12768
J. Phys. Chem. 1994, 98, 12768-12775
An Electrochemical Mechanism for the Voltammetric Oxidation of Methanol and Its Relationship with Period-Doubling Bifurcations Mark Schell,* Yuanhang Xu, and Afshin Amini Department of Chemistry, Southem Methodist University, Dallas, Texas 75275 Received: August 9, 1994; In Final Form: September 26, 1994@
The changes in behavior that lead to a period-doubling bifurcation were investigated in the application of cyclic voltammetry to the oxidation of methanol at a rotating platinum disk electrode in alkaline solution. Two parameters were separately varied, the concentration of methanol and the upper potential limit of the potential cycle. Feedback mechanisms that explain the changes in behavior are formulated from experimental data and an electrochemical mechanism. Evidence is presented that indicates a period-two cyclic voltammogram occurs due to the dual role played by the surface species PtOH. During one cycle of the period-two response, most of the PtOH that forms on the surface reacts with an intermediate of methanol oxidation. During the other cycle a substantial amount of PtOH is transformed to Pt oxides. A Mobius strip that formed before the period-doubling bifurcation was detected by examining current-potential curves. Near the point in parameter space where the Mobius strip formed the relaxation was fastest.
Introduction This paper is a continuation of our investigation of instabilities in application of cyclic voltammetry to the oxidation of methanol at a rotating platinum disk in an alkaline solution. It was demonstrated that a sequence of stable cyclic voltammetric responses corresponding to a forward and reverse U-sequence is traversed on varying the upper potential limit (upl) of the potential cycle.' At both ends of the sequence a period-two response is connected to the more commonly observed periodone response through a period-doubling bifurcation. In this paper, the focus is on the period-doubling bifurcation. We describe the period-doubling bifurcation in terms of an electrochemical mechanism. Evidence is presented that indicates instability occurs in the period-one response due to the dual role played by a species we call PtOH (surface-bonded hydroxyl radicals); PtOH can either react with an intermediate of methanol oxidation, PtCO (surface-bonded carbon monoxide), or be transformed to Pt oxides, e.g., PtO. The oxides inhibit the oxidation of methanol. The period-one response loses it stability when the same temporal-spatial distribution of PtCO and PtOH cannot be maintained for consecutive potential cycles. During one cycle of the period-two response most of the PtOH reacts with PtCO, and during the other cycle, a substantial amount of the PtOH is transformed to PtO. The evidence is obtained by directly relating the response for solutions containing small concentrations of methanol to the response for the base solution (the solution without methanol), by examining the deformation of the current-potential ( I / E ) curves as the methanol concentration is increased, and by using experimental results that demonstrate certain characteristics of the I/E curves can be identified with oxide formation and reduction. For any subharmonic bifurcation, a range of values for a bifurcation parameter must exist before the bifurcation point in which the differential flow local to the attractor in state space can be viewed to take place on a two-dimensional circular band with an odd number of twists in it, a Mobius trip.^,^ In this paper, we also present the results of experiments that followed the variations in transient I/E curves that led to the formation of a Mobius strip. Evidence is presented in support of the @
Abstract published in Advance ACS Abstracts, November 1, 1994.
theoretical proposal4 that the period-one response least sensitive to perturbations exists for the perameter value at which the Mobius strip forms.
Experimental Section Equipment, chemicals, electrodes, and experimental procedures are described in ref 1. Unless stated otherwise, the following conditions were fixed: temperature = 25.0 f 0.2 "C, [NaOH] = 0.01 M, sweep rate = 100 mV/s, lower potential limit = -660 (AgCl reference electrode with an enclosed NazSO4 electrolyte). The lower potential limit is the location of the smaller cathodic hydrogen peak in the cyclic voltammogram for the base solution.
An Electrochemical Mechanism for the Oxidation of Methanol in Alkaline Solution To relate our results to electrochemical processes, we use a mechanism that is a direct analog of a mechanism recently employed to describe results on the voltammetric oxidation of methanol in acid solution^.^ More complicated mechanisms have been proposed.6 Reaction of strongly bonded carbon monoxide controls the dynamics in the mechanism presented here. Results from a combined voltammetric and spectroscopic study' support this view. The first step in the mechanism is the adsorption of methanol from the electrode boundary layer, CH,OH,,, 4-zPt
-
PtzCH,OHad,
where Pt represents a vacant surface site and z is the number of those sites required for adsorption. Adsorption is followed by the dehydrogenation of methanol to adsorbed carbon monoxide,
+ + 40H- - PtxCO + 4H,O + ( z + n - x)Pt + 4e-
PtzCH30Had, nPt
(2)
where x is the number of sites occupied by surface-bonded carbon monoxide and n represents the additional number of sites required for the reaction to proceed. More than one type of carbon monoxide complex can occur: x = 1 for linearly-bonded CO and x = 2 or 3 for bridge-bonded C0.8 The italics in eq 2,
0022-3654/94/2098-12768$04.50/0 0 1994 American Chemical Society
Voltammetric Oxidation of Methanol
J. Phys. Chem., Vol. 98, No. 48, 1994 12769 lateral interactions.1° The multistage process for formation of a monolayer of PtOH leads to more than one peak in the CV for the base solution; see the peaks labeled 01,011, and Om in Figure lb. A proposed step for the reaction between PtOH(i) and surfacebonded carbon monoxide is given by”
’a
PtxCO
+ 2PtOH + 2 0 H - - C 0 , 2 - + 2H,O
Besides reacting with surface-bonded carbon monoxide, the hydroxyl species can participate in those processes by which an “oxide film” is formed. We only consider the processes up to the formation of Pt0:12
Potential (mV) 0111
PtOH
W
Figure 1. (a) Measured cyclic voltammograms (CVs) for a 0.5 M methanol solution: rotation rate = lo00 rpm, upper potential limit (upl) = -100 mV. The large-amplitude cycle was recorded immediately after placing the working electrode in the methanol solution. The other cycle was recorded after 90 min. (b) The stable CV for the base solution: rotation rate = 0.0 rpm, up1 = 300 mV.
as in subsequent equations, denote atoms that are generally accepted to be bonded to surface platinum atoms. The dehydrogenation, eq 2, most likely involves several successive steps involving additional intermediates, and on a millisecond time scale, one of these steps is likely rate determining as is the case in an acid e l e ~ t r o l y t e . ~However, ,~ on the time scale of the experiments presented here the rate-determining step changes to the oxidation of surface-bonded carbon monoxide. This change in the rate-determining step is indicated by decreases in the initial oxidation currents observed under certain conditions; see Figure la. These decreases are due to the accumulation of surface-bonded carbon m ~ n o x i d e . ~ We make the assumption that the average number of sites required to produce a surface-bonded carbon monoxide molecule, (n z), is greater than the average number of sites it occupies, (x), i.e.,
+
(n + z>
’(x>
(3)
Mechanistic considerations imply that the number of sites required for the production of a surface-bonded CO molecule is 4.8 Surface-bonded carbon monoxide is oxidized by reacting with coadsorbed species that are the same as those species that are adsorbed during the initial part of the oxidation of the platinum surface during the forward sweep of the cyclic voltammogram (CV) recorded for tlie base solution;8 see Figure lb. We formally represent these coadsorbed species as PtOH and assume that they originate through the discharge of OH-: OH-
+ Pt
t
PtOH(i)
+ (x + 2)Pt ( 5 )
+ e-
(4)
The parenthetical i is used in eq 4 to denote that deposition of a complete monolayer of OH must occur in more than one step. Lateral interactions prevent a full monolayer of PtOH from forming through a one-step mechanism. After sites of a sublattice become completely occupied by OH, additional deposition of OH requires a larger potential to overcome the
+ OH- -- PtO- + H,O PtO- == PtO + e-
(64 (6b)
The reactions in eqs 4 and 6 are fast, reversible processes. Long time effects observed in surface oxidation are responsible for the formation of what has been called a quasi-two-dimensional oxide phase.lo These effects imply slower processes. Proposed slower processes include place exchange: lo
- OHPt Pto - OPt
ROH
(7a) (7b)
The species that result from slow processes are reduced at values of the potential different from those values associated with the reverse reactions in eqs 4 and 6. The broad cathodic peak in Figure l b corresponds to the reduction of the oxygen-containing species. The further advanced the oxide phase becomes the lower the potential at which that cathodic peak occurs.1o
The Period-Two Cyclic Voltammogram The two parts of the current-potential curve belonging to what was called a period-two CV are plotted separately in Figure 2a,b; the complete period-two response is shown in Figure 2c. The forward and reverse parts of the curve in Figure 2a are, on the scale of the plot, superimposed except at high potentials where there is a relatively small hysteresis. The curve in Figure 2b initiates a large decrease to small current values near the end of the forward sweep, and on the reverse sweep, the curve undergoes a sharp increase to relatively large current values. We propose the period-two response is due to the dual role played by oxygenated species that are coadsorbed with methanol which we called PtOH. PtOH can react with an intermediate formed during the oxidation of methanol, eq 5, can be converted to platinum oxides, eq 6, or can be reduced during the reverse sweep, eq 4. The form of the curve in Figure 2b is the result of a substantial amount of PtOH being transformed to Pt oxides, whereas the curve in Figure 2a corresponds to the formation of a relatively small amount of Pt oxides.
Results from Using [CHJOH] as a Control Parameter We next present evidence that supports the idea that some of the surface species involved in the surface oxidation of Pt in the base solution play a fundamental role in the oxidation of methanol and that some of these species inhibit the oxidation of methanol. Relationship between the Voltammetric Oxidation of Methanol at Low Concentrations and the CV for the Base Solution. Current-potential curves, obtained from experiments in which a methanol solution was repeatedly added to the
Schell et al.
12770 J. Phys. Chem., Vol. 98, No. 48, 1994
A & I 8
-660
-180
300
Potential (mV,
,
Figure 2. A period-two CV: (a) one cycle of the period-two CV; (b) the other cycle of the period-two CV; (c) the complete period-two CV. [CH3OH] = 16.74 x up1 = 300 mV; rotation rate = lo00 rpm.
0
Figure 3. Measured CVs for different methanol concentrations. (a) The response to the fust potential cycle of a stationary electrode. [CH3M OH] = 0.0 M for the curve labeled 1 (Cl); [CH,OH] = 1.0 x M for C3; [CHsOH] = 2.0 x M for C2; [CH30H] = 5.0 x M for C5; [CH30H] = 1.0 x M for C4; [CH30H] = 4.0 x for C6. (b) Same as (a) except the stable CVs are shown. (c) The response to the first potential cycle of the working electrode rotated at lo00 rpm. The concentrations of methanol are listed in the same order M; [CH30H] = as in (a): [CH30H] = 0.0 M; [CHjOH] = 5.0 x 2.0 x M; [CHsOH] = 4.0 x M; [CH30H] = 8.0 x M; M. (d) Same as (c) except transients have [CH30H] = 1.6 x disappeared.
electrochemical cell, are shown in Figure 3. After each addition of methanol the solution was mixed by lowering the nitrogen stream into the solution. The potential was held at -660 mV for 5 min and then cycled between this value and 300 mV. The first cycle for several different methanol concentrations is shown in parts a and c of Figure 3 for respectively the stationary working electrode and the electrode rotated at lo00 rpm. These voltammograms are consistent with published result^.^ Each addition of methanol leads to a larger current
‘-660
I
-30
600k60 -i30
406
Potential (mv) Figure 4. CVs for methanol solutions superimposed on CVs for the base solution. Rotation rate = 0.0; sweep rate = 100 mVls. [CH3OH] = 6.0 x M for (a) to (d). (a) up1 = 0.0 mV. (b) up1 = 200 mV. (c) up1 = 400 mV. (d) up1 = 600 mV. [CHsOH] = 9.0 x for (e) and (f). (e) up1 = 200 mV. (0 up1 = 400 mV. [CH30H] = 3.0 x for (8) and (h). (g) up1 = 200 mV. (h) up1 = 400 mV.
peak above the location of the first PtOH peak of the voltammogram for the base solution. This is the same location where a peak occurs in IIE curves recorded during the voltammetric oxidation of carbon monoxide.’l In a spectroscopic study, Caram and Gutierrez’ provided additional evidence that surfacebonded carbon monoxide forms during the oxidation of methanol at Pt in an alkaline solution. Thus, there is strong evidence that the location of the peak is determined by the reaction between PtOH and the intermediate, PtCO, eq 5 . The current peaks decreased substantially during subsequent cycles. Stable CVs are shown in Figure 3b,d. A second peak can be seen in the stable CVs, located above the second PtOH peak in the CV for the base solution, indicating that these oxygenated species also react with CO. The CVs in Figure 3b,d also indicate the oxidation of methanol is inhibited by surface species that form during the oxidation of the platinum surface. At high potentials, the forward sweep of all CVs essentially becomes superimposed with the high-potential part of the CV for the base solution. We conclude that oxygen-containing surface species that form at the higher potentials during the oxidation of the Pt surface (PtO and other Pt oxides) inhibit the oxidation of methanol. Relationships Revealed by Adjusting the Upper Potential Limit and [CHJOH]. Further relationships between the oxidation of methanol and Pt oxides are revealed by CVs in Figure 4. These results were obtained by first recording voltammograms for the base solution, adding methanol to the solution, and then recording the stable voltammograms. We first consider the CVs in Figure 4a-d which were recorded at successively larger values of the upper potential limit (upl). The methanol concentration was fixed at 6.0 x M. An important observation is the trend followed by the potential values at which the current for the methanol solution
J. Phys. Chem., Vol. 98, No. 48, 1994 12771
Voltammetric Oxidation of Methanol I
-660
-360 0.60
-180
300
Potential (mv) 1.35
2.10
log(S) Figure 5. Plot of the cathodic peak from the CV for the base solution vs the logarithm of the sweep rate (5‘)(circles) and plots of the potential at which the current begins to rise during the reverse sweep vs the logarithm of S for different [CH30HJ. S is scaled by 1 mVls. Rotation rate = 0.0 rpm. up1 = 400 mV. [CHsOH]: triangles = 3.0 x low3 M, crosses = 12.0 x M. Each number M, rectangles = 9.0 x on the curves corresponds to the value of the slope (mV).
begins to rise during the reverse sweep with respect to increases in the value of the upl. Notice that the broad cathodic peak (the negative current peak) in the voltammograms for the base solution shifts to lower values of the potential with respect to increases in the upl. The latter result is well-known.’O Increasing the up1 allows the oxidation of Pt surface to continue to later stages. Consequently, more of the irreversible quasi-twodimensional phase forms, and a lower potential is required for its reduction. The point at which the current begins to increase during the reverse sweep in the methanol CVs follows the same trend as the cathodic peak in the CVs from the base solution. This result is evidence that the rise in current during the reverse sweep corresponds to the point where a sufficient amount of inhibiting oxides is removed to allow the resumption of the oxidation of methanol. The more advanced oxide formation becomes the lower the value of the potential at which the increase in current occurs during the reverse sweep. M (Figure Experiments using different [CH30H], 9.0 x 4e,f) and 3.0 x M (Figure 4g,h) yielded similar results. These figures also illustrate how the variation of [CHsOH] affects the coupling between the oxidation of methanol and oxidation of the Pt surface. Figure 4e has the same up1 as that of Figure 4g, and, Figure 4f has the same up1 as that of Figure 4h. A comparison of the CVs reveals that, for a fixed up1 and a fixed hydroxide ion concentration, the potential value for the rise in the current during the reverse sweep increases with respect to ingeases in [CH30H]. We conclude that oxide formation becomes less advanced with larger methanol concentrations. For larger [CH30H], surface-bonded carbon monoxide is produced at a larger rate. Consequently, a larger fraction of PtOH reacts with PtCO, eq 5, and less PtOH is converted to Pt oxides, e.g., eq 6. When instabilities are approached by increasing [CH3OH], the rule “increasing the up1 increases the amount of oxides that form” breaks down. The breakdown is directly related to the occurrence of instability and will be discussed later. Evidence for the Reduction of Oxides and Resumption of Methanol Oxidation from Tafel Plots. Evidence that the rise in current during the reverse sweep is directly related to the reduction of oxides is provided by the Tafel-type plots shown in Figure 5 . The value of the potential at which the current begins to increase during the reverse sweep is plotted against the log of the sweep rate. To ensure the initial oxide coverage was always the same, the same CV was first stabilized before
Figure 6. Continuation of the results shown in Figure 3d. (a) [CH3OH] = 4.34 x lo-’ M. (b) [CH30H] = 9.30 x lo-’ M. (c) [CH3OH] = 11.78 x lo-’ M. (d) [CH30H] = 16.74 x lo-’ M. (e) [CH30H] = 13.02 x lo-’ M. (f) Conditions the same as in (e),
transient cycles are shown. each measurement; sweep rate = 100 mV/s. Following the stabilization, the sweep rate was changed at the beginning of the reverse sweep. Also shown in Figure 5 is the potential of the cathodic peak from the CV for the base solution plotted against the log of the sweep rate (circles). It has been established that the latter plot should be linear.l0 Figure 5 reveals that the plots of the potential for the rise in current vs sweep rate are also linear. Furthermore, it has also been established for plots of the cathodic peak that the further the process of oxide film formation advances, the larger the slope.1° The results in Figure 5 reveal that the slope decreases with respect to increases in methanol concentration, a result that is consistent with the idea that oxide formation reaches a less advanced stage with increases in methanol concentration. Continuity Argument and Description of One Cycle of the Period-Two CV. The CV in Figure 6a was obtained from a continuation of the experiments that yielded the results in Figure 3d. Continually adding methanol caused the peak current in Figure 3 to increase and shift to larger potential values. Similarly, the sharp rise in the current during the reverse sweep of the CV in Figure 6a is the natural extrapolation of the rise in current that was observed using smaller methanol concentrations; the potential value at which the sharp rise occurs increases. Further additions of methanol led to the CV shown in Figure 6b. The experiments indicate that all observed characteristics associated with the rise and decrease in current during the forward sweep, and the sharp increase in current during the reverse sweep, smoothly deform with respect to increases in [CH30H]. Therefore, we propose that their physical causes remain the same: the increase in current is due to the oxidation of methanol, the decrease in current is due to the formation of inhibiting oxides, and the sharp rise in current that occurs during the reverse sweep corresponds to the reduction of inhibiting oxides and the resultant increase in the oxidation of methanol. The CV in Figure 6b has essentially the same form as the part of the current-potential curve that is exhibited on every second cycle of the period-two CV (Figure 2b). Therefore, we conclude that the physical causes for the characteristics of this part of the period-two CV are the same as those stated for the causes of the form of the period-one CV in Figure 6b. Observed Increase in Methanol Oxidation during the Reverse Sweep. A comparison of parts a and b of Figure 6 shows that continued additions of methanol eventually lead to a CV in which a large current is maintained during the first part of the reverse sweep. Oxide formation occurs, but slow enough that the current does not descend to a small value until a time during the reverse sweep. Increasing [CH30H] now shortens the region of low current during the reverse sweep at both ends. The sharp rise in current, as at lower concentrations,
Schell et al.
12772 J. Phys. Chem., Vol. 98, No. 48, 1994 shifts to larger potential values, and increasing the [CH30H] now increases the delay of the decent to low-current values during the first part of the reverse sweep. Figure 6c illustrates the continuation of this trend to a larger concentration of methanol. Proposed Ideal Limit and the Period-Doubling Bifurcation. So far we have provided evidence for the trend that as the [CH30H] increases more PtOH reacts with PtCO and less PtOH is transformed to Pt oxides. One may expect that further continuation of these trends would eventually lead to behavior in which the current would not decrease due to oxide formation. All the PtOH that forms would take place in the oxidation of methanol, and consequently, no oxide would form on the electrode. Although CO is deposited, it would be removed rapidly by reacting with PtOH, and since the oxidation of methanol is irreversible, the CV in this ideal limit would take on a form associated with an irreversible faradaic process without deposition of adspecies; see Figure 6a, ref loa. The current-potential curve obtained on the reverse sweep of such a CV would approximately follow the path traced on the forward sweep, but, of course, in the reverse direction. The CV would exhibit very little hysteresis; Le., only a small difference would exist between the current values of the forward sweep and those of the reverse sweep. Theoretically, there should always be a small contribution to the separation between the currents of the forward and reverse sweeps equal to twice the contribution to the current from charging the double layer.1° What actually does happen on further increasing [CH30H] is a period-doubling bifurcation. In Figure 6d is a CV obtained using a methanol concentration that is approximately 1.4 times the concentration used for obtaining the CV in Figure 6c. It is the same period-two CV shown in Figure 2. It is consistent with several aspects of our imagined ideal limit. Although it occurs on only every other potential cycle, most of the currentpotential curve on the reverse sweep follows the reverse of the curve obtained during the forward sweep; see Figure 2a. Relatively little hysteresis is observed during the cycle in Figure 2a. Along with the fact that this cycle was obtained as a result of increasing [CH30H], other evidence supports the contention that the response is associated with a dramatic decrease in oxide formation relative to the other cycle of the period-two CV as well as relative to the responses obtained at lower methanol concentrations. First, the part of the cycle with little hysteresis is of the same form of the CV obtained using a lower valued upl; see Figure la. If the up1 is not too large, then no oxides can form and PtOH reacts with CO. Second, the CV does not change abruptly from the form shown in Figure 6c to that in Figure 6d. A measured stable CV with a concentration close to the critical concentration of a period-two bifurcation is shown in Figure 6e. In this period-two CV both cycles exhibit the characteristics of oxide formation and reduction. As [CH30H] is increased, the inner cycle becomes smaller and changes to the form in Figure 6d. These results remain consistent with the trend established at lower concentrations; the amount of oxide that forms decreases as [CH30H] is increased, but this decrease is detected by averaging over two potential cycles. There remains the question of why the ideal limit cannot be reached, and instead, a period-two response is obtained; i.e., why do the period-one CVs not deform smoothly to the form shown in Figure 2a, the response on every second cycle of the period-two response? Two aspects of the kinetics are used for an explanation. First, strongly bound CO inhibits its own production by occupying sites. If the inequality in eq 3 holds, the inhibition will cause the rate of production of PtCO to approach zero before a monolayer forms. Consequently, the
I
-660
-330
b
-6k0
-230
4
200
Potential (mv) Figure 7. CVs illustrating the difference in response with respect to holding time at low potentials. The CVs in (a) and (c) were recorded immediately after the transfer of the working electrode to the methanol solution. The CVs in (b) and (d) were recorded after holding the electrode at -660 mV (the location of the smaller cathodic hydrogen peak in the CV for the base solution) for 5 min; rotation rate = 1000 M; up1 = 0.0 mV. (c) and rpm; (a) and (b) [CHsOH] = 3.0 x M; up1 = 200 mV. (d) [CH30H] = 6.0 x
rate of formation of other species, such as PtOH, which require only one site, can be substantial when the rate of production of CO approaches zero. Second, strongly bound CO forms at potential values less than those at which substantial amounts of PtOH form. During the last part of a cycle with little hysteresis, like the one shown in Figure 2a, PtCO will form without reacting with PtOH. During the first part of the next cycle PtCO will inhibit its own production. When a potential is reached where PtOH can form, the rate of production of PtOH will be greater than the rate of production of PtCO. Some PtOH will react with PtCO, but some will not. Since PtCO requires a large number of sites for its formation and PtOH requires only one site, small islands of PtOH will form in which some hydroxyl radicals will have only other hydroxyl radicals as neighbors. Consequently, a substantial amount of PtOH can only be converted to PtO, and the cycle exhibits the characteristics of oxide formation and reduction (Figure 2b). During the reverse sweep of the oxide cycle, a large peak current occurs at the point where oxides are reduced; see Figure 2b. The value of the current at this point is substantially larger than the values for the forward sweep of both cycles and the value for the reverse sweep of the cycle with little hysteresis; see Figure 2c. To attain such a large current, some of the oxides must be reduced to a reactive form, e.g., PtOH, and/or additional OH is deposited on the cleaned surface and reacts with PtCO. The larger current implies more CO is removed on this part of the reverse sweep of the oxide cycle than the amount removed on the equivalent part of the cycle with little hysteresis. Consequently, the response following the oxide cycle will again be a cycle with little hysteresis because the initial surface coverage is less. Less coverage increases the probability of PtOH forming at a site with either PtCO as a neighbor or with enough neighboring vacant sites to accommodate the formation of PtCO. Evidence that supports the ideas used in the explanation for the occurrence of the period-two response is contained in Figure 7. Figure 7a shows the response to a potential cycle that was measured immediately after the working electrode was transferred from the base solution to the methanol solution. Only a
J. Phys. Chem., Vol. 98, No. 48, 1994 12773
Voltammetric Oxidation of Methanol
'"@.#-
-1001
-200- e.,
I
I
, ,-
. b
0
D
,
.
I
' j
-3000
D+
-5 , -1000 -2000 a"
0
o+
-0
limited amount of carbon monoxide will have formed at the beginning of the cycle, and consistent with the above explanation, the response does not exhibit the characteristics of oxide formation and reduction. In Figure 7b is shown a response recorded under the same conditions except the electrode was held at the potential -660 mV for 5 min. Surface-bonded CO can form at this potential but not PtOH. Therefore, a large surface coverage by CO existed at the beginning of the cycle, and consistent with the above explanation, the response exhibits the characteristics of oxide formation and reduction. Figures 7c,d depicts results from experiments that followed the same procedure except a different up1 and methanol concentration were used. Note that the forms of the CVs in Figure 7a,c are similar to the cycle with little hysteresis in the period-two response (Figure 2a) and that the CV in Figure 7d is similar to the form of the other cycle in the period-two response (Figure 2b). Additional evidence that the transition to a period-two CV is in response to a decrease in oxide formation is contained in Figure 8, where the potential of the current peak obtained on the reverse sweep is plotted against [CH30H]. We have argued that the greater this potential, the less advanced oxide formation. Figure 8 reveals the potential increases with respect to increases in [CH30H] until the system cannot maintain decreases in oxide formation with a period-one response and undergoes a perioddoubling bifurcation.
Changes in the Dynamics on Approaching Bifurcation Unfortunately, it is difficult to examine dynamical changes when using [CH30H] as a control parameter. In this section we consider the approach to the period-doubling bifurcation using the up1 as a control parameter. Since the bifurcation is approached from a different direction in parameter space, the physical causes for the bifurcation are different. However, certain dynamical changes always occur in the underlying phase space preceding any ordinary subharmonic bifurcation. We first discuss the breakdown of the rule "the larger the upl, the more oxides are formed". The rule holds for [CH3OH] less than 1.5 x M. The range of up1 values where the rule fails at larger methanol concentrations can be determined from Figure 9. In Figure 9 the peak current for the forward sweep of the CV and the value of the potential for the current peak that occurs during the reverse sweep are plotted as functions of the upl. We have presented evidence that the current peak of the reverse sweep should shift to lower potentials the more advanced oxide formation becomes. Intuitively, one would expect' that increasing the up1 would increase oxide formation. However, for the up1 range of 50-200 mV, increases in the up1 increases the value of the potential where oxides are
12774 J. Phys. Chem., Vol. 98, No. 48, 1994
Schell et al.
/-
I -
I
I
1
-100
-660
-660
I
-660
-380
-350
I
I
-315
I
-40 -660
-285
30
I
-660
I
90
I
-660
-305
io
-292.5
YS -660
I
-660
I
I
-277
-270
106
I
120
Potential (mv) Figure 11. Transient cycles following large changes in the upl, 2 2 0 mV. I denotes the initial cycle, and F denotes the final cycle. The solid arrow on the right side of the cycles denotes the point where the final cycle begins to cross all previous cycles in the ZIE plane. [CH3OH] = 0.35 M. (a) up1 = 50 mV. (b) up1 = 75 mV. (c) up1 = 106 mV. (d) up1 = 120 mV. The numbers denote the order in which the cycles occurred. I
-660
-330
b
I
-660
-275
iio
Potential (mv) Figure 10. Changes in CVs caused by increasing the upl. The stable CV for the larger up1 in each diagram is solid and is labeled by the number 3. The stable CV for the smaller up1 is dashed and labeled 1. The fist cycle after increasing the up1 from the smaller to the larger value is a dotted curve labeled 2. [CH30H] = 0.35 M. (a) up1 was changed from -150 to -100 mV, (b) from -50 to -40 mV, (c) from -10 to 0.0 mV, (d) from 20 to 30 mV, (e) from 80 to 90 mV, and (Q from 105 to 110 mV.
value for the rise in current on the reverse sweep compared to the previous CV (labeled 1) and the first cycle (labeled 2); see Figure 10c,d. This is also the reason why an interval of up1 values exist in which the peak corresponding to the reduction of oxides shifts to larger potential values in Figure 9. The effects of the feedback mechanism can also be seen by examining the transients cycles recorded after an increase in the upl; see Figure 1la-c. In Figure 1l a the symbol Z refers to the initial cycle recorded, and the symbol F refers to the final cycle recorded. The solid arrow to the right of the cycles indicates the location of an apparent fold on the local twodimensional manifold that supports the transients. Note that the initial cycle is on the inside of the other cycles before the fold and on the outside after the fold. The final cycle is on the outside before the fold and on the inside after the fold. As a result of the cycles crossing in the ZIE plane, the cycle with the largest peak current is also the cycle in which, during the reverse sweep, the sharp rise in current occurs at the largest potential; i.e., less oxides are formed. As the reduction peak moves to higher potentials, the current during the remainder of the reverse sweep also becomes larger. Increasing the up1 moves the fold to a higher current; compare parts b and c of Figure 11. Further increases in the up1 moves the apparent fold upward toward the top right comer of the CV. As the fold moves to a higher current, the reverse sweep begins at a higher value of the current, which implies less oxides form. By tuning the upl, one might expect the fold to move to a current sufficiently large that a cycle will occur in which there is no oxide formation. Such a cycle is like the previously discussed ideal limit. The attainment of a cycle with little oxide formation will lead to excess CO on the electrode at low potentials, which in tum will lead to islands of surface oxides. Thus, a period-one CV without
oxide formation does not occur. Instead, a period-two response is obtained which, as before, possesses one cycle in which little or no oxides are formed and a cycle in which the characteristics of oxide formation and removal are clearly evident. The periodtwo response obtained by increasing the up1 is of the same form as those in Figure 6. Before the period-doubling bifurcation occurs, a noticeable change is revealed by the transients in Figure 1Id. In the ZIE plane each transient cycle is on the opposite side of the stable period-one CV with respect to the previous cycle. This alternating approach to the period-one CV is different from that in Figure 1la-c where the stable CV is approached from one side, i.e., a monotone approach. By examining phase portraits of the relaxation, constructed using the time-delay method,13it was deduced that the local two-dimensional manifold that supports the alternating transient cycles possesses a twist in it. This twist allows the cycles to alternate from one side to the other. The results are consistent with the idea that the twodimensional manifold is a Mobius strip.3 In experiments in which the up1 was changed by increments in 10 mV or less, the point at which the approach to the stable CV changed corresponded to the point at which most of the stable CV became superimposed on the CV that was stable at the previous upl. In Figure 10e, there is a slight but measurable difference between the two CVs, labeled 1 and 3. Figure 10f depicts the situation at a larger upl. Except for the upper right comer, the stable CV with the up1 value of 110 mV lies on top of the stable CV with the up1 of 105 mV. From this point on an altemating approach to the stable CV was observed. This result implies that, close to the point where the approach to the CV changes from monotone to altemating, the system is resistant to the effects of small parametric variations. We now tum to a question of dynamical stability. In simple one-dimensional map models with one extremum, the point at which the relaxation changes from monotone to altemating is also the point at which the relaxation to the asymptotic orbit is fastest. The asymptotic orbit is called s ~ p e r s t a b l e .Super~~ stability was defined for some differential flows4 and also corresponds to the point at which the local relaxation changes from monotone to altemating. To examine whether a correspondence exists between superstability and the point at which the Mobius strip forms, the limiting slope was calculated from
Voltammetric Oxidation of Methanol 40
J. Phys. Chem., Vol. 98, No. 48, 1994 12775
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UPL (mv) Figure 12. Plot of the slope = ~ln[AZp(t)/AZJ/At~ vs upl. AZp(t) = where Zp(r) represents peak current values measured during the forward part of the potential cycle; for altemating approaches to the period-one CV, every other peak was used; when the approach was to a period-two CV, the peaks from the cycle with oxide formation and reduction were used. Zp(-) represents the limiting value; AZ,= Z, = Zp(-); Z,represents the initial peak current. The arrow labeled “1” points to the fust data point obtained after the system began an altemating approach to the CV. The arrow labeled “2” points to the first data point obtained after the period-doubling bifurcation.
Zp(t) - Zp(-),
plots of ln(AZp(t)/AIJ vs time; AI,(?) is the difference between the peak current value measured at time t during the forward part of the potential cycle and the limiting peak current value, and AI, is the initial peak current minus the limiting value. The absolute value of the slope, or the inverse of the relaxation time, plotted against the up1 is shown in Figure 12. The largest value of the slope was obtained at a up1 value close to where the Mobius strip formed. Small values were obtained at low values of the up1 and where period-two was first observed. The results indicate the system is least sensitive to perturbations in the vicinity of where the relaxation changes from monotone to alternating.
Summary It was demonstrated that increasing the methanol concentration eventually induces a transition to a period-two state in the voltammetric oxidation of methanol at a rotating Pt disk in alkaline solution. This result, combined with the results of the
previous paper,‘ provides strong evidence that instability is a characteristic of the voltammetric oxidation of methanol. The experiments revealed that as [CH30H] was increased, more PtOH reacted with PtCO and less PtOH was transferred to pt oxides. However, instead of attaining a limit where on every potential cycle no oxides form, a bifurcation to a period-two CV occurred. One cycle of the period-two CV does not possess characteristics of oxide formtion, and the other cycle does. The transition to a period-two response was also examined using the upper potential limit as a control parameter. Prior to reaching the bifurcation point, the change from a monotone to an alternating approach to the stable period-one CV was detected. The results of measurements on the rate of decay to period-one CVs are consistent with the idea that the most stable period-one state exists at the value of the control parameter where the relaxation changes from a monotone to an alternating approach.
Acknowledgment. This research was sponsored by the Robert A. Welch Foundation, Grant N-1096. References and Notes (1) Xu, Y.; Amini, A.; Schell, M. J . Phys. Chem., preceding paper in this issue. (2) Kapral, R.; Schell, M.; Fraser, S. J . Phys. Chem. 1982, 86, 2205. (3) Mallet-Paret, J.; Yorke, J. A. Ann. N.Y. Acad. Sci. 1980, 357, 300. (4) Celarier, E. A.; Kapral, R. J . Chem. Phys. 1987, 86, 3357. (5) Gasteiger, H. A,; Markovic, N.; Ross, P. N.; Cairns, E. J. J . Phys. Chem. 1993, 97, 9771. (6) Buck, R. P.; Griffith, L. R. J . Electrochem. Soc. 1962,109, 1005. (7) Caram, J. A.; Gutierrez, C. J. Electroanal. Chem. 1992, 323, 213. (8) Parsons, R.; VanderNoot, T. J. Electroanal. Chem. 1988, 257, 9. (9) Franaszczuk, K.; Herrero, E.; Zelenay, P.; Wiekowski, A.; Wang, J.; Masel, R. I. J. Phys. Chem. 1987, 87, 1936. (10) Angerstein-Kozlowska, H.; Conway, B. E.; Sharp, W. B. A. J. Electroanal. Chem. 1973,43,9. Tilak, B. V.; Conway, B. E.; AngersteinKozlowska, H. J . Electroanal. Chem. 1973, 48, 1. Conway, B. E.; H. Bamett, B.; Angerstein-Kozlowska,H.; Tilak, B. V. J . Chem. Phys. 1990, 93, 8361. (11) Santos, E.; Giordano, M. C. J. Electroanal. Chem. 1984,172,201. (12) Damjanovic, A.; Genshaw, M. A.; Bockris, J. O’M. J . Electrochem. Soc. 1967, 114, 466. (13) Packard, N. H.; Crutchfield, J. P.; Farmer, J. D.; Shaw, R. S. Phys. Rev. Lett. 1980, 45, 712. (14) Manneville, P. Dissipative Structures and Weak Turbulence; Academic Press: New York, 1990; D 208.
