Roles of Local Deviations and Fluctuations of the Helmholtz-Layer

11186

J. Phys. Chem. B 2000, 104, 11186-11194

Roles of Local Deviations and Fluctuations of the Helmholtz-Layer Potential in Transitions from Stationary to Oscillatory Currents in an “H2O2 - Acid-Pt” Electrochemical System Yoshiharu Mukouyama, Takashi Nishimura, Shuji Nakanishi, and Yoshihiro Nakato* Department of Chemistry, Graduate School of Engineering Science, and Research Center for Photoenergetics of Organic Materials, Osaka UniVersity, Toyonaka, Osaka 560-8531, Japan ReceiVed: May 5, 2000

The mechanism of transitions from stationary to oscillatory currents has been studied for H2O2 reduction at Pt electrodes in acidic solutions. The transitions were observed in current versus time curves after the electrode potential was stepped from the rest potential to a potential where an oscillation appeared. The transitions could be classified into two types: a direct transition from a stationary to a final oscillatory current only, with slight modification in the amplitude and period of the oscillation at its initial stage; and an indirect transition via intermediary small-amplitude and short-period oscillations with complex waveforms. The direct transition was observed when the stepped potential was much more negative than the positive end of the oscillatory region in a phase diagram, whereas the indirect transition was observed when the stepped potential was close to the positive end. The appearance of the intermediary oscillatory currents with complex waveforms in the indirect transitions was mainly due to occurrence of small local oscillations at parts of the electrode surface and sudden extensions in the oscillatory area, induced by local deviations and fluctuations of the true electrode potential (or Helmholtz-layer potential), respectively. The main features of the intermediary oscillatory currents were reproduced by mathematical and experimental simulation.

Introduction Chemical and electrochemical oscillations are attractive phenomena from the point of view of dynamic self-organization of molecular systems. A number of electrochemical oscillations have been reported as summarized in recent reviews;1-4 for examples, for anodic dissolution of metals, such as Fe5 and Ni;6 oxidation of hydrogen molecules7 and small organic compounds such as formaldehyde8 and formic acid;9 deposition of metals;10 and reduction of H2O211-19 and peroxodisulfate.20 Active studies have been made on the mechanisms of electrochemical oscillations since the useful formulation by Koper and Sluyters,21,22 with an aid of mathematical simulation.7,19,23-27 The studies have recently revealed that the mechanisms can be classified into several groups.4,28 Recently, growing attention has been paid to formation of spatiotemporal patterns in electrochemical oscillations6,29-31 and their mechanisms.4,32-34 Fla¨tgen and Krischer reported that the migration (drift) current in solution played an important role in the formation of the oscillatory patterns.32 Another interesting face of the electrochemical oscillations is transitions from stationary to oscillatory states. Little is known on detailed mechanisms of the transitions. In general, an oscillation appears within a certain region of parameter values such as the electrode potential, the current density, the solution conductivity, and the concentrations of electro-active species. The transitions can thus occur when the parameter values change across the boundary of the oscillatory region. Local (stationary) deviations and fluctuations (local temporary deviations from the thermodynamic equilibrium values) of the parameter values will play important roles in the transitions when the parameter values are close to the boundary of the oscillatory region, which implies * Author to whom correspondence should be adressed. (Fax +81-66850-6236, e-mail [email protected]).

that studies on the transitions will serve for experimental elucidation of the roles of local deviations and fluctuations in nonlinear chemical dynamics. We have reported thus far that H2O2 reduction at Pt electrodes in acidic solutions show oscillations of various types, called oscillation A, B, C, D, and E. With polycrystalline Pt electrodes, oscillation A is observed in a potential region just before hydrogen evolution, whereas oscillation B is observed in a region of hydrogen evolution.35,36 Oscillations C and D are observed when small amounts of halide ions are added to the solution.25 Oscillation E is observed when an atomically flat single-crystal Pt(111) electrode is used.26 In the present work, we have studied the transitions from stationary to oscillatory currents in the “H2O2 - acid - Pt” system, with a focus placed on clarifying the general features and mechanism of the transitions and elucidating what roles the local deviations and fluctuations play in the transitions. Experimental Section Electrochemical measurements were, in most cases, made with a normal three-electrode system. Polycrystalline Pt (99.97%) disks of 1.0, 0.8, or 0.3 mm in diameter and a polycrystalline Pt (99.9%) plate of 3 × 3 mm2 in area, such as shown in Figure 1, were used as the working electrode. The counter electrode (CE) was a Pt-plate (10 × 10 mm2), and the reference electrode (RE) was a saturated calomel electrode (SCE). A four-electrode system (two working electrodes, one RE, and one CE) was also used to simulate intermediary behavior in transitions from stationary to oscillatory currents, as described in detail in the next section. The Pt-disk electrodes were prepared by cutting Pt spheres, which were obtained by heating Pt wires in a hydrogen-oxygen flame, and sealing with glass (see Figure 1). They were then

10.1021/jp001701l CCC: $19.00 © 2000 American Chemical Society Published on Web 10/26/2000

Transitions in Currents in an H2O2-Acid-Pt Electrochemical System

J. Phys. Chem. B, Vol. 104, No. 47, 2000 11187

Figure 1. Schematic illustration of working electrodes (WE) used in the present work.

polished with 0.06 µm alumina powder and immersed in 60% HNO3 for ∼1 day to remove surface contamination. The Ptplate electrodes were also polished and cleaned in the same way as the Pt-disk electrodes. Just before measurements, the electrode surfaces were further cleaned by repeated cyclic potential scans between -0.35 and +1.60 V versus SCE in 0.3 M H2SO4 (M ) mol/dm3) for ∼30 min. Electrolyte solutions were 0.3 M H2SO4 containing H2O2 in various concentrations. They were prepared using special grade chemicals and pure water, the latter of which was obtained from deionized water by purification with a Milli-Q water purification system. Current density (j) versus potential (U) and j versus time (t) curves for a three-electrode system were measured with a potentiogalvanostat (Nikko-Keisoku NPGS-301) and a potential sweeper (Nikko-Keisoku NPS-2). Those for a four-electrode system were measured with a dual potentiogalvanostat (NikkoKeisoku DPGS). The measured results were recorded with Mac ADIOS II/16 (GW Instruments) at a sampling frequency of 1 kHz. Results Figure 2A shows, for reference in later discussion, a j-U curve for a Pt-disk (φ ) 1.0 mm) electrode in 0.3 M H2SO4 + 0.7 M H2O2. The H2O2-reduction current starts at ca. +540 mV versus SCE (the rest potential) and becomes potentialindependent at about +300 mV. The potential-independent current can be expalained25,27 by considering that the H2O2 reduction is initiated by dissociative adsorption of H2O2, followed by electrochemical reduction of resultant adsorbed OH (Pt-OH), and that the former process becomes a rate-determining step in the potential region more negative than about +300 mV. The j-U curve shows a “negative slope” in a potential region from about -250 mV to about -300 mV (not corrected for the ohmic drop in the solution) for low H2O2 concentrations (e0.2 M), owing to suppression of the dissociative adsorption of H2O2 by formation of adsorbed hydrogen (under-potential deposited hydrogen, upd-H) of a nearly full coverage.25,27 Just in this potential region of the “negative slope”, an oscillation, called oscillation A, appears (Figure 2A) for high H2O2 concentrations (g0.3 M). Another oscillation, called oscillation B, appears in a potential region of hydrogen evolution below about -320 mV (Figure 2A). Figure 2B shows a j-t curve at an electrode potential of -300 mV, where oscillation A is observed. Such a stable periodic oscillation is observed in several seconds after the electrode potential was stepped to this potential (-300 mV), as described later (also see Figure 3). It continues for a long time of >1 h. Figure 3 shows j-t curves in the initial stage after the electrode potential (U) was stepped (as shown in Figure 3a)

Figure 2. (A) A j-U curve under a potential-controlled condition, and (B) a j-t curve at -300 mV versus SCE, for a Pt-disk (φ ) 1.0 mm) electrode in 0.3 M H2SO4 + 0.7 M H2O2.

from the rest potential (+540 mV) to a potential (-270, -290, or -310 mV) at which oscillation A appeared. Almost no current was observed while U was held at the rest potential. The current increased (in the absolute value) suddenly when U was stepped, and then decayed with time because of a decrease in the surface H2O2 concentration by the start of electrochemical H2O2 reduction. The current initially decayed monotonically, not showing any oscillation, while, in the meantime, it began to oscillate. The oscillation finally reached a stable periodic oscillation, such as shown in Figure 2B. The intermediary oscillatory state appearing between the initial stationary current and the final stable periodic oscillation can be called a “transition state” (see Figure 3). The oscillatory behavior in the transition state strongly depended on the values of the stepped electrode potential. Figure 4 shows the influence of the bulk H2O2 concentration on the transition states. In this experiment, the potential of the Pt-disk (φ ) 1 mm) electrode was stepped from the rest potential to -290 mV versus SCE. The transition state became more prominent as the H2O2 concentration got higher. From Figures 3 and 4, we can see that the transitions can be classified into two types; a direct transition from a stationary to a final oscillatory current only with slight modification in the magnitude and period of the oscillation in its initial stage, such as seen in Figures 3d and 4b, and an indirect transition via an intermediary small-amplitude and short-period oscillation, such as seen in Figures 3b and 4c. Similar experiments to those in Figures 3 and 4 were done at various stepped potentials and H2O2 concentrations. The results are summarized in Figure 5, which show regions of the stepped electrode potentials where the direct and indirect transitions are observed, as a function of the H2O2 concentration, together with the potential region where oscillation A is observed. We can see that the direct transition

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Mukouyama et al.

Figure 4. Effect of the H2O2 concentration on j-t curves when U was stepped to -290 mV versus SCE. The electrode was a Pt-disk (φ ) 1.0 mm) and the distance between the Pt-disk electrode and RE was 10 mm. Figure 3. (a) A schematic illustration of a potential step, and (b)-(d) j-t curves in the initial stage after the electrode potential (U) was stepped to potentials (versus SCE) given in the figures. The electrode was a Pt-disk (φ ) 1.0 mm), the electrolyte was 0.3 M H2SO4 + 0.7 M H2O2, and the distance between the Pt-disk electrode and RE was 10 mm.

is observed in case where the stepped potential is much more negative than the positive end of the potential region where oscillation A is observed, whereas the indirect transition is observed in case where the stepped potential is close to the positive end. Figure 6 shows a j-t curve in case of the indirect transition on an expanded time scale. In this experiment, the potential of the Pt-disk (φ ) 1 mm) electrode was stepped from the rest potential to -270 mV (cf. Figure 3b). A small oscillation started in ∼14.8 s after U was stepped. The amplitude (and the period) became gradually larger with time, with no essential change in the waveform, until ∼17 s. The waveform became more complex by sudden addition of another large-amplitude oscillation in a time range of ∼19.1 to 20.3 s. The large-amplitude oscillation increased in frequency with time and became predominant in ∼20.7 to 21 s, finally becoming a stable periodic oscillation in ∼24.7 s. Behavior such as that in Figure 6 was generally observed in repeated experiments for small-area Pt electrodes, though the detailed amplitude and period of the intermediary oscillations in the transition states were different

Figure 5. The regions of the stepped electrode potentials at which the direct and indirect transitions are observed, as a function of the H2O2 concentration, together with the potential region where oscillation A is observed. The electrode was a Pt-disk (φ ) 1.0 mm), and the solution was 0.3 M H2SO4 + H2O2, with the concentration shown in the figure.

from experiment to experiment even with the same electrode and under the same experimental conditions. Figure 7 shows another example of very complex intermediary oscillatory currents, that was observed using a large-area (10 × 10 mm2) Pt-plate electrode. It is to be noted that the complex intermediary oscillatory current is observed even at


Figure 6. A j-t curve on an expanded time scale when U was stepped to -270 mV versus SCE at t ) 0 s. The electrode was a Pt-disk (φ ) 1.0 mm), and the solution was 0.3 M H2SO4 + 0.7 M H2O2.

-320 mV, at which a direct transition is observed for smallarea Pt electrodes (see Figures 3 and 5). In general, the waveform in the transition state became more complex as the electrode area got larger. The waveform also became more complex as the roughness of the electrode surface got larger and the distance between the WE and RE got shorter. Experimental and Mathematical Simulation 1. Experimental Simulation. One of the prominent features of the intermediary oscillatory currents in the indirect transitions is the appearance of a small-amplitude and short-period (periodic) oscillation in the initial stage, such as seen in a time range from 15 to 17 s of Figure 6. Such an oscillation might be explained by taking into account that a small local oscillation appears at a part of the electrode surface and is coupled with a stationary current flowing at the remaining part of the electrode


Figure 7. An example of a very complex j-t curve observed for a large-area Pt-plate electrode (3 × 3 mm2) when U was stepped to -320 mV versus SCE at t ) 0 s. The solution was 0.3 M H2SO4 + 0.7 M H2O2.

surface. To investigate the validity of this model, we measured current oscillations in a four-electrode system (Figure 8), with two working Pt-disk electrodes, that were coupled with each other through the ohmic drops in the solution.37,38 Figure 9 shows a result when the electrode potentials of both the Pt electrodes were simultaneously stepped to -310 mV versus SCE, at which a direct transition was observed for a single Pt electrode (see Figure 3d). The current for one Pt electrode is exhibited in (a) and that for another Pt electrode is shown in (b). The sum of the currents (a) and (b) is shown in (c). Although the two Pt-disk electrodes were apparently identical with each other, the current for electrode (b) began to oscillate first (Figure 9A). After the oscillation for electrode (b) grew up, a small oscillation started for electrode (a) (Figure 9B). The oscillatory currents for electrodes (a) and (b) were then coupled and modulated in the period and amplitude (Figures 9C and 9D), finally resulting in one synchronized oscillation


Mukouyama et al.

Figure 8. Schematic illustration of a four-electrode electrochemical cell with two working Pt-disks (φ ) 0.8 mm) electrodes.

Figure 10. (A) Schematic illustration of a model electrode used for mathematical simulation. (B) Schematic potential profile in the region between the Pt surface and the position of SCE.

oscillation in the indirect transitions by simple mathematical simulation on the basis of the same model as just described. The following reactions were assumed, in the same way as in our previous simulation:25-27 k1

Pt + H+ + e- {\} Pt-H (upd-H)

(1)

k-1

Figure 9. Time courses of individual currents (a) and (b) for two working electrodes in a cell of Figure 8 and that of the total current (c). The electrode potentials for the working electrodes (a) and (b) were simultaneously stepped from the rest potential to -310 mV at t ) 0 s. The solution was 0.3 M H2SO4 + 0.5 M H2O2.

with the same period (Figure 9F). It is to be noted that the total current (c) in Figure 9A clearly indicates the appearance of a small-amplitude and short-period (periodic) oscillation in the initial stage, as expected. The total current (c) of Figure 9 seems to reproduce the essential features of the intermediary oscillatory currents of Figure 6, but there is a difference between them, in that only a small-amplitude oscillation adds to the preceding oscillation in Figure 9 in a time range of ∼5 to 7 s, whereas a large-amplitude (nonperiodic) oscillation adds suddenly to the preceding oscillation in Figure 6 at time of ∼19.2 s. This result implies that the sudden appearance of a large-amplitude (nonperiodic) oscillation in Figure 6 cannot be explained by assuming that another local oscillation appeared at a different part of the electrode surface. 2. Mathematical Simulation. We also investigated the appearance of the small-amplitude and short-period (periodic)

k2

2 Pt + H2O2 98 2 Pt-OH

(2)

k3

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

(3)

k4

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

(4)

k5

Pt + H+ + e- {\} Pt-H (on-top H)

(5)

k-5 k6

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

(6)

where Pt represents a surface Pt site schematically. Reaction 2 represents the dissociative adsorption of H2O2 mentioned in the preceding section. Oscillation A is caused by the suppression of the dissociative adsorption of H2O2 by formation of upd-H of a nearly full coverage.25,27 Another type of adsorbed H, called “on-top H”, contributes to hydrogen evolution.25,27 A model electrode adopted in the present work is shown in Figure 10A. The distribution of the potential near the electrode

Transitions in Currents in an H2O2-Acid-Pt Electrochemical System surface is schematically shown in Figure 10B. Although the electrical coupling of oscillations was recently treated by a rigorous but complicated function,34 we in the present work took account of it approximately by using the following equations:

U - E1 ) RΩ (IC1 + IF1 + κ IF2) ) RΩ [ ACDL(dE1/dt) + IF1 + κ IF2] (7) U - E2 ) RΩ (IC2 + κ IF1 + IF2) ) RΩ [ ACDL(dE2/dt) + κ IF1 + IF2 ] (7′) where U is the external electrode potential, Ej (j ) 1 or 2) is the true electrode potential (or the Helmholtz-layer potential) at parts 1 and 2 of the electrode surface (Figure 10A), (U - Ej) is the ohmic drop in the solution between the electrode surface at part j and the position of the reference electrode (SCE), RΩ is the solution resistance, ICj ) ACDL(dEj/dt) is the charging current at part j, A the electrode area, CDL is the double-layer capacitance per unit area, and IFj is the Faradaic current at part j. The terms κ IF2 in eq 7 and κ IF1 in eq 7′, where κ is a constant that is taken as a parameter, approximately represent a contribution of the ohmic drop by the Faradaic current at the other (neighboring) part of the electrode surface, leading to the coupling of currents at parts 1 and 2.37,38 Equations 7 and 7′ can be rewritten as

dE1/dt ) (U - E1)/ACDLRΩ - IF1/ACDL - κ IF2/ACDL

(8)

dE2/dt ) (U - E2)/ACDLRΩ - κ IF1/ACDL - IF2/ACDL (8′) The IFj (j ) 1 and 2) are given by taking account of the rates of electrochemical reactions 1, 3, 4, and 5 as follows:25-27

IFj ) AF{-k1jCH+s (1 - θHj - θOHj) + k-1jθHj k3jCH+sθOHj + k4jθOHj2 - k5jCH+s (1 - θOHj - ΘHj) + k-5jΘHj}

(9)

where CH+s is the surface concentration of H+ and θOHj, θHj, and ΘHj are the surface coverage of Pt-OH, upd-H, and ontop H at part j, respectively. CH+s is taken to be constant in the present work by considering a much higher diffusion coefficient for H+ than for H2O2. The rate constants for the ith reactions, k1, k-1, k3, k4, k5, and k-5, are expressed by the Butler-Volmer equations as follows:

kij(E) ) ki0 exp[-Ri ni F(Ej - Ei0)/RT] for i ) 1, 3, and 5 (10) kij(E) ) ki0 exp[(1 - Ri)ni F(Ej - Ei0)/RT] for i ) -1, 4, and -5 (11) where ki0 is the rate constant at Ej ) Ei0, Ei0 is the equilibrium redox potential for the ith reaction, Ri is the transfer coefficient, ni is the number of transferred electrons, F is the Faraday constant, R is the gas constant, and T is the absolute temperature. We can assume for simplicity that Ri ) 1/2 for all reactions. Because reactions 1 and -1 (and 5 and -5) are reverse reactions to each other, we obtain E10 ) E-10 and E50 ) E-50. The differential equations for time-dependent variables, Ej, CHOjs (the surface concentration of H2O2 at part j), θOHj, θHj, and ΘHj, are expressed as follows:25-27


(δHO/2) dCHOjs/dt ) (DHO/δHO)(CHOb - CHOjs) k2 CHOjs (1 - θHj - θOHj)2 (12) N0 dθOHj/dt ) k2 CHOjs (1 - θHj - θOHj)2 - k3jCH+sθOHj k4jθOHj2 (13) N0 dθHj/dt ) k1jCH+s (1 - θHj - θOHj) - k-1jθHj (14) N0 dΘHj/dt ) k5jCH+s(1 - θOHj - ΘHj) - k-5jΘHj - 2k6ΘHj2 (15) where DHO is the diffusion coefficient for H2O2, δHO is the thickness of the Nernst’s diffusion layer for H2O2, and CHOb is the concentration of H2O2 in the solution bulk. N0 represents the total amount of surface Pt sites per unit area under an assumption that it is the same for adsorbed OH, upd-H, and on-top H. Figures 11a and 11b show calculated results with no coupling (κ ) 0), whereas Figures 11c and 11d show those with coupling (κ ) 0.05). The initial surface H2O2 concentrations (at t ) 0 s) at parts 1 and 2, CHO1s0 and CHO2s0, are taken to be 0.23 and 0.70 M, respectively, to shift the initiation times of oscillations at these parts. For no coupling (κ ) 0), the currents at parts 1 and 2 (I1 and I2, respectively) oscillate with the same period, with different initiation times (different phases), and independent of each other (Figures 11a and 11b). In the presence of coupling (κ ) 0.05), the oscillations for I1 and I2 are synchronized in a region later than 0.4 s. It is to be noted that the current I1 at part 1 shows a smallamplitude and short-period oscillation in a time region from 0.1 to 0.3 s in which the other current I2 at part 2 remains stationary. This result clearly indicates that a small-amplitude and short-period oscillation appears when a local oscillation is coupled with a stationary current flowing at the remaining part of the electrode surface. Detailed analyses have shown that this phenomenon is due to a positive shift in the true electrode potential E1 at part 1 by a contribution of the ohmic drop of the stationary Faradaic current IF2 at part 2 (cf. eq 7). Discussion The transitions from stationary to oscillatory currents can be divided into two types, a direct transition and an indirect transition, as mentioned in the preceding section. The indirect transitions proceed via intermediary small oscillatory currents with complex waveforms. How can these results be explained? Let us first consider the j-t curve in case of the direct transition. Figures 12 A and 12B schematically show a j-t curve and a corresponding E-t curve expected, respectively. When the electrode potential is held at the rest potential, almost no H2O2 reduction occurs, and hence the surface H2O2 concentration (CHOs) is nearly equal to the bulk H2O2 concentration and high. Accordingly, a high H2O2-reduction current (in the absolute value) appears just after the electrode potential (U) was stepped to a negative potential, say, -310 mV. The current then decays with time because of a decrease in CHOs by the increased H2O2-reduction current by the potential step. The H2O2-reduction current induces an ohmic drop between WE and RE, leading to a positive shift in the true electrode potential (or Helmholtzlayer potential), E. The E is at the most positive just after U was stepped, because the j is the highest (in the absolute value) at this time. The E then shifts toward the negative as the j decays, as illustrated in Figures 12A and 12B. When the E reaches a certain critical potential Ecr, then an oscillation


Figure 11. Calculated j-t curves; (a) and (b) with no coupling (κ ) 0), and (c) and (d) with coupling (κ ) 0.05). Panels (a) and (c) show individual currents (I1 and I2) and panels (b) and (d) show the total current (I1 + I2). Parameter values used are as follows: U ) -300 mV versus SCE, CHOb ) 0.7 × 10 -3 mol cm-3, dHO ) 0.01 cm, DHO ) 1.7 × 10 -5 cm2 s-1, CH+b ) 0.3 × 10 -3 mol cm-3, A ) 0.01 cm2, CDL ) 2.0 × 10 -5 F cm-2, N0 ) 2.2 × 10 -9 mol cm-2, RΩ ) 60 Ω, T ) 300 K, R ) 0.5, n ) 1, k10 ) 1.0 × 10 -2 cm s-1, k-10 ) 1.0 × 10 -5 mol cm -2 s-1, k2 ) 1.0 cm s-1, k30 ) 1.0 × 10 -5 cm s-1, k40 ) 1.0 × 10 -8 mol cm -2 s-1, k50 ) 5.0 × 10 -3 cm s-1, k-50 ) 5.0 × 10 -6 mol cm -2 s-1, k ) 5.0 × 10 -6 mol cm -2 s-1, E ) E 6 10 -10 ) -190 mV versus SCE, E30 ) +800 mV, E40 ) +400 mV, and E50 ) E-50 ) -300 mV.

(oscillation A) starts to appear, where Ecr can be defined as the potential at which the H2O2 reduction starts to be suppressed

Mukouyama et al. (or the j starts to decrease) by an increased surface coverage (θH) of upd-H. The appearance of oscillation A can be explained on the basis of the previously reported mechanism25-27 as follows: When the E reaches Ecr, the j starts to decrease by an increased θH, as already mentioned. The decrease in j causes a decrease in the ohmic drop between WE and RE and hence a negative shift in E, which, in turn, leads to a further increase in θH and a further decrease in j. The process just described is a positive feedback mechanism. Thus, the j steeply decreases down to nearly zero with θH = 1. Once such a low-current state with θH = 1 is attained, almost no H2O2 reduction occurs and, thus, the surface H2O2 concentration (CHOs) increases with time by diffusion from the bulk solution. The increase in CHOs causes an increase in j and hence a positive shift in E, thus leading to a decrease in θH, which, in turn, leads to an increase in j. The latter is also a positive feedback mechanism. When the j reaches a certain critical value, the θH decreases sharply and the j increases rapidly, resulting in a high-current state with θH = 0. Repetition of such processes gives rise to oscillation A. Now, what determines the distinction between the direct and indirect transitions? The potential E is related with the stepped electrode potential (Ustep) by an equation E ) (Ustep - R I) where R I is the ohmic drop between WE and RE. (Note that the current I is cathodic and hence takes a negative value.) The E will finally reach a limiting potential Elim ) (Ustep - R Ilim) provided that no oscillation occurs, as shown by a broken curve in Figure 12B, where Ilim is the potential-independent H2O2reduction current limited by the dissociative adsorption of H2O2 (see Figure 2A). As can be seen from Figure 12B, if the potential Elim is much more negative than Ecr, the potential E will pass across Ecr for a short time. In such a case, we can expect that a stationary current changes suddenly into an oscillatory current, that is, a direct transition is observed. This argument is in harmony with the aforementioned experimental fact that the direct transition is observed in case where Ustep is much more negative than the positive end of the potential region where oscillation A appears (Figure 5). The indirect transition is, on the other hand, observed in case where Ustep is close to the positive end of the potential region of oscillation A (Figure 5). As can be understood from the aforementioned argument, this condition will correspond to that Elim is close to Ecr, as shown in Figure 12C. In such a case, the E approaches Ecr very slowly, or in other words, the E stays at potentials near Ecr for a long time. Thus we can expect that local (stationary) deviations in E, caused by, for example, inhomogeneous distributions of the current density, and fluctuations (local temporary deviations) in E play important roles in the transitions, which is responsible for the appearance of the intermediary oscillatory currents with complex waveforms. As mentioned in the preceding section, a small-amplitude and short-period (periodic) oscillation appearing in the initial stage of the indirect transition (e.g., an oscillation in a time range of 15 to 17 s of Figure 6) can be attributed to a small local oscillation starting at a part of the electrode surface. The appearance of such a small local oscillation can be explained as due to a slight local (stationary) deviation in E toward the negative, as schematically shown in Figure 12C. Both experimental and mathematical simulations have shown that the period of a local oscillation becomes shorter when it is coupled with a stationary current at the remaining part of the electrode surface. The main reason for this result is a positive shift of E for the local oscillation by a contribution of the ohmic drop of the


Figure 12. (A) A schematic representation of a j-t curve in case of a direct transition, (B) an E-t curve corresponding to the j-t curve in (A), and (C) an E-t curve in the case of an indirect transition. Schematic θH versus E curves are added to (B) and (C). Key: (Ustep) the stepped electrode potential; (Ecr) the critical potential at which the H2O2 reduction starts to be suppressed (or the j starts to decrease) by an increased surface coverage of upd-H; (Elim) the limit potential given by Elim ) (Ustep - R Ilim), where -R Ilim (>0) represents the ohmic drop between WE and RE; (Ilim) the potential-independent H2O2reduction current, limited by the dissociative adsorption of H2O2.

surrounding stationary current, as already mentioned. This phenomenon is explained in more detail as follows: In the absence of the contribution of the ohmic drop of the surrounding stationary current, the potential E in the low-current state of the local oscillation (oscillation A) nearly coincides with Ustep because the j in this state is nearly zero. However, the contribution of the ohmic drop of the surrounding stationary current keeps the E in the low-current state much more positive than Ustep (Figure 12C) and hence makes the duration of the low-current state much shorter. The shorter duration of the lowcurrent state leads to the shorter-period diffusion of H2O2 from the solution bulk and hence to the lower surface H2O2 concentration (CHOs) at the beginning of the high-current state, which, in turn, makes the duration of the high-current state shorter. It is expected from the argument just penetrated that the period of the local oscillation becomes longer as the surrounding stationary current density gets lower, which is really observed in Figure 9 in a time range from 1.0 to 5.5 s. Another interesting feature of the indirect transitions is the sudden appearance of a large-amplitude (nonperiodic) oscillation in the course of gradual growth of the preceding small oscillation, as clearly seen at a time of ∼19.2 s of Figure 6. The appearance of a large-amplitude oscillation was not


reproduced by experimental simulation (Figure 9), indicating that it cannot be explained by assuming the appearance of another local oscillation at a different part of the electrode surface, as already mentioned. It is to be noted that the sudden appearance of a large-amplitude oscillation occurs after the preceding small (local) oscillation grew up to some extent (Figure 6), suggesting that the large-amplitude oscillation arises from a certain modulation of the preceding oscillation. A possible explanation may be given by assuming that the oscillating area of the preceding local oscillation at the electrode surface extends suddenly by a fluctuation in E or fluctuations in other parameters such as j, CHOs and θH, which cause a fluctuation in E. Such a sudden extension of the oscillating area may be induced with an aid of a fluctuation in the spatial pattern of the oscillating area. The nonperiodic (random) nature of the large-amplitude oscillation in the initial stage (19-20.3 s in Figure 6) is in harmony with this argument. It may be mentioned here that the aforementioned small-amplitude and short-period oscillation (an oscillation at 15-17 s in Figure 6) is most probably preceded by a random minute oscillation in the very initial stage (at 14.7-14.8 s), induced by a fluctuation of E (see Figure 12C). In conclusion, the present work has revealed that transitions from stationary to oscillatory currents are divided into two types, direct and indirect. The indirect transitions are observed in the case where the stepped potential is close to the positive end of an oscillatory region. The intermediary oscillatory currents in the indirect transitions are, in general, complex in waveform and characterized by the appearance and growth of a small periodic oscillation in the initial stage, sudden appearances of nonperiodic large-amplitude oscillations, addition of other small oscillations, and coupling of the oscillations. The behavior can be explained by taking into account local deviations and fluctuations in E. Further studies will lead to detailed elucidation of the roles of local deviations and fluctuations in E in nonlinear chemical dynamics. Acknowledgment. This work was partly supported by a Grant-in-Aid for Scientific Research on Priority Area of “Electrochemistry of Ordered Interfaces” (No. 09237105) from the Ministry of Education, Science, Sports and Culture, Japan. References and Notes (1) Hudson, J. L.; Tsotsis, T. T. Chem. Eng. Sci. 1994, 49, 1493. (2) Fahiday, T. Z.; Gu, Z. H. Modern Aspects of Electrochemistry; Vol. 27; White, R. E., Bockris, J. O’M., Conway, R. E., Eds.; Plenum: New York 1995; p 383. (3) Koper, M. T. M. AdVances in Chemical Physics, Vol. 92; Prigogine, I., Rice, S. A., Eds.; John Wiley & Sons: New York, 1996; p 161. (4) Krischer, K. Modern Aspects of Electrochemistry, Vol. 32; Conway, B. E., Bockris, J. O’M., White R. E., Eds.; Plenum: New York 1999, p 1. (5) Nakabayashi, S.; Zama, K.; Uosaki, K. J. Electrochem. Soc. 1996, 143, 2258. (6) Lev, O.; Sheintuch, M.; Pismen, L. M.; Yarnitzhy, H. Nature 1988, 336, 458. (7) Krischer, K.; Lu¨bke, M.; Wolf, W.; Eiswirth, M.; Ertl, G. Electrochim. Acta 1995, 40, 69. (8) Okamoto, H.; Tanaka, N.; Naito, M. J. Phys. Chem. A 1998, 102, 7343. (9) Okamoto, H.; Tanaka, N.; Naito, M. Chem. Phys. Lett. 1996, 248, 289. (10) Shinohara, N.; Kaneko, N.; Nezu, H. Dinkikagaku 1995, 63, 419. (11) Tributsch, H. Ber. Bunsen-Ges. Phys. Chem. 1975, 79, 570. (12) Tributsch, H. Ber. Bunsen-Ges. Phys. Chem. 1975, 79, 580. (13) Tributsch, H.; Bennett, J. C. Ber. Bunsen-Ges. Phys. Chem. 1976, 80, 321. (14) Cattarin, S.; Tributsch, H. J. Electrochem. Soc. 1990, 137, 3475. (15) Cattarin, S.; Tributsch, H.; Stimming, U. J. Electrochem. Soc. 1992, 139, 1320. (16) Fenter, N.; Hudson, J. L. J. Phys. Chem. 1990, 94, 6506.

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Roles of Local Deviations and Fluctuations of the Helmholtz-Layer

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