New-Type Electrochemical Oscillation Caused by ElectrodeSurface

ReceiVed: June 27, 2001; In Final Form: September 1, 2001. The appearance mechanism of an electrochemical oscillation (previously called oscillation B...
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J. Phys. Chem. B 2001, 105, 10905-10911

10905

New-Type Electrochemical Oscillation Caused by Electrode-Surface Inhomogeneity and Electrical Coupling as Well as Solution Stirring through Electrochemical Gas Evolution Reaction Yoshiharu Mukouyama, Shuji Nakanishi, Hidemitsu Konishi, Yusuke Ikeshima, and Yoshihiro Nakato* Department of Chemistry, Graduate School of Engineering Science, Osaka UniVersity, Toyonaka, Osaka 560-8531, Japan ReceiVed: June 27, 2001; In Final Form: September 1, 2001

The appearance mechanism of an electrochemical oscillation (previously called oscillation B), observed for Pt electrodes in H2O2-containing acidic electrolytes in a potential region of hydrogen evolution, has been investigated. Though it is reported that electrochemical oscillations in general appear in potential regions of negative differential resistance (NDR) or hidden NDR (HNDR), impedance analyses have shown that no NDR or HNDR is present in the potential region of oscillation B. Besides, oscillation B is observed only for Pt electrodes with atomically roughened surfaces, not for electrodes with atomically flat surfaces. A possible explanation is proposed by assuming the presence of small local “active” areas in the electrode surface, in which the H2O2 reduction is not prevented by a full coverage of under-potential deposited hydrogen, contrary to the other normal “nonactive” areas occupying the major part of the electrode surface. The appearance of oscillation B is reproduced by mathematical simulation based on the model, together with the consideration of electrical coupling between the active and nonactive areas as well as solution stirring by hydrogen-gas evolution. Oscillation B can be classified into a new category of oscillators, which may be called “coupled NDR” oscillators.

Introduction Chemical oscillations are representative examples of nonlinear chemical phenomena. Recently, a large number of oscillatory phenomena have been reported, in particular in the field of electrochemistry, as summarized in recent reviews.1-4 The mechanisms of electrochemical oscillations have been studied successfully5-16 especially since the work of Koper and Sluyter.5,6 Very recently, Strasser et al. classified17 electrochemical oscillations on the basis of the mechanisms and proposed four categories, classes I, II, III (negative differential resistance [NDR] oscillators), and IV (hidden negative differential resistance [HNDR] oscillators). They also reported17 that most electrochemical oscillations fell into class III and class IV categories. We have been studying electrochemical oscillations for H2O2 reduction at Pt electrodes in aqueous H2SO4,18-28 with an emphasis placed on surface chemistry and influences of microscopic structures of the electrode surface on oscillations and vice versa.24-28 Interestingly, the “H2O2 reduction on Pt” system has shown various oscillations of different types, called oscillation A, B, C, D, and E. Detailed studies have revealed that the H2O2 reduction on Pt has two-type NDRs: one arises from the suppression of the H2O2 reduction by formation of under-potential deposited hydrogen (upd-H) in a potential region just before hydrogen evolution and the other arises from a decrease in the coverage of adsorbed OH (which is formed as an intermediate of the first step of the H2O2 reduction, i.e., the dissociative adsorption of H2O2 and acting as an autocatalyst * To whom correspondence should be addressed. Fax: +81-6-68506236. E-mail: [email protected].

for it) with a negative potential shift, in a region of more positive potentials than the NDR due to upd-H. Oscillation A appears from the NDR due to upd-H,20-22 whereas oscillation E appears from the NDR due to adsorbed OH,24,27 thus, both being classified into NDR oscillators. Oscillation E is observed only for atomically flat Pt (111) electrodes.24 The autocatalytic effect of adsorbed OH for the H2O2 reduction has been confirmed by the observation26 of two stationary states characterized by potential-independent low current densities with θOH = 0 and potential-dependent high current densities with θOH = 1, where θOH is the coverage of adsorbed OH. On the other hand, oscillations C and D are observed in the presence of a small amount of halide ions in the solution20 and are both classified into HNDR oscillators.25 Oscillation C appears from hiding of the NDR due to adsorbed OH by a decrease in the coverage (θX) of adsorbed halogen (acting as a site blocking agent) with a negative potential shift.25 Oscillation D appears from hiding of the NDR due to upd-H by not only the decrease in θX but also an addition of a transient cathodic current due to the upd-H formation.25 Oscillation B is observed in the absence of halide ions in the solution, similar to oscillations A and E. Oscillation B was discovered at the earliest stage of our work,18 but the appearance mechanism has long remained unclear. In the present paper, we report that oscillation B is an oscillation of quite a new type. Experimental Section Half-spherical single-crystal and polycrystalline Pt electrodes (about 0.8-1.0 mm in diameter) were used as the working electrode. Single-crystal Pt (111), (100), and (110) electrodes with atomically flat surfaces were prepared by the method of

10.1021/jp012461s CCC: $20.00 © 2001 American Chemical Society Published on Web 10/04/2001

10906 J. Phys. Chem. B, Vol. 105, No. 44, 2001

Mukouyama et al.

Clavilier et al.,29 as reported previously.24 The atomic flatness of the electrode surfaces was confirmed by atomic force microscopy as well as by measurements of characteristic current vs potential curves for electrochemical hydrogen adsorption and desorption.29-33 Polycrystalline Pt (poly-Pt) electrodes with atomically flat surfaces were prepared similarly by modifying the Clavilier method. Single-crystal Pt (111), (110), and (100) and poly-Pt electrodes with atomically nonflat (roughened) surfaces were also used as the working electrode. They were prepared by performing surface-roughening treatments (i.e., oxidation and rereduction procedures) in atomically flat Pt surfaces, according to the literature.34 In the present work, cyclic potential scans were repeated between -0.35 and +1.60 V vs SCE at a rate of 0.1 V/s in 0.3 M H2SO4 for a few minutes, because Pt should be oxidized above ca. 0.55 V and reduced below ca. 0.45 V. Poly-Pt electrodes, prepared just by cutting and polishing, were also used. For electrodes of this type, the electrode surface was finally polished with 1.00-0.06 µm alumina powder and immersed in 5.0 M HNO3 (M ) mol/dm3) for about 1 day, followed by repeated cyclic potential scans between -0.35 and +1.60 V vs SCE in 0.3 M H2SO4 for about 30 min just before measurements, to remove surface contamination. The contact of the well-defined Pt surface and the electrolyte was accomplished by making use of a meniscus of the electrolyte, as reported previously.24 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. Electrolyte solutions (in most cases 0.3 M H2SO4 + 0.7 M H2O2) 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. A small amount of potassium iodide (KI) was in some cases added to the solution. Current density (j) vs potential (U) curves and j vs time (t) curves were measured with a potentiogalvanostat (NikkoKeisoku NPGS-301) and a potential programmer (NikkoKeisoku NPS-2). They were recorded with a data-storing system (Mac ADIOS II/16, GW Instruments) at a sampling frequency of 1 kHz. Ohmic drops in the solution between the working electrode and the reference electrode are not corrected in the present work. 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. Results Figure 1 shows, for reference in later discussion, a reported j vs U curve for (simply cut and polished) poly-Pt in 0.3 M H2SO4 + 0.7 M H2O2 under a potential-controlled condition, together with waveforms of oscillations A and B.18 The cathodic current in a potential region of about +0.60 to -0.25 V vs SCE, in Figure 1a, is due to H2O2 reduction. The current is independent of the potential in a region of about +0.40 to -0.25 V, which is explained20,22,24 by assuming that the H2O2 reduction is initiated by the dissociative adsorption of H2O2 k1

2Pt + H2O2 98 2Pt-OH

(1)

followed by electrochemical reduction of the resultant Pt-OH k2

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

(2)

Figure 1. (a) j-U curve under a potential-controlled condition at a scan rate of 0.01 V s-1, (b) j-t curve for oscillation A at -0.27 V vs SCE, and (c) the same for oscillation B at -0.40 V. The electrode is poly-Pt. The electrolyte is 0.3 M H2SO4 + 0.7 M H2O2.

and the former is the rate-determining step. Another possibility of dissociative adsorption of H2O2 into Pt-H and Pt-OOH was discussed in a previous paper,25 though it caused no essential change in the oscillation mechanism. The j-U curve shows an NDR in about -0.25 V to -0.30 V, and just in this potential region, oscillation A appears.18,22 The NDR arises from the suppression of reaction 1 by the formation of a nearly full coverage of upd-H.18,20,22 Hydrogen evolution starts at a slightly more negative potential, say, about -0.30 V (Figure 1a). Oscillation B appears in the potential region of hydrogen evolution, i.e., in a region of “positive differential resistance”, contrary to oscillation A. Oscillation E does not appear for polyPt with atomically rough surfaces.24 An apparent NDR appearing in a potential region of 0.38-0.42 V in Figure 1a is due to the concentration polarization of H2O2 caused by j-U measurement under a potential scan at a rate of 0.01 V s-1. The waveforms for oscillations A and B, shown in Figure 1 parts b and c, respectively, are apparently similar, except that the waveform of oscillation B is somewhat disturbed by hydrogen-gas evolution. Detailed inspection of the current behavior during the low-current state (in the absolute value), however, shows that the current in this duration for oscillation A always increases with time (Figure 1b), whereas that for oscillation B decreases or is nearly constant (Figure 1c). The current in the latter sometimes increases with time, depending on experiments. A much clearer difference between oscillations A and B was observed in the influence of addition of very small amounts of halide ions to the solution. Figure 2 parts a and b show j vs U when 0.6 and 1.2 µM KI were added to 0.3 M H2SO4 + 0.7 M H2O2, respectively. Compared in Figure 1a, oscillation A was hardly affected by the addition of KI, whereas oscillation B was strongly quenched. With the increase in the KI concentration, the potential region where oscillation B was quenched extended from the positive end toward the negative. Oscillations C and D did not appear under the concentrations of H2O2 and KI of Figure 2, as reported.20

New-Type Electrochemical Oscillation

J. Phys. Chem. B, Vol. 105, No. 44, 2001 10907

Figure 2. Effect of addition of KI on j-U curves for poly-Pt, measured under potential-controlled conditions at a rate of 0.01 V s-1. The electrolyte is 0.3 M H2SO4 + 0.7 M H2O2 including (a) 0.6 × 10-6 M KI and (b) 1.2 × 10-6 M KI.

Figure 4. j-U curves for (a) atomically flat and (b) atomically roughened poly-Pt in 0.3 M H2SO4 + 0.7 M H2O2, measured under potential-controlled conditions at a rate of 0.01 V s-1.

Figure 5. Impedance (Z) diagram in a region of 1 Hz to 100 kHz for nonflat poly-Pt (meniscus) in 0.3 M H2SO4 + 0.2 M H2O2 at -0.40 V vs SCE. Figure 3. Effect of addition of KI on j-U curves for poly-Pt, measured under current-controlled conditions at a rate of 0.05 mA s-1. The electrolyte is 0.3 M H2SO4 + 0.7 M H2O2 including (a) no KI and (b) 1.0 × 10-6 M KI.

Figure 3 shows the j-U curve under current-controlled conditions. Oscillation B as a potential oscillation was clearly observed in the absence of KI (Figure 3a), whereas it was completely quenched by addition of 1.0 µM KI (Figure 3b), in agreement with the results of Figure 2. Oscillation A, which was an NDR oscillator, was not observed under currentcontrolled conditions. Similar quenching effects for oscillation B were observed when chloride (Cl-) and bromide (Br-) ions were added.20 Another clear difference between oscillations A and B was observed in the effect of surface roughening of Pt electrodes. Figure 4 compares the j-U curves for atomically flat and atomically roughened poly-Pt electrodes under potentialcontrolled conditions. Oscillation B was not observed for atomically flat poly-Pt but was observed for atomically roughened poly-Pt, though oscillation A was observed for both electrodes. The same results were obtained for atomically flat and roughened single-crystal Pt (111), (110), and (100) electrodes. The results strongly suggest that oscillation B cannot be classified into the conventional HNDR oscillators, because otherwise it should be observed for electrodes with atomically flat surfaces.

To investigate whether an HNDR was present or not in the potential region of oscillation B, impedance measurements were done. Figure 5 shows an impedance diagram obtained for nonflat poly-Pt (meniscus) in 0.3 M H2SO4 + 0.2 M H2O2 at -0.40 V vs SCE. No NDR or HNDR is observed in Figure 5, though the diagram may be somewhat affected by hydrogen-gas evolution. This conclusion is supported by the fact that the diagram of Figure 5 is nearly the same as that in H2O2-free 0.3 M H2SO4, for no NDR should exist in the H2O2-free solution. The impedance for Pt in the region of hydrogen evolution was studied in detail by Conway et al.35,36 Figure 6 shows the effect of mechanical stirring of the solution on the j-U curve. When the solution (0.3 M H2SO4 + 0.7 M H2O2) was stirred with a magnetic stirrer, oscillation A disappeared completely, whereas oscillation B was hardly affected. The potential-independent current in the region of +0.3 to -0.2 V increased by the solution stirring, suggesting that the surface H2O2 concentration was increased by the stirring. A slight shift in the potential region of oscillation B is due to the ohmic drop in the solution. Mechanistic Model of Oscillation B and Mathematical Simulation. Oscillation B appears in a potential region of positive differential resistance (Figure 1a) and shows potential oscillations under current-controlled conditions (Figure 3a). These features are typical of HNDR oscillators,4,17 but oscillation

10908 J. Phys. Chem. B, Vol. 105, No. 44, 2001

Figure 6. Effect of mechanical stirring of the solution on j-U curves for poly-Pt in 0.3 M H2SO4 + 0.7 M H2O2, measured under potentialcontrolled conditions. The solution is (a) static and (b) stirred. The scan rate is 0.01 V s-1.

Figure 7. Schematic illustration of an inhomogeneous structure of the electrode surface to explain the appearance of oscillation B, together with reactions in (a) high- and (b) low-current states.

B cannot be classified into HNDR oscillators for the following reasons: (1) The impedance analyses showed no HNDR in the potential region of oscillation B. (2) Oscillation B was not observed for Pt electrodes with atomically flat surfaces. The fact that oscillation B appears only for atomically roughened Pt (Figure 4) suggests that it is originating from certain “active” areas of the electrode surface. If they occupy only a small portion of the electrode surface, they will not affect essentially the behavior of other oscillations such as oscillations A, E, C, and D, which arise from normal “nonactive” areas. The effective quenching of oscillation B by halide ions (Figures 2 and 3) can be explained by assuming that the active areas preferentially adsorb halide ions even at the very low concentrations of about 1 µM, which leads to the loss of the active areas. Thus, we can assume as a possible explanation that oscillation B originates from an inhomogeneous structure of the Ptelectrode surface, as shown schematically in Figure 7. The electrode surface is composed of active and (normal) nonactive areas. In the (normal) nonactive areas, the H2O2 reduction is suppressed by the formation of upd-H, as assumed previously20,22 for the explanations of oscillation A. This implies that

Mukouyama et al. no H2O2 reduction can occur in the (normal) nonactive areas, in a potential region of hydrogen evolution where a full coverage of upd-H is attained. On the other hand, in the active areas, the H2O2 reduction is assumed to occur even with a full coverage of upd-H. In other words, both the hydrogen evolution and the H2O2 reduction occur in the active areas. We also assume that the active areas occupy only a small portion of the (nonflat) electrode surface, as mentioned earlier. This is reasonable because the cathodic current in the potential region of hydrogen evolution is nearly the same between atomically flat and nonflat Pt electrodes (see, e.g., Figure 4). If the active areas occupied a considerable part of the (nonflat) electrode surface, the current at this electrode would be considerably higher than that at the flat electrode having no active area. The appearance of oscillation B can be explained qualitatively on the basis of the above model as follows: When the Pt electrode is in a high-current state (Figure 7a), the active H2O2 reduction occurs throughout the electrode surface because the true electrode potential (E) is enough positive to remove upd-H owing to a large ohmic drop in the solution. More strictly, E is given by E ) U - IR, where U is the externally applied constant potential, located in the region of hydrogen evolution, and IR is the ohmic drop in the solution between the Pt electrode and the reference electrode (I is negative for a cathodic current). The active H2O2 reduction, however, leads to a decrease in the surface H2O2 concentration (CHOs) due to slow H2O2 diffusion and hence to a decrease in the current density (j) or the ohmic drop (IR), which, in turn, leads to a negative shift in E. The negative shift in E finally leads to the formation of upd-H, as U is in the region of hydrogen evolution. It is to be noted that a positive feedback mechanism works for the upd-H formation, because a negative shift in E increases the coverage (θH) of upd-H, which in turn leads to a decrease in j and hence to a further negative shift in E.21 As soon as a full coverage of upd-H is formed, the Pt electrode moves to a low-current state (Figure 7b). In a low-current state, hydrogen evolution occurs throughout the electrode surface, but the H2O2 reduction can occur only in the active area, owing to a full coverage of upd-H (Figure 7b). If the nonactive area occupies the major part of the electrode surface, as mentioned earlier, the suppression of the H2O2 reduction in the nonactive area leads to an increase in CHOs by diffusion. The CHOs is also increased by solution stirring by hydrogen-gas evolution. The increase in CHOs increases the local H2O2-reduction current density (jlocal) in the active area and thus shifts the local E (Elocal) in the active area toward the positive owing to the ohmic drop in the solution. If the CHOs is high enough, the Elocal can reach the potential region where upd-H is removed. Here we have to take into account the effect of electrical coupling between the active area and the surrounding nonactive area. Namely, the high jlocal in the active area (and the large ohmic drop in the solution near the active area) causes a positive shift in E in the surrounding nonactive area, adjacent to the active area, by electrical coupling (see Figure 8). This leads to the removal of upd-H in the surrounding nonactive area and thus to an increase in the local current density in the area. This means that there is a positive feedback mechanism with respect to the increase in the area of the high local current density. Thus, the area of the high local current density expands rapidly with time, finally expanding up to the whole electrode surface. As a consequence, the Pt electrode moves to a high-current state again.

New-Type Electrochemical Oscillation

J. Phys. Chem. B, Vol. 105, No. 44, 2001 10909 with respect to the ohmic drop, each meeting at right angles at every point, as schematically illustrated in Figure 8. The IFa and IFn are given, by taking account of electrochemical reactions 2-5, as follows:

IFa ) AaF{-k2aCH+sθOHa - k3aCH+s(1 - θHa) + k-3aθHa + k4aθOHa2 - k5aCH+s(1 - ΘHa) + k-51ΘHa} (8) IFn ) AnF{-k2nCH+sθOHn - k3nCH+s(1 - θHn - θOHn) + k-3nθHn + k4nθOHn2 - k5nCH+s(1 - ΘHn) + k-5nΘHn} (8′)

Figure 8. Schematic diagram explaining the electrical coupling between the active and nonactive areas. A cathodic current in the active area, under constant U, causes positive shifts in E not only in the active area but also in the adjacent nonactive areas.

We made mathematical simulation for oscillation B by the above model. The reaction schemes, the equivalent circuit, and the mathematical framework, adopted in the present work, are essentially the same as those reported before.20,22,24 First, the following reactions were assumed, in addition to reactions 1 and 2: k3

Pt + H+ + e- ) Pt-H (upd-H)

where CH+s is the concentration of H+ ions at the electrode surface, which is assumed to be the same between the active and nonactive areas (as discussed below) and θOH, θH, and ΘH are the surface coverages of Pt-OH, upd-H, and on-top H, respectively, with the other subscript, a and n, representing the active and nonactive areas, respectively. The currents due to the formation and disappearance of upd-H were neglected because they were small compared with the other currents. The surface H2O2 concentration, CHOs, as well as CH+s, were assumed to be the same between the active and nonactive areas, by considering the effect of rigorous solution stirring near the electrode surface by hydrogen-gas evolution in the low-current state together with the occurrence of the common H2O2 reduction in the active and nonactive areas in the high current state. The time dependence of CHOs was expressed as follows:

(3)

k-3

(δHO/2) dCHOs/dt ) (D HO/δHO)(CHOb - CHOs) -

k4

2Pt-OH 9 8 2Pt + O2 + 2H+ + 2ek

(4)

5

k5

Pt + H+ + e- ) Pt-H (on-top H)

(1 - r)k1nCHOs(1 - θHn - θOHn)2 - rk1aCHOs(1 - θOHa)2 + s(CHOb - CHOs)/CHOb (9)

For simplicity, the electrode surface was divided into two parts, part a (active area) and part n (nonactive area). The explicit expression of the (local) electrical coupling between the active and nonactive areas will be given by a very complicated function,37 and therefore, we in the present work took account of it approximately by using the following equations:23

where DHO is the diffusion coefficient for H2O2, δHO is the thickness of the diffusion layer for H2O2, and CHOb is the concentration of H2O2 in the solution bulk. The areas of parts n and a, An and Aa, are expressed as (1 - r)A and rA, respectively, where A is the total area and r is a constant. Thus, the second term on the right-hand side of eq 9 represents the decrease in CHOs by reaction 1 in the nonactive area, and the third term represents the same in the active area. The fourth term represents the increase in CHOs by the solution stirring by hydrogen-gas evolution. Under an assumption that the stirring effect is in proportion to the rate of hydrogen evolution, s is expressed as follows:

U - Ea ) RΩ[ICa + IFa + κ(ICn + IFn)]

(7)

s ) s0 {(1 - r)k6ΘHn2 + rk6ΘHa2}

U - En ) RΩ[κ(ICa + IFa) + ICn + IFn]

(7′)

ICj ) AjCDL (dEj/dt)

(7′′)

where s0 is a proportional constant, taken as a parameter. The time dependence of the other variables, CH+s, θOHj, θHj, and ΘHj, are expressed as follows:

k-5

k6

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

(5)

(6)

where Ej (j ) a or n) is the true electrode potential (Helmholtz double-layer potential) for part j (part a or part n), U - Ej is the ohmic drop between part j and the position of the reference electrode (SCE), RΩ is the solution resistance, ICj is the charging current in part j (Aj is the electrode area and CDL is the doublelayer capacitance), IFj is the Faradaic current at part j, and κ is a parameter expressing the extent of electrical coupling. The terms, κ(ICn + IFn) and κ(ICa + IFa), in eqs 7 and 7′ imply that the current at part n (or a) causes a shift in E at part a (or n) in the adjacent position. This can be understood by considering the lines of electric current and the planes of equal potential

(10)

(δH+/2) dCH+s/dt ) (D H+/δH+)(CH+b - CH+s) + (IFn + IFa)/AF + s(CH+b - CH+s)/CH+b (11) (1 - r)N0 dθOHn/dt ) k1nCHOs (1 - θHn - θOHn)2 k2nCH+sθOHn - k4nθOHn2 (12) rN0 dθOHa/dt ) k1aCHOs(1 - θOHa)2 - k2aCH+sθOHa k4aθOHa2 (12′)

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(1 - r)N0 dθHn/dt ) k3nCH+s(1 - θHn - θOHn) k-3nθHn (13) rN0 dθHa/dt ) k3aCH+s(1 - θHa) - k-3aθHa

(13′)

(1 - r)N0 dΘHn/dt ) k5nCH+s(1 - ΘHn) - k-5nΘHn 2k6ΘHn2 (14) rN0 dΘHa/dt ) k5aCH+s(1 - ΘHa) - k-5aΘHa 2k6ΘHa2 (14′) where N0 represents the total amount of surface Pt sites per unit area. The rate constants, k2j, k3j, k-3j, k4j, k5j, and k-5j, were expressed by the Butler-Volmer equations.21 Figure 9 shows calculated j-U curves under potential- and current-controlled conditions. Oscillation B was not reproduced when we assumed only the effect of solution stirring by hydrogen-gas evolution (Figure 9 parts c and d). Oscillation B was also not reproduced when we assumed only the presence of the active area and electrical coupling. The assumption of both the effects reproduced oscillation B (Figure 9 parts a and b). The potential region of oscillation A and that of oscillation B are not separated in Figure 9a. They are separated when the effect of solution stirring, s, which is assumed in eq 10 to be in proportion to the hydrogen-evolution rate, is assumed to be in proportion to the square or the third power of the hydrogenevolution rate. Figure 10 shows calculated time courses for the current, In, Ia, and I () In + Ia) at U ) -0.4 V. The current oscillation in Figure 10c reproduces the essential features of the waveform of oscillation B (Figure 1c). Discussion The experimental results and mathematical simulation have revealed that oscillation B cannot be classified into HNDR oscillators. Oscillation B can be reproduced only when we assume both the presence of the active area (and electrical coupling) and the effect of solution stirring by hydrogen-gas evolution. Oscillation B can thus be regarded as a new-type electrochemical oscillation. Oscillation B may be called “coupled NDR” or CNDR oscillator, in contrast to “hidden NDR” or HNDR oscillators, because it appears in a potential region of positive differential resistance by coupling with an NDR existing in another potential region. Electrochemical oscillations in the potential region of hydrogen evolution, apparently similar to oscillation B, were reported38,39 by Li et al. for the reduction of anions such as Fe(CN)63-, S2O82-, and IO3- on Pt in 1 M NaOH. Li et al. explained the oscillations in terms of depletion of the electroactive anions at the electrode surface by reactions and their replenishment by solution stirring due to hydrogen evolution. This mechanism, however, does not contain any autocatalytic processes and will lead to no oscillation. In fact, in the system of the present work, only the solution-stirring effect by hydrogen-gas evolution cannot reproduce oscillation B, as already mentioned. Strasser et al. later studied40 the potential oscillation for IO3- reduction on Ag in 1 M NaOH and explained it by taking into account an NDR due to a Frumkin effect (repulsion of a negatively charged electrode to electroactive anions), which was hidden by a hydrogen evolution current. It is to be noted that this mechanism cannot be applied to oscillation B because H2O2 is a neutral molecule and the

Figure 9. Calculated j-U curves, a and b with κ ) 0.9 (electrical coupling) and c and d with κ ) 0 (no electrical coupling). The solutionstirring effect by hydrogen evolution (s0 ) 5.0 × 104) is included in all cases. Curves a and c are under potential-controlled conditions, and b and d are under current-controlled conditions. The scan rates are 0.01 V s-1 and 0.01 mA s-1. The other parameter values are as follows: r ) 0.05, 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, d H+ ) 0.004 cm, D H+ ) 9.3 × 10 -5 cm2 s-1, 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, k1 ) 4.0 × 10 -2 cm s-1, k1′ ) 1.6 × 10 -1 cm s-1, k20 ) 1.0 × 10 -5 cm s-1, k30 ) 1.0 × 10 -2 cm s-1, k-30 ) 1.0 × 10 -5 mol cm -2 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, k6 ) 5.0 × 10 -6 mol cm -2 s-1, E20 ) +800 mV vs SCE, E30 ) E-30 ) -190 mV, E40 ) +400 mV, and E50 ) E-50 ) -300 mV.

Frumkin effect does not work. In short, all reported mechanisms cannot explain oscillation B. We reported previously21,22 that oscillation B appears in a region of higher concentrations of H2O2 than oscillation A. This result is in accordance with the present model because the large ohmic drop, i.e., the high local current density (in the absolute value), is necessary in the active area to induce the transfer from the low- to high-current states for oscillation B, as discussed in the preceding section. The potential region where oscillation B is observed is either separated from or in succession with the potential region where oscillation A is observed, depending on experiments (see, e.g., Figures 1a and 5a). The mathematical simulation showed that the separation depended on how to express the effect of solution stirring, s, in eq 10, as mentioned in the preceding section. It may thus be likely that the separation depends on how effectively the hydrogen-gas evolution causes the solution

New-Type Electrochemical Oscillation

Figure 10. Calculated time courses for In, Ia, and I at U ) -0.4 V vs SCE. The parameter values are the same as those in Figure 9.

stirring. In this connection, it may be noted that the separation becomes larger by addition of a small amount of iodide ions (compare Figures 1a and 2a). This can be explained by considering the loss of the active areas by preferential adsorption of iodide ions at the active areas. The appearance of oscillation B only on the negative potential side in a low concentration of iodide ions (Figure 2a) can be attributed to nonadsorption of iodide ions (or desorption of adsorbed iodine) at very negative potentials. For oscillation B to appear in the present model, the active area has to have an area of a finite size, because the ohmic drop due to the high local current in the active area (in the lowcurrent state) has to induce a large positive shift in E (large enough to remove upd-H) in the surrounding nonactive area by electrical coupling. A possible candidate for such active areas may be given by assuming the presence of holes (pits) or grooves at the Pt surface produced upon mechanical polishing, at which apparently high-density currents can flow owing to large Pt-surface areas including those of walls of the holes or grooves. It does not seem unreasonable to assume that the H2O2 reduction (or the dissociative adsorption of H2O2) is not so strongly suppressed by upd-H of a full coverage for atomically roughened surfaces. Our experiments showed, in agreement with the literature,41 that the slope of the j-U curve in the region of the NDR due to upd-H (or the magnitude of the NDR) was highest for Pt (111) and lower for Pt (110) and (100), indicating that the extent of suppression of the H2O2 reduction by upd-H depended on the crystal faces (atomic structures) of the Pt surface. Further studies are, however, necessary to clarify more details. In conclusion, the present work has revealed that oscillation B can be regarded as an oscillation of a new type, which may be called “coupled NDR” or CNDR oscillator. The appearance of oscillation B suggests a new possibility that an electrochemical reaction in a potential region of positive differential resistance can couple with an NDR in another potential region to cause an electrochemical oscillation through the presence of electrode-surface inhomogeneity as well as electrical coupling and solution-stirring by an electrochemical reaction. 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.

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