate constants are discussed. In the case of micellar solutions, the reorganization energies and driving forces were obtained. The results in these microheterogeneous systems are interpreted taking into account the long-range (Colulombic) interactions between the mixed valence complex and the micellar electric field, along with the short-range electric field derived effects, the latter coming through the dielectric saturation phenomenom produced by the micellar electric field on the solvent surrounding the binuclear complex, when it is near the micellar (CTACl) surface.

Introduction In the past few years we1 and others2 have been interested in the possibility of obtaining activation free energies for electron-transfer processes from static (that is, nonkinetic) data. The connection between these data, the band energy corresponding to the optical electron transfer, Eop, and the reaction free energy of the electrontransfer process, ∆G° ′, with the activation free energy of the associated thermal electron transfer, ∆Gq, is given by the equation3

∆Gq )

Eop2 (λ + ∆G°′)2 ) 4λ 4(Eop - ∆G°′)

(1)

which can easily be derived by assuming a linear response * To whom all correspondence should be sent. (1) (a) Pe´rez-Tejeda, P.; Lo´pez, P.; Moya´, M. L.; Domı´nguez, M.; Carmona, E.; Palma, P.; Sa´nchez, F. New J. Chem. 1996, 20, 95. (b) Pe´rez-Tejeda, P.; Benko, J.; Moya´, M. L.; Sa´nchez, F. J. Mol. Liq. 1995, 65, 261. (c) Pe´rez-Tejeda, P.; Benko, J.; Lo´pez, M.; Gala´n, M.; Lo´pez, P.; Domı´nguez, M.; Moya´, M. L.; Sa´nchez, F. J. Chem. Soc., Faraday Trans. 1996, 92, 1155. (d) Pe´rez-Tejeda, P.; Sa´nchez, F.; Gala´n, M. J. Mol. Struct. (THOCHEM) 1996, 371, 153. (e) Sa´nchez, F.; Pe´rez-Tejeda, P.; Lo´pez-Lo´pez, M. Inorg. Chem. 1999, 38, 1780. (f) Lo´pez-Lo´pez, M.; Pe´rez-Tejeda, P.; Lo´pez-Cornejo, P.; Sa´nchez, F. Chem. Phys. 1999, 50, 321. (2) (a) Graff. D.; Claude, J. P.; Meyer, T. J. In Electron-Transfer Reactions, Inorganic, Organometallic and Biological Applications; Isied, S. S., Ed.; Advances in Chemistry Series 253; American Chemical Society: Washington, DC, 1997; p 183. (b) Tominaga, K.; Kliner, D. A. V.; Jonhson, A. E.; Levinger N. E.; Barbara P. F. J. Chem. Phys. 1993, 98, 1228 and references therein. (c) Lin, T. Y.; Chen, Y. J.; Tai, C. C.; Swan, K. S. Inorg. Chem. 1999, 38, 674. (d) Nelsen, S. F.; Ismagilov, R. F.; Powell, D. R. J. Am. Chem. Soc. 1997, 119, 10213 and references therein. (3) Hush, N. S. Prog. Inorg. Chem. 1967, 92, 463. In eq 1 it is supposed that the coupling between the donor and acceptor centers is small. Otherwise a correction taking into account this coupling should be made.

of the solvent and that the free energy surfaces for the reactant and product states are paraboloids of the same curvature.4 Notice that both Eop and ∆G°′ are experimental parameters, as Eop can be obtained directly from the energy corresponding to the absorption maximum of the metalto-metal charge transfer (MMCT) band and ∆G°′ can be derived from electrochemical data (redox potentials) of the complexes involved in the electron-transfer process. The possibility of obtaining activation free energies from an independent-of-kinetic procedure is of interest, because if ∆Gq is available the determination of the rate constant through a conventional kinetic procedure permits the preexponential term in this constant to be obtained, as pointed out by Weaver5 and Bu et al.6 This term is of interest since, as is well-known, it contains information on the electronic and dynamic solvent effects of the electron-transfer reaction. On the other hand, obtaining Eop and ∆G°′ gives the reorganization free energy, λ, through:7

λ ) Eop - ∆G°′

(2)

Thus, it is possible not only to have the activation free energy but also to know, separately, the two parameters, λ and ∆G°′, controlling it. This is of interest, for example, in relation to studies on solvent effects on the kinetics of electron-transfer processes, because it is possible, having λ and ∆G°′, to know if the observed effects are mainly thermodynamic (that is on ∆G°′) or kinetic (on λ) in character. (4) Marcus, R. Annu. Rev. Phys. Chem. 1964, 15, 155 and references therein. (5) Weaver, M J. Chem. Rev. 1992, 92, 463. (6) Bu, Y.; Dong, C. J. J. Phys. Chem. 1997, 101, 1198. (7) Hush, N. S. Prog. Inorg. Chem. 1967, 8, 391.

10.1021/la000215m CCC: $20.00 © 2001 American Chemical Society Published on Web 01/25/2001

Study of Metal-to-Metal Charge Transfer

In this work, following the lines described above, we have obtained the activation free energies for the thermal (forward and reverse) electron-transfer processes within pentaammineruthenium(III)(µ-cyano)pentacyanoiron(II), (NH3)5RuIII-NC-FeII(CN)5-. These activation free energies were obtained in different reaction media, watermethanol mixtures, and electrolyte solutions (NaNO3). This mixed valence complex was chosen because it shows a clear MMCT band in water8 and because it is a localized mixed valence compound8b (class II in Robin-Day classification), which is essential in applying eqs 1 and 2. The selected species also permits us to perform electrochemical measurements on the two metalic centers, because electron transfer from or to these centers is reversible from a electrochemical point of view. Thus, generally speaking, the two parameters appearing in eq 1 can be obtained directly from experiments. It is worth pointing out that the selected system also permits us to compare for the first time, in a quantitative way, the activation free energies obtained as described above (from experimental nonkinetic data) with values of ∆Gq determined through kinetic measurements, for an intramolecular electron transfer process. This comparison will be done (in salt solutions and water-methanol mixtures) using previously published data, when available, or indirectly, by comparing their variations, as the solvent is changed, with the corresponding variations for a closely related process, when the data are impossible to be obtained. Our results show that, despite the approximations involved in the method, good agreement is found between experimental (kinetic) activation free energy values and those derived from static measurements. These approximations will be discussed later. On the other hand, our studies in micellar solutions were motivated by our interest in the study of electric field effects on reactivity, rather than by comparison of the observed and predicted rate constants in micellar systems, because there are no data for ket for this or comparable processes. As is well-known, the study of electric field effects on reactivity has been an area of growing interest in the past few years.9 In particular, in relation to electron-transfer processes, this field can have an effect on the relevant parameters controlling this kind of process, that is, the reorganization free energy and the driving force that modulates the activation free energy of the electron-transfer reactions (see eq 1). Thus, the dielectric characteristics of the medium are changed by the field through solvent saturation effects,10 so the solvent reorganization energy would be modified by the influence of an electric field. On the other hand, the electron-transfer free energy is also dependent on this field, through its influence on the solvent dielectric constant, and as a consequence on the interaction of the dipole moment of the electronic transition (optical or thermal) with the field.11 However, to produce the above-mentioned effects, that is, changes in the reorganization free energy and in the driving force, the applied electric field must be quite (8) (a) Walker G. C.; Barbara P. F.; Doorn S. K.; Dong, Y.; Hupp, J. T. J. Phys. Chem. 1991, 95, 5712. (b) Burewicz, A.; Haim, A. Inorg. Chem. 1988, 27, 1611. (9) See for example: (a) Marcus, R. A. Angew. Chem., Int. Ed. Engl. 1993, 32, 1111. (b) Molecular Electronics in Science and Technology; Aviram, A., Ed.; AIP Press: New York, 1992. (c) Franzen S.; Boxer, S. G. In Electron Transfer in Inorganic, Organic, and Biological Systems; Bolton, J. R., Mataga, N., McLendon, G., Eds.; American Chemical Society, Washington, DC, 1991; Chapter 9. (d) Hackett, J. W., II; Turro, C. Inorg. Chem. 1998, 37, 2039. (10) Bo¨ttcher, C. J. F. Theory of Electric Polarization, 2nd ed.; Elsevier Scientific Publishing Co.: Amsterdam, 1973; Vol. 1, Chapter 7. (11) Lao, K.; Franzen, S.; Stanley, R. J.; Lambright, D. G.; Boxer, S. G. J. Phys. Chem. 1993, 97, 13165.

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strong, about 107 V/m.12 Such intense fields exist, for example, in the region close to an electrode surface13 and also in the vicinity of the surface of the (charged) micelles.14 The results presented in this study show the influence of micelles on the reaction and reorganization free energies on the electron transfer within the above-mentioned binuclear complex. These results refer to micellar solutions formed by anionic (SDS) and cationic (CTACl) surfactants. Given that the binuclear complex under study bears a negative charge, one can suppose that the anionic micelles will interact with it only via long-range (Coulombic) interactions. On the other hand, in the case of cationic micelles, both Coulombic interactions and short-range effects are to be expected. Therefore, a study of both, long-range and short-range electric field effects seems feasible, the latter coming through saturation effects produced by the electric field on the solvent surrounding the binuclear complex. Experimental Section Materials. The mixed valence compound Na[(NH3)5RuIIINC-FeII(CN)5] was prepared and purified as previously described.8a,15 The visible spectrum shows a MMCT band with absorption maximum at 982 ( 1 nm (∈max ) 2988 ( 20 mol-1 dm3 cm-1), in water (ionic strength ) 5.8 × 10-4 mol dm-3, which corresponds to the concentration of binuclear complex). This wavelength corresponds to a value of Eopexp ) hυmax of 122 kJ mol-1. Sodium nitrate and methanol were purchased from Merck quality p.a. and used without further purification. Hexadecyltrimethylammonium chloride (CTACl) was purchased from Fluka as a solution containing ca. 25% in the surfactant. This solution was titrated with AgNO3 and used without further purification. Sodium dodecyl sulfate (SDS) came from Merck and was recrystallized from ethanol, washed with diethyl ether, and dried in vacuo over P2O5. Throughout the study, double distilled and deionized water, obtained from a Millipore Milli-Q system, with a conductivity of lower than 10-6 Ω-1 m-1, was used. The water-cosolvent mixtures were prepared by weight. The mole fraction of the organic compound (see Table 2) was taken in order to achieve the following dielectric constants, DS, in the media: 78.5 (pure water), 76, 74, 70, 66, 64, 60. The required weight percentages were taken from the literature.16 Spectra. The spectra of the binuclear complex in the different media were recorded in a Hitachi 150-20 UV-vis spectrophotometer at 298.2 K. To minimize the uncertainty in the absorption maximum, the derivative spectra were also recorded. Thus, the uncertainty was about (1 nm. To check up on the possible influence of the concentration of the complex on the full width at half-height and absorption maximum, a set of spectra changing the concentration of the binuclear complex in the range of 0.5 × 10-4 to 6.0 × 10-4 mol dm-3 were recorded in pure water. Both the band maximum and the full width were independent of the concentration in the above-mentioned range: constant values of λmax ) 982 ( 1 nm and ∆ν1/2 ) 4700 ( 100 cm-1 were found. Thus, concentration of the mixed valence compound was always 5.8 × 10-4 mol dm-3 in electrolyte and water-methanol solutions. In the surfactant solutions, the binuclear complex concentration was the maximum possible for compatibility with the stability of the micellar (CTACl) solutions, so it was varied depending on surfactant concentrations. The concentrations of surfactant in the solutions ranged from 1.0 × 10-2 to 3.0 × 10-1 mol dm-3 for SDS, whereas in the case of CTACl the concentration of the solutions ranged from 4.0 × 10-3 to 3.0 × 10-1 mol dm-3. The lower concentration for SDS and CTACl solutions was chosen, taking into account the correspondig values of the critical micellar (12) Farazdel, A.; Dupuis, M.; Clementi E.; Aviram, A. J. Am. Chem. Soc. 1990, 112, 4206. (13) Bockris, J. O’M.; Reddy, A. K. N. Reddy, Modern Electrochemistry; Plenum Press: New York, 1970; Vol. 2. (14) See for example: Grand, D.; Hautecloque, S. J. Phys. Chem. 1990, 94, 837 and references therein. (15) Vogler, A.; Kisslinger, J. J. Am. Chem. Soc. 1982, 104, 2311. (16) Hasted, J. B. In Water: A Comprehensive Treatise; Frank, F., Ed.; Plenum Press: New York, 1979; Vol. III; p 32.

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Table 1. Energiesa Corresponding to the Maximum of the Absorption Spectra of the MMCT Band, Eop, Redox Potentials, E°′ (Ru ) Ruthenium Ammine Center and Fe ) Iron Cyanide Center), Free Energy Change, ∆G°′, Reorganization Free Energy, λ, and Activation Free Energies (∆Gq and ∆Grq) for the Electron Transfer Process within the Binuclear Complex (NH3)5RuIII-NC-FeII(CN)5- at 298.2 K in Several NaNO3 Solutions [NaNO3]b

Eopexp c

Eopd

E°′(Ru)e

E°′(Fe)e

∆G°′

λ

∆Gq f

∆Grq g

0.2 0.6 1.0 2.0 3.0 4.0 5.0

123.4 125.1 125.9 127.4 128.7 129.0 129.3

118.0 119.7 120.5 122.0 123.3 123.6 123.9

-0.046 -0.048 -0.049 -0.049 -0.052 -0.054 -0.058

0.641 0.644 0.651 0.662 0.664 0.665 0.664

66.3 66.8 67.5 68.6 69.2 69.4 69.7

51.7 52.9 53.0 53.4 53.5 54.2 54.2

67.4 67.7 68.5 69.2 70.3 70.5 70.8

1.0 0.9 1.0 1.1 1.2 1.1 1.1

a All energies in kJ mol-1. b Salt concentration in mol dm-3. c Experimental values. d Corrected values following eq 3 (see text). e Redox potentials in V vs NHE. f Values for forward process (eq 5). g Values for reverse process (eq 12), ∆Gr°′ ) -∆G°′ and λr ) λ.

Table 2. Energiesa Corresponding to the Maximum of the Absorption Spectra of the MMCT Band, Eop, Redox Potentials, E°′ (Ru ) Ruthenium Ammine Center and Fe ) Iron Cyanide Center), Free Energy Change, ∆G°′, Reorganization Free Energy, λ, and Activation Free Energies (∆Gq and ∆Grq) for the Electron Transfer Process within the Binuclear Complex (NH3)5RuIII-NC-FeII(CN)5- at 298.2 K in Several Methanol-Water Mixtures xorg b

γc

Eopexp d

Eop e

E°′(Ru)f

E°′(Fe)f

∆G°′

λ

∆Gq g

∆Grq h

0.033 0.060 0.112 0.160 0.200 0.265

0.548 0.547 0.545 0.542 0.541 0.538

121.6 120.7 119.4 117.7 115.8 115.7

116.2 115.3 114.0 112.3 111.4 110.3

-0.043 -0.045 -0.056 -0.056 -0.066 -0.070

0.631 0.626 0.596 0.580 0.567 0.549

65.1 64.8 62.9 61.4 61.1 59.6

51.2 50.5 51.1 50.9 50.3 50.7

66.0 65.8 63.6 61.9 61.6 60.0

0.9 1.0 0.7 0.5 0.6 0.4

a All energies in kJ mol-1. b Mole fraction of the organic compound (all solutions containig a 0.2 mol dm-3 concentration of NaNO ). c γ 3 ) 1/Dop - 1/Ds; Ds values were taken from ref 10; Dop ) n2, n values from Handbook of Chemistry and Physics, 53rd ed.; CRC Press: d e f g Cleveland, OH, 1972. Experimental values. Corrected values following eq 3. Redox potentials in V vs NHE. Values for forward process (eq 5). h Values for reverse process (eq 12), ∆Gr°′ ) -∆G°′ and λr ) λ.

concentration, cmc, for both surfactants. These were 8.0 × 10-3 and 9.0 × 10-4 mol dm-3 for SDS and CTACl solutions, respectively.17 To connect strictly electrochemical with spectroscopic data (see below), the spectra in aquo-organic solutions were performed in the presence of 0.2 mol dm-3 NaNO3. On the other hand, neither the molar absorption coefficient at the maximum of the band, max, nor the full width at half-height, ∆υ1/2, showed significant modifications, in relation to the values of these parameters in water (∈max ) 2988 ( 20 mol-1 dm3 cm-1 and ∆υ1/2 ) 4700 ( 100 cm-1) in the different solutions employed in this study. All spectra were recorded using a quartz cell with a 1 cm path length. Electrochemistry. The redox potentials of both ruthenium and iron centers in the binuclear complex were obtained by cyclic voltammetry techniques in all solutions. The equipment, procedure, and electrodes have been previously described.18 The temperature was kept constant at 298.2 ( 0.1 K. The concentration of the mixed-valence compound was the same as in the experiments in which the spectra were obtained. In the case of water-methanol mixtures, sodium nitrate (0.2 mol dm-3) as a background electrolyte was used. The estimated uncertainty in redox potentials is about (2 mV, for the case of sodium nitrate, water-methanol, and SDS micellar solutions, and (5 mV for micellar CTACl solutions.

Results and Discussion (a) Electrolyte and Water-Methanol Solutions. Tables 1 and 2 give the experimental values of the maximum band energy, Eopexp ) hυmax, obtained in the NaNO3 solutions and water-methanol mixtures, respectively. These tables also show the corrected values of these parameters, Eop (the values to be used in eqs 1 and 2), calculated as

Eop ) Eopexp - δ

The δ parameter in this equation represents a correction for the spin-orbit coupling of the iron(III) center in the vibronically excited state (the asterisk in eq 4 indicates this vibronically excited character):19 hυ

(NH3)5RuIII-NC-FeII(CN)5- 98 ((NH3)5RuII-NC-FeIII(CN)5-)* (4) This correction is necessary because in the octahedral symmetry, the d5T state of the metal is split by spinorbit coupling into a higher degenerate E state and a lower A state. The energy separation of these states being (3/ 2)δ, where δ is the spin-orbit coupling parameter. Because of the existence of two excited states, the experimental charge-transfer band is the sum of two bands, corresponding to transitions from the ground state to the E and A states. These bands are at δ/2 (higher) and δ (lower) energies, respectively, than the maximum absorption observed in the composite (experimental) band, so that the transition to the lower excited state corresponds to the value of Eop as given by eq 3. A value of 450 cm-1 ) 5.4 kJ mol-1 for δ was used in this work.19b In this way Eop and ∆G°′ correspond to the same process (see below). Electron-Transfer Free Energy Changes. The standard formal redox potentials of both ruthenium and iron centers are given in Tables 1 and 2 for NaNO3 solutions and water-methanol mixtures, respectively. From these data, the values of free energy changes corresponding to the forward thermal electron-transfer process

(NH3)5RuIII-NC-FeII(CN)5- f (NH3)5RyII-NC-FeIII(CN)5- (5)

(3)

(17) van Os, N. M.; Haak, J. R.; Rupert, L. A. M. Physico-Chemical Properties of Selected Anionic, Cationic and Nonionic Surfactans; Elsevier: Amsterdam, 1993. (18) Rolda´n, E.; Domı´nguez, M.; Go´nzalez-Argona, D. Comput. Chem. 1986, 10, 187.

were calculated as (19) (a) Curtis, J. C.; Meyer T. J. Inorg. Chem. 1982, 21, 1562. (b) Brunschwig, B. S.; Ehrenson, S.; Sutin, N. J. Phys. Chem. 1986, 90, 3657.

Study of Metal-to-Metal Charge Transfer

∆G°′ ) -nF∆E°′

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(6)

with n ) 1 and ∆E°′ ) E°′(Ru) - E°′(Fe), where Ru represents the ruthenium ammine center and Fe is the iron cyanide center. The values of ∆G°′ thus obtained are also collected in Tables 1 and 2. According to the uncertainty in redox potentials, these values should have an uncertainty of about 0.5 kJ mol-1. However, it is important to realize that the redox potentials obtained for the ruthenium ammine center correspond to the process e-

} (NH3)5RuIII-NC-FeII(CN)5- {\ -e II

(NH3)5Ru -NC-FeII(CN)52- (7) and those for the ironcyanide center to -e-

} (NH3)5RuIII-NC-FeII(CN)5- {\ e

(NH3)5RuIII-NC-FeIII(CN)50 (8) Therefore, the determination of ∆G°′ by the preceding method involves implicitly the following assumption: the redox potential of each center is not affected by the oxidation state of the other. In fact, strictly speaking, the values of ∆G°′ obtained from eq 6 correspond rather to the comproportionation reaction

(NH3)5RuII-NC-FeII(CN)52- + (NH3)5RuIII-NCFeIII(CN)50 f 2(NH3)5RuII-NC-FeIII(CN)5- (9) than to the electron-transfer process in eq 5. However, it has been stated that the differences in the free energies corresponding to processes 5 and 9 depend on the donor number of the solvent.20 Such a difference is minimum when the solvent’s donor number is about 15. In view of the donor number of water, which is 14,21 the differences in free energies of processes 5 and 9, in the present case (water-rich solutions), should be small. Additional information on the question we are discussing can be obtained from Table 3. In this table, the redox potentials of the iron center in complexes of type (NH3)5M-pz-Fe(CN)5n- (pz ) pyrazine) are collected. As can be seen these redox potentials are close, with small differences caused, at least in part, by the different experimental conditions in which these potentials were obtained. Moreover, an idea of the uncertainty of ∆G°′ collected in Tables 1 and 2 can be obtained by comparing the value of the reorganization free energy, λ, corresponding to water (in fact, in NaNO3 0.2 mol dm-3, Table 1) with the value of this parameter obtained by Walker et al. (53.6 kJ mol-1).8a The difference, 1.9 kJ mol-1, could be considered the maximum value for the uncertainty of ∆G°′ values. However, taking into account the data in Table 3, it seems safer to put this uncertainty in about 3 kJ mol-1. It is important to realize that, even assuming 3 kJ mol-1 as the uncertainty in the electron-transfer free energy caused by the coupling between the metallic centers, if this coupling is a constant (as shown by the fact that the absorption coefficient of the band is a constant), this uncertainty would imply a constant shift in the values of ∆G°′ (and λ) of this magnitude (3 kJ mol-1). However, the trends in these parameters caused by changing the media would be correct. As to the values of ∆Gq this uncertainty would (20) Neyhart, G. A.; Timpson, C. J.; Bates, W. D.; Meyer, T. J. J. Am. Chem. Soc. 1996, 118, 3736. (21) Gutmann V., The Donor-Acceptor Aproach to Molecular Interactions; Plenum Press: New York, 1978; p 20.

Table 3. Redox Potentials vs NHE, E°′ (Ru ) Ruthenium Ammine Center and Fe ) Iron Cyanide Center), for Binuclear Complexes, (NC)5FeII-pz-MIII(NH3)5 at 298.2 K species

E°′(Fe)/V

E°′(Ru)/V

(NC)5FeII-pz-RuIII(NH3)5 (NC)5FeII-pz-RuII(NH3)5(NC)5FeII-pz-RhIII(NH3)5

0.720a 0.750b 0.713c 0.720a 0.737b

0.490a 0.530a

(NC)5FeII-pz-RhIII(NH3)5

a Values taken from: Yeh, A.; Haim, A. J. Am. Chem. Soc. 1985, 107, 369. b Values obtained in this lab. c Taken from: Moore, K. J.; Lee, L.; Mabbott, C. A.; Petersen, J. P. Inorg. Chem. 1983, 22, 1108.

correspond to a constant shift of about 4 kJ mol-1. Notice that these uncertainties are independent of those arising from experimental errors. It should also be pointed out that the procedure used in this paper for obtaining ∆G°′ has also been utilized and discussed recently by Lin et al.2c Reorganization Free Energies. The reorganization free energies for the electron-transfer process 5 in the different media are given in Tables 1 and 2. These values were obtained by using eq 2. It is worth pointing out that there has been some controversy over this equation, because it is written in terms of energy (Eop) and free energy (∆G°′ and λ). For this reason it has been pointed out that in eq 2 instead of λ and ∆G°′ the corresponding energetic magnitudes should appear. Nevertheless, Marcus and Sutin22 have convincingly argued that parameters λ and ∆G°′, appearing in eq 2, are better viewed as free energies. In this regard, Hupp et al.23 have noted that λ depends on the optical and static dielectric constants of the medium and ∆G°′ mainly on the static dielectric constant. As the temperature coefficients of these dielectric parameters are small, the entropic terms in λ and ∆G°′ must also be small and they, indeed, compensate to some extent. When λ is obtained from optical methods, as in the present work, an entropic term could exist derived from a change in the spin multiplicity of the ground and excited states (the nuclear contribution should be small because the positions of the nucleus are frozen in an optical transition). The corresponding electronic entropy change should be24

∆S ) R ln

Ωexc Ωg

(10)

where Ωexc and Ωg are the spin multiplicity of the excited and ground states. Thus, the corresponding free energy term should be, if any, of the order of RT, which is small in comparison with Eop and λ values. Comming back to Table 1, one can see that in the case of salt solutions there is an increase in λ corresponding to the ionic cloud effect25 and/or the ion pairing effect.26 On the order hand, the values of λ for water-methanol solutions decrease as the methanol content in the mixtures increases. This result is the expected one, taking into account the decrease of the Pekar factor in the mixtures. Thus, one can conclude that λ values are, at least, in qualitative agreement with the expectations of current theories. Unfortunately, it is difficult to go further because the electrolyte effects are difficult to quantify in concen(22) (a) Marcus, R. A.; Sutin, N. Commun. Inorg. Chem. 1986, 5, 119. (b) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. (23) Dong, Y.; Hupp, J. T. Inorg. Chem. 1992, 31, 332. (24) Marcus, R. A. J. Chem. Phys. 1956, 24, 966. (25) Marcus, R. A. J. Chem. Phys. 1965, 43, 679. (26) See for example: Nelsen, S. F.; Ismagilov, R. F. J. Phys. Chem. A 1999, 103, 5378 and references therein.

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trated solutions. On the other hand, solvent effects in mixtures with components which can participate in hydrgen bonding are also difficult to quantify.27 Activation free energies. Data in this section are the main results of this part of the work, since, as mentioned in the Introduction, one of the purposes of this work is to show the possibility of obtaining activation free energies for electron-transfer processes from independent-of-kinetic data. Thus, we have calculated the activation free energies for reaction 5 using eq 1 and the values of Eop and ∆G°′ given in Tables 1 and 2. The ∆Gq values are also shown in Tables 1 and 2. In using this equation we have not taken into account the electronic coupling between the reactants, Hab. In fact, a comparison between the values of ∆G°′ and those of λ shows that ∆G°′ exceeds λ. When this happens the reaction is at the inverted region.28,29 In such a region, the electron-transfer process is inherently nonadiabatic.30 To check the quality of the data in these tables, we had some difficulties. For example, for the forward (thermal) electron transfer there are no data and they cannot be obtained. For this reason we have checked the activation free energies for this process by an indirect procedure. This consists of comparing the variations of this parameter with the measured variations of the activation free energies for the process

Figure 1. Plot of ∆Gq for the process (NH3)5RuIII(µ-NC)FeII(CN)5- f (NH3)5RuII(µ-NC)FeIII(CN)5- versus ∆Gq for the reaction (NH3)4CoIII(µ-pzCO2)FeII(CN)5- f (NH3)4CoII(µ-pzCO2)FeIII(CN)5- in methanol-water mixtures at 298.2 K.

(NH3)4CoIII(µ-pzCO2)FeII(CN)5- f (NH3)4CoII(µ-pzCO2)FeIII(CN)5- (11) which are available.31,32 The latter binuclear complex is quite similar to the binuclear complex considered in this work: thus, both have the same charge (-1) and the peripheries of the two metallic centers are similar (in fact, identical in the case of the iron center). As the sizes of both binuclear complexes are also similar, it seems reasonable to suppose that their interactions with the solvent will be almost the same. Consequently, if the calculations of the activation free energies are correct, changes in this parameter for processes 5 and 11 should be linearly related, with the slope close to unity. Figures 1 and 2 represent plots of the activation free energies for these processes. It can be seen that, in fact, they are linearly correlated and with slopes close to unity. This result seems to support our procedure. On the other hand, for the reverse electron-transfer process II

III

-

(NH3)5Ru NC-Fe (CN)5 f (NH3)4RuIII-NC-FeII(CN)5- (12) the activation free energy can be obtained by using

∆Grq )

(λ + ∆Gr°′)2 4λ

(13)

and assuming that the reorganization free energy, λ, for both forward and reverse processes have the same value. In fact, it follows from Marcus’ assumption that the free (27) For a quantitative discussion of this subject, see ref 1f. (28) Marcus, R. A. J. Phys. Chem. 1989, 93, 3078. (29) Chem, P.; Meyer, T. J. Chem. Rev. 1998, 98, 1430. (30) Zuckerman, J. J. In Inorganic Ractions and Methods. 1986; VCH Publishers: Deerfield Beach, FL, 1986; Vol. 15; p 40. (31) Gala´n, M.; Domı´nguez, M.; Andreu, R.; Moya´, M. L.; Sa´nchez, F.; Burgess, J. J. Chem. Soc., Faraday Trans. 1990, 86, 937. (32) Moya´, M. L.; Sa´nchez, F.; Burgess, J. Int. J. Chem. Kinet. 1993, 25, 899.

Figure 2. Plot of ∆Gq for the process (NH3)5RuIII(µ-NC)FeII(CN)5- f (NH3)5RuII(µ-NC)FeIII(CN)5- versus ∆Gq for the reaction (NH3)4CoIII(µ-pzCO2)FeII(CN)5- f (NH3)4CoII(µ-pzCO2)FeIII(CN)5- in sodium nitrate solutions at 298.2 K.

energy curves of the reactant and product states are parabolas of the same curvature.4 Values of the ∆Grq for reaction 12 are also included in Tables 1 and 2. From these tables it follows that reaction 12 is practically barrierless due to a compensation effect betwen λ and ∆Gr°′ (see Figure 3). To check the values of activation free energy for reaction 12, we have estimated the value of ket for this process. According to the model of Jortner and Bixon,33 by employing up to the second-order power of the electronic coupling, the preexponential factor of ket gives a value of 4.8 × 1012 s-1. Thus, the value of ket obtained was 3.2 × 1012 s-1 for 0.2 mol dm-3 NaNO3, in close agreement with that obtained in water by Walker et al,8a by using transient pump-probe measurements (1012-1013 s-1). (33) Jortner, J.; Bixon, M. J. Chem. Phys. 1988, 88, 167.

Study of Metal-to-Metal Charge Transfer

Langmuir, Vol. 17, No. 4, 2001 985 Table 4. Energiesa Corresponding to the Maximum of the Absorption Spectra of the MMCT Band, Eop, Redox Potentials, E° ′ (Ru ) rutheniumammine center and Fe ) ironcyanide center), Free Energy Change, ∆G° ′ and Reorganization Free Energy, λ for the Electron Transfer Process within the Binuclear Complex (NH3)5RuIII-NC-FeII(CN)5- at 298.2 K in SDS Micellar Solutions [SDS]b

Eopexp c

Eop d

E°′(Ru)e

E°′(Fe)e

∆G°′

λ

0.010 0.050 0.10 0.20 0.25 0.30

122.3 123.8 124.1 127.0 127.4 128.0

116.9 118.4 118.7 121.7 122.0 122.6

-0.029 -0.049 -0.055 -0.070 -0.076 -0.082

0.644 0.625 0.620 0.619 0.616 0.612

64.9 65.1 65.2 66.4 66.7 67.0

52.0 53.4 53.5 55.3 55.3 55.6

a All energies in kJ mol-1. b Surfactant concentration in mol dm-3. Experimental values. d Corrected values following eq 3 (see text). e Redox potentials in V vs NHE. c

Figure 3. Free energy surfaces (FSE) for the reactant and product states in the Marcus inverted region showing the characteristic magnitudes for the optical (vertical transition) and thermal (movement of representative point along the reaction coordinate) electron transfer.

The above results support the idea that it is possible to obtain the activation free energies (or at least a reasonable estimation of their variations) as well as electron-transfer rate constants from independent-of-kinetic data. This possibility is interesting for reasons indicated in the introductory section. Indeed, it permits us to obtain, independently, variations of λ and ∆G°′. This possibility is also of interest in order to gain a deeper insight into causes of the changes in reactivity when the reaction medium is changed. Thus, from data of the tables it is possible to conclude that variations of the activation free energy for the forward electron-transfer process in methanol-water mixtures are fundamentally thermodynamic in character, as ∆G°′ in these mixtures changes in about 5 kJ mol-1 and λ in about 0.5 kJ mol-1. On the other hand, in salt solutions the variations of ∆G°′ and λ are similar (about 3 kJ mol-1), in such a way that the variations of reactivity in these solutions are equally due to changes in the thermodynamic and the reorganization energetics of the process. (b) Micellar Solutions. Once the suitability of our approach has been tested, we will consider the data corresponding to micellar solutions. These are Eopexp, Eop, redox potentials, reaction free energies, and reorganization free energies (Tables 4 and 5). Electron-Transfer Free Energy Changes. As to the ∆G°′ values, Tables 4 and 5 show that these values in the presence of the cationic surfactant demonstrate an opposite trend to that corresponding to anionic surfactant solutions. According to these values, the thermal reaction (eq 5) becomes more favorable from a thermodynamic point of view in CTACl solutions while this electron-transfer process is more unfavorable in SDS solutions when the concentration of both surfactants increases. This behavior, obviously, is a consequence of the variations of redox potentials with the surfactant concentration shown also in Tables 4 and 5. In micellar (SDS) solutions, the performance of the standard formal redox potential, E°′ for both centers is the expected one, considering the charges at each center: the rutheniumammine (cationic) center becomes a less potent oxidant when the SDS concentration increases. This is in agree-

Table 5. Energiesa Corresponding to the Maximum of the Absorption Spectra of the MMCT Band, Eop, Redox Potentials, E°′ (Ru ) Ruthenium Ammine Center and Fe ) Iron Cyanide Center), Free Energy Change, ∆G°′, and Reorganization Free Energy, λ, for the Electron Transfer Process within the Binuclear Complex (NH3)5RuIII-NC-FeII(CN)5- at 298.2 K in CTACl Micellar Solutions [CTACl]b

Eopexp c

Eopd

E°′(Ru)e

E°′(Fe)e

∆G°′

λ

0.004 0.005 0.007 0.010 0.050 0.10 0.20 0.25 0.30

118.1 118.0 117.8 117.4 117.4 117.5 117.1 117.3 117.0

112.7 112.6 112.5 112.0 112.1 111.7 111.8 111.6 111.4

-0.032 -0.029 -0.025 -0.019 -0.017 -0.026 -0.007 -0.024 -0.003

0.656 0.660 0.652 0.651 0.636 0.616 0.618 0.604 0.615

66.4 66.5 65.3 64.7 63.0 61.9 60.4 60.7 59.6

46.3 46.1 47.1 47.3 49.0 50.2 51.3 51.1 52.0

a All energies in kJ mol-1. b Surfactant concentration in mol dm-3. Experimental values. d Corrected values following eq 3 (see text). e Redox potentials in V vs NHE. c

ment with expectations, taking into account that the formal potentials are given by34

E°′ ) E° +

fox RT ln F fred

(14)

where E° is the standard redox potential and fox and fred are the activity coefficients of the oxidized (ox) and reduced (red) species of the redox couple. In the presence of a negatively charged micelle both fox and fred must decrease (fred corresponds to the reduced form of ruthenium(III) ammine center; that is, to a ruthenium(II) ammine species), but the decrease in fox will be greater than that corresponding to fred owing to the higher charge of the oxidized form of the couple. So a decrease of E°′ results. As to the iron cyanide center of the binuclear complex, which has an anionic character, the reduced form will have a higher negative charge. Therefore, this form will be more destabilized by the interaction with the field of the negatively charged micelles, and consequently, a decrease of E°′ is also found for this center in the presence of anionic micelles. (34) Equation 14 follows from the Nernst expression, when this equation is written using concentrations instead of activities:

E ) E° +

(

)

aox fox [ox] RT RT ln ) E° + ln + ln ) nF ared nF fred [red] E°′ +

[ox] RT ln nF [red]

986

Langmuir, Vol. 17, No. 4, 2001

The more favorable thermodynamic character of the reaction in CTACl solutions arises from the fact that the ruthenium ammine center becomes a more potent oxidant and the iron cyanide center a more potent reductant in these solutions (see Table 5). The variations in the redox potential of the oxidant center are the expected ones on the basis of the electrostatic interaction of this center with the field of the positively charged micelles. However, the iron cyanide center at the binuclear complex bears a negative charge, which is greater in the reduced form than in the oxidized form of this couple. Thus, fred should be expected to decrease more than fox for this center, as a consequence of the interaction with the electric field arising from a positively charged micelle. This would produce, according to eq 14, an increase in E°′, which is opposite to the observed decrease. However, the behavior of E°′ for the iron cyanide center observed in this work has been observed previously: the redox potentials of the couples of opposite sign charge to the charge in the micelles can vary in the opposite sense expected under electrostatic grounds only.35,36 Indeed, in CTACl solutions a decrease in the redox potentials of the Fe(CN)63-/4-couple was found, in agreement with data in Table 5 (E°′ ) 0.406 V for [CTACl] ) 0.01 mol dm-3 and E°′ ) 0.393 V for [CTACl] ) 0.2 mol dm-3).37 These results can be explained by considering that the centers of opposite charge sign to the micellar charge are placed at the Stern layer of the micelles.36 In this layer, the strong micellar field causes a strong decrease of the local dielectric constant, as a consequence of the dielectric saturation effects. This decrease in the local dielectric constant will produce an increase of both fox and fred in eq 14, but more marked in fred since this corresponds to a species with a higher charge (absolute value). These results are schematically shown in Figure 4. So the decrease in the redox potential of the reductant is due not so much to the direct effect of the field on this center as to the effect of the field on the solvent, which produces a dielectrically more saturated state of the medium (solvent). Notice that the positively charged center must be, according to the changes in the redox potential of this center, outside of the Stern layer. Thus, the binuclear complex must be at the limit of the Stern layer and oriented perpendicularly to the surface of the micelles. Reorganization Free Energies. The values of the reorganization free energies, λ, in micellar solutions are also given in Tables 4 and 5. A comparison between the values of λ for the same range of the surfactant concentrations, 1.0 × 10-2 to 3.0 × 10-1 mol dm-3, reflects a rise in the reorganization free energy for both surfactants (3.6 and 4.9 kJ mol-1 for SDS and CTACl solutions, respectively). This fact suggests that the same effect can be the cause of such an increase in λ (but not of their values, see Tables 4 and 5). This effect is that corresponding, in the case of micellar solutions, to the ionic cloud effect on electron-transfer reactions when electrolytes are present in the medium: an additional contribution to the reorganization free energy appears, owing to the reorganization of ion positions,24 as is observed in the case of NaNO3 solutions (see Table 1). However, this ionic cloud effect is bigger in surfactant solutions as a consequence of the strong micellar electric field, which strongly couples the reactants to micelles. (35) Ohsawa, Y.; Shimazaki, Y.; Aoyagui, S. J. Electroanal. Chem. 1980, 114, 235. (36) Davies, K. M.; Hussam, A.; Rector, B. R., Jr.; Owen, I. M.; King, P. Inorg. Chem. 1994, 33, 1741. (37) Sa´nchez, F.; Lo´pez-Lo´pez, M.; Pe´rez-Tejeda, P. Langmuir 1998, 14, 3672.

Neto-Ponce et al.

Figure 4. Scheme of the influences of different effects of the micellar electric field on the chemical potential levels corresponding to the reduced (Red) and oxidized (Ox) species of the iron center at the binuclear complex (NH3)5RuIII(µ-NC)FeII(CN)5-.

It is noteworthy that the values of λ for CTACl solutions are smaller in about 4 kJ mol-1 than those for SDS solutions. This result can be explained by considering the different dielectric properties of the headgroup shell region and the surrounding water of the micellar system and assumig that the binuclear complex will be preferentially placed at the limit of the Stern layer in CTACl micelles and outside this region in SDS micelles, according to the arguments presented when the reaction free energies were discussed. Thus, following the Marcus treatment,4 the solvent reorganization energy is given by

(

λsolv ) NAe2

)

1 1 1 + - γ 2a1 2a2 R

γ ) Dop-1 - Ds-1

(15) (16)

where Dop and Ds are the optical and the static bulk dielectric constants of the medium, respectively, a1 and a2 are the acceptor and donor radii, and R is the donoracceptor distance. As the geometric factor (1/2a1 + 1/2a2 - 1/R) can be considered to be a constant, independent of the reaction medium, the difference observed between the values of the reorganization free energy in CTACl and SDS solutions will depend basically on the different values of the dielectric characteristics in the reaction medium surrounding the binuclear complex: the Stern layer in the first case and the aqueous phase (or the GouyChapman region) in the case of anionic micelles. The dielectric properties of the headgroup region (Stern layer) are expected to be intermediate between that corresponding to water and those corresponding to the micellar hydrocarbon core, taking into account that a micellar system can be modeled by three concentric spheres according to Tavernier et al.38 These authors have estimated the values of the static, Ds, and optical, Dop, (38) Tavernier, H. L.; Barykin, A. V.; Tachiya, M.; Fayer, M. D. J. Phys. Chem. B 1998, 10, 6078.

Study of Metal-to-Metal Charge Transfer

dielectric constants for the surface shell of the CTABr (hexadecyltrimethylammonium bromide) micelles, their values being 4 and 1.88 for Ds and Dop, respectively.38 These values originate a great decrease in the Pekar factor, γ, in the micellar surface (0.28) in relation to the value of this parameter for the surronding water (0.55). Since the headgroup region is similar in CTABr and CTACl micellar systems, a similar decrease of the Pekar factor can be expected in the case of the CTACl surface. Therefore, due to the fact that the binuclear complex will place preferentially at the Stern layer of the CTACl micelles and outside this layer in SDS micelles, it seems reasonable to consider that the origin of the smaller value in the reorganization energy for cationic surfactant as compared to anionic surfactant (and salt) solutions is a consequence of the decrease of Pekar factor in the micellar surface of CTACl in relation to those in aqueous bulk. Once again, the dielectric saturation effect of the solvent, induced by the micellar electric field of the cationic surfactant, originates the decrease observed in the reorganization energy for CTACl solutions in relation to this parameter for SDS or NaNO3 solutions. Thus, the dielectric saturation effect implies a more favorable free energy change as well as a lower reorganization free energy. Conclusions We have presented here an approach for obtaining the main factors controlling the activation free energy of the electron-transfer reactions in different media constituted by electrolyte, water-cosolvent, and micellar solutions. It has been shown that despite the uncertainties derived from the influence of the coupling between the metallic centers on the reaction free energies, as these influences are constant in the different reaction media, it is possible to obtain, at least, the trends in the parameters controlling the activation free energy (λ, ∆G°′) in these media. Thus, it has been possible to know that variations in the reactivity in water-methanol mixtures are mainly caused by the thermodynamics of the process. In the case of salt solutions, both the reaction free energy and the reorganization free energy influence the kinetics, decreasing the rate of reaction. In SDS micellar solutions, in which it is expected that, on the average, the negatively charged binuclear complex is far from the micelles, a similar

Langmuir, Vol. 17, No. 4, 2001 987

behavior to that observed in salt solutions is found. Finally, in the case of CTACl solutions there is a decrease of the reaction free energy and an increase in the reorganization free energy, when the concentration of the surfactant increases. Both effects would produce an important decrease in the activation free energy in these media. On the order hand, the results in CTACl micellar solutions reveal that the ruling effect is that derived from the dielectric saturation of the solvent caused by the micellar electric field, while for anionic micelles the long-range (Coulombic) interactions are those that prevail between the binuclear complex and the micelles. List of Symbols Eopexp ) experimental energy of the metal-to-metal charge transfer (MMCT) band υmax ) frequency corresponding to the maximum of the experimental MMCT band Eop ) Eopexp - δ δ ) correction for spin-orbit coupling of the iron(III) center in the vibronically excited state produced in the optical transition λ ) reorganization free energy ∆G°′ ) reaction free energy ∆Gq ) activation free energy ∈max ) molar absorption coefficient at the maximum of the experimental band Ds ) static dielectric constant of the medium λmax ) wavelength corresponding to the maximum of the experimental band ∆υ1/2 ) full width at half-height of the band E°′ ) standard formal redox potential of the a given redox couple Ω ) spin multiplicity of a given electronic state ket ) rate constant for the thermal electron transfer f ) activity coefficient of a given species in a given medium γ ) Pekar’s factor Dop ) optical dielectric constant ()n2) n ) refractive index of a given medium

Acknowledgment. This work was financed by D.G.C.Y.T. (PB-98-04233), the Consejerı´a de Educacio´n y Ciencia de la Junta de Andalucı´a and the University of Sevillla by finantial support from the Plan Propio. LA000215M