Spatio-temporal pattern formation during the reduction of peroxodisulfate in the bistable and oscillatory regime: a surface plasmon microscopy study

ELSEVIER

Journal of Electroanalytical Chemistry 409 (1996) 183-194

Spatio-temporal pattern formation during the reduction of peroxodisulfate in the bistable and oscillatory regime: a surface plasmon microscopy study ’ G. Fl’itgen, K. Krischer *, G. Ertl Fritz-Haber-Institut der Max-Plan&Gesellschaft,

Faradayweg 4-6, D-14195 Berlin (Dahlem), Germany

Received 6 November 199.5;in revised form 1I December 1995

Abstract Using surface plasmon microscopy we demonstrate that oscillations as well as transitions in the bistable regime during the reduction of

S,Oi- at Ag electrodesare accompanied by wave phenomena. Typical velocitiesof the wavesrangefrom somecentimetersper second to meters per second, depending on the conductivity

of the electrolyte.

The characteristic

length of the patterns is determined

by the

temporaldynamicsof the potentialdrop acrossthe doublelayer at high masstransportand by the dynamicsof the concentrationof S,Oiat the electrode at low mass transport. The first gives rise to potential fronts with front widths between 0.1 and 0.5 mm; the second leads to smooth structures on the order of centimeters. Further, the influence of the electrode boundary on the pattern formation in

electrochemicalsystemsis discussed, aswell asthe generalityof the above-mentioned characteristictimesandlengths. Keywords:

Surface plasmon microscopy; Pattern formation; Oscillations; Reduction of peroxodisulfate

1. Introduction

Oscillating currents or potentials were observed with a large variety of electrochemical reactions under certain experimental conditions [l-3]. Oscillations in these global and easily measurablequantities are accompaniedby oscillating concentrations of reacting speciesat or close to the electrode surface. Generally, speciesin a solid (liquid interface cannot be mixed by any kind of convection. Therefore, it cannot be expected that the whole electrode reacts homogeneously. Rather, it is likely that parallel to the temporal oscillations spatial patterns are formed at the electrode Ielectrolyte interface which consist of spatially varying concentrationsas well as varying current densities. The latter are connected with different potential drops acrossthe double layer. In contrast to the large number of publications on temporal oscillations (in a recent review [2] about 500 are cited), there are only very few reports on spatial pattern formation. Except for the system considered here, all

* Corresponding author. ’ This paper is based on a presentation given during the Snowdonia Conference on Electrified Interfaces, Harlech, Wales, UK, 17-21 July 1995.

0022-0728/96/$15.00 PII SOO22-0728(96)045

0 1996 Elsevier Science S.A. All rights reserved I 1-l

examples come from metal dissolution or metal deposition [4-lo]. These reactions have the advantage that spatial inhomogeneities can be easily observed, as oscillations during metal dissolution are often accompaniedby visible reflectivity changesdue to the formation and dissolution of passivating films with thicknessesfar beyond a monolayer. Hence, the patterns can be directly recorded with a video camera or any other charge coupled device (CCD). However, in order to understand the basic rules which govern pattern formation in electrochemical systems,metal dissolution reactions seem far too complicated to serve as suitable model systemsfor several reasons.The kinetics of the formation of the passivating films is complex and only poorly understood, transport of speciesthrough the films has to be considered, and the electrode surface changes continuously. However, in systems free of complications of this kind, i.e. if the electrode acts only as an electron donor and acceptor or as a catalyst and the mechanismof the oscillations is well understood,patterns which might be connected with the dynamic instabilities are not visible under light microscopy. In the studies on metal dissolution mentioned above, besideslight microscopy, stationary potential probes were also employed in order to visualize patterns in the current density. This method is less restrictive in the sensethat, whenever dynamic instabilities in electrochemical reac-

184

G. Fliirgen

er al.//ournnl

of Electroanalytical

tions lead to patterns on the electrode, the patterns also occur in the current density. Recently, micro potential probes were used successfully to demonstrate the existence of spatial self-organization in a simple oscillatory system, the reduction of peroxodisulfate at a quasi-one-dimensional ring electrode [11,12]. Besides its advantages of general applicability and comparatively simple experimental setup, there is also the severe drawback of limited resolution in space and time, resulting from the disturbance of the kinetics through the measurement. Fast motion of the probe induces convection of the electrolyte, and the probe itself affects the diffusion of the reactive species. As these difficulties are more severe when a two-dimensional electrode is investigated, the use of potential probes for the observation of spatio-temporal dynamics has been confined to one-dimensional geometries. Two-dimensional images during electrocatalytic oscillations became accessible only recently by the introduction of surface plasmon (SP) microscopy [131. In this paper we use SP microscopy to study the reduction of peroxodisulfate at Ag electrodes in the bistable and oscillatory regime. Special emphasis is laid on the question of characteristic times and lengths as well as on the influence of the electrode boundary on pattern formation. Furthermore, we discuss in which systems similar results can be expected. Oscillations during the reduction of peroxodisulfate had already been observed by Gokhshtein and Frumkin [ 141 in the 1960s. As old as the discovery of the oscillations is the idea that the negative differential resistance due to an electrostatic repulsion between an anion and the electrode for potentials negative of the pzc as well as a high series resistance are essential for the occurrence of the oscillations. Meanwhile, extensive experimental studies and model calculations [15,16] support this early conjecture. Furthermore, it turns out that there are many systems which can be described by models exhibiting the same mathematical structure [17]. In Section 2 we summarize briefly the experimental findings and simulations of the temporal, i.e. global, behavior found during the reduction of S,Oi- at Ag electrodes. This represents the basis for the main part of the paper, the studies on spatial phenomena. In Section 3 SP microscopy is introduced, and in Sections 4 and 5 the experimental data are represented and discussed respectively.

2. The global behavior

of the S,Oi-

reduction

Fig. 1 displays current-voltage characteristics of the reduction of S,Oi- at a rotating electrode for different rotation frequencies. At low rotation rates there exists an interval of the externally applied voltage U in which the current exhibits oscillatory behavior, whereas at high rotation rates bistability is observed. The same scenario is seen when the concentration of S,Oi- or the ionic strength is varied: at low S,Oi- concentrations or low conductivity

Chemistry

409 (1996)

-oL -20

183-194

; ______ Lb-----1.6

-i6

-l.L

-l.Z

U.&V

-1.0

-126

-0.6

-0.L

-0.2

(vs. SCE)

Fig. 1. Current-voltage characteristics of the reduction of ~$0:~ at different rotation rates. The current displays oscillations at low rotation rates (-, f= 5 Hz) and bistable behavior at higher rotation rates (---, f= 20 Hz; ------, f= 40 Hz). Electrolyte 1 mM Na,S,O,, 0.5 mM Na,SO,, pH 5 (H,SO,).

the reaction exhibits bistable behavior, at higher concentrations or high conductivity oscillations appear. These features can be readily understood by analyzing, on the one hand, the dependence of the reaction current on the potential drop across the double layer and, on the other hand, the stability of a simple equivalent circuit representing the electrochemical cell. Frumkin pointed out that in a dilute solution the variation of the potential inside the double layer may affect the electrode kinetics in two ways: firstly, the potential difference driving the electrode reaction has to be corrected by the potential drop r& across the diffuse double layer, and secondly, owing to electrostatic attraction or repulsion, the concentration of charged species at the outer Helmholtz plane is different from the bulk concentration [l&19]. These effects have become known as Frumkin effects and can be incorporated into the Butler-Volmer equation leading to the following expression for the dependence of the current density on the potential drop c& across the double layer hea, = -nFkcexp[-anF/RT(&,-E,)] Xexp[(

an - z)F/RT(

A>]

(1)

In our context the most important consequence of the Frumkin effects is that they can lead to a negative slope in the polarization curve for low ionic strengths. Fig. 2(a) displays such a current-potential curve calculated from Eq. (1) with rate constant and transfer coefficient suitable for the reduction of S,Oi[15,16] and a total ionic strength of 15 mM. Whenever the cell resistance R, is large enough, the steady state which possesses a negative polarization slope is unstable. In quantitative terms, ‘large enough’ means m R, > l&l = IkW,,/dZl . order to destabilize the steady state [17,20]. This result can be readily obtained by linear stability analysis of a common equivalent circuit for an electrochemical cell as shown in Fig. 2(b): the electrode is represented by a capacitance C in parallel with a faradaic impedance Z, and is connected in series with the uncompensated cell resistance R,. The potentiostatic operation

G. Frdrgen

i$yi-q .,‘ -1.0 -0.5

0.0

%L

et al./Journal

0.5

of Electroanalyrical

1.0

v

u

b

C

R.

GJ

Fig. 2. (a) From FQ (1). calculated dependence of the reduction current on the potential drop across the double layer (4DL given with respect to pzc of -0.6 V (SCE)). Parameters n= 2, k = 2.5X lo-“, z = -2, LY= 0.13. I& calculated implicitly [42] using Gouy-Chapman theory [19] with 5 mM Na,SO, and 0.1 mM Na,S,O, in the bulk electrolyte. (b) Simple equivalent circuit for an electrochemical cell under potentiostatic control.

mode is described by the constant voltage U across the electrode and electrolyte. The equation, describing the potential evolution across the double layer, results from a charge balance of this equivalent circuit

dd%L u-&x c -= dt

Re

(2)

- Jmc

Assuming that the concentration of the active speciesis constant (which correspondsto ‘infinitely fast masstransfer’), the dynamics of the reaction are fully described by Eq. (2), and the dynamic behavior which can occur is either mono- or bistable. In many experimental situations, however, the slower masstransport of the reactants has to be taken into account, adding another degree of freedom to the system. The temporal change in concentration of the reactive species at the electrode is then given by the difference between the reactive consumption and the diffusive transport of the specieswhich, to a first approximation, can be assumedto be proportional to the difference between the concentrations in the bulk and double layers dc 12 -=-_. dt 8nFJreac

+ LD(c,6’

c)

where 6 is the thickness of the diffusion layer, D the diffusion constant and cb the bulk concentration. For slow masstransport, Eqs. (2) and (3) predict oscillatory behavior. For fast masstransport the small value of S ensuresa fast adjustment of the steady state concentration such that at these parameter values the dynamics are governed by &. (21, resulting again in bistable behavior. This dependence of the dynamics on the thickness of the diffusion layer was seen in the experiments (cf. Fig. 1) and, as is

Chemisrry

409 (1996)

185

183-194

evident from the general nature of Eqs. (2) and (31, is not specific to our particular system, reduction of S,Oi-, but is common to many systems which possessa negative polarization slope (for a detailed discussionseeRef. [17]). So far, we have only consideredthe temporal behavior, i.e. we have implicitly assumedthat the whole surface reacts homogeneously. The aim of this paper is to extend this picture to the spatial dimension. In order to obtain a feeling of the patterns that might form, it is worthwhile to again consider the two stable steady statesin the bistable regime. Fig. 3 shows a schematic of the potential distribution perpendicular to the electrode for the two states.The active state is characterized by a high current density, implying a high ohmic potential drop inside the electrolyte and, as the experiments were carried out under potentiostatic conditions, a small potential drop across the interface. For the passive state the opposite is true: both the current and ohmic potential drop acrossthe double layer are high. Now, consider a situation in which part of the electrode is in the active state and part in the passive state. In the interfacial region of the two states there exists an electric field component parallel to the electrode, inducing migration currents parallel to the electrode. As a consequence of these cross currents, the double layer recharges; hence, the interface starts to move, and potential fronts will be observed. Fronts were observed in other chemical systems that exhibit bistability, for example homogeneously catalyzed reactions like the iodate-arsenous acid system [2 l-231 or heterogeneouscatalysis [24,25]. In these systemsthe two states are characterized by different concentrations of the reacting species and the fronts constitute concentration waves. In exothermic catalytic reactions, the steady states also possessdifferent temperatures,giving rise to propagating temperature profiles [26-281.

3. Experimental setup The central element of our electrochemical cell suitable for spatio-temporal measurementsis a glassprism of high refractive index (LASF 35, Schott, Mainz, Germany), onto one side of which a 50 nm thick Ag film is evaporated (Fig. 4). The silver film servesas a working electrode, and the glassprism permits the excitation of surface plasmons by a p-polarized laser beam which is passedthrough the

passive

active

z

z

Fig. 3. Schematics of the potential distribution perpendicular to the electrode for the passive and active steady state in the bistable regime.

186

G. FIiitgen

et aI./Journal

ofElectroandytica1

Chemistry

409 (1996)

-2.2

183-194

-2.0

-1.8 UN

b

Fig. 4. Schematics

of the experimental

-1.4

-

-1.6

-1.4

-1.2

(SCE)

,

setup for SP microscopy.

prism onto the Ag film with a certain angle of incidence. This configuration has become known as the Kretschmann configuration [29]. In the experiments described below a He-Ne laser was used, and in some experiments a small sapphire plate was brought into optical contact with a sapphire or glass prism of nearly identical refractive index (SFLS6, Schott, Mainz, Germany). In these cases CH,J, served as index-matching liquid. The excitation of SPs occurs in a narrow interval of the angle of incidence, at which the energy and momentum of the incoming photons and SPs are matched. The SP excitation manifests itself as a strong decrease in intensity of the reflected laser beam. In the late 1970s several groups studied the excitation of surface plasmons in an electrochemical environment and showed that the dispersion relation of the SPs changes with the applied potential in a certain potential range (see Section 5) [30-401. Fig. 5 displays two typical resonance curves, obtained at two different values of the potential, which are clearly shifted relative to each other. Obviously, if the potential drop is different at two different locations at the electrode, the intensity of the reflected laser beam at a certain angle of incidence should be different. Hence, spatially resolved pictures of the potential distribution along the electrode can be obtained if the laser beam is broadened and the irradiated part of the electrode is imaged onto a screen, which can be recorded with a CCD (Fig. 4). A Dalsa CCD with full-frame transfer architecture allowed us to store

-1.6

48;

-2.2

-2.0

-1.8 UN

(SCE)

Fig. 6. (a) Current-voltage and (b) intensity-voltage characteristics of the peroxodisulfate reduction. The electrolyte (2 mM Na,S,O,, 0.05 mM Na,SO,. 0.01 M NaOH) was stirred by an impinging jet.

800 frames per second with 128 X 128 pixels. This high temporal resolution is necessary in order to resolve the fast dynamic characteristics for oscillatory electrochemical reactions. The camera was connected to an image processing board, and the digitally available images were further processed in order to eliminate intensity differences due to the Gaussian intensity profile of the laser beam or inhomogeneities in the film thickness. The glass prism was mechanically pressed to an electrochemical cell. A defined convection was achieved with an impinging jet which was placed close to the freely accessible working electrode. A Pt plate served as counter electrode and a Hg IHg,SO, electrode was used as reference a

o.oy,

4.64, -1.8

,

,

,

,

,

,I

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.8

-0.6

$,N

(SCE)

200 2

150.

? z 2

lOG-

50 48-l 50.0

50.5

51.0

51.5

52.0

52.5

$10

Fio (Sk)

5. Surface plasmon resonance (left curve) and - 0.3 V (SCE)

curves measured at II = - 1.0 V (right curve) in 0.1 M NaF, pH 10.

-1.6

-1.6

-1.4 @n/V

-1.2

-1.0

(SCE)

Fig. 7. (a) Current-voltage and (b) intensity-voltage data of Fig. 6 after IR correction; R = 3.6 kR.

characteristics

of the

a

0

b

3mm

100

200

300

400

timelms

99 ms

108 ms

117 ms

126 ms

135 ms

157.5 ms

180 ms

202.5 ms

279 ms

Fig. 8. (a) Time trace of the global current during a transition in the bistable microscope. Electrolyte 1 mM Na,S,O,, 0.1 mM Na,SO,. 0.01 M NaOH,

regime, (b) images of the electrode during N, saturated, impinging jet stirring.

the transition

obtained

with the SP

a

0

I

I

I

100

I

I

300

200

timelms b

8mm

56 ms

96 ms

226 ms

64 ms

86 ms

116 ms

158 ms

264 ms

300 ms

Fig. 9. (a) Time trace of the global current during a transition in the bistable regime at parameter values closer to the oscillatory regime than in Fig. 8. Note that the relaxation to the active steady state is not completely shown. (b) Images of the electrode during the transition obtained with the SP microscope. (The color scale is reversed in comparison with Fig. 8 as the angle of incidence lies on the other side of the resonance minimum.) Electrolyte I mM Na,S,O,, 0.1 mM Na,SO,, 0.01 M NaOH, N, saturated, slower impinging jet stirring than in Fig. 8.

a

0

I

I

I

I

I

I

I 100

1

I 200

I

-1 --

-2 * b

6mm

44 ms

--

300

timelms

48 ms

50 ms

54 ms

62 ms

80 ms

100 ms

120 ms

236 ms

-...

Fig. 10. (a) Time trace of the global current during an oscillation. (The oscillation frequency was about 2 Hz.) (b) Images of the electrode during oscillation obtained with the SP microscope. Electrolyte 2 mM Na,S,O,, 0.1 mM Na,SO,, 0.1 M NaOH, N, satmated, impinging jet stirring.

the

190

G. Fliitgen

et al./Journal

ofElectroanalytica1

electrode. All experiments were carried out under potentiostatic control. The electrolyte was prepared with triple distilled water and p.a. grade chemicals (Na,SO,, Na,S,O,, NaOH, HzSO,, all Merck).

4. Results Fig. 6(a) displays current-voltage characteristics of the peroxodisulfate reduction in a parameter regime in which the reaction exhibits bistable behavior. In parallel to the current the average intensity of the reflected beam at a constant angle of incidence was recorded (Fig. 6(b)). Obviously, the two steady states in the bistable regime are characterized by different reflectivities and can be clearly distinguished. A careful comparison of how current and intensity change with voltage reveals that the optical measurement contains more information than the current: outside the bistable regime the current density does not exhibit any hysteresis. In contrast, the intensity of the reflected beam is somewhat higher in the positive than in the negative scan. As the measurements were carried out under potentiostatic conditions, this indicates that the amount, or possibly also the nature, of chemisorbed species is different in the two scan directions. As discussed in the Introduction, the solution resistance cannot be neglected under conditions where bistable or oscillatory behavior is observed. Hence, the externally applied voltage is not equal to the potential drop 4oi, across the double layer, which determines current density and resonance conditions for the SP excitation. For this reason, it is instructive to investigate how both quantities depend on 4oL. This can be easily done if the uncompensated resistance is known. Corresponding plots for the data of Fig. 6 are shown in Fig. 7. From the dependence of the reaction current on +uL the region of negative resistance can be clearly seen. The unstable steady state, which is, of course, not seen in the experiment, is indicated by the dashed line. Fig. 7(b) shows that the intensity of the reflected beam depends, to a first approximation, linearly on the potential. In the following, we present the spatio-temporal behavior of the electrode in three dynamically different regimes. The simplest behavior can be expected during a transition from one steady state to another in the bistable regime. Such an example is displayed in Fig. 8. Fig. 8(a) shows how the total current changes during a transition from the low-current density state (passive) to the high-current density state (active): at time t = 99 ms the magnitude of the current starts to rise monotonically until it has reached the active steady state at about 140 ms. A sequence of images recorded during the transition is shown in Fig. 8(b). At the moment at which the current starts to rise, a small nucleus of the active state appears at the lower left rim of the disk-shaped electrode. This nucleus expands and the image taken at t = 157.5 ms appears nearly homogeneous. The

Chemistry

409 (19961 183-194

growing active state in the first five images corresponds well to the increasing current. However, as can be seen in the last four images, the reflectivity of the electrode changes further on a slower time scale while the current stays constant. In repetitions of the experiment, the first wave always originates at the rim of the electrode, though from different positions. If the convection is reduced, the bistable behavior changes into oscillatory behavior. The oscillations are preceded by more complex transients in the bistable regime: during a transition from the passive to the active state, the current does not monotonically increase but overshoots its active steady state value and relaxes slowly towards it from high current values. Such a situation is depicted in Fig. 9(a). The spike of Fig. 6 also stems from such a more complex transition. Just like the global behavior, the spatio-temporal picture also becomes more complex in this parameter regime (Fig. 9(b)). The current starts to increase after 54 ms and reaches its maximum value after about 86 ms. The relaxation back to the final steady state lasts for several hundred milliseconds and is not completely shown. The first three images are taken during the rising part of the current and give the impression that two waves, one originating at the left edge and the other at the right edge a little later, are propagating across the surface. As discussed below, it is also possible that a variation in the current is accompanied by circular waves starting at the whole border of the electrode at the same time. Owing to the comparatively high noise level of the data, it is hard to decide which of these two possibilities is realized in this example. At t = 116 ms, i.e. somewhat after the current maximum, the electrode acquires an approximately homogeneous state, which is characterized by the highest intensity. From this state a nearly radially symmetric wave starts at the rim of the disk and propagates towards its center, finally leaving a homogeneous state whose reflectivity is only slightly different from the passive state. The spatio-temporal behavior during a period of oscillation is shown in Fig. 10. The time trace of the current resembles that in the complex bistable regime: an oscillation can be roughly divided into three regimes, the regime of fast increase, followed by one of slow relaxation to its original value, and a quasi-stationary phase. This sequence occurs with a distinct frequency of about 2 Hz. The images in Fig. 10(b) show that as soon as the current starts to rise, a nucleus of a second phase is formed in the lower right-hand comer. This nucleus expands across the electrode. Again. the maximum intensity is attained some time after the current has reached its highest value. From the nearly homogeneous state of maximal intensity the intensity decreases slowly. Owing to the high noise level it is hard to decide whether the decrease in intensity is accompanied by a radial wave with a broad interface, or whether it occurs homogeneously. Finally, we would like to mention that at more positive values of the potential close to the onset of oscillations, i.e.

G. Friitgen

et al./Journal

of Electroanalytical

A Ak k,

/

/ Uth Fig. 1 I. Schematics of potential. A change in SP to a change in coverage specific adsorbing anion.

U

the dependence of the SP wave vector on resonance is only observed if the potential leads of a chemisorbed species, as for example a The adsorption starts at the potential cl,,,.

close to the Hopf bifurcation [411, no spatial structures were discernible so we can assume that the homogeneous oscillation is stable in this parameter regime.

5. Discussion

We have shown that oscillations as well as transitions in the bistable regime during the reduction of S,Oiare accompanied by wave phenomena at the electrode. These wave phenomena were recorded with SP microscopy. For a more detailed interpretation of the dynamics it is essential that we clarify the influence of electrode potential on the SP resonance. The linear dependence of the reflectivity on the electrode potential (Fig. 7(b)) suggests that the reflectivity probes the potential. However, experiments and calculations by different groups [34-37,39,40] show that the situation is more complicated. All published resonance curves exhibit an asymmetric behavior of the SP resonance with potential, as schematically depicted in Fig. 11. At potentials negative to a characteristic potential V,, the SP resonance is nearly independent of the potential; only positive of this threshold is a considerable shift of the SP wave vector with potential observed. This dependence could be reproduced in calculations which revealed that a change of electron density in the metal exhibits only a minor effect on the SP dispersion. However, the change of electron density in the metal is directly coupled to a change of charge density in the double layer. Positive to the pzc the double layer charge is carried by anions which often specifically adsorb at the electrode. The shift of the wave vector with potential is attributed to a change in the coverage of specifically adsorbing species. Hence, although thesurface plasmon resonance changes with electrode potential over a wide range, it is not affected directly by the electrode potential but by the influence of the electrode potential on the coverage of adsorbed species. From these considerations, we have to conclude that in our experiments also the change in intensity is connected with coverage. From this point of view, it is surprising that

Chemistry

409 (1996)

183-194

191

we observe changes in the intensity at potentials as negative as - 1.6 V (SCE) (Fig. 7(b)). At present, we do not have a convincing interpretation of the nature of the adsorbed species within the passive regime of the S,Oireduction, i.e. at potentials negative of the pzc. (The pzc of Ag(l11) is -0.69 V (SCE), Ag(100) -0.91 V (SCE), Ag(ll0) - 1.01 V (SCE) [42]; that for polycrystalline Ag is expected to be somewhere between the pzcs for Ag(1 11) [35] and Ag(l10) [42]. Although we have not determined the pzc for our Ag films, we can assume that the passive branch lies negative to it, as (i) the potentials differ by several hundred millivolts from the data mentioned above, and (ii) according to the mechanism leading to the bistability, the passive branch should be negative of the pzc.) When going from the passive to the active state, the potential changes from values negative of the pzc to those positive of the pzc, and it is likely that SO:-, produced at a very high rate, adsorbs at the electrode. The change in coverage due to the recharging of the electrode occurs at the same time scale at which the potential changes and, in this sense, the waves observed during the fast increase of the current in Figs. 8-10 represent potential waves. In other words, we observed the dynamic of the variable tiDL (Eq. (2)) and not that of c (Eq. (3)). Besides these fast variations representing the potential front, the reflected intensity also changes on a much slower time scale, as apparent in the last four images in Fig. 8. This slow decrease in intensity is not connected with any observable change in current density. This means also that the potential drop across the double layer stays constant, and these slow intensity variations do not reflect the potential evolution; they have to result from changes in composition of the double layer (without any change of the double layer charge) or state, i.e. roughness, of the Ag surface. Both seem to be possible during the reduction of S,Oi-. We observed macroscopic restructuring of the Ag film on the order of hours, and attributed it to the oxidation of Ag by the reaction intermediate SO,’ and successive redeposition of Ag+. However, since we expect that such a restructuring of the surface occurs on an even slower time scale than the intensity variations in Fig. 8, we consider it more likely that the change in resonance originates from a second species adsorbing at the electrode. Desilvestro and Weaver [43] deduce from SERS measurements. at Au electrodes that in the presence of S,Oi- the oxide region extends towards more negative potentials than without S,Oi-. At a first glance, it seems likely that the same happens at Ag, and we will test this conjecture in future experiments. Changes in SP intensity that do not correspond to changes in potential can also be seen in other data, i.e. in Figs. 6, 9 and 10. The hysteresis within the active and passive branches in Fig. 6(b) has no counterpart in the current shown in Fig. 6(a). In Figs. 9 and 10 the intensity maximum occurs somewhat later than the current maximum. These observations point again to a slower change in

192

G. Fliitgen

et al./Journal

of EIectroarudytical

the composition of the double layer or the roughness of the Ag surface. At present, we believe that these changes do not influence the pattern formation. Although there remain some uncertainties in the interpretation of the intensity images, several conclusions on characteristic times and lengths of patterns in electrochemical systems can be drawn. Firstly, consider the transition in the bistable regime shown in Fig. 8. The potential front propagates across the electrode with a velocity of about 10 cm s- ’ ; from other experiments we know that the velocity increases with the conductivity of the electrolyte and reaches, at ionic strengths of 20 mM, velocities on the order of meters per second. These velocities are lo3 to lo6 orders of magnitude faster than typical front velocities observed in other chemical systems like, for example, the Belousov-Zhabotinsky reaction [44] or CO oxidation at Pt single crystal surfaces [45,46]. The front width lies between 0.1 and 0.5 mm, which again is several orders larger than in the above-mentioned systems. The data of Fig. 8 were obtained at high mass transfer rates at which, as discussed in Section 2, the dynamics are governed by the temporal evolution of the potential drop across the electrode, while the concentration of S,Oiin front of the electrode adjusts rapidly to the changed potential. For very thin diffusion layers the restoration of the consumed species occurs nearly instantaneously. (Note that in Eq. (3) consumption and restoration of S,Oiat the electrode are proportional to l/S and l/6* respectively.) Hence, in this parameter regime, potential and concentration profiles look like those sketched in Fig. 12. This is different when the diffusion layer becomes thicker due to less efficient mass transport. The steady state concentrations of the active and passive states are now considerably different and the dynamics of the concentration are slow. Owing to these slow dynamics the concentration remains nearly constant during the transition of the potential from the active to the passive state. As the concentration of S,Oi- is larger in the passive than in the active state, the current density is higher immediately after

/

/-

ct Fig. 12. Schematic potential and concentration profile of a front in the bistable regime at high mass transfer, corresponding to the experimental situation shown in Fig. 8.

Chemistry

409

(1996)

183-194

‘;l-J cI--I

+ x

Fig. 13. Schematic potential and concentration profile of a front bistable regime at comparatively low mass transfer, corresponding experimental situation shown in Fig. 9.

in the to the

the transition than in the steady state value of the active branch; but after the transition, S,Ol- is consumed faster by the ongoing reaction than it is replenished by diffusion, and the current density decreases along with the concentration, until both quantities have reached their respective steady state values. With these considerations we can rationalize the more complex behavior shown in Fig. 9. The first five images show two fast potential fronts emerging from two opposing sites of the disk (the left one somewhat later than the right one). After the front has passed, the current slowly decreases due to a decrease of the surface concentration of S,Oi- and, hence, the potential becomes more negative again. As depicted in Fig. 13, the spatial profile of the potential front is now composed of two parts, a fast increasing part which is governed by the fast dynamics of the potential and a slow relaxation to the steady state where the potential adjusts adiabatically to the decreasing concentration. The concentration, being the slow variable, exhibits throughout the transition only smooth changes. (Note that the slow dynamics of the surface concentration of S,Oiare not related to changes in the intensity due to a restructuring of the silver surface or the formation of an oxide. Rather, changes in the surface concentration of S,Oi- result in potential changes which are seen via a changing SOi- coverage; in the images in Figs. 9 and 10 both effects are superimposed.) During the oscillations shown in Fig. 14, almost the same scenario occurs: the fast potential wave is followed by a slow consumption of S,Oi-. Now, however, the system does not relax back to a steady state in the active branch. Rather, the decreasing concentrations drive the potential back to its starting point at which the reaction rate is low and, consequently, the concentration recovers. When the concentration has exceeded a threshold, the potential front is induced again, initiating a new cycle. Obviously, the total wavelength of this pulse-like structure is determined by the slow dynamics of the concentration field. Fig. 14(a) depicts snapshots of the spatial profiles of during an oscillation. In the potential 4 DL and Cs,o,2-

G. Friirgen

et al./Journal

of Electroanalytical

Chemistry

409 (1996)

183-194

193

potential is radially symmetric, with large slopes close to the edge of the disk and small slopes inside the disk. A higher current density at the rim reduces the perturbation necessary to induce a transition from the passive to the active state. Hence, the probability that the potential wave starts from the rims is high, whereas the specific location along the rim at which the transition starts should be random. It seems likely that the rotationally symmetric passivation waves observed during the oscillatory dissolution of Fe [8,47] also originate from such a boundary effect [48,49]. b

“[L!I

6. Conclusions

x

LL

u L I-----l I4

4

Fig. 14. (a) Schematic potential and concentration profiles during an oscillation, corresponding to the experimental situation shown in Fig. 10. (b) Evolution of the potential during an oscillation if the electrode is smaller than the wavelength of the potential wave. Such a situation is observed in the experiments.

profile two characteristic lengths can again be identified: the front of the ‘pulse’ over which the potential rises quickly, determined by the temporal evolution of the potential f&, and the ‘pulse’ tail which is controlled by the slower dynamics of the concentration of S,Og-. This length is larger than the extension of the electrode, resulting in the impression that a front travels across the electrode, leaving it in a more or less homogeneous state which relaxes back towards its original value. This sequence is sketched in Fig. 14(b). The comparable order of magnitude of wavelength and electrode dimension suggests also that the boundary conditions play an important role for the patterns. In our experiments it was striking that the potential waves always originated from the rim of the electrode. This effect can be understood if the influence of the boundary on the potential or current distribution is considered. The boundary is characterized by a transition from a conductor, the Ag electrode, to an isolator, the glass prism. Newman [I] showed that these boundary conditions exclude the existence of homogeneous potential distributions. Rather, the

Wave phenomena occurring during the reduction of S,Oi- could be recorded with SP microscopy. The intensity in the image is affected by two processes: firstly, the change in coverage of specifically adsorbing anions which, over wide parameter range, directly reflect changes of the electrode potential, and secondly, a change in roughness or a partial oxidation of the Ag electrode. We discussed the essential dynamics in terms of the dynamics of the potential and the concentration of S,Oi- at the electrode, and hence restricted our considerations concerning the spatiotemporal dynamics to spatial changes in these two variables. The observed patterns are characterized by two time and two length scales, associated with the temporal dynamics of a two-variable model (Eqs. (2) and (3)). This model describes a variety of electrochemical oscillators that possess a negative polarization slope in connection with an, at least partly, mass transport controlled reaction. Assuming that the capacitance C and the diffusion constant D are approximately equal in all systems, there are three important parameters in the model: the uncompensated resistance R,, the diffusion layer thickness S and the rate constant of the electrochemical reaction entering kc. Two of them, S and R,, do not depend on the specific reaction, and hence can be controlled individually. They determine time and length scales in a specific system. The velocity of the fronts was found to be mainly affected by the electrolyte resistance, pointing to the importance of the spatial coupling via migration currents (as opposed to diffusion). At low mass transfer the extension of the front in the bistable, or of the wavelength in the oscillatory, regime is determined by 6. Whereas the trend for wave speed and length change with R, and S should be reaction independent, the quantitative values will be affected by the reaction constant in individual cases. So far, all arguments concerning time and length scales have been phenomenological and based on a model describing the temporal dynamics of the variables; the spatio-temporal behavior can of course only be simulated if the model is extended by the spatial dimension. This was done in Ref. [.50] for the spatially one-dimensional case. So

G. Fliitgen

194

et al./Journal

ofElectroandytica1

far, only simulations with constant concentrations, i.e. for the limiting case of infinitely fast mass transfer, have been carried out. These simulations reproduced the dependence of the front velocity on the conductivity. We hope that future calculations with the two-variable model will also verify the proposed influence of the diffusion layer on the patterns.

Acknowledgements We thank Karl Doblhofer for many fruitful discussions and Bruno Pettinger for his help with all questions concerning SPs and the optics of the SP microscope.

References [l] [2] [3] [4] [5] [6] [7] [8] [9] [lo] [l 11 [12] [13] [14] Il.51 [ 161 [17] [IS]

J. Wojtowicz, Oscillatory Behavior in Electrochemical Systems, Butterworths, London, 1973. J.L. Hudson and T.T. Tsotsis, Chem. Eng. Sci., 49 (1994) 1493. M.T.M. Koper, Oscillations and Complex Dynamical Bifurcations in Electrochemical Systems, in press. K.F. Bonhoeffer, Z. Elektrochem., 47 (1941) 147. U.F. Franck, Z. Elektrochem., 55 (1951) 154. 0. Lev, M. Sheintuch, H. Yamitsky and L.M. Pismen, Chem. Eng. Sci., 45 (1990) 839. R.D. Otterstedt, N.I. Jaeger and P.J. Plath, Int. J. Bifurc. Chaos, 4 (1994) 1265. J.L. Hudson, J. Tabora, K. Krischer and I.G. Kevrekidis. Phys. Len. A, 179 (1993) 355. E. Raub and A. Schall, Z. Metallkunde, 30 (1938) 149. F. Argoul, J. Huth, P. Merzeau, A. Ameodo and H.L. Swinney, Physica D, 62 (1993) 170. G. Flltgen and K. Krischer, Phys. Rev. E, 51 (1995) 3997. G. Fbdtgen, K. Krischer and G. Ertl, Z. Naturforsch. Teil A, 50 (1995) 1097. G. Fl%tgen, K. Krischer, B. Pettinger, K. Doblhofer, H. Junkes and G. Ertl, Science, 269 (19951 668. A.Y. Gokhshtein and A.N. Frumkin, Proc. Acad. Sci. USSR Phys. Chem. Sect., 132 (1966) 409. W. Wolf, J. Ye, M. Purgand, M. Eiswirth and K. Doblhofer, Ber. Bunsenges. Phys. Chem., 96 (1992) 1797. W. Wolf, Oszillatorische Dynamik zweier elektrochemischer Reaktionen, FU-Berlin, 1994. M.T.M. Koper. Electrochim. Acta, 37 (1992) 1771. A. Frumkin, Z. Phys. Chem., 164A (1933) 121.

Chemistry

409 (1996)

183-194

Methods, Wiley, New [191 A.J. Bard and L.R. Faulkner, Electrochemical York, 1980. hoc. Acad. Sci. USSR, Phys. Chem Sect., 133 DOI Y.A. Chizmadzhev, (1960) 745. 1211 J. Harrison and K. Showalter, J. Phys. Chem., 90 (1986) 225. [221 A. Saul and K. Showalter, in RJ. Field and M. Burger @ds.), Oscillations and Traveling Waves in Chemical Systems, Wiley, New York, 1985. [231 R.H. Harding and J. Ross, J. Chem. Phys., 92 (1990) 1936. A.v. Oertzen, H.H. Rotermund and G. Ertl, J. Chem. [241 S. Nettesheim, Phys., 98 (1993) 9977. zu Hysterese- und Oszillationserschein[251 M. Berdau. Untersuchungen ungenbei der katalytischen CO-Oxidation auf Platinmetallobert&hen, KBster, Berlin, 1994. 1261V.V. Barelko, 1.1. Kurochka, A.G. Merzhanov and K.G. Shkadinskii, Chem. Eng. Sci., 33 (1978) 805. [271 G. Philippou, M. Somani and D. Luss. Chem. Eng. Sci., 48 (1993) 2325. [281 D. Luss, Physica A, 188 (1992) 68. [291 E. Kretschmamr, Opt. Commun., 6 (1972) 185. [301 R. Katz, D.M. Kolb and J.K. Sass, Surf. Sci., 64 (1977) 359. 1311 D.M. Kolb. J. Phys., 38 (1977) C5. [=I F. Chao, M. Costa, A. Tadjeddine, F. Abbles, T. Lopez-Rios and M.L. Theye, J. Electroanal. Chem., 83 (1977) 65. (331 F. Chao, M. Costa and A. Tadjeddine, J. Phys., 38 (1977) C5. and D.L. Mills (Eds.), Surface [341 D.M. Kolb. in V.M. Agranovich Polaritons: Electromagnetic Waves at Surfaces and Interfaces, North-Holland, Amsterdam, 1982, p. 299. [351 J.G. Gordon and S. Ernst, Surf. Sci., 101 (1980) 499. A.A. Komyshev, A. Tadjeddine and M.I. Ur[361 P.G. Dzhavakhidze, bakh, Electrochim. Acta, 34 (19891 1677. J. Electroanal. Chem., 169 (1984) 129. 1371 A. Tadjcddine, [381 A. Tadjeddine, A. Rahmani, G. Piazza and M. Costa, Electrochim. Acta, 34 (1989) 1681. Acta, 34 (1989) 29. [391 A. Tadjeddine, Electrochim. J. Electroanal. Chem., 329 [401 F. Chao, M. Costa and A. Tadjeddine, (1992) 313. [41] J.M.T. Thompson and H.B. Stewart, Nonlinear Dynamics and Chaos, Wiley, Chichester, UK, 1984. [42] G. Valette and A. Hamelin, J. Electroanal. Chem., 45 (1973) 301. [43] J. Desilvestro and M.J. Weaver, J. Electroanal. Chem., 234 (1987) 237. [44] J.D. Murray, Mathematical Biology, Springer-Verlag. Berlin, 1990. [45] M. Eiswirth and G. Ertl, in R. Kapral and K. Showalter @Is.), Kluwer. Dordrecht, 1994, p. 447. [46] R. Imbihl and G. Ertl, Chem. Rev., 95 (1995) 697. [47] A. Pigeau and H.B. Kirpatrick, Corrosion, 25 (1969) 209. [48] I. Epelboin, C. Gabrielli, M. Keddam, J.-C. Lestrade and H. Takenouti, J. Electrochem. Sot., 119 (1972) 1632. [49] M.E. Orazem and M.G. Mliller, J. Electrochem. Sot., 134 (1987) 392. [50] G. Flatgen and K. Krischer, J. Chem. Phys., 103 (1995) 5428.