J. Phys. Chem. C 2007, 111, 8283-8290
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Homogeneous versus Heterogeneous Catalysis at Electrodes Modified with a Thin Organic Layer: Theoretical and Experimental Study under Conditions of Square-Wave Voltammetry Valentin Mircˇ eski,*,† Franc¸ ois Quentel,‡ Maurice L’Her,‡ and Catherine Elleouet‡ Institute of Chemistry, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius UniVersity, P.O. Box 162, 1000 Skopje, Republic of Macedonia, and Laboratoire de Chimie Analytique, UMR-CNRS 6521, UniVersite´ de Bretagne Occidentale, 6 aVenue Victor Le Gorgeu, C.S. 93837, 29238 Brest Cedex 3, France ReceiVed: December 22, 2006; In Final Form: January 30, 2007
A catalytic mechanism at thin film-modified electrodes is studied both theoretically and experimentally under conditions of square-wave voltammetry (SWV). The electrode system considered consists of a solid electrode covered with an electrochemically inactive thin film (e.g., a layer of a water-immiscible organic solvent) containing a neutral redox probe (R1). The modified electrode is immersed in an electrolyte solution (typically an aqueous electrolyte solution) that contains a second redox probe (R2) present in large excess compared to R1. The product of the assumed one-electron electrode reaction O1+, confined within the film, is transformed back to initial reactant R1 by means of a catalytic redox reaction with R2. If the permeation of R2 in the thin film is significant, then the catalytic reaction is a homogeneous process confined within the boundaries of the thin film. Otherwise, the catalytic reaction is a heterogeneous process involving electron transfer across the interface between the thin film and the electrolyte solution. Simple numerical solutions for both mechanisms have been derived with the aid of the step-function-modified method (Mircˇeski, V. J. Electroanal. Chem. 2003, 545, 29), and a comparative analysis of their theoretical voltammetric responses has been performed. SWV provides clear criterions for discriminating between two mechanisms. The studied catalytic mechanisms are of particular importance for assessing the electron transfer across the interface between two immiscible liquids by means of thin-organic-film-modified electrodes. Theoretical predictions have been confirmed by experiments with lutetium bis(tetra-t-butylphthalocyaninato) as a redox probe dissolved in a thin nitrobenzene film deposited on the surface of an edge-plane pyrolytic graphite electrode in contact with an aqueous solution of [Fe(CN)6]3- or [Fe(CN)6]4-.
1. Introduction Square-wave voltammetry (SWV) is a versatile technique that unifies the advantages of pulse voltammetric techniques and cyclic voltammetry.1 It is a particularly appealing method for analytical applications, mechanistic studies, and kinetic measurements. Beside, it has been recently demonstrated that SWV can resolve complex electrode mechanisms such as those complicated by both adsorption equilibriums and chemical reactions.2-4 An example is the adsorption-complicated EC mechanism comprising two types of follow-up chemical reactions (i.e., a chemical reaction proceeding in the diffusion layer and a surface chemical reaction confined to the electrode surface3). These two types of follow-up chemical reactions are indistinguishable in cyclic voltammetry; however, they can be discriminated under conditions of SWV. The differences between the two types of follow-up chemical reactions are particularly emphasized in the case of the adsorption-complicated EC′ (catalytic) mechanism (i.e., the electrode mechanism in which the follow-up chemical reaction regenerates the initial electroactive reactant4). Moreover, when the rate of the surface catalytic redox reaction is synchronized with the duration of the potential pulses, SWV exhibits extreme sensitivity toward the electroactive reactant, which is of particular analytical utility. * Corresponding author. E-mail:
[email protected]. † Ss. Cyril and Methodius University. ‡ Universite ´ de Bretagne Occidentale.
In the present study, we extend our consideration to a catalytic mechanism when the electroactive reactant is embedded in a thin film imposed on the electrode surface. Recent applications of SWV to thin-organic-film-modified electrodes5-8 and threephase electrodes9-11 showed the power of the technique in probing the kinetics and thermodynamics of ion-transfer reactions across the interface between two immiscible liquids. The electrode assembly considered consists of a solid electrode (e.g., graphite electrode (GE)) covered with a thin electrochemically inactive film (e.g., a thin film of an organic solvent (O)) containing a neutral redox probe R1 (Scheme 1). The electrode is immersed in an electrolyte solution (typically an aqueous electrolyte (AQ)) that contains a second redox probe R2, which is present in large excess compared to R1. At the electrode|film interface, the following electrode reaction occurs:
R1(o) a O+1(o) + e (electrode|film)
(1)
The product of the electrode reaction O+1(o) is assumed to be confined within the film. In a general case, considering the partition of R2 between the electrolyte solution and the thin film, the following two catalytic redox reactions are possible:
O1+(o) + R2(o) a R1(o) + O2+(o) (within the thin film)
10.1021/jp068880c CCC: $37.00 © 2007 American Chemical Society Published on Web 05/18/2007
(2)
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O1+(o) + R2(aq) a R1(o) + O2+(aq) (film|electrolyte solution) (3) Reaction 2 is a homogeneous process occurring in the organic film, whereas reaction 3 is a heterogeneous process involving electron transfer across the film|electrolyte solution (O|AQ) interface. If R2 rapidly permeates the film, then it can be assumed that the contribution of reaction 3 to the overall electrocatalytic mechanism is insignificant. An experimental example of this case is the reduction of dioxygen catalyzed by a redox mediator dissolved in a thin organic film.13 Thus, the general catalytic mechanism 1-3 can be represented by reactions 1 and 2 only (Scheme 1A). This limiting case is termed a homogeneous catalytic mechanism in thin-film voltammetry. On the contrary, if the permeation of R2 in the film is very low, then homogeneous reaction 2 can be neglected. Thus, the second limiting situation, represented by reactions 1 and 3, is termed a heterogeneous catalytic mechanism (Scheme 1B). The latter mechanism has been frequently encountered experimentally.13-20 Recently, using the method of finite differences, the heterogeneous catalytic mechanism has been simulated under conditions of linear scan voltammetry.20 The main objective of this study is to develop methodology to discriminate between the two foregoing limiting reaction pathways. These electrode mechanisms are of particular importance for studying heterogeneous electron-transfer reactions at the interface between two immiscible liquids with the help of thin-organic-film-modified electrodes.13-20 A comparative theoretical study of these two electrochemical processes is carried out to extract properties of the response that can serve as diagnostic criterions for recognizing the operative electrode mechanism. Both homogeneous and heterogeneous catalytic mechanisms are mathematically modeled by means of Laplace transforms and a modified step-function numerical method.21 Although the mathematical procedure is very complex, the final solutions are represented by a few recursive formulas that can be easily implemented in any mathematical or spreadsheet software package available (Supporting Information). Theoretical results are illustrated with experiments performed with lutetium bis(tetra-t-butylphthalocyaninato) (Lu[tBu4Pc]2) dissolved in a thin nitrobenzene (NB) film and then deposited on the surface of an edge-plane pyrolytic graphite electrode (EPPGE). This strongly hydrophobic redox probe can be oxidized and reduced to a stable monovalent cation and anion, respectively.22,23 In the presence of [Fe(CN)6]3-/[Fe(CN)6]4- in the aqueous phase, the overall process can be transformed into a catalytic mechanism.24,25 2. Experimental Section Lu[tBu4Pc]2 was synthesized as described elsewhere.22,23 All other chemicals were of high purity and were used as received. The redox compound was dissolved in water-saturated nitrobenzene. Besides the redox compound, nitrobenzene contained 0.1 mol/L (C4H9)4NClO4 (TBAClO4) as an electrolyte. In all experiments, the common ClO4- ion was present in both the organic and aqueous phases. A disk (0.32 cm2) of pyrolytic graphite (edge plane) was used as a working electrode. The preparation of the electrode and its pretreatment are described elsewhere.6 A nitrobenzene solution was deposited on the graphite electrode with the help of a micropipette; the organic solution spreads spontaneously over the electrode surface. The thin-film-modified electrode was immersed in an aqueous electrolyte and used in a conventional three-electrode cell.
Mircˇeski et al. SCHEME 1: Homogeneous (A) and Heterogeneous (B) Catalytic Mechanisms in Thin-Film Voltammetry
Square-wave voltammograms were recorded using Autolab equipment (Eco-Chemie, Utrecht, The Netherlands). A KCl saturated calomel electrode (SCE) was used as a reference electrode, and a platinum wire was used as an auxiliary electrode. Nitrobenzene-saturated water (Millipore Q) was used to prepare all aqueous solutions. 3. Results and Discussion 3.1. Theoretical Results. Both homogeneous (Scheme 1A) and heterogeneous (Scheme 1B) catalytic mechanisms combine the features of a thin-film electrode mechanism26 and a simple catalytic electrode mechanism.27 Voltammetric features of an electrode reaction in thin-film voltammetry are primarily controlled by the thickness parameter Λ ) Lxf/D and the electrode kinetic parameter K ) ks/xDf, where L is the thickness of the film, f is the SW frequency, and D is a common diffusivity of an electroactive species. Λ represents the effect caused by the restricted diffusion of electroactive species within the boundaries of the thin film. The electrode kinetic parameter K has a well-understood physical meaning that is common to most kinetically controlled electrode mechanisms.1 Besides Λ and K, the homogeneous catalytic mechanism is attributed to a dimensionless catalytic parameter, κh ) kh/f. Here kh (s-1) is a pseudo-first-order catalytic rate constant defined as kh ) k/hcR/ 2(o), where k/h is the real second-order homogeneous rate constant in units of mol-1 cm3 s-1 and cR/ 2(o) is the concentration of reactant R2 in the film, which is assumed to be constant in the course of the voltammetric experiment. The corresponding parameter for the heterogeneous catalytic mechanism is defined as κht ) kht/xDf. kht (cm s-1) is a pseudofirst-order heterogeneous rate constant defined as kht ) k/ht cR/ 2(aq), where k/ht (mol-1 cm4 s-1) is the real second-order heterogeneous rate constant and cR/ 2(aq) is the bulk concentration of reactant R2(aq) in the aqueous phase. The difference between dimensionless catalytic parameters reflects the intrinsic discrepancy in the two mechanisms. For the homogeneous catalytic mechanism, redox reaction 2 takes place uniformly within the entire film, whereas for the heterogeneous mechanism, the product of the electrode reaction O1+(o) has to diffuse toward the film|electrolyte solution interface before being chemically converted. For these reasons, the heterogeneous catalytic parameter (κht) unifies the heterogeneous rate constant (kht) with the diffusivity (D) and the time window of the voltammetric experiment (f). For both mechanisms, the effect of the catalytic reaction varies depending on the thickness of the film and the kinetics of the
Catalysis at Organic-Layer-Modified Electrodes
Figure 1. Theoretical results. Effect of the rate of the catalytic reaction on the net peak current studied for different thicknesses of the film for the homogeneous (A) and heterogeneous (B) catalytic mechanisms. The values of thickness of the film were L ) 2 (1), 3 (2), 4 (3), and 5 µm (4). The other conditions of the simulations were diffusion coefficient D ) 10-5 cm2 s-1, anodic electron-transfer coefficient β ) 0.5, temperature T ) 298.15 K, standard electrode rate constant ks ) 0.01 cm s-1, frequency f ) 10 Hz, amplitude Esw ) 50 mV, and potential step dE ) 10 mV.
electrode reaction. Figure 1 shows comparatively the effects of the catalytic reactions on the dimensionless net peak currents (∆ψp) for different thickness of the film. Ordinates display the ratio ∆ψp/∆ψp,0, where ∆ψp is the net peak current measured at a corresponding rate of the catalytic reaction and ∆ψp,0 is the peak current measured when the rate of the catalytic reaction is insignificant. With this additional normalization, only the increase in the net peak current due to the catalytic reaction is presented, enabling a consistent comparison between the two mechanisms. For the homogeneous catalytic mechanism (Figure 1A), ∆ψp increases nonlinearly with log(kh) for any film thickness. The thinner the film, the stronger the effect of the catalytic reaction. In a very thin film, the total amount of R1(o) is rapidly converted to O1+(o), thus increasing the rate of catalytic reaction 2. For the heterogeneous mechanism (Figure 1B), the effect of kht is similar to the previous one only if the thickness of the film is very low (Λ < 0.4, curves 1-3 in Figure 1B). However, for a thicker film (Λ g 0.5), the voltammetric behavior is dramatically different (curve 4 in Figure 1B). Over the interval -3 e log(kht/cm s-1) e -1.8, the net peak current
J. Phys. Chem. C, Vol. 111, No. 23, 2007 8285
Figure 2. Theoretical results. Effect of the rate of the catalytic reaction on the net peak current studied for various rates of the electrode reaction for the homogeneous (A) and heterogeneous (B) catalytic mechanisms. The electrode kinetic parameter values were log(K) ) -1.5 (1), -1 (2), 0 (3), and 1 (4) in plot A and -1.5 (1), -1 (2), -0.5 (3), 0 (4), and 1.4 (5) in plot B. The thickness of the film was L ) 5 µm. All other conditions were the same as for Figure 1.
decreases by increasing the heterogeneous catalytic rate constant. After reaching the minimum value, ∆ψp commences increasing by further acceleration of the catalytic reaction (curve 4 in Figure 1B). The position of the minimum of parabolic curve 4 in Figure 1B depends on the thickness of the film and the kinetics of the electrode reaction. For instance, by increasing the thickness of the film, the minimum shifts toward higher values of kht. Therefore, voltammetric features of the heterogeneous catalytic mechanism are considerably different than those of the homogeneous mechanism. Before providing an explanation for such behavior, it is useful to inspect the effect of the catalytic reaction for different apparent reversibilities of electrode reaction 1. The apparent reversibility of the electrode reaction depends mainly on the electrode kinetic parameter K.26 For the homogeneous catalytic mechanism (Figure 2A), the sensitivity of ∆ψp to the catalytic reaction increases by increasing the apparent
8286 J. Phys. Chem. C, Vol. 111, No. 23, 2007 reversibility of the electrode reaction (compare curves 1 and 4 in Figure 2A). However, within the quasi-reversible kinetic region (-1 < log(K) < 1) the situation is the opposite. Comparing curves 2 and 3 in Figure 2A, which are simulated for log(K) ) -1 and 0, respectively, one observes that the slower electrode reaction is more sensitive to the catalytic redox reaction. For the heterogeneous catalytic mechanism (Figure 2B), all curves are associated with a minimum, except for the curve simulated for a very fast electrode reaction (curve 5 in Figure 2B). The position of the minimum of all curves is shifted toward lower values of kht by increasing the apparent reversibility of the electrode reaction. Results in Figures 1B and 2B imply that the parabolic dependence of ∆ψp versus log(kht) stems from combined kinetic effects of both the electrode and the catalytic redox reactions. Hence, to provide further insight into the voltammetric characteristics of the studied mechanisms, it is useful to inspect in more detail the effect of the electrode kinetic parameter K for various rates of the catalytic reaction. For both mechanisms, ∆ψp depends parabolically on log(K), forming a sharp maximum positioned within the quasi-reversible kinetic region (Figure 3). This is an intrinsic property of a kinetically controlled electrode reaction in thin-film SW voltammetry, known as a quasireversible maximum.26 This phenomenon originates from the specific choronoamperometric properties of an electrode reaction occurring in a restricted diffusion space and the current sampling procedure used in SWV. When the rate of the electrode reaction fits with the duration of the potential pulse of the SW modulation, the maximal dimensionless current is measured. This occurs for a certain critical value of the kinetic parameter, Kmax. For the homogeneous catalytic mechanism, the position of the maximum is virtually independent of the catalytic rate constant (Figure 3A). However, for the heterogeneous mechanism the position of the maximum shifts toward lower Kmax by increasing of the rate of the catalytic reaction (Figure 3B). This shift is illustrated by the inset of Figure 3B, which is associated with a linear dependence of log(Kmax) versus log(kht). For high rates of the heterogeneous catalytic reaction, the quasi-reversible maximum vanishes (curve 4 in Figure 3B). Therefore, the behavior of the quasi-reversible maximum could serve as a second diagnostic criterion for discriminating between the two catalytic mechanisms in thin-film voltammetry. The peculiar voltammetric behavior of the heterogeneous catalytic mechanism is a consequence of the specific chronoamperometric features of the electrode reaction confined within the restricted diffusion space,26 the current sampling procedure used in SWV,1 and the restriction of the catalytic reaction to act only at the film|electrolyte solution interface. Generally, the catalytic reaction regenerates the electroactive material, thus causing an increase in the voltammetric response. However, the catalytic reaction increases the apparent reversibility of the electrode reaction, enabling the redox equilibrium of the O1/R1 couple to be rapidly achieved in the course of a single potential pulse. Thus, at the end of the pulse, when the current is sampled in SWV, a low current remains to be measured. This effect is manifested as a diminishing of the current by an increase in the rate of the catalytic reaction. Therefore, the overall result of the catalytic reaction is a compromise between these two opposite effects. Finally, it is useful to note that under certain experimental conditions the net SW peak of a quasi-reversible electrode reaction confined in a thin film splits into two peaks.26 The splitting is a consequence of the large potential separation between the forward and backward components of the SW
Mircˇeski et al.
Figure 3. Theoretical results. Effect of the rate of the electrode reaction on the net peak current studied for various rates of the catalytic reaction for the homogeneous (A) and heterogeneous (B) catalytic mechanisms. The homogeneous catalytic rate constant values were log(kh/s-1) ) -2 (1), -1 (2), and 0 (3) in plot A, and the heterogeneous catalytic rate constant values were log(kht/cm s-1) ) -4 (1), -3 (2), -2 (3), and -1.5 (4) in plot B. The thickness of the film was L ) 5 µm. All other conditions of the simulations were the same as for Figure 1. The inset in B shows the dependence of the logarithm of the critical electrode kinetic parameter Kmax on the logarithm of the heterogeneous catalytic rate constant.
response. The splitting can be tuned by the amplitude and frequency of the potential modulation. The higher the SW amplitude, the larger the potential separation between the split peaks. The splitting can be effectively exploited to discriminate between the two catalytic mechanisms. Figure 4 depicts the effect of the catalytic reaction on the shape of net SW peak for the two mechanisms. The conditions of the simulations, such as the film thickness, electrode kinetic parameter, and SW amplitude, are adjusted to be close to their critical values
Catalysis at Organic-Layer-Modified Electrodes
J. Phys. Chem. C, Vol. 111, No. 23, 2007 8287 tion.26 This is another indication that the heterogeneous catalytic redox reaction increases the apparent reversibility of the electrode reaction in thin-film voltammetry. 3.2. Experimental Results. The foregoing theoretical results are partially illustrated by experiments with Lu[tBu4Pc]2 at thinorganic-film-modified electrodes.6-8,11 In an organic solvent, Lu[tBu4Pc]2 can be both oxidized and reduced in reversible oneelectron steps to form a chemically stable cation and anion, respectively. At a thin-film electrode consisting of a nitrobenzene solution of Lu[tBu4Pc]2 deposited on the surface of EPPGE, which is immersed in an aqueous electrolyte, the electrode reactions of the redox probe are accompanied by corresponding ion transfers across the AQ|NB interface. In the presence of ClO4- in both liquid phases, the oxidation is accompanied by the transfer of ClO4- from water to nitrobenzene, whereas the reduction is accompanied by an expulsion of the same ion from the organic phase. These processes are represented by the following equations:
Lu[tBu4Pc]2(nb) + ClO4-(aq) a Lu[tBu4Pc]2+(nb) + ClO4-(nb) + e (4) Lu[tBu4Pc]2(nb) + ClO4-(nb) + e a Lu[tBu4Pc]2-(nb) + ClO4-(aq) (5)
Figure 4. Theoretical results. Effect of the rate of the catalytic reaction on the evolution of net SW voltammograms for the homogeneous (A) and heterogeneous (B) catalytic mechanisms. (A) log(kh/s-1) ) -3 (1), -1 (2), and -0.2 (3). (B) log(kht/cm s-1) ) -5 (1), -3 (2), and -1.8 (3). The other conditions of the simulations were L ) 6 µm, ks ) 0.01 cm s-1, and Esw ) 80 mV. The other conditions were the same as for Figure 1.
required for splitting the response. Figure 4A shows that the acceleration of the homogeneous catalytic reaction causes a proportional increase in the response without significantly affecting the shape of the peak. On the contrary, for the heterogeneous catalytic mechanism, the response decreases substantially by increasing the rate of the catalytic reaction (Figure 4B). When the heterogeneous catalytic redox reaction is sufficiently fast, the splitting appears (curve 3 in Figure 4B). Therefore, this property can be exploited as a simple, clear criterion for distinguishing between the two catalytic mechanisms. It is interesting that a similar effect can be observed for a simple quasi-reversible reaction in thin-film SW voltammetry by increasing the apparent reversibility of the electrode reac-
Under conditions of SWV, both processes are kinetically controlled, with the ion transfer being the rate-determining step.6-8,11,28 In the presence of [Fe(CN)6]4- and [Fe(CN)6]3in the aqueous phase, the oxidation (reaction 4) and the reduction (reaction 5) of Lu[tBu4Pc]2 can be transformed into oxidative and reductive catalytic mechanisms in thin-film voltammetry, respectively. As will be further evidenced, the voltammetric behavior of both catalytic systems is rather peculiar, and without previous theoretical results, it is difficult to resolve their complexity. Voltammetric properties depend predominantly on the amount of NB solution deposited on the electrode surface, the concentration of the aqueous redox probe, the concentration of the transferring ions in both liquid phases, and the frequency and amplitude of the potential modulation. The film thickness is controlled by the amount of NB solution deposited on the electrode surface. In general, the catalytic effect increases by decreasing the thickness of the NB film. For instance, by studying the oxidative catalytic system, it was observed that the net SW peak current increases linearly with the concentration of [Fe(CN)6]4- over the interval of 0 e c([Fe(CN)6]4-)/mmol L-1 e 14. The slope of the line increases from 19.74 to 32.29 to 43.65 mA mol-1 L by decreasing the amount of deposited NB solution from 2 to 1.5 to 0.5 µL. The kinetics of the catalytic redox reaction was controlled by adjusting the concentration of the redox probe in the aqueous phase. This experimental analysis corresponds to the variation of the rate constant of the catalytic redox reaction in the theoretical models. Figure 5 shows the evolution of the reductive net SW voltammograms of Lu[tBu4Pc]2 under increasing concentration of [Fe(CN)6]3- in the aqueous phase. The net peak current increases in proportion to the concentration of [Fe(CN)6]3-, confirming the catalytic nature of the system. However, on the basis of these experiments only, it is difficult to recognize the type of catalytic mechanism. These experiments have been performed in contact with 0.1 mol/L LiClO4 aqueous electrolyte. Increasing the concentration of the aqueous electrolyte from 0.1 to 1 mol/L while keeping all other experimental conditions
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Figure 5. Experimental results. Net SW voltammograms for the reduction of Lu[tBu4Pc]2 recorded in contact with 0.1 mol/L LiClO4 aqueous solution containing 0 (1), 2 (2), 4 (3), 6 (4), 8 (5), 10 (6), and 15 mmol/L [Fe(CN)6]3- (7). The thin film was formed by depositing 1 µL of NB solution containing 1 mmol/L Lu[tBu4Pc]2 and 0.1 mol/L TBAClO4. The other experimental conditions were f ) 20 Hz, Esw ) 50 mV, and dE ) 0.15 mV.
constant caused a dramatic change in the voltammetric behavior of the system. In contact with 1 mol/L LiClO4, instead of increasing, the net SW peak slightly decreases with the concentration of [Fe(CN)6]3- (Figure 1A in Supporting Information). Moreover, at 10 mmol/L [Fe(CN)6]3- the net SW peak splits. Such voltammetric behavior indicates that a heterogeneous catalytic mechanism that involves an electron transfer from Lu[tBu4Pc]2-(nb) to [Fe(CN)6]3-(aq) is operative. As demonstrated in previous studies, the electrode kinetics for both the oxidation and reduction of Lu[tBu4Pc]2 at thinfilm electrodes is gated by the rate of the accompanying iontransfer reaction across the liquid interface.6-8,11,28 Thus, the apparent kinetics of the electrode reaction can be controlled by adjusting the concentration of the transferring ion in the liquid phases. Increasing the concentration of the transferring ion in the aqueous phase causes an acceleration of the ion-transfer reaction across the liquid interface, causing a corresponding increase in the apparent reversibility of the electrode reaction. Hence, the increase in the transferring ion concentration is equivalent to the increase in the electrode kinetic parameter K in the theoretical analysis. Moreover, the concentration of the transferring ion plays another important role in the overall mechanism. Because the experiments are performed in excess transferring ions compared to the environment of the redox probes, the concentration of the ions at the AQ|NB interface is assumed to be constant throughout the voltammetric experiment. Hence, the potential difference at the AQ|NB interface is predominantly controlled by the concentration of the transferring ions in the two liquid phases. The Galvani potential difference defined as ∆nb aq φ ) φnb - φaq, where φ is the inner potential, is related to the activities of the common ion as follows: aqfnb ø ∆nb φX- + aq φ ) ∆
RT a(X(nb)) ln F a(X- ) (aq)
Here, X- is the common anion, ∆aqfnbφXø - is the standard potential of the anion transfer from water to nitrobenzene, and
Mircˇeski et al.
Figure 6. Experimental results. Net SW voltammograms for the oxidation of Lu[tBu4Pc]2 recorded in contact with 0.1 mol/L LiClO4 aqueous solution containing 0 (1), 2 (2), 4 (3), 6 (4), 8 (5), 10 (6), and 14 mmol/L [Fe(CN)6]4- (7). The thin film was formed by depositing 0.5 µL of NB solution. The frequency was 8 Hz. All other conditions were the same as for Figure 5.
the other symbols have their usual meanings. Increasing the concentration of the anion in the aqueous phase makes the potential difference at the liquid interface less positive, which accelerates the rate of electron transfer from Lu[tBu4Pc]2-(nb) to [Fe(CN)6]3-(aq). Therefore, the concentration of the transferring ion in the aqueous phase affects both the apparent kinetics of the electrode reaction and the kinetics of the heterogeneous electron-transfer reaction across the liquid interface. As predicted by theoretical results in Figures 1B and 2B, for a quasi-reversible electrode reaction, the heterogeneous catalytic reaction causes a decrease in the net SW response; moreover, the splitting of the net SW peak can emerge because of the fast electron exchange at the film|aqueous electrolyte interface (Figure 4B). The experimental behavior of both reductive (Figure 1A in Supporting Information) and oxidative (Figure 6) systems strongly confirms the theoretical predictions. The foregoing experimental results reveal that the studied processes proceed according to a heterogeneous catalytic reaction scheme in thin-film voltammetry. The heterogeneous catalytic redox reaction for the reductive mechanism is represented by the following equation:
Lu[tBu4Pc]2-(nb) + [Fe(CN)6]3-(aq) + ClO4-(aq) a Lu[tBu4Pc]2(nb) + [Fe(CN)6]4-(aq) + ClO4-(nb) (6) The corresponding catalytic reaction for the oxidative mechanism is
Lu[tBu4Pc]2+(nb) + [Fe(CN)6]4-(aq) + ClO4-(nb) a Lu[tBu4Pc]2(nb) + [Fe(CN)6]3-(aq) + ClO4-(aq) (7) To estimate the heterogeneous catalytic rate constant for the oxidation system, the ratio ∆Ip/∆Ip,0 was measured for different concentrations of [Fe(CN)6]4- and compared with the theoretical ratio ∆ψp/∆ψp,0, calculated via the model under conditions corresponding to those in the experiments. ∆Ip and ∆Ip,0 are net peak currents measured in the presence and absence of
Catalysis at Organic-Layer-Modified Electrodes
J. Phys. Chem. C, Vol. 111, No. 23, 2007 8289 4. Conclusions
Figure 7. Experimental results. Quasi-reversible maximums for the reduction of Lu[tBu4Pc]2 measured in contact with 0.1 mol/L LiClO4 aqueous solution containing 0 (1), 2 (2), 12 (3), and 18 mmol/L [Fe(CN)6]3- (4). The thin film was formed by depositing 1.5 µL of NB solution containing 0.5 mmol/L Lu[tBu4Pc]2 and 0.1 mol/L TBAClO4. The other experimental conditions were Esw ) 50 mV and dE ) 0.15 mV.
[Fe(CN)6]4-, respectively. The best fitting was observed for the heterogeneous catalytic rate constant of k/h ) 1.5 × 103 cm4 mol-1 s-1 (Figure 2A in Supporting Information). The inset of the Figure shows a correlation diagram between the theoretical and experimental data associated with the following regression line: y ) 0.992x + 0.025 (R ) 0.96). The intercept and the slope of the regression line are close to the idealized values 0 and 1, respectively, indicating good agreement between the theoretical and experimental data. Using the same methodology for the reduction system of Lu[tBu4Pc]2 in the presence of [Fe(CN)6]3-, the heterogeneous catalytic rate constant k/ht ) 5 × 102 cm4 mol-1 s-1 has been estimated. The correlation diagram is associated with the following regression line: y ) 1.107x - 0.184 (R ) 0.90) (data not shown). Finally, the evolution of the quasi-reversible maximums for the reductive catalytic system has been studied. The results are presented in Figure 7. During this analysis, the apparent reversibility of the electrode reaction has been varied by changing the frequency of the potential modulation for a variety of [Fe(CN)6]3-(aq) concentrations. It should be noted that the experimental analysis is more complex than the theoretical one presented in Figure 3 because the variation of the frequency simultaneously affects both the electrode kinetic parameter K and the catalytic parameter κht. Nevertheless, the experimental results clearly show that the position of the maximum shifts toward higher critical frequencies by increasing the rate of the catalytic redox reaction, which is in agreement with the theoretical prediction presented in Figure 3B. These results confirm that the catalytic redox reaction affects the apparent reversibility of the system and provide additional evidence for the heterogeneous nature of the catalytic system.
To the best of our knowledge, this is the first attempt to characterize both homogeneous and heterogeneous catalytic redox reactions by using SWV at thin-film electrodes. SWV is capable of discriminating between the homogeneous catalytic mechanism that involves the catalytic reaction within the thin film and the heterogeneous catalytic mechanism concerned with electron transfer across the interface between the thin film and the electrolyte solution. For both mechanisms, a numerical method for the simulation of the voltammetric response has been developed and is represented by a few recursive formulas. For the homogeneous catalytic mechanism, the height of the voltammetric response increases in proportion to the rate of the catalytic reaction, which is a common feature of various regenerative electrocatalytic systems. On the contrary, the performance of the heterogeneous catalytic mechanism is much more complex. Frequently, instead of increasing, the net peak current decreases with an acceleration of the rate of the heterogeneous catalytic reaction. Though the origin of this feature is rather complex, it can serve as a simple diagnostic criterion for discriminating between the two catalytic mechanisms in thin-film voltammetry. The evolution of both the splitting of the net SW peak and the quasireversible maximum under the influence of the catalytic reaction can also serve as an additional diagnosis of the operative mechanism. For the homogeneous catalytic mechanism, the splitting and the quasireversible maximum are insensitive to the rate of the catalytic reaction, which is opposite to the heterogeneous catalytic mechanism. The experiments with lutetium bisphthalocyanine dissolved in a thin film of nitrobenzene in contact with an aqueous electrolyte containing the [Fe(CN)6]3-/[Fe(CN)6]4redox couple fit the theoretical predictions for the heterogeneous catalytic mechanism involving electron transfer across the water|nitrobenzene interface. Acknowledgment. The financial support of the ministries of science of France and the Republic of Macedonia is acknowledged. V.M. also acknowledges the financial support of A. v. Humboldt-Stiftung. Supporting Information Available: Mathematical model describing the procedure for the derivation of the final recurrent formulas for calculating SW voltammograms, list of symbols and abbreviations, and plots showing (i) the effect of [Fe(CN)6]3on the net SW voltammograms for the reduction of the redox probe and (ii) the fitting between experimental and theoretical data for the purpose of estimating the heterogeneous catalytic rate constant. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Lovric´, M. In Electroanalytical Methods: Guide to Experiments and Applications; Scholz, F., Ed.; Springer-Verlag: Berlin, 2002; pp 111133. (2) Mircˇeski, V. J. Electroanal. Chem. 2001, 508, 138. (3) Mircˇeski, V.; Lovric´, M. J. Electroanal. Chem. 2004, 565, 191. (4) Mircˇeski, V.; Quentel, F. J. Electroanal. Chem. 2005, 578, 25. (5) Mircˇeski, V.; Gulaboski, R. J. Phys. Chem. B 2006, 110, 2812. (6) Quentel, F.; Mircˇeski, V.; L’Her, M. Anal. Chem. 2005, 77, 1940. (7) Quentel, F.; Mircˇeski, V.; L’Her, M. J. Phys. Chem. B 2005, 109, 1262. (8) Mircˇeski, V.; Quentel, F.; L’Her, M.; Pondaven, A. Electrochem. Commun. 2005, 7, 1122. (9) Marken, F.; Webster, R. D.; Bull, S. D.; Davies, S. G. J. Electroanal. Chem. 1997, 437, 209. (10) Scholz, F.; Komorsky-Lovric´, Sˇ.; Lovric´, M. Electrochem. Commun. 2000, 2, 112.
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