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Stabilizing Nonstationary Electrochemical Time Series Raphael Nagao,† Elton Sitta,† and Hamilton Varela*,†,‡,§ Institute of Chemistry of Sa˜o Carlos, UniVersity of Sa˜o Paulo, CP 780, CEP 13560-970, Sa˜o Carlos, SP, Brazil Institute of AdVanced Studies, UniVersity of Sa˜o Paulo, CP 72012, CEP 05508-970, Sa˜o Paulo, SP, Brazil, and Ertl Center for Electrochemistry and Catalysis, GIST, Cheomdan-gwagiro 261, Buk-gu, Gwangju 500-712, South Korea ReceiVed: October 5, 2010; ReVised Manuscript ReceiVed: NoVember 5, 2010
Electrochemical systems are ideal working-horses for studying oscillatory dynamics. Experimentally obtained time series, however, are usually associated with a spontaneous drift in some uncontrollable parameter that triggers transitions among different oscillatory patterns, despite the fact that all controllable parameters are kept constant. Herein we present an empirical method to stabilize experimental potential time series. The method consists of applying a negative galvanodynamic sweep to compensate the spontaneous drift and was tested for the oscillatory electro-oxidation of methanol on platinum. For a wide range of applied currents, the base system presents spontaneous transitions from quasi-harmonic to mixed mode oscillations. Temporal patterns were stabilized by galvanodynamic sweeps at different rates. The procedure resulted in a considerable increase in the number of oscillatory cycles from 5 to 20 times, depending on the specific temporal pattern. The spontaneous drift has been associated with uncompensated oscillations, in which the coverage of some adsorbed species are not reestablished after one cycle; i.e., there is a net accumulation and/or depletion of adsorbed species during oscillations. We interpreted the rate of the galvanodynamic sweep in terms of the time scales of the poisoning processes that underlies the uncompensated oscillations and thus the spontaneous slow drift. 1. Introduction Many natural and man-made open systems are known to undergo spontaneous self-organization when kept far from thermodynamic equilibrium. Rather than mere curiosity, the establishment of the nonequilibrium thermodynamics1 made the study of such processes an exciting research field and also an intellectually respected enterprise.2 Particular interest is focused on the noticeable analogy with many processes that occur in living systems.3-6 Chemical systems are very attractive for studying spatiotemporal pattern formation. Since the discovery of the famous Belousov-Zhabotinsky reaction,7 examples of self-organization in chemical systems have become very abundant in both homogeneous and heterogeneous environments. Due to the integration between experimental and theoretical approaches, some experimentally observed patterned states are presently reasonably understood. Oscillatory behavior in chemical reactors operating in batch is characterized by transient dynamics, which reflects the decrease in the overall free energy as reactants are consumed and the system evolves toward the thermodynamic equilibrium, the ultimate attractor in closed systems.8 To keep the system in a nonequilibrium stationary state, reactants are continuously fed into the reaction reservoir and reaction products are constantly removed, in a way that the reactor volume remains constant. Under those conditions, entropy produced due to irreversible chemical reactions is exported, allowing at the spontaneous emergence of temporal self-organized states. Such studies are usually carried out in the so-called continuous-flow-stirred-tankreactor (CSTR).2,9-12 * Corresponding author. E-mail:
[email protected]. † Institute of Chemistry of Sa˜o Carlos, University of Sa˜o Paulo. ‡ Institute of Advanced Studies, University of Sa˜o Paulo. § GIST.
This qualitative description is also applicable to chemical reactions that occur at the electrified solid/liquid interface. Electrochemical systems are regarded as open systems in which the control volume around the electrified solid/liquid interface is connected to inexhaustible reservoirs. From the electrode side, the system is open to the electron flow, whereas from the solution side it is in contact with the bulk solution, which remains virtually unchanged, regardless of the consumption of reactants and the formation of products.13 Both potentiostatic and galvanostatic operation modes can support the emergence of sustained oscillations, examples include harmonic, relaxation, mixed mode oscillations, and chaos.14-26 One important problem when dealing with experimental time series is the fact that they are usually found to evolve in time, despite the fact that all controllable parameters are kept constant. These systems can be described as consisting of two coupled rhythms: a core system underlying the observed oscillations and the long-term slow evolution that drives the core system through different parameter regions. As a consequence of the slowvarying component, analyses of the dynamic behavior are normally restricted to considerably short time windows. In general terms, the coupling among different time scale characterizes all rhythms in living systems, since some aging is always superimposed when intrinsic rhythms are measured. In spite of the vast literature on the control of chaotic dynamics,27-30 and the stabilization of unstable fixed points through feedback control techniques,31-33 we are not aware of previous work on the compensation of the long-term slow drift to stabilize experimental time series. We introduce in this paper an empirical procedure to stabilize nonstationary oscillatory time series obtained in an electrochemical experiment. Oscillations were conducted under galvanostatic control and the temporal patterns were stabilized individually by a negative galvanodynamic sweep (NGS). Simple periodic and mixed mode oscil-
10.1021/jp109554r 2010 American Chemical Society Published on Web 12/01/2010
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lations time series were successfully stabilized. The procedure is exemplified for the oscillatory electro-oxidation of methanol on platinum, but the strategy is suggested to be of general nature and could be easily extended to other comparable systems. 2. Experimental Section A conventional glass cell equipped with three electrodes was used in our experiments. The working electrode was a smooth polycrystalline platinum with real area AR ) 0.3 cm2 and roughness factor of about 1.1, estimated in terms of the hydrogen monolayer charge of 210 µC cm-2 (see references 34 and 35 for a survey on the issue of area determination). A mesh of platinized platinum with a very large area was utilized as the counter electrode. A reversible hydrogen electrode (RHE) prepared with identical composition and concentration of that used in the supporting electrolyte was used as reference electrode. All the solutions were prepared with high purity water (system Millipore Milli-Q, 18 MΩ cm), perchloric acid (Merck, suprapur 70-72%), and methanol (J.T. Baker, chromatography grade 99.9%). The system Pt|HClO4, H3COH was selected because it exhibits different temporal patterns as quasi-harmonic and mixed mode oscillations at the same oscillatory time series. Prior to electrochemical experiments, the cell was purged with argon (AGA 99.997%) for at least 20 min and kept in an inert atmosphere during all experiments to avoid the presence of dissolved molecular oxygen. The working electrode was flameannealed with butane/air flame and then cooled in an argon atmosphere. Afterward the electrode was immersed in the electrochemical cell and cycled between 0.05 and 1.50 at 1.00 V s-1 until a time-invariant profile is reached. Galvanodynamic experiment at dj/dt ) 3.32 µA s-1 cm-2 was then performed to find the oscillatory region (i.e., current interval where stable potential oscillations appears). The applied current density j is defined as I/AR, in which I is the applied current. Galvanostatic experiments were conducted at a sampling rate of 10 Hz. Before each electrochemical experiment, the working electrode was subjected to 10 cycles between 0.05 and 1.50 at 0.10 V s-1. All measurements were carried out at room temperature T ) 25 ( 1 °C with concentrations of HClO4 ) 0.1 mol L-1 and of H3COH ) 0.5 mol L-1 and monitored by a potentiostat/ galvanostat (Autolab/Eco-Chemie, PGSTAT3002) equipped with the SCANGEN module. 3. Results Figure 1 gives a general overview of our system: curves in black account for the cyclic voltammetries conducted at 0.05 V s-1 from 0.05 to 1.50 V for (a) aqueous perchloric acid media at 0.1 mol L-1 and (b) after addition of methanol to a final concentration of 0.5 mol L-1. In both cases, the voltammetric signatures reveal the quality of our surface and experimental setup, as well as the cleanness of the system. Details of the profiles themselves can be found elsewhere for the polycrystalline platinum surface in perchloric acid36 and in the presence of methanol.37-39 To investigate the region of instability where potential oscillations emerge, a slow galvanodynamic sweep (at dj/dt ) 3.32 µA s-1 cm-2) was carried out under conditions identical to that presented in the cyclic voltammogram; results are given in the red curve in plate (b). Note that at low potentials, the galvanodynamic curve nearly coincides with the voltammetric curve up to about 0.70 V, where the stable stationary state loses its stability and undergoes a subcritical Hopf bifurcation, i.e., explosive birth of the oscillations. Following the current increase, oscillations become less harmonic and with larger
Figure 1. Cyclic voltammograms recorded at dU/dt ) 0.05 V s-1 (black) in (a) 0.1 mol L-1 HClO4 electrolyte and (b) containing 0.5 mol L-1 H3COH. Galvanodynamic sweep at dj/dt ) 3.32 µA cm-2 s-1 (red) for the composition given in (b).
Figure 2. Potential time series during galvanostatic (j ) 1.00 mA cm-2) electro-oxidation of methanol. The following sequence spontaneously evolves: the birth of harmonic oscillations from a stationary state (ss), the transition to mixed mode oscillations, and the death of oscillations at 371 s.
amplitude, ending with mixed mode oscillations close to the upper limit of the oscillatory region. At higher currents, the limit cycle collides with the focus saddle-point of the oxygen evolution branch, and oscillations are extinguished. In Figure 1b this transition is given as a discontinuity in the abrupt jump in the red curve from the low to the high potential branch. Figure 2 shows an example of oscillatory time series of the electrode potential obtained under galvanostatic conditions at j ) 1.00 mA cm-2. High amplitude, nearly harmonic oscillations are born after the induction period and remain stable up to about 290 s. Spontaneous homoclinic transition to mixed mode oscillations is then observed. These oscillations are characterized by intercalating large (L) and small (S) amplitude cycles and spontaneously evolve in the following LS sequence: 10 f 11 f 12 f 13 f 1n (with n > 3). Overall, this sequence closely resembles the one shown along the galvanodynamic sweep in Figure 1b, reflecting the quasi-stationary nature of the galvanodynamic experiments. However, in contrast to the current-driven
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transitions presented in the galvanodynamic experiments, the transitions observed in Figure 2 are spontaneous and therefore occur in spite of the fact that all controllable experimental parameters are kept constant. Comparing the dynamic and static experiments presented in Figures 1b and 2, respectively, it becomes clear that the spontaneous drift observed in the galvanostatic measurements is equivalent to that caused by the deliberately induced current increase in the galvanodynamic experiments. Therefore, the spontaneous drift plays the role of a time-dependent bifurcation parameter, whose dynamics is considerably slower than that of the potential oscillations and which is somewhat connected to an increase in the applied current. Mechanistic insights on the nature of this drift can be gained from the analysis of the potential regions visited as oscillations evolve. In this regard, the increase in the mean electrode potential at each cycle is clearly discernible in the monotonic increase in the upper limit of the electrode potential and also in the time spent at high potentials in the mixed mode states. In quantitative terms, we estimate the evolution of the mean electrode potential, Um, at each oscillation cycle, and the rate dUm/dt was then obtained as the system slowly evolves. The following rates were estimated, for the induction period 0.519 mV s-1, and for the oscillatory states 10 0.192 mV s-1, 11 0.264 mV s-1, 12 0.177 mV s-1, and 13 0.145 mV s-1. The electrode potential informs on the mean composition of the actual surface coverage. During one oscillatory cycle, the potential values visited reflect the oscillations observed in the coverage of some intermediate species.40 Ideally, the surface composition would be re-established after one full loop, in such a way that the population of adsorbed species would be identical before and after the cycle, so that the system remains essentially in the same region of the phase space. As in most experimental cases, the situation observed here is different and the potential slowly increases after each cycle. Since the increase in the electrode potential and the consequent observed patterns is equivalent to an increase in the applied current, it is intuitive to try to compensate this spontaneous drift by slowly decreasing the applied current. The following procedure was adopted to accomplish this goal: a stationary experiment was initiated at constant current density until one of the sequential patterns given in Figure 2 is observed, then a NGS is applied. Stabilized temporal patterns are exemplified in Figure 3. NGSs were applied at different rates for an initial current density of j ) 1.00 mA cm-2. Comparing Figures 2 and 3, it becomes apparent that simple period one and mixed mode LS states are nicely stabilized when the NGS is applied. In addition, we found an incomplete Farey sequence with a concatenation of two other states, namely 1011 and 2011, between the transition from 11 to 10 (not shown), as predicted by the firing numbers.26 As already mentioned, the spontaneous slow increase in the mean electrode potential under the oscillatory regime is associated with transformations in the surface composition. To verify the efficacy of the stabilization procedure, we applied NGSs at different rates, and computed the number of oscillatory cycles for each temporal pattern. Results are compiled in Table 1. The number of cycles obtained for the nonstabilized cases are given for the zero sweep rate in the first line. Except for the highest sweep rate for the 11 state, the imposed linear decrease in the applied current results in an increase in the number of cycles. Each temporal pattern in Table 1 was performed separately in different days to avoid the influence of contamination and reagent evaporation in long experiments. In spite of the rigorous pretreatment and general experimental procedures, the number
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Figure 3. Period-one and mixed mode oscillations stabilized by a negatiVe galVanodynamic sweep of different rates for an initial current density of 1.00 mA cm-2: (a) - 2.39 µA s-1 cm-2; (b) - 1.00 µA s-1 cm-2; (c) - 1.33 µA s-1 cm-2; (d) - 0.58 µA s-1 cm-2.
of cycles recorded was found to slightly vary around a mean value. The discrepancies in the number of cycles remain smaller than 40%, but the rate in which the maximum number of cycles is observed is very stable and is fully reproducible. This aspect reinforces the argument developed below in which the surface poisoning rate is compared to the optimum stabilization rate. In Table 1, the initial current density of j ) 1.59 mA cm-2 was utilized to measure the oscillatory time for the 10 pattern and j ) 1.00 mA cm-2 for the 11, 12, and 13 cases. The increase of the initial current was necessary due to the large time-window presented by period-one which allowed to keep the same acquisition frequency. In any case, the efficacy of the stabilization, i.e., the increase in the number of cycles, increases with the sweep rate up to a maximum and then decreases. In the optimum NGS, i.e., the one that produces the longest time series of a given stabilized pattern, a pronounced increase in the stability of the time series is observed. Increases from about 5 to more than 20 times were observed in the number of stable cycles for patterns 13 and 10, respectively. The optimum stabilization rate can, however, be as unique in the sense it reflects the rate in which the surface transformations occur for a given pattern. This aspect is important and will be further discussed below. In spite of both the small deviation in the number of cycles and the difference in the initial current in the data presented in Table 1, the observed trend is completely representative of the stabilization achieved. 4. Discussion The problem presented here consists of the slow drift observed in the potential time series registered during the electro-oxidation of methanol on platinum. This drift is often observed in electrochemical systems, and, in the case of methanol, it has been associated to the slow change in the mean coverage of
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TABLE 1: Number of Oscillatory Cycles as a Function of the Rate of the NGS (µA s-1 cm-2) 10
11
12
13
-dj/dt
cycles
-dj/dt
cycles
-dj/dt
cycles
-dj/dt
cycles
0 0.78 1.59 2.39 3.18 4.78 6.37 7.96
18 125 165 382 271 172 124 81
0 0.33 0.50 0.66 0.83 1.00 1.16 1.33
15 19 23 25 50 87 37 12
0 0.33 0.66 1.00 1.16 1.33 1.49 1.66
6 7 10 17 21 54 24 6
0 0.17 0.33 0.41 0.50 0.58 0.60 0.66
7 9 24 25 31 35 16 10
adsorbed species in the course of oscillations.18 This change results from uncompensated oscillations, in which the coverage of some adsorbed species are not reestablished after one cycle; i.e., there is a net accumulation and/or depletion of adsorbed species during oscillations. We initially discuss in this section the main surface processes leading to these two processes. Afterward, a mechanism associated to the short and long-term dynamics is suggested. Finally, our results are discussed in connection with the problem of nonstationary time series in more general terms. Surface Reactions. The electro-oxidation of methanol on platinum and platinum based surface has been extensively investigated by means of different techniques. The electrooxidation of methanol is commonly rationalized in terms of the so-called dual pathway mechanism,41 in which parallel pathways occur simultaneously. Carbon monoxide is recognized as an important adsorbed intermediate that severely blocks the electrode surface at relatively low potentials. It is believed to be formed via three dehydrogenation steps42 (notation: the underlined element indicates the very atom by which the molecule is adsorbed),
H3COH f H2C _ OH + H+ + e-
(r1a)
H2C _ OH f HC _ OH + H+ + e-
(r1b)
HC _ OH f C _ OH + H+ + e-
(r1c)
C _ OH f C _ O + H+ + e-
(r1d)
the first process involves the adsorption of methanol by the carbon, which requires at least three contiguous sites to break the C-H bonds.43,44 In the indirect pathway, adsorbed carbon monoxide is oxidized only at high overpotentials via a Langmuir-Hinshelwood (LH) step in the Ertl reaction,45
C _ O + (H)xO _ f CO2 + xH+ + xe-
(r2)
where (H)xO (with x ) 0, 1, or 2) generically represents the adsorbed oxygenate species. In the direct pathway, it is believed that the methanol molecule adsorbs by the oxygen atom, promoting the methoxy species,46,47
H3COH f H3CO _ + H+ + e-
(r3a)
H3CO _ f H2CO _ + H+ + e-
(r3b)
which generates formaldehyde, H2CO, that desorbs from the surface48,49 and exists in its hydrated form: methylene glycol, H2C(OH)2,50
H2CO _ f H2CO + H2O h H2C(OH)2 In its turn, methylene glycol might lose two hydrogen atoms and rearrange itself, forming HCOOH. Formic acid generates adsorbed carbon monoxide, which is oxidized, cf. reaction r2, via a Langmuir-Hinshelwood step. Formic acid might also form adsorbed formate, HCOOad, which acts as a spectator species during the electro-oxidation of methanol, contributing with an insignificant percentage to the carbon dioxide yield.51 Finally, formic acid reacts with methanol molecules in solution, giving rise to methylformate, HCOOCH3.52 This complex mechanism is strongly dependent on a number of experimental variables, including electrolyte composition and concentration, temperature, crystalline structure of the surface, etc. Under some circumstances, the steady state coverage distribution of adsorbed intermediates may become unstable, so that the electro-oxidation of methanol displays current or potential (as in the present case) oscillations. In short, the oscillatory regime in electrocatalytic reaction systems is mechanistically described by the competition between potential-dependent adsorption isotherms of carbonaceous and oxygenated species.53 Short- and Long-Term Dynamics. In terms of surface reactions, the phenomenon reported here consists of two processes with distinct time scales. The core dynamics occurs in the short time scale and underlies the potential oscillations with frequency about 0.2-1 Hz. The secondary, slow, dynamics reflects the changes in the mean coverage of some adsorbed species and is responsible for the spontaneous drift that drives the system through different oscillatory patterns. Interesting transitions among different oscillatory states have been reported for the electro-oxidation of formaldehyde and methanol on platinum.21-23 We have recently reported comparable transitions from periodic to chaotic states during the electro-oxidation of ethylene glycol on platinum and in alkaline media.54 The increase observed in the electrode potential is common to these systems and has been recognized as a process of surface deactivation.21-23 The authors21-24 described the continuous drift as a monotonic sequence series of dynamic states, in such a way that time was suggested to subsume two or more parameters. Finally, they suggested that the drift is caused by surface, rather than transport processes. Boscheto et al.18 used in situ ATR-SEIRAS (surface enhanced infrared absorption spectroscopic in attenuated total reflection configuration) to follow the changes in the surface composition
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during the electro-oxidation of methanol on a platinum film and in sulfuric acid media. The authors found in the long term dynamics, a continuous decrease of the COL coverage with rate -4.5 × 10-4 to -0.9 × 10-4 cm-1 s-1 along the transition from the induction period to the well developed oscillations in the range between 0.34 and 0.20 ML, whereas the coverage of COB varied smoothly from 0.06 to 0.04 ML. The core dynamics was characterized by considerably smaller oscillations in the CO coverage, ∆θCOL ∼ 0.04-0.05 ML and comparable potential oscillations as the one reported here. The band intensity of adsorbed formate remained quite small without significant time changes. In agreement with our results, they found dUm/dt rates of +0.066 and +0.011 mV s-1 during the induction period and oscillations, respectively.18 In our case, the following rates for the evolution of the mean electrode potential amounts to +0.519 mV s-1 (the induction period), +0.192 mV s-1 (10), +0.264 mV s-1 (11), +0.177 mV s-1 (12), and +0.145 mV s-1 (for the 13 pattern). Following the mechanistic scenario reviewed above, the surface coverage θ during the electro-oxidation of methanol on platinum can be written as
AF ) AR(1 - θCO - 2θHCOO - θ(H)xO)
Although the real area AR remains constant (and equal to 0.3 cm2; see the Experimental Section) during the oscillations, the free area AF, changes due to the slow modification of the mean values of surface coverage of some intermediate species. Therefore, the actual current density becomes a function of time, J ) J(t). As time evolves, e.g., from t1 to t2, the residual coverage of poisoning species increases, so that the free area decreases: AF,t1 > AF,t2, and thus Jt1 < Jt2. Since the applied current I is kept constant during stationary experiments, the product JAF remains constant, and the time derivative of this product leads to
AF
dAF dJ +J )0 dt dt
(4)
or
dJ J dAF )dt AF dt
θ ) (θC-H + θO-C + θCO + 2θHCOO + θ(H)xO + θA)
(1) where θC-H and θO-C represent the coverage of different adsorbed methanol residues. θCO represents the coverage of carbon monoxide, θHCOO the bridge bonded formate, θ(H)xO the oxygenate species, and θA the adsorbed anions from supporting electrolyte. Note that in the range of potential where the galvanostatic oscillations develop, around 0.60-0.85 V vs RHE, the main contribution to the electro-oxidation reaction can be reduced to
θ ) (θCO + 2θHCOO + θ(H)xO)
(3)
(2)
Simplification of eq 1 to eq 2 is justified as follows. (a) The oxidative removal of carbon monoxide by reaction r2 is the rate determining step in the potential range where sustained oscillations emerge.44,55-57 It indicates the inability of the platinum electrode to dissociate water in adsorbed oxygenated species, which made the adsorbed COad not a catalytic poison but rather an intermediate of the oxidation reaction.51 (b) Experimental results support the idea that formate acts as a spectator species during methanol electro-oxidation. The band intensity of the adsorbed formate did not follow the increase of faradaic current with the addition of methanol concentration.51 The same hypothesis is thought to hold during the electro-oxidation of formic acid.58 (c) The interaction of water with the surface increases as the potential is made more positive.59 Water competes with the organic molecules for adsorption sites and plays a crucial role in the overall reaction rate;60 see reaction r2. It acts as an “activated” precursor, donating the oxygen element to CO2 formation.61 (d) The perchlorate anion has the smallest adsorption energy among the classical anions used as supporting electrolyte,62 so that its contribution can be neglected. Poisoning species adsorbed at the electrode surface decrease the electrode area, changing the actual local current density J, which is defined by the applied current I, normalized by the nonpoisoned free area AF. Note that j ) I/AR is different from J ) I/AF by the following relationship,
(5)
deriving eq 3,
(
dθ(H)xO dAF dθCO dθHCOO ) -AR +2 + dt dt dt dt
)
(6)
and inserting it in eq 5, results in
(
dθ(H)xO AR dθCO dθHCOO dJ )J +2 + dt AF dt dt dt
)
(7)
Emphasizing the local current density J as function of applied current density j,
(
dθ(H)xO dθCO dθHCOO dJ j ) +2 + 2 dt dt dt (1 - θ) dt
)
(8)
which can be written as
(
dθ(H)xO dθCO dθHCOO dJ )κ +2 + dt dt dt dt
)
(9)
in which the term κ is strictly positive. The decrease in the nonpoisoned area AF is reflected in the net increase of the surface population of adsorbed species,
(
)
dθ(H)xO dθCO dθHCOO >0 +2 + dt dt dt
(10)
According to experimental data of the long-term dynamics for the methanol system under consideration, it has been observed that dθ(H)xO/dt > 0, dθCO/dt < 0, and dθHCOO/dt f 0.18 Therefore, condition 10 is satisfied and the uncompensated oscillations result in a net slow accumulation of oxygenated, (H)xO, at the electrode surface. As already stressed, this
Nonstationary Electrochemical Time Series accumulation occurs in a rather slow time scale in the uncompensated oscillations and therefore it is not discernible in the short term dynamics. Although the applied current, j ) I/AR, is kept constant during stationary experiments, the actual current that flow through the nonpoisoned area, J ) I/AF rises up. The spontaneous increase in J during the oscillations, see (9) and (10), drive thus the system to different states as exemplified in Figure 2. The application of a negative galvanodynamic sweep introduced here accounts for the compensation of this spontaneous drift. In the ideal case, the rate of the NGS would match the time scale of the slow drift, resulting in a totally efficient stabilization. The results presented in Table 1 illustrate this aspect and show how the rate in which the current is decreased influences the stabilization of a given pattern. The empirical approach presented here assumes a linear evolution of the spontaneous drift, which obviously results from a linear evolution of the net surface population during the uncompensated oscillations. This is of course a rough assumption, and we have shown that the time evolution of the carbon monoxide coverage is nonlinear.18 In addition, the oversimplification of our treatment becomes apparent when we realize that the NGS becomes less efficient at high potential, where more complicated patterns appear. Rather than a comprehensive/ sophisticated stabilization procedure, our methodology simply applies previous knowledge of the short and long-term dynamics. Nevertheless, increasing the number of oscillations in a given state from 5 to 20 times might be already enough to characterize short-lived temporal patterns squeezed in a certain parameter window. In the next we discuss how nonstationarity can provide mechanistic information on the poisoning process. Nonstationarity. The coupling among different time scales (mass transport, adsorption, and reaction) present in electrochemical systems result in very rich dynamics including a plethora of complex patterns.13-25,53,63-65 The nonstationary nature of experimental time series may be an unwanted feature when one is focused on the characterization of those patterns. The method proved to be of help in this sense, since it was shown to efficiently stabilize different oscillatory states by increasing its number of cycles. However, nonstationarity not only means an experimental imperfection to be avoided but also can indeed be used to inform on mechanistic aspects. The coexistence of different time scale is an important issue in experimental nonlinear dynamics and has been referred to as the problem of time-scale separation in which a hidden slow process causes nonstationarity in a fast system.66 The identification of this slow process can help to predict the deleterious effects of the slow accumulation of damage/fatigue in mechanical/biomechanical measures. The so-called nonlinear damage tracking method66,67 has been used to follow slow changes in movement kinematics as an attempt to identify physiologic fatigue and related changes.68-70 Very important, it has been suggested that this approach can help extracting information from apparently nonaccessible biological processes from easily obtainable biomechanical data. The premature identification of slowly evolving injury/disease via its tracking might impact the way to deal with many biological questions. In fact, the occurrence of coupled rhythms is ubiquitous in nature, and understanding how different these rhythms are coupled is essential to explore the richness behind experimentally obtained physiological time series. Examples of engineering-related questions include damage evolution, failure prediction, the drifting out of alignment of machinery parts, corrosion process in structural components, performance degradation, etc.66,67,71
J. Phys. Chem. C, Vol. 114, No. 50, 2010 22267 In reacting systems, this issue remained unexplored so far, and the dynamics of the hidden, slow subsystem can provide valuable information for instance on the slow deactivation of a catalytic specie, cf. an enzyme, or of a catalytic surface, as in the present case. Again, predicting full deactivation in early stages might prevent drastic performance decrease. As a general conclusion, it has been suggested that rather than a simple a nonstationarity to be avoided, the slowly evolving process can be the main process to analyze.71 In the case discussed here, the optimum stabilization rate is connected to the evolution of surface poisoning. Of course, our linear, empirical approach only gives a general idea of the relative time scale of the slow process, more rigorous treatment of slowly evolving time series is needed to further understand the interplay between surface population changes and the fast dynamics. We are currently working on the application of nonlinear damage tracking method66-68 to electrochemical systems. 5. Conclusions and Outlook We report in this paper an empirical approach to stabilize experimental oscillatory time series. The method was applied for the electro-oxidation of methanol on a polycrystalline platinum surface in perchloric acid aqueous media. The system was studied under galvanostatic regime and spontaneous temporal transition from nearly sinusoidal shape to mixed mode oscillations (LS: 10 f 11 f 12 f 13 f 1n, with n > 3) was observed in a wide range of applied current density. Each temporal pattern was stabilized by a negatiVe galVanodynamic sweep at different rates, showing a stabilization improvement on the oscillatory time, at least, 5 times for the 13 pattern to more than 20 times for the 10 state. The results presented here open the perspective to investigate temporal patterns present in the squeezed parameter region. Methods to characterize time series are currently needed for the experimental investigation of two-dimensional phase diagrams numerically anticipated for this class of systems.72 The main experimental difficulty in realizing such high-resolution phase diagrams is the identification of some temporal patterns confined in tiny parameter regions. The method reported here is certainly an alternative to circumvent this limitation. Besides the stabilization itself, it has been suggested that rather than an experimental problem to be avoided, nonstationarity can indeed be used to provide valuable mechanistic information. Since the time-dependent bifurcation parameter observed in stationary experiments is connected to the surface poisoning, the optimum stabilization rate informs on the rate of changes in the surface coverage. Although tested for the electro-oxidation of methanol, the approach is certainly valid for other similar systems, since the poison accumulation seems to be universal for a wide class of organic molecules. Stabilizing specific patterns might also impact the efficiency increase or dissipation decrease observed in some systems operating under oscillatory regime.73 Specifically in the context of fuel cells, it has been shown that under oscillatory regime the performance increase strongly depends on the morphology (period and amplitude) of the oscillations.74-78 Stabilizing electrochemical oscillations in such a way that the time that the system remains in the high conversion state is maximized is obviously an important target. Acknowledgment. We express our gratitude to E. Boscheto and E. G. Machado for fruitful discussions. R.N. acknowledges Fundac¸a˜o de Amparo a` Pesquisa do Estado de Sa˜o Paulo (FAPESP) for the scholarship (# 09/00153-6) and H.V. ac-
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