Mechanistic aspects of oscillations during CO electrooxidation on Pt in the presence of anions: Experiments and simulations

Catalysis Today 202 (2013) 144–153

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Mechanistic aspects of oscillations during CO electrooxidation on Pt in the presence of anions: Experiments and simulations S. Malkhandi a , P.R. Bauer a , A. Bonnefont b , K. Krischer a,∗ a b

Physik Department, Nonequilibrium Chemical Physics, TU München, James-Franck-Str. 1, 85748 Garching, Germany Institut de Chimie de Strasbourg, UMR7177, CNRS et Université de Strasbourg, 4 rue Blaise Pascal, 67000 Strasbourg, France

a r t i c l e

i n f o

Article history: Received 27 February 2012 Received in revised form 2 May 2012 Accepted 4 May 2012 Available online 20 July 2012 Keywords: Electrooxidation Electrocatalysis Oscillations Nonlinear dynamics Chloride adsorption platinum

a b s t r a c t The electrooxidation of carbon monoxide on platinum in the presence of anions is one of the very few strictly potentiostatic oscillators, in which the electrode potential takes the role of a parameter rather than an essential variable. In this paper we investigate the oscillatory behavior as a function of five parameters: applied voltage, rotation rate of the electrode, anion concentration, electrolyte resistance and external resistor. The experiments exhibit regular oscillations also in parameter regions in which the hitherto assumed mechanism predicts only the existence of stable fixed points, and they show irregular oscillations in wide parameter ranges. Model considerations reveal that an asymmetric inhibition of the adsorption of CO and OH by adsorbed anions introduces a positive feedback loop. This so far undetected source of oscillations could be responsible for the wide oscillatory range found in the experiments. These oscillations are solely driven by the reaction kinetics and do not involve transport processes or, as the overwhelming number of electrochemical oscillators, an IR drop in the electric circuit. Furthermore, observations are compiled which suggest that the irregular oscillations are a manifestation of spatial pattern formation. © 2012 Elsevier B.V. All rights reserved.

1. Introduction The electrochemical oxidation of CO on Pt is a prototypical electrocatalytic reaction. Its study has provided us with a deeper understanding of surface electrochemistry and has shed light on many microscopic details of adsorption, desorption and reaction processes (for reviews see [1–3]). Also when viewed as a dynamical system, CO electrooxidation on Pt plays an outstanding role. Bulk CO electrooxidation is one of the very few electrochemical systems with an S-shaped polarization curve [4–10], which have been coined S-NDR systems [11,12]. S-NDR systems are susceptible to a variety of further dynamic instabilities [13–25], their pattern forming properties being potentially as rich as those of CO oxidation under UHV conditions [26]. CO oxidation is thus also an important model system for the study of dynamic instabilities in electrochemical systems. In bulk CO electrooxidation, the S-shaped, and thus bistable, polarization curve results from an interplay of the Langmuir–Hinshelwood mechanism and mass transport limitation. In the bistable potential region, the system adopts either a reactive state with a diffusion limited current density, or a poisoned state, in which the electrode is CO covered and the

∗ Corresponding author. E-mail addresses: [email protected], [email protected] (K. Krischer). 0920-5861/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.cattod.2012.05.018

current density negligible. The bistability is the manifestation of a positive feedback loop: Assume that the system is in the poisoned state close to the so-called ignition potential at which the system undergoes a transition to a high current state. Then, a small increase of the free surface sites (or equivalently decrease of the CO coverage) prompts the adsorption of both, CO molecules and OH species from the oxidation of water, thereby also initializing the oxidation reaction between adsorbed CO and OH species. This process frees the adsorption sites again and allows for an ongoing, yet still slow, reaction. With time, however, the CO concentration in front of the electrode will slightly decrease, and therefore, the relative rates of CO and OH adsorption are shifted in favor of a faster OH adsorption. As a consequence, the CO monolayer is reacted off and the system attains the diffusion limited high current state. It is this change in relative adsorption rates of the mass transport limited CO adsorption and the mass transport independent OH adsorption that produces the positive feedback and leads to the observed bistability. When reducing the voltage on the diffusion limited current branch, the system undergoes the transition to the CO poisoned state only at much lower potential values, reversing the autocatalytic steps: A small decrease in the number of free surface sites reduces the reaction rate somewhat, which leads to a slight increase of the CO concentration in front of the electrode, and thus also to an increase of the CO adsorption rate, while the OH adsorption rate stays constant, resulting in an autocatalytic built-up of the CO adsorption layer.

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The described scenario takes place in concentrated sulfuric acid or perchloric acid base electrolyte. The addition of a small amount of strongly adsorbing anions, such as BF− or Cl− , renders the sys4 tem oscillatory [27,28]. The anion coverage plays the role of an inhibitory variable which causes the system to switch back and forth between the two, formerly stable states in an oscillatory manner: when the system is on the reactive branch, a slow net adsorption of the anions causes a decrease of the number of free surface sites and, thus, initiates a transition to the CO-poisoned state. In the poisoned state, the small number of remaining free surface sites lets the adsorption rate of the anions drop below their desorption rate so that empty surface sites become available again, which, in turn, commences a transition back to the reactive state. This mechanism was transformed into a simple model which reproduced the oscillations [27]. In this paper, we explore the existence range of the oscillations as a function of five parameters, voltage, mass transport rate, anion concentration, conductivity of the electrolyte and magnitude of an external series resistor, and we demonstrate that the oscillations also occur with Br− instead of Cl− ions. The experiments are then confronted with simulations using the skeleton model as introduced in [27], as well as a modified model taking into account an asymmetric inhibition of adsorption of CO and OH by anions. The modified adsorption terms introduce a further self-enhancing loop into the kinetics and make the oscillations independent of the prior discussed mass transport dependent feedback loop. They also widen the oscillatory parameter range considerably. 2. Experimental The working electrode (WE) was a polycrystalline platinum (99.999%) disk electrode (geometrical area: 0.2 cm2 , roughness factor: 1.65; note that all current densities are given with respect to the geometrical area) embedded in a Teflon cylinder. The custom-built electrode system was attached to a Pine Instrument rotator. Unless otherwise stated, the rotation rate was 1200 rpm. Prior to each experiment the electrode was cleaned in a 1:1 mixture of H2 SO4 (96%, for analysis, Merck) and H2 O2 (30%, for analysis, Merck) following a procedure described in detail in [27]. A Pt wire bent to a ring served as counter electrode. It was placed symmetrically to the WE in the main compartment of the cell. The reference electrode was a Hg|Hg2 SO4 electrode kept in a separate compartment. All potential values below are converted to the RHE scale. The electrolytes were prepared from HClO4 (70%, Suprapure, Merck) or H2 SO4 (96%, Suprapure, Merck) and water from a Millipore MilliQ system (18.2 M  cm, TOC < 4 ppb). The Cl− and Br− ion concentration was adjusted with HCl (37%, for analysis, Merck) and KBr (for analysis, Merck), respectively. The electrolyte was purged with CO (Linde 4.7) for 25 min before the first experiment was carried out as well as during the experiments. During the initial purging time the electrode potential was cycled between 10 mV and 1270 mV. 3. Results 3.1. Experiments Fig. 1a shows the positive potential region of a cyclic voltammogram (CV) of a rotating polycrystalline Pt-disk electrode in 0.5 M H2 SO4 electrolyte containing 1 ␮M Cl− ions. The CV exhibits oscillations in the current density in a small potential region which separates a poisoned state at lower potentials and a high current branch at more positive potentials. The oscillations occur in both sweep directions of the potential. In Fig. 1b short portions of time series obtained at constant, and from left to right

145

increasing values of the applied voltage are depicted. The oscillation amplitude attains large values, even overshooting the high current branch, close to the low potential oscillatory instability, while only small amplitude oscillations around the high current state are seen at the high potential limit. Furthermore, it is striking that the oscillations are fairly regular only in the intermediate potential range. The simple periodic oscillations are flanked by irregular time series of the current for higher and lower voltages. To obtain a more complete picture of the dynamics of this strictly potentiostatic oscillator, systematic parameter studies were carried out. Let us first look at the influence of the rotation rate. In Fig. 2a time series measured at 1200 rpm and 600 rpm and the same value of the applied voltage are compared. At the slower rotation rate, the oscillation period is longer, the system spending more time on a high current plateau, and the oscillation amplitude is somewhat smaller. These trends seem to be a direct consequence of the reduced mass transfer rate of CO to the electrode, which leads to a smaller diffusion limited current and to a slower poisoning of the active branch through adsorbing CO (and possibly also Cl− ions). The existence region of oscillations in the rotation rate – applied voltage parameter plane is depicted in Fig. 2b for rotation rates between 400 rpm and 1200 rpm. The parameter region in which regular oscillations were observed (black squares in the red hatched region) shifts to slightly less positive voltages and becomes somewhat narrower with decreasing rotation rates. As already observed in Fig. 1a, this region is to both sides, i.e. smaller and larger voltages, encircled by a region in which the system oscillates irregularly, the transition from the irregular oscillations to a steady state behavior being at approximately the same value of U independent of the rotation rate. An overview of the impact of the chloride concentration on the oscillatory dynamics can be seen with the time series depicted in Fig. 3a–c. They were obtained at Cl− concentrations of 10−4 M (a), 10−5 M (b) and 10−7 M (c), respectively. (For 10−6 M see Figs.1b and 2a). At the highest anion concentration, sustained regular oscillations could not be obtained anymore, though irregular oscillations prevailed. At potential values negative to irregular oscillations, spike-like current bursts appeared randomly and with different amplitudes on a relatively low current level, though mostly only during a transient period of time (Fig. 3a). Between 10−5 M and 10−7 M regular oscillations developed in some voltage interval, the period of the oscillation increased by an order of magnitude when lowering the anion concentration from 10−5 M to 10−7 M (Fig. 3b and c). The decrease in oscillation frequency is mainly due to progressively longer decreasing current flanks. This suggests that at low Cl− -concentration the oscillation period is to a large part determined by the rate of anion adsorption. The two-parameter phase diagram in the Cl− -concentration – applied voltage plane depicts the existence region of the different dynamic regimes (Fig. 3d). Non-stationary current densities were found for Cl− -concentrations varying by three orders of magnitude, the voltage interval supporting oscillations being with about 80 mV broadest at 10−6 M Cl− . It reduced to just 10 mV at 10−7 M Cl− . At concentrations of 10−5 M and 10−4 M Cl− , transient current bursts at irregular time intervals occurred in a potential interval positive to the one in which sustained irregular oscillations were obtained. With increasing Cl− -concentration this potential range increased, while the one, in which sustained, non-stationary behavior occurred, decreased. Also in this parameter plane, the parameter range in which periodic oscillations exist is encompassed by a region with aperiodically varying current time series. An ohmic resistance in series to the working electrode affects the dynamics of electrochemical systems in various ways. First, it is a parameter of the local dynamics. As outlined above, the oscillations are linked to an S-shaped current–potential curve, and thus also to

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Fig. 1. (a) Positive potential region of a CV of a Pt rotating disk electrode in CO saturated 0.5 M H2 SO4 + 1 ␮M HCl, scan rate 1 m V/s. (b) Current oscillations during CO electrooxidation on Pt at different values of U. The potential values are given above the time traces. Electrolyte: CO saturated 0.5 M H2 SO4 + 1␮M HCl.

the bistability found in the system without the presence of strongly adsorbing anions. When increasing the cell resistance, or, equivalently, adding an external series resistance, the bistable potential interval becomes smaller, and eventually it is extinguished in a cusp bifurcation. Beyond the cusp bifurcation, the S-shaped steady state curve is unfolded and, in the spatially lumped model the middle, unstable branch is stabilized by the quickly varying electrode potential. This suggests that in the presence of anions also uniform oscillations are suppressed if the oscillations are linked to the same autocatalytic feedback loop. Second, an ohmic resistor affects the spatial coupling, and thus pattern formation. There are two sources of ohmic series resistances, the electrolyte resistance and an ohmic series resistance in the outer electric circuit, which have a different impact on spatial coupling. The electrolyte conductivity determines the strength of migration coupling and thus plays a similar role as the diffusion coefficient for diffusional coupling [29,12]. A series resistance in the outer circuit introduces a global coupling into the system: any local change of the current density affects the potential drop across the double layer at every position on the electrode [30,15]. Thus, the two resistance sources influence spatial pattern formation differently. Studying the dynamics as a function of both, electrolyte conductivity and series resistance, provides some insight into possible spatial instabilities. Fig. 4a and b compares the oscillating parameter regions in reciprocal resistance – voltage planes, where in Fig. 4a the cell resistance was varied by changing the conductivity of the supporting electrolyte, while in Fig. 4b the base electrolyte was 0.5 M H2 SO4 and different ohmic resistors were inserted in the external circuit.

First of all, it is striking that oscillatory behavior occurs in both cases also with the highest values of the ohmic resistance (i.e. lowest supporting electrolyte concentration in Fig. 4a). Here, it should be emphasized that oscillations were indeed observed at resistance values at which the bistability in the anion free electrolyte was completely unfolded and thus the above discussed autocatalysis for the uniform system suppressed. Hence, there is either a spatial bifurcation to oscillatory structures, or there is another autocatalysis which leads to oscillations of the uniform dynamics. Furthermore, with an external resistance regular oscillations also establish at very large resistance values, while already in electrolyte solutions of 50 mM H2 SO4 only irregular oscillations were obtained when no external ohmic resistor is added. The most regular time series measured in 50 mM supporting electrolyte concentration is reproduced in Fig. 5a. The time series shown in Fig. 5b and c were obtained in 0.5 M H2 SO4 with an external resistor of 350  and 700 , respectively. The cell resistance in our cell geometry equals around 250  for a 10 mM solution, which is considerably lower than the external resistances with which the regular time series of Fig. 5 were obtained. The qualitatively different oscillatory behavior in equal parameter ranges of the local dynamics strongly suggests that in case of the irregular time series the oscillations are accompanied by spatial structure formation. When replacing Cl− by Br− ions, no qualitative changes are observed, as can be seen from the time series depicted in Fig. 6. The two topmost time series displaying regular oscillations were obtained in 0.5 M sulfuric acid and 0.1 ␮M or 1 ␮M KBr, respecand for Cl− containing tively. As was shown previously for BF− 4 electrolytes [27,28], no regular oscillations could be adjusted in

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Fig. 2. (a) Current time series of a Pt-disk electrode at two different rotation rates in CO saturated 0.5 M H2 SO4 + 1 ␮M HCl solution at 910 mV. (b) Regions of regular (finely hatched) and irregular (coarsely hatched) oscillations in the rotation rate – applied voltage parameter plane. (Points at which experiments were carried out are marked with symbols.) Electrolyte: CO saturated 0.5 M H2 SO4 + 1 ␮M HCl.

perchloric acid electrolytes. The most coherent time-patterns obtained with Br− ions in 0.5M HClO4 are depicted in the two bottom plates of Fig. 6. Obviously, the ions of the supporting electrolyte do not only determine the conductivity of the electrolyte but also actively participate in the dynamics, where it appears most likely that their different chemical nature affects the spatial coupling more strongly than the local dynamics.

site. Since at potentials above the ignition potential the oxidation current becomes diffusion controlled, also the transport of CO molecules from the bulk solution (COb ) to the surface has to be taken into account, which can be formally written as

3.2. Model

X− + ∗  Xad + e−

CO electrooxidation on Pt is known to proceed through the Langmuir–Hinshelwood mechanism, i.e., the reaction occurs between adsorbed CO and adsorbed O-containing species, and simulations are usually based on three elementary reaction steps, adsorption of CO (Eq. (1)), oxidative adsorption of water (Eq. (2)) and reaction of adsorbed CO and OH molecules (Eq. (3)):

The reaction scheme (1–5) possesses four time-dependent quantities, the surface coverages CO, OH and anions as well as the concentration of CO in front of the electrode. In [27], the resulting four variable model was formulated and shown to predict oscillations at some parameter values. In the following we compare the oscillatory ranges predicted by the model with our experimental studies discussed above. We do this, however, with a reduced two-variable model as our studies revealed that in the interesting voltage range the dynamics predicted by this reduced model is not significantly different from the one of the original four-variable model. As demonstrated in [10], as long as the OH-coverage remains small, the reaction rate can be expressed without taking explicitly the coverage of OH into account:

COs + ∗ → COad

(1) +

H2 O + ∗  OHad + H + e−

(2)

COad + OHad → CO2 + H+ + e− + 2∗

(3)

Here, the subscripts ‘s’ and ‘ad’ indicate a molecule in the reaction plane, i.e., immediately in front of the electrode, and a species adsorbed on the electrode, respectively. ∗ denotes a free adsorption

COb → COs

(4)

In [27] it was shown that the additional competitive adsorption of anions may induce oscillations:

COad + H2 O + ∗ → CO2 + 2H+ + 2e− + 2∗

(5)

(6)

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Fig. 3. (a)–(c) Current oscillations at different Cl− ion concentrations. (a) 10−4 M HCl, U = 955 mV, (b)10−5 M HCl, U = 955 mV, (c) 10−7 M HCl, U = 895 mV. (d) Regions of regular (finely hatched) and irregular (coarsely hatched) oscillations and of (transient) current spikes (horizontal stripes) in the HCl concentration – applied voltage plane. (Points at which experiments were carried out are marked with symbols.) Base electrolyte: CO saturated 0.5 M H2 SO4 .

i.e., water adsorption and CO oxidation are described with a single effective Butler–Volmer type rate constant. Furthermore, any temporal changes of the concentration of CO in front of the electrode, cs , occur on a time scale which is comparable to the one of the CO-coverage, which suggests that it is not an independent degree of freedom. In fact, when eliminating cs adiabatically, the predictions of the model differ only slightly from the full one (such as a 10% increase of the oscillation period), but they never show large quantitative or even qualitative differences for slow reaction rates. We therefore incorporated in all simulations shown below the adiabatic assumption, i.e., we expressed cs by an algebraic equation, which was obtained by setting the temporal derivative of Eq. (1) in [27] to 0. Note that changes of cs are still an integral part of the positive feedback in the reaction mechanism. When setting cs to a constant value, the model does not reproduce the observed bistability between the poisoned and the reactive branch in the system without anions.

The model, thus, consists of two ordinary differential equations for the evolution of the CO and the anion coverages, CO and X : ˙ CO = ads − reac  CO

(7)

˙ X= 

(8)

ads X

des − X

where the corresponding adsorption, desorption and reaction rates are given by the following expressions: ads ads CO = kCO cs (0.99 − CO − X )

cs =

cb D ads ı (1 −  D + Stot kCO CO − X )

(9) (10)

reac = kreac R(1 − CO − X /xinhib )CO exp(2 ˛f)

(11)

ads X

(12)

=

ads kX cX R(0.99 − CO

− X /max X ) exp(nx ˛f)

des des X = kX X exp(nx (˛ − 1)f)

(13)

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Table 1 Meaning of the parameters entering the model and their standard values. Meaning

Parameter

Value

Bulk CO concentration Anion concentration Reactive surface site density Diffusion layer thickness Transfer coefficient Maximum anion coverage Anion adsorption rate constant Anion desorption rate constant Anion valency CO adsorption rate constant Reaction rate constant Irregular anion blocking coefficient Diffusion coefficient Double layer capacitance Electrode area Faraday constant/(gas constant × temperature) Faraday constant

cb cx Stot ı ˛ max X kXads des kX nx ads kCO kr xinhib D CDl A F f = RT

10−6 mol cm−3 = 1 mM 10−8 mol cm−3 = 10 ␮M 2 × 10−9 mol cm−2 1.64 × 10−3 cm 0.5 0.8 1 cm3 s−1 mol−1 106 s−1 1 5 × 107 cm3 s−1 mol−1 8 × 10−15 s−1 1 1.5 × 10−5 cm2 s−1 2 × 10−5 F cm−2 0.33 cm2 38.7 V−1

F

96485 C mol−1

 R(x) =

0

if x ≤ 0

x

if x > 0

(14)

Although the overall surface coverage is constrained to 1, the introduction of max and xinhib may lead to unphysical negative X reaction or adsorption rates, which is prevented by the ramp function (eq. 14). The reaction current is determined by the rates of the charge transfer steps according to Ireac = Stot F(2 reac + nx (Xads − Xdes ))

Fig. 4. (a) Regions of regular (stripe hatched) and irregular (square hatched) oscillations in the H2 SO4 concentration – applied voltage plane. (Points at which experiments were carried out are marked with symbols.) Electrolyte: CO saturated H2 SO4 + 1 ␮M HCl. (b) Regions of regular (stripe hatched) and irregular (square hatched) oscillations in the 1/R – applied voltage plane. (R: external resistance, points at which experiments were carried out are marked with symbols.) Electrolyte: CO saturated 0.5 M H2 SO4 + 1 ␮M HCl.

(15)

Meaning and values of all parameters are compiled in Table 1. The model contains two parameters which were in the previous model not accounted for, but turned out to be important. These are max and xinhib . max ≤ 1 limits the maximum anion coverX X age to a value lower than one (or more precisely 0.99, since this is the maximum total coverage allowed so that a full CO coverage does not inhibit the reaction completely), and, more importantly, it introduces an asymmetric inhibition of adsorption: CO can still adsorb on a surface with the maximum anion coverage max , but X anions cannot adsorb on a fully CO covered surface. Furthermore, < xinhib also the reaction is not fully suppressed on as long as max X

Fig. 5. Current oscillations at different ohmic resistances. Top: high electrolyte resistance (50 mM H2 SO4 (CO saturated), no external series resistance), middle and bottom: external series resistance of 350  and 700  and CO saturated 0.5 M H2 SO4 . In all three cases 1 ␮M HCl.

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Fig. 6. Current oscillations with Br− as inhibiting anion in CO-saturated 0.5 M H2 SO4 electrolyte (top two panels) and CO-saturated, 0.5 M HClO4 electrolyte (lower two panels).

an anion covered surface. The picture behind is that the anions form a rather open structure with ‘holes’ sufficiently large such that CO and OH molecules can still adsorb, whereby Eq. (11) implies that the latter immediately react with CO. The introduction of xinhib allows in addition to weighten the inhibition of anions differently for CO and OH, where we varied xinhib between the two limits xinhib = 1 (CO adsorption and reaction are equally inhibited by adsorbed anions) and xinhib = max (the reaction is completely inhibited by an anion X covered surface and can only proceed on 1% of the surface that is kept free of anions and CO). Below we demonstrate that a value of xinhib < 1 introduces a further positive feedback loop in the system and may lead to oscillations in parameter ranges where the above explained autocatalytic loop does not exist. 3.3. Simulations A simulated cyclic voltammogram, together with the steady state curve, is shown in Fig. 7a, typical time series after transients have died out at low, intermediate and high voltage, respectively, in Fig. 7b. The characteristic features of the two plots are very similar to those of the experiments (Fig. 1). The current oscillates on both forward and backward scan in a small voltage interval, the oscillations possessing large amplitudes on the low voltage border of the oscillatory region and decay with small amplitudes at large potentials. An analysis of the stability of the steady state explains the different behavior of the oscillations at the low and high voltage region: Coming from low potentials, the fixed point becomes unstable through a subcritical Hopf bifurcation (HB), but at a higher voltage, it stabilizes again in a supercritical HB. The subcritical HB implies that the border of the oscillatory range does not coincide with the location of the HB. But, in general, the oscillations cease to exist very close to it so that the locations of the HBs are good approximations of the oscillatory parameter regions. Calculations were done for max = 0.8 and xinhib = 1. The behavior was rather X ; the influence of xinhib is discussed insensitive to a variation of max X below in more detail. Figs. 8–10 display the location of the Hopf-bifurcation (which encircles approximately the oscillatory parameter domain) in the rotation rate–voltage, anion concentration–voltage, and

Fig. 7. (a) Thick lines: calculated polarization curve with stable (solid) and unstable (dashed) steady states. Thin curves: Calculated cyclic voltammogram; positive (dotted) and negative (dashed) potential scan. The stars are at the potential values of the time series shown in (b). Their current value corresponds to their respective mean current density values during the oscillations. Scan rate: 0.3 mV/s. Other parameters as listed in Table 1. (b) Time series for different potential values.

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3000 2700

Rotation rate / rpm

2400

HB 300 rpm 600 rpm 1200 rpm 2400 rpm

2100 1800 1500 1200 900 600

mA 1 cm 2

300 0 0.92

5s 0.93

0.94

0.95

U/V Fig. 8. Location of the Hopf bifurcation (black lines) in the rotation rate – U parameter plane. The time series insets depict the oscillatory behavior at the marked points (◦). Remaining parameters as given in Table 1.

conductivity–voltage planes, respectively. As for the dependence of the oscillations on the rotation rate (Fig. 8), experiment and calculations compare quite favorable, both concerning the oscillation shapes as well as the location of the oscillatory region in the parameter plane. Though, the oscillatory voltage interval is clearly larger in the experiments than in the simulations. (Note that the variation of rotation rates in the simulations (Fig. 8) is much larger than in the experiments.) Again the good concurrence does not depend on the value of max . X This is very different when considering the dependence of the oscillations on the anion concentration. The dashed curved in Fig. 9 was calculated with max = 1, xinhib = 1, i.e. assuming a symmetric X inhibition as in the original model [27]. For these parameter values, the anion concentration can be varied at most by a factor ≈3 without leaving the oscillatory region, while in the experiments the range of Cl− concentrations in which regular and irregular oscillations were observed extended over more than two and three orders of magnitude, respectively. Setting max = 0.8 but leaving xinhib = 1 X (solid curve in Fig. 9), extends the oscillatory range in the anion concentration already considerably (to nearly a factor of 100). The oscillatory concentration interval becomes even larger when lowering xinhib to 0.8 (dotted curve, Fig. 9), and the oscillatory voltage interval is significantly enhanced, giving thus a much better agreement with the experiments. Note, however, that we do not show the border of the oscillatory region at positive voltage since it only occurs at values at which in the experiment the OH coverage cannot be neglected anymore, i.e., at parameter values at which the model is not valid anymore. The most remarkable impact of the asymmetric inhibition becomes apparent in Fig. 10 where the location of the Hopf bifurcation is shown in the conductance–voltage plane. For these calculations, one needs to make allowance for a change of the electrode potential with the IR drop across a series resistor (electrolyte or external resistor). Therefore, Eqs. (7) and (8) were augmented by the following coupled equation which results from the charge balance at the interface. ˙ = 1  CDl

Fig. 9. Location of the Hopf bifurcation in the U–cx parameter plane for three combinations of the parameters max , xinhib , as given in the inset. Remaining parameters X as given in Table 1.

Fig. 10. Location of the Hopf bifurcation in the U–1/R parameter plane for three , xinhib , as given in the inset, and cx = 1 ␮M, combinations of the parameters max X and location of the saddle node bifurcation in the system without anions (cx = 0 ␮M) (dotted line). Remaining parameters as given in Table 1.

151

U −  RA



− Stot F(2reac + nx (Xads − Xdes ))

(16)

For the meaning of the symbols see Table 1. In Fig. 10 the loca= 1, xinhib = 1 (long tions of the Hopf bifurcation are shown for max X dashed), max = 0.8, xinhib = 1 (solid line), max = 0.8, xinhib = 0.8 X X (short dashed). The first two curves exhibit again several orders of magnitude discrepancy to the experimental data. The maximum resistances at which oscillations can still be obtained (for an electrode size A = 0.33 cm2 , i.e., the real electrode size in the experiment) are 80  and 95  in the first two cases, while in the experiments even with an external resistor of 700  the system still exhibited oscillations. The resistance range broadens clearly in the third case where max = 0.8, xinhib = 0.8, though it is still somewhat X smaller than in the experiments. What is, however, more important than the better quantitative agreement is that now oscillations are obtained for resistance values that are larger than the one at which the cusp bifurcation occurs (the point in the parameter plane at which the bistability ceases to exist) in the system without anions. The location of the saddle node bifurcations for cX = 0, encircling the bistable parameter region, is shown as dotted line in Fig. 10. In the case of xinhib = 1, the principle loss of the autocatalytic feedback loop at Rcusp was corroborated with nullcline-type plots ˙ CO = 0 and  ˙ DL = 0 are calculated where the simultaneous roots  with X as a parameter. For any R > Rcusp and any value of U, the resulting curve f(X ) is not S-shaped anymore, and thus lacks an unstable branch. Therefore, all intersections with the inhibitor nullcline (which is a monotonic curve) are stable fixed points of the full system. Note that this is the case, even though the steady

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U = 0.943 V

j / mA cm-2

coverage

1

j

0.8

0.6

0.4

0.2

0

0

10

20

30

40

Time / s Fig. 11. Calculated time series with (xinhib = 0.8) and a constant value of the CO concentration in front of the electrode: cs = cb . Remaining parameters as given in Table 1 and cx = 1 ␮M.

state current of the anion-containing system is much smaller than without anions. In contrast, in the case of xinhib = 0.8, the oscillatory range extends to conductivities below the cusp bifurcation, i.e., to parameter values at which the positive feedback from the CO-subsystem is not present anymore. This, in turn, implies that the asymmetric inhibition of CO and OH adsorption (or equivalently the oxidation reaction) by the anion coverage introduces a further positive feedback loop. Above, we have seen that in the CO-subsystem the origin of the self-enhancing loop is that the rates of CO and OH adsorption respond differently to a change of the number of free surface sites. This different response was brought about by the limited mass transport rate of CO. Qualitatively, an asymmetric inhibition of the adsorption of CO and OH by the anion coverage does the same, namely leading to different changes of CO and OH adsorption (respectively reaction) rates upon a change in the anion coverage, thereby promoting the avalanche like built up or removal of CO coverage. However, in this case, the oscillatory instability depends on chemical reaction terms only; neither mass transport limitation nor an ohmic drop in the external circuit is involved in the necessary feedback loops. Hence, here, the system is not only a strictly potentiostatic oscillator (where oscillations are possible at constant electrode potential) but could also be termed a strictly electrocatalytic oscillator, to indicate that it is exclusively the reaction kinetics that induces oscillations. In fact, setting cs to the bulk value cb , the oscillations are preserved in simulations with asymmetric inhibition (Fig. 11). 4. Discussion The experimentally determined oscillatory parameter regions in three different parameter planes made possible a critical assessment of the simplest model giving rise to oscillatory behavior during CO oxidation in the presence of anions, which, in turn, revealed important details of the adsorption and reaction kinetics. In the most simple form of the model, which we will call model 1, the anions competitively adsorb with CO and OH on the surface, each molecule, independent of its chemical nature, consuming the same number of free surface sites. (In Eqs. (11) and (12) this corresponds to xinhib = 1 and max = 1.) The model correctly X predicts oscillations in a small voltage range that connects the CO-poisoned electrode at low potentials and the reactive state at higher potential. Furthermore, it captures the hard onset of

current oscillations at low voltages and the extinction of the oscillations through diminishing amplitudes at high voltages. It also satisfactorily reproduces oscillations in the experimentally investigated rotation rate range. However, the predictions of the oscillatory range in two other parameters, anion concentration and series resistance, are 2–3 orders of magnitude too small. Let us first focus on the anion kinetics. For oscillations to occur, the anion coverage should take on an intermediate value in the voltage range in which OH adsorption, and therefore also the oxidation of CO, sets in. Let us assume that kXads and kXdes are chosen such that this is the case for some intermediate concentration of Cl− ions. Clearly, changing the Cl− bulk concentration in model 1 by more than an order of magnitude toward larger or smaller values shifts the isotherm such that around the onset potential of the reaction the anion coverage is either negligibly small or close to its maximum coverage. In the first case, the CO oxidation remains unaffected by the presence of anions, in the second case adsorption of CO and OH, and thus the reaction, are precluded by the high anion coverage. Therefore, it is expected that in model 1 oscillations occur only in a small anion concentration range. Seen from the other side, the enormously wide parameter range, extending over three orders of magnitude, in which the chloride concentration can be changed experimentally without leaving the oscillatory range, provides evidence of a more complex interaction between the adsorbing species. There are only very few relevant studies of Cl− or Br− adsorption on Pt [31–36]. Some of them provide evidence of repulsive interactions between adsorbed Cl− ions and also between adsorbed Cl− and OH species [31,32]. In CO stripping experiments in Cl− containing electrolytic solutions Lopez-Cudero et al. [36] find a substantial inhibition of OH adsorption and a shift of the onset of CO oxidation to more positive potentials by anion adsorption while they rule out coadsorption of Cl− and CO. In our opinion, this latter finding can be traced back to the very low desorption rate of CO at usual adsorption potentials of stripping experiments, which leads to a slow displacement of adsorbed Cl− by CO. Our experiments provide clear-cut evidence that at potentials where CO oxidation takes place there is co-adsorption of CO and Cl− or Br− ions. In an effort to keep the model as simple as possible we chose to introduce only a small modification of the adsorption kinetics, namely different space requirement of the three adsorbing species: anions, CO and OH. We discussed two limiting situations: 1. Choos= 0.8 and xinhib =1, assumes an equal and smaller space ing max X requirement of CO and OH than of anions and allows for some adsorption of CO and OH on an anion covered surface. This, in turn, also enables oscillations at considerably larger anion concentrations than the originally completely symmetric inhibition of adsorption. 2. Setting max = 0.8 and xinhib =0.8 assumes that X the place requirement of Cl− and OH is equal but the one of CO is considerably smaller. With other words, on a fully chloride covered surface only CO can still adsorb but not OH and thus also the reaction cannot proceed. This formulation widens the oscillatory range in the chloride concentration as well as in the applied voltage further and thus formerly exhibits a better agreement with the experiments. Two remarks are noteworthy at this point: First, all our attempts to introduce repulsive interactions through a Frumkin isotherm did not lead to the same trends, unless the asymmetric inhibition was also taken into account. Second, a mathematical formulation of co-adsorbing species similar to ours was used in [37] to explain the enhancement of electrocatalytic reactions in supporting electrolytes with differently inhibiting anions present. Experiments in the presence of an external resistance revealed finally the most astonishing result: Oscillations existed even at parameter values at which the fast and inhibiting response of the electrode potential, which becomes a degree of freedom in the presence of a series resistance, suppresses the positive feedback loop

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stemming from mass transport limitation with respect to uniform perturbations. Therefore, also uniform oscillations originating from this autocatalytic loop should be suppressed, as could be verified with simulations. Consequently, the oscillations observed at high series resistance must stem from a spatial instability, or they are caused by a different feedback mechanism. While with the present experiments we cannot discriminate between the two possibilities, our model studies revealed that already rather small changes of the adsorption dynamics lead to a second positive feedback loop: An asymmetric inhibition of CO and OH adsorption through anions gives rise to a self-enhancing built-up or removal of the CO coverage and leads to an oscillatory instability in the lumped model. We emphasize that, at this stage, it remains open whether these small changes indeed capture the actual essential interactions of the adsorption kinetics. The value of the simulations is to identify the kinetic processes that are insufficiently described in model 1 and to demonstrate how already very small changes of the adsorption kinetics can introduce quantitative changes by more than an order of magnitude and even introduce new feedback loops that qualitatively alter the dynamics. Further carefully designed experiments are needed to validate or falsify the second positive feedback loop. Note that this autocatalytic feedback is similar to the one occurring in CO oxidation under UHV conditions where the different space requirement of adsorbing CO molecules (1 site) and O2 molecules (2 adjacent sites) causes the destabilizing feedback [38]. So far, we have completely neglected that in the experiments the oscillations were irregular in large parameter ranges. Clearly, more complex oscillations cannot be described by a two-variable model, and in principle, we cannot exclude that the irregular oscillations emerge from a more complex homogeneous dynamics with further degrees of freedom. However, we consider this option unlikely. In all simulations, in which OH coverage and cs were treated as independent variables, we only observed simple periodic behavior, never more complex oscillations. This, of course, is not a proof that they do not exist in the extended model, nor that other degrees of freedom, not considered at all, such as different adsorbed OH species [5,39], are present. However, in the experiments we never found transition scenarios from periodic to aperiodic behavior as typical in systems with a few degrees of freedom. Instead, irregular current oscillations emerged directly at the transition from the stationary to the oscillatory region, which when going deeper into the oscillatory region eventually transformed into periodic oscillations. These facts indicate that the irregular oscillations are accompanied by spatial structures on the electrode surface. This conjecture is further supported by a comparison of the time series obtained with low electrolyte conductivity and high electrolyte conductivity but an external series resistor. Although for the uniform dynamics the effect of electrolyte and external resistor is the same, the oscillatory dynamics exhibited marked differences. These differences must originate from a different spatial order on the electrode surface, entailed by the different spatial coupling modes of the two experimental arrangements. In fact, traveling waves were observed in first spatially resolved FTIR experiments during CO oxidation in the presence of Br− ions [40], underlying the necessity to incorporate spatial degrees of freedom in a mathematical description of the observed oscillatory instability. The global measurements and lumped model simulations reported in this paper present thus only a footing for a more comprehensive picture of the nonlinear dynamics of CO electrocatalysis. 5. Conclusions Our studies demonstrated that the coadsorption of anions, CO and OH may lead to nontrivial interactions among the different adsorbed species that introduce additional feedback loops into the

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