J . Phys. Chem. 1990, 94, 7137-7143
7137
Bistabiiity and Oscillations in the Eiectrocatalyzed Oxidation of Formaldehyde Yuanhang Xut and Mark Schell* Department of Chemistry and the Center for Nonequilibrium Structures, Southern Methodist University, Dallas, Texas 75275 (Received: February 12, 1990)
A variety of nonlinear phenomena, which was observed during the electrochemical oxidation of formaldehyde at a rotating platinum disk, is described. The experiments were conducted under galvanostatic conditions and the applied current was treated as a bifurcation parameter. The oxidation process exhibited bistability; both high-potential and low-potential states were found within the same range of values of current. However, most of the low-potential stationary behavior was either nonexistent or unstable in the region of coexistence and, instead, oscillations were observed. Period-doubling bifurcations, leading to chaos, were found by changing the current. Waveforms were recorded that represented dynamical states belonging to a periodie-chaotic sequence which was previously characterized under other conditions. The results presented here include dynamical states that were measured further into the sequence. New types of states within the sequence were also discovered. These latter states possessed characteristics that made them appear similar to dynamical states recently measured in an experimental investigation of the oxidation of formic acid. However, an examination of their symbolic patterns, which were obtained from one-dimensional mappings, reveals that they were different. The observation of yet other types of oscillations suggests that the oxidation of formaldehyde is coupled to more than one of the stages of the process in which oxide layers are formed on the platinum electrode.
Introduction This paper reports the results of an experimental investigation of nonlinear phenomena that accompany the electrochemical oxidation of hydrated formaldehyde at a platinum electrode.'-13 The focus is on oscillations that replace, as stable behavior, stationary states which apparently belong to part of the lower branch of a bistable curve. Nonlinear phenomena are characterized by using measurements, which were taken under galvanostatic conditions (constant current), of the potential difference between the working electrode and a reference electrode. Models have been presented'*3that describe possible underlying causes for oscillatory behavior, but during the time since their formulation additional details of the oxidation process have been revealed. Therefore, we first summarize those aspects of the present understanding of the oxidation process which provide a plausible explanation for the occurrence of oscillations. Following this summary, we state the motivations and objectives for the present study. A Mechanism for the Oxidation of Formaldehyde. In an acidic electrolyte, most of the formaldehyde is hydrated to methylene glycol.'4 The overall electrochemical oxidation of the glycol is represented by the following chemical equation4 C H 2 ( 0 H ) 2 C 0 2 + 4H+ + 4e(1) The mechanism for the oxidation process consists of at least two paths. I n one path, the direct path, radicals bond with surface platinum atoms producing intermediates that possess relatively short lifetimes. A proposed mechanism for the direct path4 is written as follows: C H 2 ( 0 H ) 2 A + H+ + e(2) A B + H + + e(3) B GOOH + H+ + e(4) C 0 2 + H+ + eGOOH (5) where A and B originally represented schematic intermediates, but more recently, they have been po~tulated'~ as HC(OH), and HCOOH (formic acid), respectively.I6 Several alternative schemes for the direct path have been p r ~ p o s e d . l ~ - ~ ~ I n a second path, an intermediate is formed on the electrode, which, at sufficiently low values of the potential difference, essentially remains inert, and thus it behaves as a poison and blocks the direct route. The identity of the poison is a controversial subject. Experimental evidence supports a variety of candidates
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'Permanent address: Department of Chemistry, Xiamen University, Xiamen, Fujian, China.
0022-3654/90/2094-7 137$02.50/0
that include COH,S98,'7918HC0,20 and CO (both C=O and C=O).69'2918,19Mechanisms for the formation of a given can-
didate have also been suggested. Two reactions proposed for the formation of carbon monoxide2' are represented by
COOH + 2COOH
-
-
+ H20 GO + H20 + C02 GO
(7)
At sufficiently high potentials, hydroxyl radicals from water will bond with surface platinum atoms,22-24and this complex reacts with the poison:22
( I ) Buck, R. P.; Griffith, L. R. J . Electrochem. SOC.1962, 11, 1005. (2) Bagotzky, V. S.; Vasilyev, Yu. B. Electrochim. Acta 1964, 9, 869. (3) Shropshire, J. A. Electrochim. Acta 1967, 12, 253. (4) Hunger, H . F. J. Electrochem. Soc. 1968, 115, 492. (5) Breiter, M. W. Electrochemical Processes in Fuel Cells; Springer: New York, 1969. (6) Loucka, T.; Weber, J. J. Electroanal. Chem. 1969, 21, 329. Sidhesuaran, P.; Lal, H. J. Electroanal. Chem. 1972, 34, 173. (7) Vielstich, W. Fuel Cells; Wiley: New York, 1970. (8) Kazarinov. V. E.; Tysyachnaya, G. Ya. Electrokhimiya 1972.8. 592. (9) Kazarinov, V. E.; Tjsyachnaia, G. Ya.; Andreev, V. N. J . Electroanal. Chem. 1975, 65, 391. (10) Motoo. S.: Shibata. M. J . Electroanal. Chem. 1982. 139. 119. ( I 1 ) Custro Luna, A. M.; Giordano, M. C.; Arvia, A. J. J. Electroanal. Chem. 1989, 259, 173. ( I 2) Nishimura, K.; Ohnishi, R.; Kunimatsu, K.; Enyo, M. J . Electroanal. Chem. 1989, 258, 219. (13) Schell, M.; Albahadily, F. N.; Safar, J.; Xu, Y. J . Phys. Chem. 1989, 93, 4806. (14) Loudon, G . M. Organic Chemistry; Benjamin/Cummings: Menlo Park, CA, 1988; p 777. ( 1 5) Beltowska-Brzezinska, M.; Heitbaum, J.; Vielstich, W. Electrochim. Acta 1985, 30, 1465. (16) Following ref 15, we have also replaced H C O O with COOH. The underbar on an atom denotes bonding to surface platinum atoms; we do not distinguish the type or number of bonds. The chemical equations are written with the understanding that the reactions occur on platinum. (17) Spasojevic, M. D.; Adzic, R. R.; Despic, A. R. J . Electroanal. Chem. 1980, 109. 26 I . (18) Kazarinov, V. E.; Vassiliev, Yu. B.; Andreev, V. N.; Kuliev, S. A. J. Electroanal. Chem. 1981, 123, 345. (19) Solomun, T. Surf. Sei. 1986, 176, 593. (20) Kamath, V. N.; Lal, H. Electroanal. Chem. 1968, 19, 137. (21) Kunimatsu, K.; Kita, H . J. Electroanal. Chem. 1987, 218, 155. (22) Sun,S. G.; Clavilier, J. J. Electroanal. Chem. 1988, 240, 147. (23) Gilroy, D.; Conway, B. E. Can. J . Chem. 1968.46, 875. (24) Laitinen, H. A.; Enke, C. G., J . Electrochem. SOC.1960, 107, 773.
0 1990 American Chemical Society
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The Journal of Physical Chemistry, Vol. 94, No. 18. 1990
+ + + - + +
H20
OH
H+
e-
(8)
OH GO COz H+ e(9) Wojtowicz et al.25have proposed that the rate of a reaction, which is analogous to reaction 9, is proportional to the surface density of vacant sites. (The cited paperz5considered reactions in which intermediates of the direct route reacted with OH.)If the rate of reaction 9 is proportional to the density of sites, the reaction is autocatalytic; the reaction produces at least two vacant sites for every molecule of C 0 2 produced. Such a reaction has an explosive nature. The more vacant sites produced, the faster the reaction. This property is consistent with cyclic voltammograms2* and, as will be noted, with some features of our measurements on oscillations. Reactions 2-9 provide a scheme that can be used to explain the occurrence of oscillations under galvanostatic conditions. Reactions 6 and 7 lead to the formation of a poison which partially blocks the direct path, reactions 2-5. It then follows that, in order to satisfy the requirements of the applied current, the system responds with an increase in potential so that the rate of reactions will increase. At sufficiently high potentials, OH is formed, reaction 8, and subsequently reacts with the poison, reaction 9. This latter reaction cleans the electrode surface and, consequently, the potential drops. Objectices. One of the motivations for the present study arises from our previous work13in which we found qualitative differences between the two bifurcation structures associated with the oxidation of formic acid and the oxidation of formaldehyde. Within the oscillatory regions, both reactions displayed an ordered set of periodic, mixed-mode, oscillations. In this set, each oscillatory state possessed, within one period, one large oscillation followed by a number of small oscillations; the set was ordered in such a way that, for each new member in the set that appeared in the direction of decreasing applied current, the number of small oscillations within a period increased by one. However, the character of the dynamical states found intermediate to two adjacent members of the set differed drastically between the two reactions. In the oxidation of formic acid, only periodic states were found, and the full sequence of states could be defined as a Farey sequence, i.e.. a sequence of states in which a one-to-one correspondence can be made with an ordered sequence of rational numbers.26 In the case of the oxidation of formaldehyde, subharmonics of the mixed oscillations and chaotic states were found. These results are somewhat surprising in view of other investigation~~.**’ where current-potential diagrams were obtained for the oxidation of methanol, formaldehyde, and formic acid; the peaks along the potential axis were located at the same positions for all three reactions. The results of these studies imply that reactions 2 and 3 are fast and that the remaining mechanism is qualitatively similar to that for the oxidation of formic acid. Therefore, we have initiated a series of experiments that will examine the oxidation of formaldehyde under several different conditions. The objective is to find whether our previous results for the oxidation of formaldehyde are robust, and whether any similarities can be found in the bifurcation structure with that of the oxidation of formic acid. The study presented here examines the response of a system that has a 50% increase in acid concentration over that used in our previous study. Although we report additional periodic states that appear similar to periodic states observed in the oxidation of formic acid, a close inspection of one-dimensional mappings, which were constructed from measured time series, reveals that their symbolic patterns*’ (unique sequences of binary symbols, one for each periodic solution of certain one-dimensional maps, constructed according to whether each point in the solution is mapped to the left or the right) are different. The only type of (25) Wojtowicz, J.; Marincic, N.; Conway, B. E. J . Chem. Phys. 1968, 48, 4333 (26) Ringland. J.; Schell, M. Phys. Lett. A 1989, 136, 379. Ringland, J.; h a , N.; Schell, M. Phys. Reu. A 1990, 41, 4223. (27) Metropolis, N.; Stein. M. L.; Stein, R. R . J Combinatorial Theory A 1973, IS, 25
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B2 10 15 Current ( PA ) Figure 1. The response of the potential (vs SCE) plotted against the applied current. Open squares (closed squares) represent data collected when the applied current was changed in the forward (reverse) direction. Between BI and B2, the system exhibited oscillations on the lower branch. The absolute minimal and maximal values of the potential are plotted for each oscillatory state. The point labeled with a T represents one case where the system had not relaxed. In separate experiments, it was found that a long relaxation, following the perturbation of the system in the vicinity of the low current end of the upper branch, was a common event. Typically, after the current was decreased, the system would immediately exhibit a rapid decrease in potential. However, the rate of change in the potential would slow and eventually the potential would begin to increase, and the system would finally return to a state on the upper branch. The working-electrode disk used in the experiment was 0
81
5.0 mm diameter in platinum.
conclusion we can make so far on the mechanisms of the oxidation of formaldehyde and the oxidation of formic acid, which is based on our investigations of oscillatory behavior, is that there may exist fundamental differences. A second objective of the present study is to place the location of oscillatory behavior relative to the region where the formation of an oxide layer occurs. It is well-known that, if a large enough current is applied, the system will respond with the evolution of oxygen. This evolution is preceded by the formation of an oxide layer. Reaction 8 is considered the initial step in oxide formation. We are interested in discovering whether, in addition to the initial stage, oscillations involve later stages of oxide formation. Our results show that this is indeed the case.
Experimental Section The experiments were conducted under galvanostatic conditions using a cell containing a 400-mL solution of 0.4 M formaldehyde and 3.0 M H2S04. All solutions were prepared by using distilled water which was further purified by processing it through a Millipore deionization unit. Two different sizes of polycrystalline platinum rotating disks were employed as working electrodes; one was 5.0 mm diameter in platinum and the other was 7.0 mm diameter. The experimental setup, equipment, chemicals, other conditions and cleaning procedures were the same as those described in ref 13. Before each set of experiments the working electrode was electrochemically cleaned and then the system was allowed to relax under open-circuit conditions (zero applied current). A steady potential was reached after an average time of 130 min. The procedure for preparing the system for measurements on oscillations, which was followed after the system reached an opencircuit, steady potential, is described in the next section. Results and Discussion Bistability. A relationship between measured potential responses and the applied current is shown in Figure 1. The data used for the plot was collected from an experiment conducted in the following way: after the working electrode was cleaned, the system was allowed to relax under open-circuit conditions. Next, the current was increased in increments (51.0 KA) to a value of
Electrocatalyzed Oxidation of Formaldehyde
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 7139
14.0 PA, and then it was decreased (in decrements) back to the value of zero. Between changes in the current, the current was held constant for at least 3 min and, in most cases, no longer than 12 min; if the observed potential (or peak potential in the case of oscillations) changed less than 1% over a time span of 2 min, the value of the potential was saved and the current was changed. One of the points in Figure 1, labeled T, was recorded more than 30 min after the current was last changed. At this point the system was still far from its final state; separate experiments indicate that the system would have eventually relaxed back to the upper branch. For oscillatory states, both the peak and minimal values of the potential are shown in Figure 1. The results of the experiment show that sustained oscillations can be realized over a substantial range of values for the applied current. The interval (BI, B2) in which sustained oscillations were observed is identified in Figure 1. An even larger range of values was found for which at least two “asymptotic” behaviors can coexist under the same conditions. This phenomenon, bistability, is common and has been observed in many electrochemical proc e ~ s e sas ~ ~ well , ~ as in several other types of chemical p r ~ c a s e s . ~ ~ - ~ The bistability studied here has additional complications due to the coupling with oscillations. We first present an explanation of bistability which does not account for the occurrence of oscillations. This is done by imagining a system that is the same I ’ 1 as the one under consideration but, with the following exceptions: 0 120 240 ( 1 ) no poison is formed from the fuel and (2) no reactions occur Timeb) in which the reactants include both the species that partake in Figure 2. Several measured waveforms from a subharmonic sequence. the process in which oxide layers are formed and the species that Measured potential is plotted against time. The potential range is partake in the oxidation of formaldehyde. The explanation, for 350-650 mV. Working electrode was 5.0 mm diameter in platinum. (a) the most part, is based on the reported behaviors of oxide forPrimary oscillatory state, period-one oscillations; Current density (1,) = ma ti or^,*^-^'-^^ including the important observation of h y ~ t e r e s i s . ~ ~ 29.0 pA/cm2; (b) period-two oscillations, Id = 25.5 pA/cm2; (c) period-two oscillations, Id = 24.5 pA/cm2; (d) period-four oscillations, Id = At open-circuit conditions and at small values of the applied 23.0 pA/cm2; (e) period-four oscillation, Id = 22.0 pA/cm2; (f) a time current, the system can meet the requirements imposed by the series that was measured very close to or within the region where pericurrent through relatively low activation energy (low-potential) od-eight oscillations were stable, Id = 21.6 pA/cm2. oxidation reactions, like those in eqs 2-5. When the current is increased in small increments, the system responds with increases for the applied current is reached. At this value, high activation in the potential in order that the rates of reactions increase to energy, oxidation reactions cannot take place at a slow enough values that meet the requirements of the current. Eventually, the rate to satisfy the requirements of the small current. Hence, the potential becomes large enough that the initial stage of oxide layer oxide layers break up allowing the low activation energy reactions formation occurs, reaction 8.23*24 Formation of oxide layers to satisfy the imposed requirements; reduction reactions, which proceeds in several stages, some of which do not produce current, involve both the fuel and oxides and which accelerate the breakup, e.g., the transformation of weakly bound oxygen to strongly bound have been proposed.34 oxygen.32 Consequently, a feedback mechanism can be initiated The responses of the system are more complicated than those that operates as described in the following: a potential is reached described due to the formation of the poison during the oxidation at which oxide formation occurs. Since oxides block the oxidation of hydrated formaldehyde and the occurrence of oscillatory beof organic molecules at the bare electrode, the potential rises havior. The formation of the poison causes substantial increases further, and in turn, the increase in potential increases the rate in the potential a t values of the applied current that are smaller of oxide formation. Therefore, once initiated, the feedback process than that at which oxide formation would lead to equivalent can continue until the system reaches a potential that is large increases in the hypothetical system. However, the poison reacts enough that high activation energy oxidation reactions, e.g., the with the species involved in the initial stage of oxide formation. evolution of oxygen, can take place on “or within” the oxide layers. The removal of both the poison and oxide by this reaction causes These reactions satisfy the requirements imposed by the current, the potential to decrease until substantial amounts of poison are and the system relaxes toward a high-potential, stationary state. again formed. Transition to a high-potential, stationary state takes After the system relaxes to a stationary state that belongs to place when the amount of oxide formed is greater than the amount the branch of high-potential states, decreasing the current in small consumed by reactions involving the poison. Our measurements amounts causes the system to respond with small decreases in the on the oscillations indicate that not only does the initial stage of potential (see the upper branch in Figure 1) until a critical value oxide formation strongly couple to the oxidation of formaldehyde, but so does at least one of the later stages. The results of ex(28) Russell, P. P.; Newman, J . J . Electrochem. SOC.1983, 130, 547. periments in which we focused on measuring the different types Mark Jr., H. B.; Kenyhercr, T. M.; Kissinger, P. T. In Electrochemical of oscillatory behaviors are presented in the remainder of this Studies of Biological Systems; Sawyer, D. T., Ed.; ACS Symposium Series; section. American Chemical Society: Washington, DC, 1977, p 1. Preparation of the System Previous to Measuring Oscillatory (29) Zimmermann, E. C.; Ross, J. J . Chem. Phys. 1984, 80, 720. Laplante, J. p.; Borckmans, p.; Dewel, G.; Gimenez. M.; Micheau, J. c.J . Phys. Behavior. Previous to recording oscillatory responses, the working Chem. 1987, 91, 3401. Laplante, J . P. J . Phys. Chem. 1989, 93, 3882. electrode was first cleaned and then the system was allowed to (30) Ganapathisubramanian,N.; Showalter, K. J . Phys. Chem. 1985.89, relax under open-circuit conditions. Next, the current was in21 18. Ganapathisubramanian, N.; Reckley, J. S.;Showalter, K. J . Chem. creased by the amount of 0.5 pA every 3 min until it was clear Phys. 1989, 91, 938. Epstein, 1. R. J . Chem. Educ. 1989, 66, 191. (31) Kozlowska, H. A.; Conway, B. E.; Sharp, W. B. A. J . Electroanal. that the system was beginning a transient approach to a state on Chem. 1973, 43, 9. the upper branch in Figure 1. Decreases in the current were (32) Hammond, J. S.;Winograd, N. J . Electrochem. SOC.1977, 78, 5 5 . initiated before the system reached a high-potential, stationary Conway. B. E.; Mozota, J. J . Chem. SOC..Faraday Trans. I 1982, 78, 1717. Roscoe, S.G.;Conway, B. E. J . Electroanal. Chem. 1987, 224, 163. (33) Biegler, T.; Woods, R. J . Electroanal. Chem. 1969, 20,73. Hoare, J. P. J . Electrochem. SOC.1985, 132, 301.
(34) Hoffman, A.; Kuhn, A. T. Electrochim. Acta 1964, 9, 835.
Xu and Schell
7140 The Journal of Physical Chemistry, Vol. 94, No, 18. 1990
1
0
125 Time(s)
230
0
Figure 3. Measured waveforms, potential plotted against time. Potential range is 360-580 mV. Electrode was 7.0 mm diameter in platinum. (a) Period-four oscillations, Id = 19.5 pA/cm2; (b) chaotic oscillations, Id = 18.5 pA/cm2.
0 Vmin(m)
125 Time(s)
250
Figure 5. Measured waveforms from (a) a period-three state, Id = 19.0 pA/cm2, and (b) its subharmonic,a period-six state, Id = 19.0 pA/cm2.
1
Figure 4. Plots of the ( N + l ) t h minimum in a time series against the Nth minimum. (a) Constructed from the time series in Figure 3a. (b) Constructed from the time series in Figure 3b. The iterates outline a map function with one extremum.
state. By continually decreasing the current and allowing the system to relax at each value, the behavior in Figure 2a was always eventually found and stabilized. In each set of experiments that was conducted on oscillations, qualitative similar behavior was always found on changing the current from a value at which the behavior shown in Figure 2a occurred. The predominate dynamical states were always obtained and their order of appearance, with respect to the direction in which the current was changed, remained the same. On the other hand, the absolute value of the current at which a given state was observed could vary substantially. The main contribution to this variation is a drift, which was previously de~cribed,'~ and that persists under the conditions used for the present study. Nevertheless, we report the current values for measured waveforms in order to give both the approximate location of different behaviors and the approximate relative distances between them. We now describe the different dynamical behaviors that were observed upon decreasing the current from a value at which the state shown in Figure 2a occurred. Period-Doubling Bifurcations. Slowly decreasing the current led to the appearance of a sequence of period-doubling bifurcations. In Figure 2, we show waveforms, plots of the measured potential vs time, for the primary oscillatory state, a period-two state, a period-four state, and a period-eight state; waveforms for both the period-two and period-four states are shown for two different values of the applied current. No other states belonging to the subharmonic sequence could be found. We also point out that the state corresponding to Figure 2f could not always be observed. Upon decreasing the current further, chaotic oscillations were found to follow the last observed subharmonic state. In Figure 3, waveforms are shown that correspond to a period-four state and a chaotic state. One-dimensional mappings, constructed from the waveforms in Figure 3, are shown in Figure 4. The iterates in Figure 4b outline a map function that is capable of producing the stretching and folding characteristics of chaotic behavior. Principal States. The bifuracation structure that was revealed through further decreases in the current can be described as a periodic-chaotic sequence: a sequence that consists of intervals of periodicity separated by intervals in which only chaotic behavior is located. A waveform of a periodic state, which appeared through a tangent bifurcation from a chaotic state, is shown in Figure Sa (the verification of a tangent bifurcation was done in the same way as described in refs 13 and 35). In turn, this periodic state
T i m e (s ) Figure 6. Principal states. Measured waveforms from dynamical states that belong to the set IM, where the number 1 represents the Occurrence of one large oscillation in a period and M represents the number of small oscillations: (a) a 1' state, Id = 18.3 pA/cm2; (b) the first subharmonic of the principal state in (a), Id = 17.9 pA/cm2; (c) a i'state, Id = 17.3 pA/cm2; (d) a i s state, Id = 17.0 pA/cm2; (e) a I6 state, Id = 16.8 pA/cm2. Potential range is 310-580 mV. The electrode was 7.0 mm diameter in platinum.
was found to undergo a period-doubling bifurcation. See Figure 5b. The system was then observed to return to a chaotic state at a value of the current slightly less than that used in Figure 5b. Similar sequences were found at lower values of the current; in each case a periodic state was found to bifurcate from a chaotic state. Upon decreasing the current, this bifurcation was followed by the observation of a limited number of subharmonics and the eventual return of the system to a chaotic state. The waveforms shown in Figure 6, with the exception of the state represented in Figure 6b, correspond to a set of periodic states where each state is the initial state of an interval of periodic behavior. It is easily seen that these states form an ordered set. In fact, the number of elements of the set can be extended to include those states represented by Figures 2a,c and 5a. Each member of the set can be labeled by the notation IM, where the number 1 represents the one large oscillation and M represents the number of small oscillations in each period. Each state in this set occupies, locally, the largest interval of periodicity. Therefore, we call these states principal states. The results presented so far on the periodic-chaotic sequence are qualitatively similar to those obtained at a lower acid concentration (2 mol/L) except that here we were able to obtain measurements on periodic states further into the sequence, Le., for larger values of M , the number of small oscillations (compare Figure 6 with Figure 5 of ref 13). Upon decreasing the current (35) Schell, M.; Albahadily, F. N. J . Chem. Phys. 1989, 90. 822.
The Journal of Physical Chemistry, Vol. 94, No. 18, 1990 7141
Electrocatalyzed Oxidation of Formaldehyde
400' 0
5
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125 Timeb)
J
35
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100
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m
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Figure 7. Measured waveforms from (a) a possible I7-state, Id = 16.5 pA/cm2, and (b) from a state where small oscillations have either disappeared or are too small to measure, Id = 16.3 pA/cmZ. Potential range
E
1
f" 380 0
and electrode size are the same as Figure 6.
4 50; 0
234
468
Time(s)
Figure 8. Measured waveform from an oscillatory state that occurs close to the end of the periodic-chaotic sequence in the direction of decreasing
current: Id = 10.0 pA/cm2. Potential range 290-600 mV;electrode was 5.00 mm in platinum.
from that value at which the l 6 state occurred, the amplitudes of some of the oscillations became so small that eventually it was impossible to identify a state or verify periodicity. Examples of these difficulties are revealed by the waveforms shown in Figure 7. Although the state in Figure 7a appears to be a l 7 state, the deviation in the peak height of every seventh small oscillation can be a substantial percentage of the average amplitude. This percentage could not be measured within the accuracy of the experiment. At values of the current slightly lower than that value at which the behavior shown in Figure 7a occurred, the system exhibited a response like that shown in Figure 7b where even the number of small oscillations cannot be determined. An example of a waveform recorded near the low-current boundary point for these types of oscillations is shown in Figure 8. The waveforms in Figures 6-8 cover a potential range within which OH is expected to be adsorbed on the electrode.22 Since the potential rises only to peak values that are well below those values where later stages of the formation of oxide layers occur and, in addition, the system clearly undergoes oscillations, which include sharp decreases in the potential, it is reasonable to believe reactions take place that involve the poison and either OH or some other closely related species that is present in the initial stage of oxide formation. The rate law proposed for the reaction involving OH and CO (reaction 9) r = (OH)(CO)Sk (10) where round brackets denote surface concentrations, S is the surface concentration of vacant sites, and k is a rate coefficient, is consistent with the measured behavior shown in Figure 8 that consists of a sudden drop in potential following a long sojourn at relatively high potential values. Observation of Quasiperiodic Oscillations. In principle, other dynamical behaviors should have been found in an interval of current values between the location of the type of oscillations shown in Figure 8 and where steady-state behavior first appeared on lowering the current. We were unable to obtain solid evidence on the type of dynamical behaviors that exist in this interval, or whether such an interval exists. If such an interval does exist, it is small. Nevertheless, indications of the type of bifurcation structures that might exist in this region are contained in some of our measurements. These measurements were recorded during experiments in which we slowly increased the current from a value at which the system exhibited steady-state behavior, but close to where sustained oscillations were found. Close to a value of the current where oscillations first appeared, the system was found to relax in an oscillatory fashion. Damped
.. 234 Time(s)
468
Figure 9. Damped oscillations and two-frequency behavior. Potential is plotted against time. (a) Id = 6.0 pA/cm2; (b) Id = 10.0 pA/cm2; (c) quasiperiodic oscillations, Id = 12.5 pA/cmZ.
oscillations are shown in Figure 9, a and b. Increasing the current by a small amount from a value at which a response like that in Figure 9b was observed led to the appearance of sustained oscillations. Initially, these oscillations were of small amplitude. However, at the same fixed value of the current, the oscillations proceeded to become larger, and eventually, the response appeared to develop two frequencies, i.e., quasiperiodic oscillations. An example of this "quasiperiodic response" is shown in Figure 9c. Although these oscillations persisted for a long period of time, they could not be stabilized. As can be seen in Figure 9, the average amplitude continued to increase. Furthermore, the system would eventually settle down into a state of mixed oscillations that was beyond that of Figure 8; i.e., a decrease in the current was required to obtain oscillations like those in Figure 8. Decreasing the current from a value at which oscillations like those in Figure 8 occurred always led to stationary behavior. The quasiperiodic behavior was not observed. No local bistability was detected; experiments were carried out in which perturbations were imposed when the autonomous system exhibited a response like that shown in Figure 9c and when the system was in a state like the one represented in Figure 8. The experimental observation of the behaviors shown in Figure 9 preceding the Occurrence of mixed oscillations might be explained by the occurrence of at least three bifurcations, two Hopf bifurcations (a double Hopf is also possible) followed by a bifurcation involving the breakup of a torus. (Quasiperiodic oscillations and the breakup of a torus have been characterized in a different of these bifurcations electrochemical p r o c e ~ s . ~ ~The , ~ ~occurrence ) within a small region of parameter space would produce a system which was difficult to stabilize in that region. Since, in the direction of increasing current, the quasiperiodic behavior was the last type of behavior observed before the occurrence of mixed oscillations, it is possible that a point at which a torus breaks up is an end point of the periodic-chaotic sequence; this was the case for a sequence of mixed oscillations in a different electrochemical process.38 However, the evidence in the case studied here is far from conclusive and other phenomena, such as long lasting complicated transients, may explain the results. Nonprincipal Stares. We also measured periodic states within the periodic-chaotic sequence that were neither principal states nor their subharmonics. Examples of such measurements are shown in Figure 10. By use of the number of consecutive small (36) Bassett, M . R.; Hudson, J. L. J . Phys. Chem. 1989, 93, 2731. (37) An interesting transition from a doubled torus to chaos is reported in: Basset, M . R.; Hudson, J. L. Physic0 D 1989, 35, 89. (38) Albahadily. F.N.; Ringland, J.; Schell, M.J . Chem. Phys. 1989, 90, 813.
7142 The Journal of Physical Chemistry, Vol. 94, No. 18. 1990
I
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I
120 Time(s)
240
Figure 10. Nonprincipal states. Measured waveforms from (a) a period-five state, (b) a period-seven state and a period-nine state.
Figure 11. A one-dimensional mapping constructed by plotting the ( N 1)th minimum against the Nth minimum of the time series shown in Figure loa.
+
and large oscillations, the corresponding states can be labeled 121 I, Figure loa; 1 3 1 2 , Figure lob; and 131211, Figure 1Oc. The waveforms appear as if they were constructed from concatenations of other waveforms; the I 2 l 1 state looks like a combination of the l 1 and l 2 states, the 1312 state appears like a combination of the 1 and 1 states, and the 1 3 l 21 I state resembles a combination of the l 3 and I 2 1 l states. Labeling states according to the number of consecutive small and large oscillations may not account for vital information and care should be taken with interpretations based on this method. The 1' 1 state, Figure 1Oa, provides a good example. This perid-five state was observed at a value of the current between those values at which the l 2 and l 3 states were found. The location is consistent with the U-sequence since the period-five state has the symbolic pattern RL2R and is listed (element 51 in ref 27) between that of the l 2 state (period three) and the l 3 state (element 94). The symbolic pattern for the period-five state is explicitly revealed by following the mappings in Figure 11: begin at the highest point and 'iterate" until the preimage of that point is reached while denoting whether you move to the left (L) or the right (R) after each iteration. The more detailed characterization of the temporal pattern in Figure 10a is important as it distinguishes this period-five state from the " 1 ' 1 2 state" observed in experiments conducted on the oxidation of formic acid.13 The latter state was located between the 1 and l 2 principals, and it has a different symbol sequence; it does not belong to the standard U-sequence, but rather, it is a Farey intermediate.26 Oscillations with Large Peak Potentials. We now describe the changes in oscillatory behavior that were observed by increasing the current after the l o state (Figure 2a) was stabilized. Slowly increasing the current in small increments from a value at which the state shown in Figure 2a occurred eventually led to the appearance of a response like that shown in Figure 12. The waveform consists of several oscillations that appear like those of the l o state. At a fixed value of the current the 10-like oscillations were interrupted by a small oscillation. This small oscillation possessed a lower turning point at a value of the potential significantly higher than that of the lower turning points
Xu and Schell
Figure 12. Measured waveforms of dynamical states that were found at values of the current that were larger than the value at which the l o state, Figure l a , was found to exist: (a) I d = 30.0 gA/cm2, (b) I d = 42.5
pA/cm2. of the 10-like oscillations (see Figure 12a), and it was the first of a number of sequential oscillations in which each consecutive amplitude decreased, whereas each consecutive mean value of the potential increased. The sequence of small oscillations was terminated by a large sudden drop in potential which was then followed by the return of oscillations similar to those of the l o state; the corresponding part of the waveform actually gives the impression the system was relaxing to the l o state. Although the waveform in Figure 12a at a coarse-grained level may appear periodic, periodicity was once again difficult to judge because of the small size of some of the oscillations. Upon increasing the applied current, the behavior represented in Figure 12a was found to deform in such a way that the small oscillations and the maximal peak potential became broader in time; Le., the peak potential appeared to almost remain constant over a rather large period of time and this period increased with respect to increases in the current. Eventually, the system displayed asymptotic behavior like that shown in Figure 12b. The time series contains lo-type oscillations that are interrupted by a sudden rise in potential. Following the sudden increase in potential, the potential changed very little for a substantial length of time after which it suddenly dropped to a low value. The system then returned to Io-type behavior and the "cycle" was repeated. The behavior shown in Figure 12b was observed in the immediate region of the transition point at which the system jumped to a high-potential, steady state. The value of the peak potential in Figure 12b is over 200 mV larger than the value of the peak potential of Figure 8. The value of the former potential is within the range where oxide film is considered to be present on the surface of the working electrode.32 These results strongly suggest that the oxidation of the fuel couples to more than one stage of oxide formation. A similar type of rate law as that written in eq 10 could describe the large oscillation in Figure 12b; however, the physical situation is more consistent with a different mechanism that was also proposed by Wojtowicz et aLz5 The authors hypothesized that, although reactions involving the fuel and intermediates could take place on top of an oxide film, the most catalytically facile reaction would occur at the edges of two-dimensional holes that nucleate during high oxide coverage. The increased catalytic activity at these sites is due to the presence of both vacant metal sites and oxide species. Such a reaction would again be autocatalytic; the reaction would increase the size of the holes, and hence, it would also increase the number of sites with high catalytic activity. Summary Nonlinear behavior was studied in an electrochemical process in which hydrated formaldehyde is oxidized at a rotating platinum disk under constant-current conditions. A bistable region, in which both high- and low-potential states were found to coexist, was characterized. Instead of low-potential stationary behavior, a variety of oscillatory behaviors was observed throughout most of the region of coexistence. The oscillatory phenomena included period-doubling bifurcations and a periodic-chaotic sequence consisting of mixed-mode
J . Phys. Chem. 1990, 94, 7143-7153
7143
periodic-chaotic sequence other types of oscillations occurred which possessed peak potentials that were within a range where later stages of oxide formation occur. These results provide strong evidence that the oxidation of formaldehyde couples to at least two different stages of the process in which oxide layers form. The coupling between the oxidation of formaldehyde and the process by which oxide layers form, which we postulated as the cause of the oscillatory response, removes a "poison" and prevents the catalyst, the platinum electrode, from becoming inactivated. In addition, the coupling also shifts the value of the applied current, at which oxide film formation can be completed, to larger values.
oscillations. Within the periodic-chaotic sequence, there was a predominance of periodic states, which we call principal states, that belong to a set in which the elements can be labeled as I M , where the integer 1 represents the one large oscillation and M represents the number of small oscillations that occur within one period. Other states were observed within the sequence that appeared very similar to states measured between adjacent principals in a recent study of the oxidation of formic acid.13 However, one-dimensional mappings were constructed from the time series of the nonprincipal states and the symbolic patterns obtained from these mappings revealed that they were different. The peak potentials of the oscillations within the periodic chaotic sequence were within a range that is consistent with the adsorption of OH on the electrode surface. On the high-current side of the
Acknowledgment. This research was supported by the Welch Foundation and the Texas Advanced Technology Program.
Chiral Dynamics in the Excited State of a Stereochemicaily Labile Metal Complex. Enantiomer Interconversion Kinetics, Enantloselective Quenching, and Chlroptical Activity of Eu(cda)," in H,O and D,O' David H. Metcalf,**tSeth W. Snyder,$J. N. Demas: and F. S. Richardson**t Chemistry Department and Biophysics Program, University of Virginia, Charlottesville, Virginia 22901 (Received: March 13, 1990)
Time-resolved chiroptical luminescence measurements are used to characterize the excited-state chiroptical activity and chelidamate) in H20and D20solutions at temperatures between 293 and 353 racemization kinetics of E ~ ( c d a ) ~(cda & K. Racemic E ~ ( c d a ) ~is&excited with circularly polarized light to create an enantiomeric excess of one optical (configurational) isomer in an excited electronic state, and then comparisons between time-resolved total luminescence and circularly polarized luminescence spectra are used to monitor the time dependence of the enantiomeric excess. Decay of the enantiomeric excess is related to interconversion of optical isomers (i.e., racemization) within the excited-state population of complexes, and rate constants are determined for the excited-state racemization of Eu(cda),& in both H20and D20over a 60 OC temperature range. Arrhenius parameters and thermodynamic activation parameters are derived from the temperature-dependent rate data, and the results obtained in H 2 0 and D 2 0 are compared and discussed. The racemization lifetimes (the reciprocal of the racemization rate constants) determined for 293 K solutions (16.9 and 79.5 ms in H 2 0 and DzO,respectively) are long compared to the emission lifetimes ( 1 .I6 and 2.26 ms, respectively). The racemization process is interpreted in terms of an intramolecular mechanism without any (complete or partial) ligand dissociation. The complex passes through an achiral transition state of either D3,,or Cb symmetry during interconversions between the two D3 enantiomers. Circularly polarized luminescence spectra are presented for the 'Fo ,,2 5D0transition regions of europium(II1) in Eu(cda),&, and circularly polarized excitation spectra are reported for the 5Fo,l 5D,transition regions. The latter are analogous to circular dichroism spectra one would obtain from resolved (nonracemic) samples of Eu(cda)t- in solution. In our experiments, they are the consequence of chiral photoselection in the excitation of a racemic mixture with circularly polarized light. Time-resolved & chiroptical luminescence measurements are also used to investigate enantioselective quenching of E ~ ( c d a ) ~excited-state populations by the chiral transition-metal complex i i - C ~ ( e n ) ~ ~It +is. shown that one excited-state enantiomer of E ~ ( c d a ) ~ & is quenched at twice the rate of the opposite enantiomer. The quenching is attributed to electronic-energy-transfer processes within E u ( ~ d a ) ~ ~ - - C o ( e ncollisional )~~+ complexes, and enantioselectivity in the quenching reflects chiral discriminatory contributions to intermolecular interactions between A - c ~ ( e n ) , ~and + the two enantiomers of Eu(cda)t-.
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Introduction Chiroptial luminescence spectroscopy has been used extensively to study the electronic-state structure and stereochemical propflies of lanthanide complexes in solution and in crystals,z Most chiroptical luminescence measurements reported in the literature have been based on steady-state excitation/emission-detection techniques, but time-resolved measurements have also been reported r e ~ e n t l y . ~ , Time-resolved ~ chiroptical luminescence measurements are particularly valuable for studying the dynamics of chirality-related processes, and they have been used to investigate the kinetics of excited-state racemization processes3 and enantioselective excited-state quenching processes4 in solution. Both steady-state and time-resolved chiroptical luminescence
* Author to whom correspondence should be addressed. 'Chemistry Department, University of Virginia. *Biophysics Program, University of Virginia. Present address: Argonne National Laboratory, Argonne, IL 60439. 0022-3654/90/2094-7 143$02.50/0
measurements have been reported for samples that contain a racemic mixture of enantiomeric specie^.^^^ These measurements were performed by using circularly polarized light to preferentially excite one enantiomer population of the racemic ground-state ( I ) cda denotes a triply deprotonated chelidamic acid ligand. Chelidamic acid 4-hydroxypyridine-2,6-dicarbxylicacid. (2)(a) Richardson, F.S. J . Less-Common Met. 1989,149, 161-177. (b) Riehl, J. P.; Richardson, F. S. Chem. Rev. 1986,86, 1-16. (c) Brittain, H. G. Coord. Chem. Rev. 1983,48,243-276. (d) Brittain, H. G. In Molecular Luminescence Spectroscopy: Methods and Applications; Schulman, S . G . , Ed.; Wiley: New York, 1985; Chapters 5 and 6, pp 547-582, 583-620. (3)Metcalf, D. H.; Snyder, S. W.; Demas, J. N.; Richardson, F. S. J . Am. Chem. Soc. 1990,112, 469-479. (4)(a) Metcalf, D. H.; Snyder, S. W.; Wu,S.; Hilmes, G. L.; Riehl, J. P.; Demas, J. N.; Richardson, F. S. J . Am. Chem. SOC.1989,111,3082-3083. (b) Metcalf, D. H.; Snyder, S.W.; Demas, J. N.; Richardson, F. S. J . Am. Chem. Soc. 1990, 112, 5681-5695. (5) (a) Hilmes, G. L.; Riehl, J. P. J . Phys. Chem. 1983,87,3300-3304. (b) Hilmes, G. L.; Timper, J. M.; Riehl, J. P. Inorg. Chem. 1985, 24, 1721-1722. (c) Hilmes, G.L.; Riehl, J. P. Inorg. Chem. 1986,25,2617-2622.
0 1990 American Chemical Society
