Nonideal Electrochemical Behavior of Biomimetic Iron Porphyrins

Tobias, H.; Soffer, A. J. Electroanal. Chem. 1983, 148, 221−232. .... Katherine E. Moore , Benjamin S. Flavel , Jingxian Yu , Andrew D. Abell , Jose...
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Anal. Chem. 2003, 75, 494-502

Nonideal Electrochemical Behavior of Biomimetic Iron Porphyrins: Interfacial Potential Distribution across Multilayer Films Irina M. Shiryaeva, James P. Collman,* Roman Boulatov, and Christopher J. Sunderland

Department of Chemistry, Stanford University, Stanford, California 94305

The electrochemical behavior of multilayer films formed by iron porphyrins deposited on an edge plane graphite electrode has been examined under anaerobic conditions. In the scan rate interval (1-250 mV/s) where the electrode reaction is reversible, CV diagrams of these films demonstrate substantial deviations from ideality in broadening and separation of the peaks. A model that describes the observed behavior is proposed by taking into account the potential distribution at the electrode/film interface and the concentration dependence of surface activity coefficients. The peak separation is described in terms of the electric double layer that affects the potential difference driving the electrode reaction. The effective potential difference deviates from the applied value due to the potential distribution across the film. The interfacial potential distribution depends on the ionic concentration inside the film. When different ionic concentrations are assumed for oxidation and reduction, different shifts from the applied potential lead to a hysteresis of the peaks. The peak broadening is modeled by using the lattice theory expression for the surface activity coefficients. The model shows that the midpoint potentials of the redox centers depend on the ionic concentration inside the film. At low ionic concentrations, they are remarkably close to the midpoints of the cytochrome c oxidase heme a3/CuB site. Modified electrodes find extensive application in studying heterogeneous electrocatalysis,1-10 redox proteins,11-18 biological * Corresponding author. E-mail: [email protected]. (1) Murray, R. W. Molecular Design of Electrode Surfaces; Wiley: New York, 1992. (2) Kadish, K. M.; Smith, K. M.; Guilard, R. The Porphyrin Handbook; Academic Press: San Diego, Vol. 11, in press. (3) Bard, A. J.; Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications, 2nd ed.; Wiley: New York, 2001. (4) Andrieux, C. P.; Saveant, J. M. J. Electroanal. Chem. 1982, 142, 1-30. (5) Andrieux, C. P.; Saveant, J. M. J. Electroanal. Chem. 1982, 134, 163-166. (6) Andrieux, C. P.; Dumas-Bouchiat, J. M.; Saveant, J. M. J. Electroanal. Chem. 1982, 131, 1-35. (7) Anson, F. C.; Shi, C.; Steiger, B. Acc. Chem. Res. 1997, 30, 437-444. (8) Collman, J. P.; Hendricks, N. H.; Leidner, C. R.; Ngameni, E.; L’Her, M. Inorg. Chem. 1988, 27, 387-393. (9) Collman, J. P.; Fu, L.; Herrmann, P. C.; Zhang, X. Science 1997, 275, 949951. (10) Boulatov, R.; Collman, J. P.; Shiryaeva, I. M.; Sunderland, C. J. J. Am. Chem. Soc. 2002, 124, 11923-11935. (11) Haas, A. S.; Pilloud, D. L.; Reddy, K. S.; Babcock, G. T.; Moser, C. C.; Blasie, J. K.; Dutton, P. L. J. Phys. Chem. B 2001, 105, 11351-11362.

494 Analytical Chemistry, Vol. 75, No. 3, February 1, 2003

electron transfer,19-26 fuel cell technology,27,28 etc. Electrodes modified with multilayer films can be particularly efficient in catalyzing redox reactions.1,4-6 Numerous iron and cobalt porphyrins deposited on the electrode surface have been used extensively in the biomimetic studies of oxygen reduction catalyzed by cytochrome c oxidase (CcO).2,7-10 Artificial structural analogues of the heme a3/CuB site have been recently characterized29 and found to operate as functional models of the enzyme, catalyzing 4-electron reduction of oxygen to water at physiological potentials and pH.10 Deposited on the electrode surface, they demonstrate nonideal electrochemical behavior. Wave broadening and scan rate-independent peak separation (i.e., hysteresis) appear in their CV diagrams. A redox film undergoing a reversible electrode reaction obeys the Nernst equation.3,30 When surface activity coefficients of reduced and oxidized species are independent of their concentration (i.e., the film behaves as an ideal system), CV diagrams have the following characteristics: (i) symmetric waves of 90.6/n mV width; (ii) scan rate-independent peak potentials corresponding to the standard potential, with zero separation of the anodic and cathodic peaks; and (iii) direct proportionality of the peak current (12) Bourdillon, C.; Demaille, C.; Moiroux, J.; Saveant, J.-M. J. Phys. Chem. B 1999, 103, 8532-8537. (13) Bartlett, P. N.; Birkin, P. R.; Wang, J. H.; Palmisano, F.; De Benedetto, G. Anal. Chem. 1998, 70, 3685-3694. (14) Hirst, J.; Armstrong, F. A. Anal. Chem. 1998, 70, 5062-5071. (15) Vreeke, M. S.; Yong, K. T.; Heller, A. Anal. Chem. 1995, 67, 4247-4249. (16) Chen, Q.; Kenausis, G. L.; Heller, A. J. Am. Chem. Soc. 1998, 120, 45824585. (17) Scott, D. L.; Bowden, E. F. Anal. Chem. 1994, 66, 1217-1223. (18) Bourdillon, C.; Demaille, C.; Gueris, J.; Moiroux, J.; Saveant, J. M. J. Am. Chem. Soc. 1993, 115, 12264-12269. (19) Murgida, D. H.; Hildebrandt, P. J. Phys. Chem. B 2001, 105, 1578-1586. (20) Fedurco, M. Coord. Chem. Rev. 2000, 209, 263-331. (21) Avila, A.; Gregory, B. W.; Niki, K.; Cotton, T. M. J. Phys. Chem. B 2000, 104, 2759-2766. (22) Lecomte, S.; Hildebrandt, P.; Soulimane, T. J. Phys. Chem. B 1999, 103, 10053-10064. (23) Anicet, N.; Bourdillon, C.; Moiroux, J.; Saveant, J.-M. J. Phys. Chem. B 1998, 102, 9844-9849. (24) Lecomte, S.; Wackerbarth, H.; Soulimane, T.; Buse, G.; Hildebrandt, P. J. Am. Chem. Soc. 1998, 120, 7381-7382. (25) Hu, N.; Rusling, J. F. Langmuir 1997, 13, 4119-4125. (26) Nassar, A.-E. F.; Zhang, Z.; Hu, N.; Rusling, J. F.; Kumosinski, T. F. J. Phys. Chem. B 1997, 101, 2224-2231. (27) Miller, D. O.; Rusek, J. J. Proceedings of the First International Conference on Green Propellants for Space Propulsion 2001, SP-484, 337-342. (28) Park, S.; Gorte, R. J.; Vohs, J. M. Appl. Catal., A 2000, 200, 55-61. (29) Collman, J. P.; Sunderland, C. J.; Boulatov, R. Inorg. Chem. 2002, 41, 22822291. (30) Murray, R. W. Electroanal. Chem. 1984, 13, 191-368. 10.1021/ac025918i CCC: $25.00

© 2003 American Chemical Society Published on Web 12/21/2002

to the total surface coverage.3,30 Experimental CV diagrams of surface-confined films frequently deviate from these predictions: waves become broader31-34 or narrower;33-36 and hysteresis of the peak potentials appears.33-35 Models that have been offered to describe this behavior take into account surface activity effects,33,35,37 inhomogeneity of the electroactive film,32,36 or interfacial potential distribution across the film.38 Incorporation of a concentration dependence of surface activity coefficients into the Nernst equation accounts for specific interactions between redox centers and allows description of broad and narrow peaks. The commonly used assumption that the film behaves as a strictly regular solution of oxidized and reduced species gives the following expression of the surface activity coefficients:39,40

ln γi ) r(1 - χi)2

(1)

where χi and γi are the mole fraction and the activity coefficient of reduced (or oxidized) species in the film, respectively, and r is the interaction coefficient41 that reflects the difference between the interaction energies of similar (Ox-Ox or Red-Red) and dissimilar (Ox-Red) species in the nearest-neighbor sites of the lattice. Positive interaction parameter corresponds to the film where pure forms (oxidized or reduced) are favored resulting in narrow voltammetric peaks. Negative interaction parameter implies that mixtures of oxidized and reduced species are energetically preferable over the pure forms leading to the peak broadening. Another group of models that also describe peak broadening takes into account details of the film microstructure such as formation of microdomains36 or surface inhomogeneity.32 Physical causes of the hysteresis of CV peaks are different swelling of the oxidized and reduced forms and changes in solvation or in the molecular conformations.30 A qualitative theory describing hysteresis in electroactive films is based on a concept of “N-shaped free energy curve”.36 Irreversible phase change occurring inside the film in the course of CV experiments was offered as an explanation of its hysteretic behavior. Hysteresis of narrow spikelike peaks was predicted in the framework of the lattice theory when an instability region appears in a film (at r g 4, eq 1).33-35 However, these approaches have not been used for quantitative description of experimental CV diagrams revealing hysteresis.33-36 Electrochemical behavior of electroactive species can be affected substantially by electrostatic phenomena at the electrode surface.3 The model of Smith and White38 ascribes the nonideal (31) Steiger, B.; Anson, F. C. Inorg. Chem. 1994, 33, 5767-5779. (32) Albery, W. J.; Boutelle, M. G.; Colby, P. J.; Hillman, A. R. J. Electroanal. Chem. 1982, 133, 135-145. (33) Laviron, E.; Roullier, L. J. Electroanal. Chem. 1980, 115, 65-74. (34) Laviron, E. J. Electroanal. Chem. 1981, 122, 37-44. (35) Sadkowski, A. J. Electroanal. Chem. 1986, 208, 69-76. (36) Feldberg, S. W.; Rubinstein, I. J. Electroanal. Chem. 1988, 240, 1-15. (37) Laviron, E. J. Electroanal. Chem. 1979, 105, 35-42. (38) Smith, C. P.; White, H. S. Anal. Chem. 1992, 64, 2398-2405. (39) Nikitas, P. J. Chem. Soc., Faraday Trans. 1 1985, 81, 1767-1787. (40) Prigogine, I.; Defay, R. Chemical thermodynamics; Longmans: London, 1969. (41) The Frumkin adsorption isotherm corresponds to this approach when the adsorbed electroactive species are present in the bulk solution. Laviron,37 who first incorporated the Frumkin isotherm into the Nernst equation, used the following terminology: “repulsive interactions” when r < 0 and “attractive interactions” when r > 0.

behavior of monolayers, such as distortion of voltammetric peaks, dependence of the peak potentials on the electrode coverage, and shift of the peak potentials from the standard value, to the electric double layer (EDL) at the electrode surface. These effects are significant when the entire interfacial potential drop is not localized within the distance between the electrode surface and the redox centers at the plane of electron transfer (PET). Thus, the effective potential difference driving the electrode reaction becomes lower than the applied one. The potential at the PET depends on the oxidation state of the redox centers, the molecular structure of the film, the electrolyte concentration, and the dielectric constant. Herein we propose a quantitative approach to describe the nonideal behavior of electroactive films that reveal a hysteresis of broad peaks. Our model takes into account the interfacial potential distribution inside the film and the concentration dependence of the surface activity coefficients. We apply the proposed model to describe experimental CV diagrams of biomimetic iron porphyrins. EXPERIMENTAL SECTION Apparatus. A BAS CV-50W potentiostat (Bioanalytical Systems) was used to record CV diagrams. All experiments were carried out in custom-made cells (100 mL) with a tightly fitting Teflon lid at ambient temperature 20.0 ( 0.2 °C. A low flow rate saturated calomel electrode (SCE), ESCE ) 0.241 V versus normal hydrogen electrode (NHE), and a Pt mesh were used as the reference and auxiliary electrodes, respectively. The working electrode was an edge-plane graphite (EPG) electrode from Pine Instruments, Inc. Reagents. The synthesis and characterization of the iron porphyrins (Figure 1b-d) were described elsewhere.29 All chemicals were of the highest purity commercially available. KPF6 was recrystallized at least twice from a basic solution (pH ) 10); the pH of ∼0.5 M solution of the recrystallized KPF6 was 6.9 ( 0.2 and this solution displayed a single 19F NMR peak. Procedures. The EPG disk (0.195 cm2) was cleaned with a 600-grit SiC paper and sonicated for 1 min in methanol immediately prior to depositing a film. A sample of a complex in the reduced form (0.1 µmol) was dissolved in methanol (200 µL) and oxidized in air. The solvent was removed and the solid redissolved in dimethoxyethane to give a solution of the complex with a desired concentration and then placed in a microvial. Samples were stored at -22 °C when not in use. The oxidized complexes are chemically stable in air for at least 1 month but were discarded after 5 days to prevent changes in the sample concentration through solvent evaporation. One microliter of the complex solution was syringed onto a cleaned, vertically positioned, rotating (300 rpm) electrode and allowed to evaporate for 2 min in air, followed by 2 min under a stream of N2. The prepared electrode was immediately immersed into a N2-saturated (for 1 h before use) solution containing supporting electrolyte and phosphate buffer (pH ) 7, KH2PO4-Na2HPO4, 0.07 M total concentration) where CV experiments were carried out. RESULTS AND DISCUSSION Presentation of the results is organized in the following order. In subsection I, we provide a description of measured CV diagrams followed by their qualitative interpretation. This explanation represents the main idea that is further developed quantitatively Analytical Chemistry, Vol. 75, No. 3, February 1, 2003

495

Figure 1. (a) Heme a3/CuB site of bovine cytochrome c oxidase:10 The C atoms are light gray, the N and O atoms are black, and the Fe and Cu atoms are dark gray. (b)-(d) General chemical structures of the complexes (for synthesis and spectroscopic characterization, see ref 29).

Figure 2. CV diagrams of the monometallic complexes: (1) Fe(NMe), (2) Fe(NH), and (3) Zn(NMe). Scan rate is 50 mV/s, and supporting electrolyte is 0.1 M KPF6.

in subsection II. The calculated results are compared with the experimental data in subsection III. I. Experimental Current-Potential Waves. Typical diagrams of the monometallic complexes, Fe(NMe) and Fe(NH), are depicted in Figure 2. The background current was obtained with a nonelectroactive complex Zn(NMe), which is structurally identical to Fe(NMe). Subsequent CV diagrams are shown with the background subtracted.42 496 Analytical Chemistry, Vol. 75, No. 3, February 1, 2003

The cathodic waves of CV diagrams for the bimetallic complex, Fe(NMe)Cu (Figure 1d), are shown in Figure 3. The single peak indicates that both metals in this complex have similar redox potentials (cathodic peak potential, 0.15 V vs NHE) close to the potential of iron in the monometallic analogue, Fe(NMe) (0.16 V vs NHE). The peak current drops off rapidly during the first several cycles that most likely corresponds to loss of copper from the bimetallic complex when in contact with an aqueous solution.10 Due to uncertainty in composition of the Fe(NMe)Cu films during CV experiments, further analysis is focused on the monometallic complexes. The CV diagrams show no diffusion tailing of the current (Figure 2). The peak potentials are independent of the scan rate over the interval 1-250 mV/s but shift in opposite directions at higher scan rates (Figure 4). This indicates that the electron (42) The estimation of the charging current by replacing a redox-active film with an electroinactive structural analogue has been shown to be inaccurate for monolayers.38 At low electrolyte concentrations in the bulk solution, a minimum of the charging current has been predicted near the peak potential, because the charge at the PET changes in the course of the electrode reaction. This effect is significant for chemically attached films in which redox-active centers are immobile. Our complexes are retained at the electrode surface by physical adsorption due to their limited solubility in water. Mobile electroinactive ions from the bulk solution penetrate into the film. Consequently, the EDL structure in our films resembles that in solutions rather than the EDL in monolayers. Moreover, the concentration of supporting electrolyte in our experiments was high: g0.1 M (see Table 1). Therefore, simple subtraction of the background current is appropriate in our case.

Figure 3. Decrease of the cathodic peak current for Fe(NMe)Cu in subsequent cycles. Scan rate is 50 mV/s, and supporting electrolyte is 0.1 M KPF6.

Figure 6. CV diagrams of the Fe(NMe) at different electrode coverages: 1-0.65, 2-0.4, and 3-0.15 nmol. Inset: dependence of the cathodic peak current on the electrode coverage. Scan rate is 50 mV/s, and supporting electrolyte is 0.1 M KPF6. Table 1. Influence of Supporting Electrolyte and Its Concentration in Solution on the Peak Potentials and Separation supporting electrolyte

Figure 4. Dependence of the peak potentials of Fe(NH) on the scan rate. Supporting electrolyte is 0.1 M KPF6.

Figure 5. Peak current of Fe(NH) as a function of the scan rate. Supporting electrolyte is 0.1 M KPF6.

transfer to the electroactive centers is reversible up to 250 mV/s and becomes quasireversible thereafter. In this reversible interval, the peak current is directly proportional to the scan rate (Figure 5) and to the surface coverage (Figure 6), as expected for a surface Nernstian electrode reaction. The proportionality of the peak current to the scan rate and the absence of diffusion tails indicate that electron transfer through these multilayer films is fast and is not limited by diffusion. Nonideal characteristics of the CV diagrams are wave broadening and hysteresis of the peak potentials. The wave width at the half-height is ∼200 mV (Figure 2). Because our complexes (Figure 1) are approximately spheres of a uniform size in both oxidized and reduced states, the film can be described as a strictly regular solution.39 In this approach, wave broadening corresponds to a negative value of the interaction parameter r (eq 1).

NaClO4 NaClO4 NaClO4 NaClO4 NaClO4 KNO3 KPF6 NEt4Cl NBu4Cl N(C6H5)Et3Cl

effective ionic radius,52 Å concn, M cation anion Ep,c, V Ep,a, V ∆Ep, V 0.1 0.25 0.5 1.0 0.1 0.1 0.1 0.1 0.1 0.1

4.0 4.0 4.0 4.0 4.0 3.0 3.0 6.0 10.0 8.0

3.5 3.5 3.5 3.5 3.5 3.0 2.5 3.0 3.0 3.0

0.18 0.17 0.15 0.14 0.07 0.06 0.03 0.10 0.16 0.14

0.27 0.26 0.24 0.23 0.17 0.17 0.13 0.21 0.28 0.25

0.09 0.09 0.09 0.09 0.10 0.11 0.10 0.11 0.12 0.11

redoxactive complex Fe(NMe) Fe(NMe) Fe(NMe) Fe(NMe) Fe(NH) Fe(NH) Fe(NH) Fe(NH) Fe(NH) Fe(NH)

The scan rate-independent hysteresis of the peaks (Figure 4) is not affected by the nature of the supporting electrolyte or by its concentration (Table 1). It does not disappear when the scan is reversed well before the completion of the electrode reaction (Figure 7). Our explanation of this hysteresis is based on the idea that the electric double layer is formed inside the film. Due to the interfacial potential distribution across the film, the applied electrode potential is modified by the potential at the PET. The latter potential depends on the ionic concentration within the film. We suggest that the ionic concentration within the film depends on its redox state. The oxidized film is likely to be hydrophilic because the electroactive centers are charged, whereas the reduced film is rather hydrophobic as electroactive centers are neutral. Therefore, the swelling and ionic concentrations in the oxidized and reduced films would be different. We assume two metastable states of the film that are reached at the end of the electrode reaction. These states are (1) the reduced film with the ionic concentration corresponding to the oxidized film (hydrophobic film with high ionic concentration) and (2) the oxidized film with the ionic concentration corresponding to the reduced film (hydrophilic film with low ionic concentration). When the potential is reversed, the film transfers from the metastable to its stable state; thus, according to our assumptions, the direct and reverse electrode reactions proceed at different ionic concentrations. For instance, the film would retain the ionic concentration of the oxidized form during the reduction process (Ox + e - f Red) and reach the metastable state in which the reduced film contains high ionic concentration. When the potential is reversed, Analytical Chemistry, Vol. 75, No. 3, February 1, 2003

497

Figure 8. EDL structure (a) and the potential distribution at different concentration of ions (b) inside the film.

Figure 7. CV diagrams of Fe(NMe) with a cycle reversal at different potentials. (a) Full cycle; (b) before the oxidation is completed; (c) before the reduction is completed; and (d) both reactions are uncompleted. The arrows show the direction of potential sweep, the scan rate is 50 mV/s, and supporting electrolyte is 0.1 M KPF6.

the metastable reduced film converts into its stable state with low ionic concentration. Therefore, we explain the observed hysteresis in terms of irreversible phase transition between the metastable and stable films with different ionic concentrations. Ions entering the film from the bulk solution influence the ionic concentration within the film. The distribution of ions between the solution and the film depends on the nature of the electrolyte, its concentration in the bulk solution, and the redox state of the film. Experimental data show that the reduction peak is more negative than the oxidation peak (Figure 2). According to our previous consideration, the reduction process occurs at high ionic concentration in the film, whereas the oxidation process corre498 Analytical Chemistry, Vol. 75, No. 3, February 1, 2003

sponds to low ionic concentration. Therefore, the lower the ionic concentration in the film, the more positive the peak potential becomes. The effect of the nature of the supporting electrolyte on the peak potentials is illustrated in Table 1. The positive shift correlates with the increase of effective radius of either cation or anion in the supporting electrolyte. Apparently due to size restrictions, large ions preferentially partition into the aqueous phase, and consequently, their concentration inside the film is lower compared with the concentration of small ions. The increase of the electrolyte concentration in the bulk solution leads to a negative shift of the peak potentials (Table 1). This observation suggests that the ionic concentration inside the film rises with the increase of the electrolyte concentration in the bulk solution. II. Model Description. We propose a model that takes into account the interfacial potential distribution to describe the CV diagrams of a surface-confined multilayer film. We consider a reversible electrode process that is not complicated by diffusion. This means that (i) the electrode reaction is described by the Nernst equation, (ii) transport of nonelectroactive ions and solvent molecules are not rate-limiting, and (iii) electron propagation through the film is fast, so that at any time the concentrations of the reduced and oxidized species obey the Nernst equation throughout the film. We assume that the dielectric constant of the film is identical regardless of the film’s redox state (see below). We describe the film as an unstructured phase with a large concentration of redox-active centers (Figure 8a) that have a Poisson distribution. This assumption enables us to describe the EDL inside the film within the framework of the classical theory developed for solutions.3 We use this simplification as a first approximation to illustrate our explanation of the hysteresis of the peak potentials in the simplest quantitative way. The potential distribution across the film is shown in Figure 8b. The PET corresponds to the plane of the redox centers at the

The potential profile through the interface can be expressed in terms of the electric field. The magnitude of the electric field (|E B| ) -{dΨ}/{dx}) in each region shown in Figure 8a is given by

Table 2. Characteristics of the Film and the EPG Electrode Used in Calculations quantity

value

EPG Electrode geometric area (A) roughness factor3 (g) microscopic area (Am) zero charge potential46 (EPZC)

0.195 cm2 3 0.585 cm2 411 mV vs NHE 170 mV vs SCE

Film constant43

dielectric () molecular surface area8 (a) complex radius (x1) amount of the complex in one layer (ΓM) concentration of the complex in the film (C)

scan rate (v) amt of complex in the film (ΓA) number of layers (N) thickness of the film (δ) ionic concn in the oxidized film (COx) ionic concn in the reduced film (CRed) interaction coeff in the oxidized film (rOx) interaction coeff in the reduced film (rRed)

40 250 Å2 8.9 Å 0.039 nmol 0.37 M

[

xδ

(3)

Applying the condition of the continuity of the electric field at point x1 (valid when the dielectric constant does not change through the boundary), we obtain from eq 3

Figure 9a (FeNH)

Figure 9b (FeNMe)

50 mV/s 0.50 nmol 12.9 230 Å 1M 0.0065 M -2.5 -2.8

50 mV/s 0.41 nmol 10.6 189 Å 1M 0.008 M -2.8 -3.6

closest approach to the electrode surface and is determined by their molecular radii. The potential decays linearly from Ψel to Ψ1 in this region. In the diffuse layer inside the film, the potential distribution is described by the Gouy-Chapman model.3 We assume that the entire potential drop occurs inside the film. This assumption is supported by the following factors. The thickness of the film is estimated at 200 Å (Table 2). According to the literature data, in aqueous solutions, the thickness of the diffuse layer extends to 96.2 Å at the electrolyte concentration of 10-3 M.3 The estimated ionic concentration in the films is higher for both redox forms (Table 2). Moreover, the dielectric constant is lower in the film compared to the aqueous solution (Table 2). The diffuse layer is thinner at lower values of the dielectric constant. Our calculations of the potential profiles across the films have shown that the potential drops to zero inside the film: it decays to 0 V at ∼20 Å for the oxidized and at ∼150 Å for the reduced films (Figure 8b). The solution of the Poisson-Boltzmann equation with the boundary conditions dΨ/dx ) 0, Ψ ) 0 at x ) δ, where δ is the film thickness, gives the expression for the potential profile3 in the film diffuse layer:

tanh[(zeΨ)/(4kT)] ) exp{- κ(x - x1)} tanh[(zeΨ1)/(4kT)]

|E B| )

0 (Ψel - Ψ1)/x1

(2)

where z is the charge number of an ion (the equation is valid for z:z electrolyte), e is the electron charge (C), k is Boltzmann’s constant (J K-1), T is the temperature (K), x is the distance from the electrode (m), x1 is the distance of the PET from the electrode (m), Ψ is the potential at position x (V), Ψ1 is the potential at the PET (V), κ is the inverse Debye length in the film (m-1) given by κ ) ze(2Cf/0kT)1/2, Cf is the concentration of ions in the film (m-3),  is the relative dielectric constant of the film, and 0 is the permittivity of vacuum (C2 N-1 m-2).

[ ]

Ψel - Ψ1 2kT zeΨ1 κ sinh ) x1 ze 2kT

(4)

A detailed thermodynamic description of the reversible electrode reaction in terms of the interfacial potential distribution is given by Smith and White.38 Since ions undergoing electron exchange with the electrode are located at the PET, the effective potential difference, E - Ψ1, driving the electrode reaction is lower than the applied difference E by the value of Ψ1 (so-called Ψ effect).3 Taking into account this effect, the standard Nernst equation is modified as

E - Ψ1 ) E0 +

RT [Ox] ln nF [Red]

(5)

where E is the applied potential difference defined as E ) Ψel EPZC - ERef (V, EPZC is the potential of zero charge of the uncoated electrode, ERef is the potential of the reference electrode) and E0 is the standard potential of the redox couple (V); [Ox] and [Red] are surface concentrations of oxidized and reduced centers, respectively; R is the molar gas constant (J mol-1 K-1); F is the Faraday constant (C); and n is the number of electrons participating in the electrode reaction. Equation 5 transforms into the Nernst equation, when Ψ1 is zero, i.e., when the entire potential drop occurs between the electrode and PET. Conditions at which Ψ1 tends to zero can be easily found if eq 4 is rewritten for a limiting case of low potentials (sinh[eΨ1/2kT] f eΨ1/2kT):

Ψ1 ) Ψel/(1 + x1κ)

(6)

This equation shows that at high ionic concentrations (large κ, x1κ > 1) Ψ1 f 0 and the effective electrode potential (Ψel Ψ1) is close to the applied one, Ψel. In contrast, at low ionic concentrations (small κ, x1κ < 1), Ψ1 approaches Ψel, and the effective electrode potential substantially differs from the applied one. Therefore, at a particular applied potential, the effective potential difference driving an electrode reaction would be different depending on the ionic concentration inside a multilayer film. The expression for the Faradic current flowing through the electrode surface when the electrode reaction occurs is given by

I ) nFAΓ(dχ/dt)

(7)

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499

Figure 9. Peak separation (∆Ep) as a function of the difference in the ionic concentrations inside the film. Curves 2-6 are calculated by taking into account the EDL effect (eq 9). Reduction peak 2-5 M ionic concentration inside the film. Oxidation peaks: 2-5, 3-1, 4-0.1, 5-0.01, and 6-0.001 M ionic concentration inside the film. Separation of the reduction peak 2 and the oxidation peaks are as follows: 2, ∆Ep ) 0 V; 3, ∆Ep ) 0.03 V; 4, ∆Ep ) 0.085 V; 5, ∆Ep ) 0.145 V; 6, ∆Ep ) 0.2 V. Curve 1 is an ideal CV diagram (eq 8). Parameters used in calculations: ΓA ) 5.0 nmol, v ) 50 mV/s, and other parameters were the same as in Table 2.

where I is the current (A), A is the electrode surface area (m2), Γ is the surface coverage of the electrode (mol m-2), and χ is the mole fraction of the reduced form of the electroactive species given by χ ) [Red]/Γ. The cathodic current Ox + e- f Red is taken to be positive. In CV experiments, the electrode potential difference is changed linearly with time (E ) Estart + vt, where Estart is the starting potential difference (V), v is the scan rate (V/s), and t is the time (s)). The expression for the current in the ideal case is given by

I ) (F2vΓA/RT)χ(1 - χ)

(8)

where χ ) 1/(1 + η), η ) exp{(nF/RT)(E - E0)} is obtained from the Nernst equation. When Ψ effect is accounted for, eq 8 modifies to

I)

[

dΨ1 F2vΓA χ(1 - χ) 1 RT dΨel

]

(9)

where χ ) 1/(1 + η′), η′ ) exp{(nF/RT)(E - Ψ1 - E0)} is obtained from eq 5. The dependence of Ψ1 on the applied potential Ψel at a given ionic concentration (κ) is obtained from eq 4:

dΨ1 1 ) dΨel 1 + x1κ cosh[zeΨ1/2kT]

(10)

Equations 9 and 10 show that the current depends on the ionic concentration (κ) due to the potential distribution in the film. Figure 9 illustrates the effect of the difference of ionic concentrations during oxidation and reduction processes on the peak separation. In the present work, the experimental peak broadening has been described by taking into account the concentration depend500

Analytical Chemistry, Vol. 75, No. 3, February 1, 2003

Figure 10. Effect of the interaction parameter r on the peak broadening. 1 is a CV diagram calculated by taking into account different ionic concentrations inside the film: reduction 5 M, oxidation 0.001 M (eq 9); 2 is a CV diagram calculated by taking into account both different ionic concentrations and interaction parameter: r ) -1.0 (eq 11). Parameters used in the calculations are the same as in Figure 9.

ence of the surface activity coefficients of the redox centers in the framework of the lattice theory (eq 1). The applicability of the lattice theory to our films has been discussed in the previous subsection. Substitution of eq 1 into eq 5 leads to the following expressions:

for the Faradic current I)

[

dΨ1 χ(1 - χ) F2vΓA 1RT 2rχ(1 - χ) - 1 dΨel

]

(11)

and

η′ )

1-χ exp{r(2χ - 1)} ) exp{(nF/RT)(E - Ψ1 - E0)} χ (12)

Figure 10 illustrates the peak broadening when r in eq 11 is negative in accordance with the literature data.31,33,34 As mentioned in the introduction, the negative value of the interaction parameter corresponds to a situation when a mixture of oxidized and reduced molecules is the energetically preferable state, leading to the peak broadening. Thus, eq 11 expresses the reversible voltammetric response of a multilayer film when the interfacial potential distribution and concentration dependence of surface activity coefficients of the oxidized and reduced molecules are taken into account. At each applied potential, a value of Ψ1 is calculated from eq 4. Substitution of the calculated value into eqs 10 and 12 gives dΨ1/dΨel and χ, respectively. The Faradic current is obtained with these values from eq 11. The presented model includes two adjustable parameters that are determined by fitting the experimental CV diagrams: the ratio of ionic concentrations in the oxidized and reduced films, responsible for the peak separation; and the interaction coefficient, describing the peak broadening. The film parameters are listed in Table 2. The distance of the PET from the electrode (x1) is taken to be equal to the molecular radius of the complexes. The film thickness, volume, and

Figure 11. Calculated (eq 11) (lines) and experimental (dots) CV diagrams of Fe(NH) (a) and Fe(NMe) (b) at different scan rates. Supporting electrolyte is 0.1 M KPF6; film and electrode characteristics used in the calculations are listed in Table 2.

concentration of the complexes are estimated under the assumption that molecules are arranged in layers of a molecular diameter thickness. The total amount of electroactive species on the electrode surface (ΓA) is calculated by integrating the experimental current-potential curves. The number of molecules in one layer is estimated as ΓM ) a/Am, where a is the surface area occupied by one molecule and Am is the microscopic surface area of the electrode. A microscopic surface area is used instead of the geometric area since the scale of roughness of the edge plane graphite electrode is of the order of 1 µm,3 which is significantly larger than the size of one molecule. The number of layers is estimated as N ) Γ/ΓM; film thickness is δ ) Nd, where d is the molecular diameter; film volume is V ) Amδ; and the concentration of the complexes is C ) ΓA/V (M). In the oxidized film, the ionic concentration is assumed to be at least twice higher than C due to the presence of counterions. The ionic concentration in the reduced film is used as an adjustable parameter and fitted to the experimental peak separation. The second adjustable parameter, the interaction coefficient r, is fitted to describe the experimental peak width. The values obtained for the interaction coefficient (Table 2) are in agreement with those reported in the literature for other porphyrin complexes.31 The value of the dielectric constant of the film (Table 2) is taken from the literature.43 The numerical calculations of the dielectric constant of cytochrome c in a water droplet show that, although the bulk of the protein has a very low dielectric constant of 3 ( 1, the overall value is 25 ( 10, arising almost entirely from charged side chains.44,45 The polar groups of the protein that are present around redox cofactors form a polar surrounding that increases the dielectric constant to values larger than 30 even inside the protein.43 Taking into account these findings, we assume that the dielectric constant of the films formed by the complexes studied (Figure 1) is close to that around redox cofactors inside proteins and is unaffected by the swelling of, or the ionic (43) Warshel, A. Computer Modeling of Chemical Reactions in Enzymes and Solutions; Wiley: New York, 1991. (44) Simonson, T. J. Am. Chem. Soc. 1998, 120, 4875-4876. (45) King, G.; Lee, F. S.; Warshel, A. J. Chem. Phys. 1991, 95, 4366-4377.

concentration in, the film. This assumption is supported by the observation that the charging current is identical for electroinactive films formed by [Zn(NMe)]0, [Al(TPP)]+ (TPP ) tetraphenylporphyrin) or the nonmetalated free-base porphyrin [H2(NMe)]0; thus, it does not depend on the redox state of the film. The determination of the potential of zero charge (EPZC) for graphite electrodes is rather complicated due to their large-area, and poorly defined surfaces.46-48 In the present work, we use literature data on experimental EPZC of a carbon electrode.46 Similar to the EPG electrode,30 the carbon electrode is characterized by a large concentration of surface oxygen groups. This explains the positive value of the PZC (Table 2). III. Calculated Results. The calculated CV diagrams for the monometallic complexes (Figure 11) are in a good agreement with the experimental data. Figure 11 demonstrates that the model correctly reflects the peak separation when different ionic concentrations are assumed in the oxidized and reduced films. This result supports our assumptions and the idea that the peak potentials depend on the ionic concentration inside the film due to the EDL at the electrode surface. This effect should be accounted for when quantitative parameters measured for surfaceconfined redox-active centers are compared with characteristics of related natural systems. An accepted standard for characterization of the protein redox sites is the midpoint potential corresponding to the system in which the concentrations of oxidized and reduced forms are equal.49,50 For the heme a3/CuB center two midpoints have been found depending on the redox state of the other groups in the protein (Table 3).49-51 (46) Golub, D.; Soffer, A.; Oren, Y. J. Electroanal. Chem. 1989, 260, 383-392. (47) Oren, Y.; Soffer, A. J. Electroanal. Chem. 1986, 206, 101-114. (48) Tobias, H.; Soffer, A. J. Electroanal. Chem. 1983, 148, 221-232. (49) Wikstrom, M.; Krab, K.; Saraste, M. Cytochrome Oxidase. A Synthesis; Academic Press: London, 1981. (50) Graber, P.; Milazzo, G. Bioenergetics; Birkhaeuser: Basel, 1997; Vol. 4. (51) Farver, O.; Einarsdottir, O.; Pecht, I. Eur. J. Biochem. 2000, 267, 950954. (52) Dean, J. A. Lange’s handbook of chemistry; McGraw-Hill: New York, 1992.

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Table 3. Midpoint Potentials of the Complexes vs the Potentials of the Heme a3/CuB49-51 Center

complex

E0,a V vs NHE

Fe(NMe)/Fe(NMe)Cud Fe(NH) a3/CuB

0.08 -0.03 0.21-0.25/0.33-0.38

(E0 + Ψ1)b COx ) 1 M

(E° + Ψ1)c CRed ) 0.008 M Fe(NMe) CRed ) 0.0065 M Fe(NH)

0.16 0.03

0.29 0.13

a Standard potential. b Reduction, ionic concentration in the film is large (0.1 M KPF supporting electrolyte). c Oxidation, ionic concentration 6 in the film is small (0.1 M KPF6 supporting electrolyte). d Since the peak potentials of the bimetallic complex, Fe(NMe)Cu, are similar to those of Fe(NMe) (see subsection I), the parameters for this monometallic complex have been used to characterize the bimetallic analogue.

The peak and midpoint potentials are identical for surface symmetrical CV diagrams. They are equal to the standard potential E0 in an ideal system obeying the Nernst equation. However, in the presence of EDL (eq 5), the midpoint potentials are equal to E0 + Ψ1. Table 3 shows that the midpoint potentials depend on the ionic concentration inside the redox film and have more positive values at low ionic concentrations. It is notable that at low ionic concentrations, best approximating the environment around redox cofactors within the protein matrix,20 the midpoint potentials of the Fe(NMe)/Fe(NMe)Cu complexes, which are the closest structural analogues of the CcO active site, are satisfactorily close to those of the heme a3/CuB center. CONCLUSIONS In this paper, the interfacial potential distribution in electroactive multilayer films and its effect on the cyclic voltammograms has been described for the first time. Based on the general theory of the electric double layer, we have obtained expressions that relate the Faradic current with the ionic concentration inside the film. Assuming different ionic concentrations inside the film in

502 Analytical Chemistry, Vol. 75, No. 3, February 1, 2003

the oxidized and reduced forms, we have shown that a transition between these two states is responsible for the experimental peak separation. The peak potentials that correspond to the midpoint potentials differ from the standard potential and depend substantially on the ionic concentration inside the film. Under conditions of low ionic concentrations, the midpoint potential of the synthetic analogues of the heme a3/CuB site approaches that of CcO. This result is particularly important since the film with the low ionic concentration correctly reflects the microenvironment around the heme a3/CuB site of CcO. ACKNOWLEDGMENT We gratefully acknowledge Prof. C. E. D. Chidsey (Stanford) for valuable discussions. We thank NSF, NIH, and a Stanford Graduate Fellowship (R.B.) for financial support.

Received for review July 3, 2002. Accepted November 25, 2002. AC025918I