Mechanisms of Two Electrochemical Oscillations of Different Types

7246

J. Phys. Chem. B 2001, 105, 7246-7253

Mechanisms of Two Electrochemical Oscillations of Different Types, Observed for H2O2 Reduction on a Pt Electrode in the Presence of a Small Amount of Halide Ions Yoshiharu Mukouyama, Shuji Nakanishi, Takehiro Chiba, Kei Murakoshi, and Yoshihiro Nakato* Department of Chemistry, Graduate School of Engineering Science, Osaka UniVersity, Toyonaka, Osaka 560-8531, Japan ReceiVed: February 5, 2001; In Final Form: May 16, 2001

Two electrochemical oscillations, previously called oscillation C and D, are observed for H2O2 reduction on a Pt electrode in an acidic solution when a small amount of halide ions is added to the solution. Detailed studies, including impedance analyses and in-situ light reflectance measurements as well as mathematical simulations, have revealed that both oscillations C and D fall into hidden negative differential resistance (HNDR) oscillators, though oscillation D can be classified into a new-type HNDR oscillator not reported thus far. The H2O2 reduction on Pt has two-type NDR's: One arises from a decrease in the coverage of adsorbed OH (acting as an autocatalyst for the H2O2 reduction) with a negative potential shift, and the other arises from suppression of the H2O2 reduction by formation of under-potential deposited hydrogen (upd-H) in further negative potentials. Oscillation C appears from hiding of the former NDR by a decrease in the coverage (θX) of adsorbed halide ions (acting as a site blocking agent) with the negative potential shift. Oscillation D appears from hiding of the latter NDR by not only the decrease in θX but also an addition of a transient cathodic current due to the upd-H formation, indicating that oscillation D is really a new-type HNDR oscillator.

Introduction Electrochemical oscillations have attracted growing attention as typical examples of nonlinear chemical phenomena. Studies on electrochemical oscillations are also interesting from a point of view of investigation of mechanisms of electrochemical reactions themselves, because such studies sometimes enable us to reveal new mechanisms that will otherwise not be clarified, such as an autocatalytic effect of adsorbed OH on H2O2 reduction,1-3 an important reaction in connection with O2 reduction. Electrochemical oscillations have been reported for a variety of systems, as summarized in recent reviews,4-7 including anodic metal dissolution,8,9 cathodic metal deposition,10 oxidation of hydrogen molecules11,12 and small organic compounds such as formic acid,13,14 formaldehyde,15,16 and methanol,15 and reduction of hydrogen peroxide,1-3,17,18 persulfate ions,19 etc. The electrochemical oscillations have thus far been classified by the kind of oscillating reactions or the conditions under which oscillations are observed. Recently, with progress of mechanistic studies, the classification on the basis of mechanism has been tried.7,20,21 Strasser et al. reported21 that electrochemical oscillations could be classified into four categories, Class I, Class II, Class III (negative differential resistance [NDR] oscillators), and Class IV (hidden negative differential resistance [HNDR] oscillators). They also reported21 that most of electrochemical oscillations fell into Class III and Class IV categories, and Class IV could be further divided into at least three subcategories, called IV-1, IV-2, and IV-3. We reported previously1,3,22-27 that H2O2 reduction on Pt electrodes in acidic solutions is quite an interesting oscillatory * To whom correspondence should be addressed. Fax: +81-6-68506236. E-mail: [email protected].

Figure 1. Experimental setup for measuring light reflectance changes at the Pt-electrode surface, occurring concurrently with potential oscillations.

system, showing five electrochemical oscillations of different types, called oscillation A, B, C, D, and E (cf. Figures 2 and 3, discussed later). Oscillations A and B are observed for polycrystalline Pt electrodes.23,25,26 Oscillation A is also observed for atomically flat Pt (111), (110), and (100) electrodes,3 whereas oscillation B is not observed for such atomically flat Pt electrodes.27 On the other hand, oscillation E is observed only for atomically flat Pt (111) electrodes.3 Oscillations C and D are observed when small amounts of halide ions are added to the solution.1,24 With respect to the oscillation mechanism, oscillation A is classified into an NDR oscillator,25,26 with underpotential deposited hydrogen (upd-H) as an NDR-inducing species. Oscillation E is also classified into an NDR oscillator,3 with adsorbed OH (acting as an autocatalyst for the H2O2

10.1021/jp0104381 CCC: $20.00 © 2001 American Chemical Society Published on Web 07/07/2001

Mechanisms of Electrochemical Oscillations

Figure 2. General view of oscillations A, B, C, D, and E, observed under potential-controlled conditions for H2O2 reduction on Pt in an acidic solution. Electrode: poly-Pt, except (c) for which single-crystal Pt (111) was used. The solution: 0.3 M H2SO4 containing (a) 0.1 M H2O2, (b) 0.7 M H2O2, (c) 1.0 M H2O2, (d) 1.2 M H2O2 + 1.0 × 10-3 M KCl, and (e) 0.7 M H2O2 + 1.0 × 10-4 M KBr.

reduction) as an NDR-inducing species. Oscillation B was classified27 into an oscillator of a new type, called a “coupled NDR” or CNDR oscillator, contrary to a suggestion in the literature.21 In the present work we have studied the mechanisms of oscillations C and D in detail, using impedance analyses and in-situ light reflectance measurements as well as mathematical simulations. The studies have revealed the essential difference between oscillations C and D, which remained unclear in a previous paper,1 together with the crucial role of adsorbed halide ions acting as an NDR-hiding species. It is concluded that oscillation C is a typical example of the IV-2 oscillators, according to the classification of Strasser et al.,21 whereas oscillation D can be classified into a new subcategory of Class IV oscillators, which may be named IV-4. Experimental Section Polycrystalline Pt (poly-Pt) disks or single-crystal Pt (111) disks of about 1.0 mm in diameter were used as the working electrode. The disks were obtained by the method of Clavilier et al.28 or a modified one. Namely, they were obtained by heating Pt wires (99.97% in purity) in a hydrogen flame to prepare poly- or single-crystal Pt spheres, followed by cutting and polishing with diamond slurry.3 The poly-Pt disks were used

J. Phys. Chem. B, Vol. 105, No. 30, 2001 7247

Figure 3. Oscillations B, C, and D under current-controlled conditions: (a) and (b) j-U curves and c-f time courses (U-t curves), where (c) is for oscillation C at j ) -0.32 A cm-2 in (a), and (d) and (e) are for oscillation D at j ) -0.25 and -0.38 A cm-2, respectively, in (b). Curve (f) is a simple expansion of curve (e). Electrode: polyPt. The solution: 0.3 M H2SO4 containing (a) 0.7 M H2O2 + 1.0 × 10-3 M KCl and (b) 0.7 M H2O2 + 1.0 × 10-4 M KBr.

as prepared, except immersing in 60% HNO3 for about 1 day to remove surface contamination. Just before measurements were taken, cyclic potential scans were repeated between -0.35 and +1.60 V vs SCE in 0.3 M H2SO4 (M ) mol/dm3) for about 30 min to clean the electrode surface. The single-crystal Pt (111) disks were, after polishing, annealed in a hydrogen flame for 30 s and immediately quenched in Ar-bubbled pure water in order to obtain atomically flat surfaces. Both the polycrystalline and single-crystal disk electrodes were held such that only the flat surface was in contact with the electrolyte by use of its meniscus, as reported previously.3 Current density (j) vs potential (U) curves were measured with a potentiogalvanostat (Hokuto-Denko, HA501) and a potential programmer (Nikko-Keisoku NPS-2), and recorded with a data-storing system (instruNET, GW Instruments) with a sampling frequency of 1 or 10 kHz. A Pt plate (10 × 10 mm2) was used as the counter electrode, and a saturated calomel electrode (SCE) or a hydrogen electrode (HE) was used as the reference electrode. The electrolyte solutions were in most cases 0.3 M H2SO4 + 0.7 M H2O2, to which small amounts of halide ions were added when necessary. They were kept stagnant in all measurements. The solutions were prepared using special grade chemicals and pure water, the latter of which was obtained by purification of deionized water with a Milli-Q water purification system. The ohmic drops in the solution between the Pt electrode and the reference electrode were not corrected in the present work, though they were estimated23 to be about 0.02-0.03 V at j ) 1 mA mm-2.

7248 J. Phys. Chem. B, Vol. 105, No. 30, 2001

Mukouyama et al.

Impedance measurements were carried out with a Solartron 1260 impedance analyzer combined with a Solartron 1287 electrochemical interface potentiostat. The amplitude of modulation potential was 5 mV. The electrode potential was held at a potential at which measurements were done, for about 180 s just before the measurement in order to accomplish steady distributions of the surface H2O2 concentration, the coverage of adsorbed halide ions, etc., under given experimental conditions. Light reflectance changes at the electrode surface by electrochemical oscillations were measured by use of an experimental setup shown in Figure 1. A Pt plate of about 38 mm2 in area was used as the working electrode in this case. A 300 W xenon lamp was used as the light source. Monochromatic light of 550 nm was obtained with a Jobin Yvon-Spex monochromator. The reflected light intensity was measured with a photomultiplier (Hamamatsu R928) and a lock-in amplifier (NF Electronic Instruments LI-575), with either external rectangle waves or electrochemical potential oscillations being used as the reference signal. Results For reference in later discussion, we first summarize the reported oscillatory behavior of H2O2 reduction on Pt electrodes1,3,22-27 in Figures 2 and 3, where j-U curves under potential- and current-controlled conditions, respectively, are shown. Figure 2a is a j-U curve for poly-Pt in a relatively low H2O2 concentration (0.3 M H2SO4 + 0.1 M H2O2), in which no oscillation is observed.23,25,26 The H2O2-reduction current starts at about 0.6 V vs SCE and is nearly independent of the potential in a region of about 0.45 to -0.25 V. The nearly potential-independent current is explained1,3,26 by assuming that the H2O2 reduction is initiated by dissociative adsorption of H2O2 k1

2 Pt + H2O2 98 2Pt-OH

(1)

followed by electrochemical reduction of the resultant Pt-OH k2

Pt-OH + H+ + e- 98 Pt + H2O

(2)

and that the former (reaction 1) is the rate-determining step. A “negative differential resistance (NDR)” is observed in a region of about -0.25 to -0.30 V. The NDR arises from suppression of the dissociative adsorption of H2O2 (reaction 1) by formation of underpotential deposited hydrogen (upd-H).1,3,26 Hydrogen evolution starts at about -0.30 V. Figure 2b is a j-U curve for poly-Pt in a slightly higher H2O2 concentration (0.3 M H2SO4 + 0.7 M H2O2). Oscillations A and B are clearly observed as reported.23,25,26 Oscillation A appears in the potential region of the above-mentioned NDR. (A slight shift in potential is due to an increase in the ohmic drop in the solution between the Pt electrode and the reference electrode.) Oscillation B appears in the region of hydrogen evolution. Figure 2c is a j-U curve for single-crystal Pt (111) in 0.3 M H2SO4 + 1.0 M H2O2. In addition to oscillation A, oscillation E appears at about 0.0 to -0.2 V, as reported.3 Oscillation E is observed only for Pt (111) and appears from another NDR, which is not apparent in Figure 2a for poly-Pt. The NDR arises from a decrease in the surface coverage (θOH) of adsorbed OH (Pt-OH) with a negative potential shift.3 This is explained as follows: The adsorbed OH is formed by the dissociative adsorption of H2O2 (reaction 1) and also acts as an autocatalyst

Figure 4. Impedance diagrams: (a) for Pt (111) in 0.3 M H2SO4 + 0.3 M H2O2 at -0.02 V vs SCE, (b) for poly-Pt in 0.3 M H2SO4 + 0.3 M H2O2 at 0.2 V, and (c) for poly-Pt in 0.3 M H2SO4 + 0.3 M H2O2 + 2.0 × 10-3 M KCl at 0.2 V.

for this reaction itself, which is the rate-determining step in the potential region of oscillation E. Thus, a decrease in θOH with a negative potential shift, caused by an increase in the rate of the electrochemical reduction of Pt-OH (reaction 2), leads to a decrease in the H2O2-reduction current (j), namely, the appearance of an NDR. The autocatalytic effect of the adsorbed OH is most prominent for single-crystal Pt (111). This is the reason oscillation E is observed only for Pt (111).3 Figure 2d,e show j-U curves for poly-Pt in Cl-- and Br-added solutions (0.3 M H2SO4 + 1.2 M H2O2 + 1.0 × 10-3 M KCl and 0.3 M H2SO4 + 0.7 M H2O2 + 1.0 × 10-4 M KBr), respectively. Oscillations C and D appear on the positive side of the potential regions where oscillations E and A appear, respectively.1,26 Figure 3a,b show oscillations C and D under currentcontrolled conditions.1,26 Oscillations A and E, which are NDR oscillators, do not appear under current-controlled conditions. Figure 3c-f show waveforms of oscillations C and D under current-controlled conditions.1,26 It is to be noted that the potential in the low-potential state for oscillation C shifts toward the positive (Figure 3c), whereas that for oscillation D shifts toward the negative (Figure 3d-f), suggesting the essential difference in the mechanism between these oscillations. Figures 4 and 5 show impedance diagrams in relation with oscillations C and D, respectively. Figure 4a is an impedance diagram for Pt (111) in 0.3 M H2SO4 + 0.3 M H2O2 at -0.02 V vs SCE, near which oscillation E appears in higher H2O2 concentrations (see Figure 2c). The diagram clearly shows the presence of NDR, suggesting that oscillation E is indeed classified into NDR oscillators. A similar diagram is observed even for poly-Pt at 0.2 V, as shown in Figure 4b, indicating that the NDR is present even for poly-Pt, though this is not clear in the j-U curve (Figure 2a). Figure 4c shows an impedance diagram for poly-Pt in a Cl--added solution (0.3 M H2SO4 + 0.3 M H2O2 + 2 × 10-3 M KCl) at the same potential as (b), near which oscillation C appears in higher H2O2 concentrations (Figure 2d). This figure shows a diagram typical of the presence of an HNDR4,19,20 (negative differential resistances in a region of intermediate frequencies and positive



Figure 5. Impedance diagrams for poly-Pt at -0.15 V in (a) 0.3 M H2SO4 + 0.3 M H2O2 and (b) 0.3 M H2SO4 + 0.3 M H2O2 + 1.0 × 10-4 M KBr.

differential resistances in low frequencies), indicating that oscillation C is indeed classified into HNDR oscillators. Figure 5a shows an impedance diagram for poly-Pt at -0.15 V, at which the NDR due to upd-H is present. The figure clearly shows the presence of NDR, indicating that oscillation A is an NDR oscillator. Figure 5b is an impedance diagram for polyPt in a Br--added solution (0.3 M H2SO4 + 0.3 M H2O2 + 1.0 × 10-4 M KBr) at the same potential as (a), near which oscillation D appears in higher H2O2 concentrations (Figure 2e). A diagram typical of the presence of an HNDR is obtained,4,19,20 similar to Figure 4c, suggesting that oscillation D is classified into HNDR oscillators. If oscillations C and D are HNDR oscillators with adsorbed halide ions as an NDR-hiding species, the surface coverage (θX) of the adsorbed halide will change concurrently with potential oscillations, as schematically shown in Figure 6(a). We thus measured light reflectance changes (∆F) at the Pt-electrode surface in a Br--added solution, because ∆F is reported to be in proportion to ∆θX (coverage change).29 First we measured the maximum reflectance change ∆Fm [) (R0 - Rm)/R0], where R0 is the reflected light intensity at a potential where θX = 0 and Rm is that at a potential where θX = θX,max (maximum of θX) for a given concentration of halide ions. From the reported θX vs U curves30-32 for Br-, shown in Figure 6b, we can see that θX = 0 at U ) -0.25 V vs SCE and θX = θX,max = 0.5 at U ) 0.45 V for 4.0 × 10-5 M Br-, which is the concentration used in the present reflectance measurements (Figure 6c,d). Next we measured the reflectance change ∆Fosc [) (RLP - RHP)/R0] occurring concurrently with a potential oscillation, where RLP and RHP are the reflected light intensities at the low- and highpotential states of a potential oscillation, respectively. The average coverage change (∆θX) occurring concurrently with the potential oscillation (see Figure 6a) was calculated by an equation ∆θX ) θX,max (∆Fosc/∆Fm). If the coverage (θX) of the adsorbed halide is a slow variable (i.e., the adsorption and desorption of halide ions are slow compared with the potential change), the coverage change (∆θX) will show a phase shift (∆φ) with respect to the potential oscillation, as also schematically shown in Figure 6a. Figure 6c,d plot the measured ∆θX and ∆φ values, respectively, for oscillations C (b) and D (×), as a function of the oscillation frequency (f). The measurements were done with the high and low potentials kept unchanged throughout the frequencies. The ∆θX values for both oscillations C and D were only about 3% in maximum (though only average values were measured as illustrated in Figure 6a) and decreased with the increasing frequency, indicating that θX changes more slowly than the

Figure 6. (a) Schematic illustration of a potential oscillation and an expected change of θX. (b) Reported θX vs potential, ()) for poly-Pt30 in a solution of 1.0 × 10-5 M Br- and (O and ×) for Pt (111) and (110), respectively,31,32 in a solution of 8.0 × 10-5 M Br-. (c) and (d) Observed ∆θX and ∆φ vs oscillation frequency (f) for (b) oscillation C and (×) oscillation D, with a poly-Pt plate used as the electrode and 0.3 M H2SO4 + 0.3 M H2O2 + 4.0 × 10-5 M KBr as the solution.

oscillating potential. The phase shift ∆φ, especially that for oscillation C, increased with the increasing frequency, also indicating the slow changes of θX. The small change in ∆φ with the frequency for oscillation D may arise from its complicated waveform (Figure 3d-f). These results support that θX is a slow variable. We investigated the effect of solution stirring on oscillations C and D to confirm that the surface H2O2 concentration was a nonessential variable for these oscillations. The oscillations remained nearly unchanged when the electrolyte solution was stirred with a magnetic stirrer, really confirming the above concept. On the contrary, oscillations A and E disappeared as soon as the solution stirring was started. Oscillation Mechanism and Mathematical Simulation. The experimental results show that both oscillations C and D are classified into HNDR oscillators, with adsorbed OH and upd-H as NDR-inducing species, respectively. Also, it seems to be evident that the coverage (θX) of adsorbed halide acts as a slow variable. To confirm this model and clarify the essential difference between oscillations C and D, we made mathematical simulation by taking account of the site-blocking effect of adsorbed halide ions, together with the autocatalytic effect of adsorbed OH3 and the site-blocking effect of upd-H.1,3,26 (The difference from our previous model1 will be described later in this section.) The calculation reproduced well the essential features of both oscillations C and D, as shown in Figure 7. For mathematical simulation, we assumed essentially the same reactions and equivalent circuit as those reported.1,3,26 The


Mukouyama et al. about 0.45 to -0.25 V (Figure 2a) but also the appearances of oscillation E and the corresponding NDR in this potential region (Figure 2c). In our early papers,23,25 the nearly potentialindependent current was explained in terms of electrochemical reduction of H2O2 into HO‚ and OH- and the diffusion limit of H2O2, which could not explain the occurrence of oscillation E. Another dissociative adsorption of H2O2

2 Pt + H2O2 f Pt-OOH + Pt-H

Figure 7. Calculated j-U curves under current-controlled conditions, with k1 expressed as k1 ) k10 + γθOH. The parameter values: (a) γ ) 0.6 cm s-1, E70 ) E-70 ) 0.1 V vs SCE, CXs ) CXb ) 3.0 × 10-3 mol cm-3, k70 ) 5.0 × 10 -4 cm s-1, k-70 ) 5.0 × 10 -7 mol cm -2 s-1, and (b) γ ) 0 cm s-1 (which was assumed to simplify the calculation), E70 ) E-70 ) -0.23 V, CXs ) CXb ) 5.0 × 10-4 mol cm-3, k70 ) 5.0 × 10 -5 cm s-1, and k-70 ) 5.0 × 10 -8 mol cm -2 s-1. In (b), a ) 0.3 and (1 - a′) ) 0.3 were assumed for the forward and backward processes of reactions (4), respectively (see text for details). The other parameters are common for (a) and (b): CHOb ) 0.7 × 10 -3 mol cm-3, δHO ) 0.01 cm, DHO ) 1.7 × 10 -5 cm2 s-1, CH+b ) 0.3 × 10 -3 mol cm-3, δH+ ) 0.004 cm, DH+ ) 9.3 × 10 -5 cm2 s-1, A ) 0.01 cm2, Cd ) 2.0 × 10 -5 F cm-2, N0 ) 2.2 × 10 -9 mol cm-2, T ) 300 K, n ) 1, a ) 0.5, k10 ) 4.0 × 10 -2 cm s-1, k20 ) 1.0 × 10 -5 cm s-1, k30 ) 1.0 × 10 -8 mol cm -2 s-1, k40 ) 1.0 × 10 -2 cm s-1, k-40 ) 1.0 × 10 -5 mol cm -2 s-1, k ) 5.0 × 10 -3 cm s-1, k -6 mol 50 -50 ) 5.0 × 10 -2 -1 -6 -2 -1 cm s , k6 ) 5.0 × 10 mol cm s , E20 ) 0.8 V, E30 ) 0.4 V, E40 ) E-40 ) -0.15 V, and E50 ) E-50 ) -0.32 V. The scan rate is (a) 0.05 mA s-1 and (b) 0.01 mA s-1.

following reactions were assumed, in addition to reactions 1 and 2 described in the preceding section. k3

2Pt-OH 98 2Pt + O2 + 2H+ + 2e+

(3)

may be a possible candidate for the initiation of the H2O2 reduction, because resultant Pt-OOH, or Pt-OH produced from it, will also have an autocatalytic effect on the dissociative adsorption by a similar mechanism to that reported,3 Pt-H being readily oxidized into Pt and H+ in the potential region of oscillation E. If this is the case, no essential change will occur in the main conclusions in the present work. Under current-controlled conditions, the following differential equations can be derived for mass balances, a current balance, and reaction rates:1,26

(δHO/2) dCHOs/dt ) (D HO/δHO)(CHOb - CHOs) k1CHOs (1 - θH - θOH - θX)2 (9) (δH+/2) dCH+s/dt ) (D H+/δH+)(CH+b - CH+s) k2CH+sθOH + k3θOH2 - k4CH+s(1 - θH - θOH - θX) + k-4θH - k5CH+s(1 - ΘH) + k-5ΘH (10) dE/dt ) I/ACd - IF/ACd

(11)

IF ) AF{- k2CH+sθOH + k3θOH2 k4CH+s(1 - θH - θOH - θX) + k-4θH - k5CH+s(1 - ΘH) + k-5ΘH + k7CXs (1 - θH - θOH - θX) - k-7θX} (11′) N0 dθOH /dt ) k1CHOs (1 - θH - θOH - θX)2 k2CH+sθOH - k3θOH2 (12) N0 dθH /dt ) k4CH+s (1 - θH - θOH - θX) - k-4θH (13)

k4

-

(8)

Pt + H + e y\z Pt-H (upd-H)

(4)

k-4

N0 dΘH /dt ) k5CH+s(1 - ΘH) - k-5ΘH - 2 k6ΘH2 (14)

k5

Pt + H+ + e- y\z Pt-H (on-top-H)

(5)

N0 dθX /dt ) k7CXs (1 - θH - θOH - θX) - k-7θX

(15)

k-5 k6

Pt-H (on-top-H) + Pt-H (on-top-H) 98 H2

(6)

k7

Pt + X- y\z Pt-X + e-

(7)

k-7

Reaction 7 represents the electrochemical adsorption and desorption of halide ions (X-). The formation and disappearance of upd-H (reaction 4) are observed experimentally as cathodic and anodic current peaks in a potential region from 0.0 to -0.25 V vs SCE just before hydrogen evolution.3 It is also reported that hydrogen evolution occurs via a different type of adsorbed hydrogen (see reactions 5 and 6), as discussed in detail in previous papers.23,25,26 The dissociative adsorption of H2O2 (reaction 1) was assumed in our recent papers1,3,26 to explain not only the nearly potential-independent current in a region of

where CHOs, CH+s, and CXs are the surface concentrations of H2O2, H+, and X-, respectively, and CHOb, CH+b, and CXb are the bulk concentrations of H2O2, H+, and X-, respectively. In the present work, CXs ) CXb is assumed because ∆θX is small (Figure 6c) and X- is not consumed by electrochemical reactions. θOH, θH, ΘH, and θX are the surface coverage of adsorbed OH (Pt-OH), upd-H, on-top H, and adsorbed halogen (X), respectively. E is the true electrode potential, U the externally applied potential (U ) E + IR, where IR is the ohmic drop between the electrode surface and the reference electrode, I being negative for a cathodic current), IF the Faradaic current, A the electrode area, Cd the electrode capacity, N0 the total amount of surface sites per unit area, δHO and δH+ the thickness of diffusion layers for H2O2 and H+, respectively, and DHO and DH+ the diffusion coefficients of H2O2 and H+, respectively. The site-blocking effects of upd-H, adsorbed OH, and adsorbed X were taken into account by introducing such terms



as (1 - θH - θOH - θX) in rate equations, which means that the corresponding reactions occur only on naked Pt sites, not covered with upd-H, Pt-OH, and Pt-X. It was assumed that upd-H and on-top-H existed on different sites and thus θH and ΘH can change independently of each other.1,26 The autocatalytic effect of adsorbed OH on the dissociative adsorption of H2O2 (reaction 1) was taken into account by adopting the following equation:3

k1 ) k10 + γθOH

(16)

where k10 is a normal rate constant and γ is a proportional constant. At present we have no direct experimental evidence for this effect, but it can explain many experimental results such as the appearance of oscillation E, that of the corresponding NDR, and their crystal-face dependence, as discussed in detail in a previous paper.3 Besides, our recent studies showed33 that adsorbed halogen has a similar catalytic effect on the dissociative adsorption of H2O2, supporting the above concept. Moreover, our recent studies have shown34 that the H2O2 reduction on atomically flat Pt in relatively high H2O2 concentrations shows another stationary state of a very high (potentialdependent) current density, quite different from a state of the nearly potential-independent low current density in Figure 2a. This implies34 that, in the stationary state of the high current density, the rate of reaction 1 becomes very high and exceeds that of reaction 2, giving strong support to the presence of the autocatalytic effect of adsorbed OH. The rate constants (ki) for electrochemical reactions were expressed by the conventional Butler-Volmer equations:

ki(E) ) ki0 exp[-anF(E - Ei0)/RT] for reduction reactions (17) ki(E) ) ki0 exp [(1 - a)nF(E - Ei0)/RT] for oxidation reactions (18) where ki0 is the rate constant at E ) Ei0 for the ith reaction, Ei0 the equilibrium redox potential, a the transfer coefficient, and n the number of transferred electrons. In the present work a ) 0.5 was assumed for all reactions for simplicity, except for reaction 4. Reaction 4 is actually composed of two or more processes occurring at different adsorption sites, as is seen from the appearance of two or more (cathodic and anodic) current peaks due to the upd-H formation and disappearance.3,23 As it is difficult to consider individual processes at different sites separately, we approximately considered averaged forward and backward processes of reaction 4 and assumed independent a and (1 - a′) values for the forward (k4) and backward (k-4) processes. The a and (1 - a′) values were determined to be both 0.3 so that they could explain the observed wide distributions of the cathodic and anodic current peaks over a range from 0.0 to -0.25 V vs SCE.3,23 Which of oscillations C and D was reproduced was determined essentially by the equilibrium potential (E70) for halide adsorption (reaction 7). Namely, if E70 was in (or near) a potential region of the NDR due to the autocatalytic effect of adsorbed OH, oscillation C was reproduced. If E70 was in (or near) a potential region of the NDR due to upd-H, oscillation D was reproduced. The reproduction of oscillation D was more difficult than that of oscillation C, i.e., oscillation D was reproduced only under limited ranges of the parameter values. Besides, oscillation D was reproduced only when the transient current due to the upd-H formation was included, indicating that this current played a crucial role in the appearance of oscillation D.

Figure 8. (a-c) Calculated E, θx, and θOH vs time for oscillation C at -1.2 mA of Figure 7a, respectively, and (d-g) calculated E, θx, θOH, and θH vs time for oscillation D at -0.2 mA of Figure 7b, respectively. The same parameter values as Figure 7 were used. A rather steep change of E in (d), in a time region of a nearly constant θx marked by an arrow (rf) in (e), is caused by a rapid exponential decay of θOH that is not seen in (f).

It is to be mentioned here that we reported in a previous paper1 that eq 16 adopted in the present work was not suitable for explanation of oscillations C and D. This was because the calculation with eq 16 showed the appearance of a current oscillation assignable to oscillation C even with no halide adsorption, in disagreement with the experiment. In a previous paper1 we thus adopted the following rather complex equation, instead of eq 16.

k1 ) k10 + γ′θXθOH

(19)

However, we later discovered experimentally the presence of oscillation E near a potential region of oscillation C in the absence of halide ions3 (see Figure 2c). Thus, we can now assign the above-mentioned current oscillation calculated from eq 16 to oscillation E.3 This implies that eq 16 is not unsuitable for explanation of oscillations C and D. Therefore, we adopted this equation in the present work, which made the understanding of the mechanisms of oscillations C and D much easier. Figure 8 shows calculated potential oscillations for oscillations C and D in (a) and (d), respectively, together with time courses of some important variables such as θX, θOH, and θH. The calculated potential oscillations in (a) and (d) reproduce the essential features of oscillations C (Figure 3c) and D (Figure 3d-f), respectively. Discussion It is clear from the experiments and mathematical simulation that both oscillations C and D are classified into HNDR oscillators. This conclusion is also supported by the fact that both oscillations C and D show potential oscillations under current-controlled conditions (Figure 3), contrary to oscillations A and E. As mentioned in the Introduction section, Strasser et al. reported21 that HNDR (Class IV) oscillators could be further


Figure 9. Schematic waveforms of observed oscillations C and D under constant current densities (j), together with main factors affecting the waveforms.

divided into at least three subcategories, called IV-1, IV-2, and IV-3. The results in the present work show that oscillation C can be regarded as a typical example of the IV-2 oscillators, in which the electrode potential E (or U) acts as a fast variable and the coverage (θX) of an adsorbed species acts as a slow variable.21 On the other hand, oscillation D cannot be classified into either of the IV-1, IV-2, and IV-3 subcategories. Oscillation D can be regarded as a new-type HNDR oscillator, as explained below. Let us first consider the mechanism of oscillation C on the basis of the results of mathematical calculation (Figure 8a-c). The upper part of Figure 9 illustrates a schematic waveform of an observed potential oscillation for oscillation C under a constant current density (j) (Figure 3c), together with main factors affecting the waveform. In a high-potential (HP) state just after a transition from a low-potential (LP) state, the temporary θX value is lower than the equilibrium θX value (θX,eq) in the HP state. Thus, θX increases slowly with time (θX: a slow variable). This leads to a slow decrease in the coverage (θnaked) of naked Pt sites where the H2O2 reduction occurs, and thus to a slow negative shift in the true electrode potential (E) to keep the constant j by an increase of the rate of reaction 2, R2. It is to be noted here that R2 in the HP state is not so high that θOH is enough high to maintain the autocatalytic process for the dissociative adsorption of H2O2 (i.e., k1 . k10 in eq 16). When E shifts toward the negative, as mentioned above, θOH decreases owing to an increase in R2. When θOH approaches nearly zero, the autocatalytic process cannot be maintained, and thus a rapid negative shift in E occurs to keep the constant j. Then the system goes to an LP state. In an LP state, the temporary θX is higher than the equilibrium value (θX,eq) in the LP state because high θX was reached in the foregoing HP state. Thus, θX decreases with time. The decrease in θX leads to an increase in θnaked and hence to a

Mukouyama et al. positive shift in E to keep the constant j. The positive shift in E leads to an increase in θOH owing to a decrease in R2. When θOH becomes high enough to maintain the autocatalytic process, the θOH starts to increase rapidly, which leads to the rapid positive shift in E. This leads to the recovery of an HP state. Next let us consider the mechanism of oscillation D, which is more complex than that of oscillation C. The lower figure of Figure 9 illustrates a schematic waveform of observed potential oscillations for oscillation D (cf. Figure 3d-f) and main factors affecting the waveform. The potential for oscillation D shifts stepwise from the HP to LP state, via an intermediate potential (IP) state. The transition from the HP to IP state can be explained in a similar way to the transition from the HP to LP state for oscillation C, by taking account of the autocatalytic effect of adsorbed OH. For oscillation D, the temporary θX in the IP state is still lower than θX,eq in this state, and therefore θX still increases, leading to a further slow decrease in θnaked and a further slow negative shift in E. When E reaches the potential at which the upd-H formation starts, a rapid increase in θH and hence a rapid decrease in θnaked occurs, which induces a rapid negative shift in E to keep the constant j. Thus, the system goes to the LP state. The rapid negative shift in E is, however, retarded and finally inverted to a positive shift because there arise two factors leading to positive shifts in E in the LP state. One is an increase in θnaked owing to the desorption of adsorbed X (i.e., a decrease in θX) at very negative potentials. The other is an addition of the transient cathodic current due to the upd-H formation (and the desorption of adsorbed X) to the H2O2-reduction current. The behavior of E in the LP state for oscillation D is thus determined mainly by the three factors, the increase in θH, the decrease in θX, and the addition of the transient cathodic current. The mathematical simulation showed that oscillation D was reproduced only when the transient current due to the upd-H formation was included, as mentioned in the preceding section. This implies that this current plays a crucial role in the appearance of oscillation D. The appearance of oscillation D could not be explained if we considered only the coverage (θX) of adsorbed halide as the slow variable. Once the potential starts to shift toward the positive in the LP state, a rapid decrease in θH and hence a rapid increase in θnaked start owing to a low θX reached in the foregoing stage. This, in turn, leads to a rapid positive shift in E to keep the constant j. Thus, the HP state is recovered again. It is to be noted here that the calculated potential in the LP state for oscillation C shifts toward the positive from the beginning (Figure 8a), whereas that for oscillation D still shifts toward the negative in the beginning (Figure 8d), thus the lowest potential lying nearly in the middle of the LP state. Such behavior explains the essential difference of the observed time courses between oscillations C (Figure 3c) and D (Figures 3d∼(f)), indicating the validity of the above argument. We can say that oscillations C and D are really of different types. We can also say that oscillation D has both the characters of the IV-2 subcategory (having the coverage of an adsorbed species as a slow variable) and the IV-3 subcategory (having an additional current as an NDR-hiding factor). Oscillation D may thus be classified into a new subcategory, named IV-4. In conclusion, the present studies, using impedance analyses and in-situ light reflectance measurements together with mathematical simulation, have revealed that both oscillations C and D are classified into HNDR (Class IV) oscillators, with adsorbed OH and upd-H as NDR-inducing species, respectively. Detailed analyses of the oscillatory behavior showed that oscillation C


Figure 10. Improved classification of electrochemical oscillations on the basis of mechanisms, with newly added categories indicated by enclosure with rectangles.

is classified into the IV-2 sub-category, whereas oscillation D is classified into a new subcategory, named IV-4, according to the classification of Strasser et al.21 Figure 10 shows, for reference, an improved classification of electrochemical oscillations, in which the above IV-4 subcategory is included together with a “coupled” NDR or CNDR (Class V) oscillator reported in a separate paper.27 Acknowledgment. This work was partly supported by Grantin-Aid for Scientific Research on Priority Area of “Electrochemistry of Ordered Interfaces” (Grant 09237105) from the Ministry of Education, Science, Sports and Culture, Japan. References and Notes (1) Mukouyama, Y.; Nakanishi, S.; Konishi, H.; Nakato, Y. J. Electroanal. Chem. 1999, 473, 156. (2) Fla¨tgen, G.; Wasle, S.; Luˆbke, M.; Eickes, C.; Radhakrishnan, G.; Doblhofer, K.; Ertl. G. Electrochim. Acta 1999, 44, 4499. (3) Nakanishi, S.; Mukouyama, Y.; Karasumi, K.; Imanishi, A.; Furuya, N.; Nakato, Y. J. Phys. Chem. B 2000, 104, 4181. (4) Hudson, J. L.; Tsotsis, T. T. Chem. Eng. Sci. 1994, 49, 1493. (5) Fahiday, T. Z.; Gu, Z. H. Modern Aspects of Electrochemistry; White, R. E., Bockris, J. O’M., Conway, R. E., Eds.; Plenum: New York, 1995; Vol. 27, p 383. (6) Koper, M. T. M. AdVances in Chemical Physics; Prigogine, I., Rice, S. A., Eds.; John Wiley & Sons: New York, 1996; Vol. 92; p 161. (7) Krischer, K. Modern Aspects of Electrochemistry, Conway, B. E., Bockris, J. O’M., White, R. E., Eds.; Plenum: New York, 1999; Vol. 32; p 1.

J. Phys. Chem. B, Vol. 105, No. 30, 2001 7253 (8) Franck, U. F.; FitzHugh, R.; Z. Elektrochem. 1961, 65, 156. (9) Nakabayashi, S.; Zama, K.; Uosaki, K. J Electrochem. Soc. 1996, 143, 2258. (10) Bohannan, E. W.; Huang, L.-Y.; Miller, F. S.; Shumsky, M. G.; Switzer, J. A. Langmuir 1999, 15, 813. (11) Wolf, W.; Luˆbke, M.; Koper, M. T. M.; Krischer, K.; Eiswirth, M.; Ertl, G. J. Electroanal. Chem. 1995, 399, 185. (12) Krischer, K.; Luˆbke, M.; Wolf, W.; Eiswirth, M.; Ertl, G.; Electrochim. Acta 1995, 40, 69. (13) Strassser, P.; Luˆbke, M.; Raspel, F.; Eiswirth, M.; Ertl, G. J. Chem. Phys. 1997, 107, 979. (14) Strassser, P.; Eiswirth, M.; Ertl, G. J. Chem. Phys. 1997, 107, 991. (15) Okamoto, H.; Tanaka, N.; Naito, M. J. Phys. Chem. A 1997, 101, 8480. (16) Okamoto, H.; Tanaka, N.; Naito, M. J. Phys. Chem. A 1998, 102, 7343. (17) Neher, G.; Pohlmann, L.; Tributsch, H. J. Phys. Chem. 1995, 99, 17763. (18) Koper, M. T. M.; Chaparro, A. M.; Tributsch, H.; Vanmaekelbergh, D. Langmuir 1998, 14, 3926. (19) Treindl, L.; Doblhofer, K.; Krischer, K.; Samec, Z. Electrochim. Acta 1999, 44, 3963. (20) Koper, M. T. M. J. Electroanal. Chem. 1996, 409, 175. (21) Strasser, P.; Eiswirth, M.; Koper, M. T. M. J. Electroanal. Chem. 1999, 478, 50. (22) Hommura, H.; Mukouyama, Y.; Matsuda, T.; Yae, S.; Nakato, Y. Chem. Lett. 1996, 91. (23) Matsuda, T.; Hommura, H.; Mukouyama, Y.; Yae, S.; Nakato, Y. J. Electrochem. Soc. 1997, 144, 1988. (24) Mukouyama, Y.; Konishi, H.; Nakanishi, S.; Nakato, Y. Chem. Lett. 1998, 1009. (25) Mukouyama, Y.; Hommura, H.; Nakanishi, S.; Nishimura, T.; Konishi, H.; Nakato, Y. Bull. Chem. Soc. Jpn. 1999, 72, 1247. (26) Mukouyama, Y.; Nakanishi, S.; Nakato, Y. Bull. Chem. Soc. Jpn. 1999, 72, 2573. (27) Mukouyama, Y. New Aspects in Appearance Mechanism and Improved Classification of Electrocatalytic Oscillations. Ph.D. Thesis, Osaka University, 2001. Mukouyama, Y.; Nakanishi, S.; Konishi, H.; Ikeshima, Y.: Nakato, Y. J. Phys. Chem. B Submitted for publication. (28) Clavilier, J.; Faure, R.; Guinet, G.; Durand, D. J. Electroanal. Chem. 1980, 107, 205. (29) Takamura, T.; Takamura, K.; Yeager, Y. J. Electroanal. Chem. 1971, 29, 279. (30) Bagotzky, V. S.; Vassilyev, Y. B.; Weber, J.; Pirtskhalava, J. N. J. Electroanal. Chem. 1970, 27, 31. (31) Markoviæ, N. M.; Lucas, C. A.; Gasteiger, H. A.; Ross, P. N. Surf. Sci. 1996, 365, 229. (32) Gasteiger, H.; Markoviæ, N. M.; Ross, P. N. Langmuir 1996, 12, 1414. (33) Nakanishi, S.; Mukouyama, Y.; Nakato, Y. J. Phys. Chem. B 2001. In press. (34) Mukouyama, Y.; Nakanishi, S.; Konishi, H.; Karasumi, K.; Nakato, Y. Phys. Chem. Chem. Phys. 2001. In press.

Mechanisms of Two Electrochemical Oscillations of Different Types

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