18962
J. Phys. Chem. 1996, 100, 18962-18969
Mechanism for the Electrocatalyzed Oxidation of Glycerol Deduced from an Analysis of Chemical Instabilities Mark Schell,* Yuanhang Xu, and Zoran Zdraveski Department of Chemistry, Southern Methodist UniVersity, Dallas, Texas 75275 ReceiVed: April 24, 1996; In Final Form: June 11, 1996X
The electrocatalyzed oxidation of glycerol in alkaline solution is compared with the oxidations of ethylene glycol and methanol. An analysis of behaviors caused by instabilities provides strong evidence that the elementary reactions that dominate the oxidation of glycerol are the same as those that dominate the oxidation of methanol. These reactions include the formation of surface bonded CO and its reaction with surface bonded hydroxyl radicals. The reactions that precede the dominant reactions in the oxidation of glycerol are relatively fast and must involve cleavage of C-C bonds. Evidence from phase diagrams indicates that the most probable sequence for the fast reactions requires a sufficient number of neighboring vacant sites to produce three surface-bonded CO complexes for each glycerol molecule. Reaction sequences that lead to zero, one, or two CO complexes occur with small probability.
1. Introduction In this paper, we claim to deduce the elementary reactions that dominate the electrocatalyzed oxidation of glycerol at Pt in alkaline solution.1,2 Dominant reactions are defined as those that control the obserVed dynamics and include the slow reaction steps. Information on the fast reactions that precede the dominant reactions is also deduced. The deductions are made by analyzing behaviors caused by chemical instabilities.3 We use the following approach: Consider a complex reaction process that exhibits instabilities and for which you seek information on its kinetic mechanism. One method is to find a more fundamental but related process for which information on its mechanism is assumed known. If both processes exhibit the same behaviors, then this is strong evidence that the elementary reactions that dominate the complex process are the same as those that dominate the fundamental process. The behaviors cannot be limited to uniVersal behavior,4 behavior exhibited by a broad class of chemical and nonchemical processes, but, rather, they must include nonuniversal behaviors. Specific conclusions about the complex process require that the nonuniversal behaviors include behavior directly related to the mechanism for the fundamental process. We apply cyclic voltammetry5 and theories of electrochemical instabilities6 to the electrocatalyzed oxidation of glycerol. The cyclic voltammetric responses are compared with those of more fundamental reactions, the oxidations of ethylene glycol and methanol. First, it is shown that all three reaction processes display a sequence of periodic states that are ordered in the same way as members of a forward and reverse U-sequence.7,8 The U-sequence is universal.8 Here, and in most cases,9 it is a necessary condition (not sufficient) that a complex process and a more fundamental process exhibit the same universal behavior to conclude that both processes have the same dominant reactions. Next, it is demonstrated that the three processes share nonuniversal behaviors. One such behavior is a characteristic of transients that occur close to period-doubling bifurcations. We show that these transients can be used to define a specific point on a limit cycle; the exact location of the point is determined by the underlying deterministic laws. The point has X
Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)01195-1 CCC: $12.00
the same location for all three oxidation processes. A second nonuniversal behavior is the form of the current-potential curve for different periodic states. The forms of these curves are sufficiently complex that they can be used as analogues to spectral signatures. All three processes match these signatures. We also examine nonuniversal changes that occur on approaching the primary instability. All three processes exhibit the same changes. For methanol oxidation, these changes were directly related to its mechanism through several experimental results.10 The results provide strong evidence that the dominant reactions in the oxidation of glycerol are the same as those in the oxidation of methanol. These reactions begin with the formation of surface bonded CO (PtCO) and include the reaction of PtCO with surface bonded hydroxyl radicals. For glycerol, reactions preceding the formation of PtCO clearly involve cleavage of at least one C-C bond and are relatively fast. The stated universal and nonuniversal behaviors do not reveal other information on the fast reactions. By comparing curves located in parameter space where instabilities occur, evidence is obtained in support of the conjecture that the most probable sequence for these fast reactions is one in which three PtCO complexes are produced for each glycerol molecule. 2. Experiment Glycerol and ethylene glycol (spectrophotometric grade) were acquired from Aldrich, Milwaukee, WI. Methanol (OmniSolv Purge and Trap grade) was obtained from EM Science, Gibbstown, NJ. A standard three-electrode electrochemical cell was used.7 The working electrode, the electrode where reactions under study occur, was a polycrystalline Pt rotating disk. The electrode had a geometric area of 0.45 cm2 and a ratio for the actual “area” to the geometric area of 1.1. The counter electrode was a Pt wire. An AgCl electrode (Fisher Scientific, modified for use in Cl- titrations) was used as the reference electrode. Potentials are stated using the reversible hydrogen-electrode scale (rhe). The reference electrode was placed either in a separate compartment or, for a large electrochemical cell (500 mL), 3.5 cm from the working electrode. The location essentially eliminates anions that may leak from the reference electrode from interfering with the reactions at the working electrode. The © 1996 American Chemical Society
Mechanism Deduced from Instabilities
J. Phys. Chem., Vol. 100, No. 49, 1996 18963
Figure 1. Response of a 0.25 M glycerol solution to a cycling potential. Current density is plotted against time. (a) Period-one (P1) state, upl ) 1030 mV (rhe); (b) P2 state, symbol sequence (ss) ) R, upl ) 1180 mV; (c) P4 state, ss ) RLR, upl ) 1260 mV; (d) P3 state, ss ) RL, upl ) 1270 mV; (e) P6 state, ss ) RLLRL, upl ) 1350 mV; (f) P7 state, ss ) RLLRRL, upl ) 1390 mV; (g) P10 state, ss ) RLLRRLLRL, upl ) 1440 mV; (h) P3 state, ss ) RL, upl ) 1520 mV, (i) P4 state, ss ) RLR, upl ) 1590 mV; (j) P2 state, ss ) R, upl ) 1640 mV. The Rs and Ls are assigned to peaks to their immediate right as described in the text.
location causes a large uncompensated resistance (Ru). For results using the stated reference electrode, Ru ) 250 Ω. Experiments were conducted to examine the effects of Ru. A Luggins-Haber capillary with a thin U-shaped end was used for placing the reference electrode close to the working electrode; Ru was obtained as described in ref 11. Unless stated otherwise, the following conditions hold: temperature ) 25.0 ( 0.2 °C, [NaOH] ) 0.01 F, rate of cycling the potential (S) ) 100 mV/s, rotation rate ) 1000 rpm, lower potential limit (lpl) ) 270 mV (rhe). All other details on procedures and equipment are in refs 7 and 11. 3. Universal Sequence In cyclic voltammetry, the current is measured while an applied potential is cycled at a constant rate between two points. Time-series representations for the response of the oxidation of glycerol to a cycling potential are shown in Figure 1. The results are from experiments in which the upper potential limit (upl) of the cycle was increased in variable increments. The system was held at each upl until transient behavior disappeared. Only period-one responses occur at small upls, Figure 1a. Increasing the upl leads to the successive appearance of a periodtwo response (the response has a period that is twice that of the potential cycle), Figure 1b, a period-four response, Figure 1c, a period-three response, Figure 1d, and a period-six response, Figure 1e. The responses in Figure 1 can be connected to an ordered set called the U-sequence8 by assigning a symbol sequence to each response. Beginning with the tallest peak, peaks within a period are given an R if the preceding peak is shorter. Otherwise, they are given an L. The last symbol in each sequence, an L, is not included. Peaks that occur on the reverse potential scan, the narrow peaks in Figure 1, are ignored. The symbol sequences for the responses in Figures 1b-e are R, RLR,
RL, and RLLRL. The order and symbol sequence of these responses are the same as those that belong to members of the U-sequence.8 Additional responses corresponding to members of the U-sequence are shown in Figure 1f,g. At large upls, responses occur with the same symbol sequences as those for responses seen at smaller upls. Periodthree, period-four, and period-two responses, recorded at large upls, are shown in Figure 1h-j. The result reveals that increasing the upl causes the U-sequence to be eventually traversed in the reverse direction. Forward and reverse U-sequences are generated in the voltammetric oxidations of methanol7 and ethylene glycol12 by varying the same constraint, the upl. However, the U-sequence represents universal behavior. Therefore, this observation, by itself, is inadequate to be considered as evidence that the mechanisms for the three oxidation processes are related. It is necessary to show that chemical processes share nonuniversal behaviors before it can be concluded that relationships exist among their mechanisms. 4. Universal and Nonuniversal Transient Behavior The nonuniversal behavior we first discuss involves transients that occur close to a period-doubling bifurcation. Preceding any period-doubling bifurcation, the approach to the limit cycle in phase space changes from a monotone to an alternating one (universal behavior).13-15 Figure 2 displays current-density Vs potential curves (i/E curves) that represent alternating approaches to the limiting state; part a is for methanol, part b is for ethylene glycol, and part c is for glycerol. During each cycle, the i/E curve is on the side of the limiting cycle that is opposite to the side it was on during the previous cycle. A nonuniversal characteristic can be obtained by considering a phase point where odd numbered cycles cross even numbered cycles in the limit of reaching the asymptotic state. We call
18964 J. Phys. Chem., Vol. 100, No. 49, 1996
Figure 2. Alternating approaches to a period-one state. Current density is plotted against applied potential. The numbers indicate the order in which the cycles occurred. (a) [CH3OH] ) 0.35 M, upl ) 1050 mV; (b) [C2H4(OH)2] ) 0.30 M, upl ) 1300 mV; (c) [glycerol] ) 0.05 M, rate of cycling (S) ) 150 mV, upl ) 1230 mV.
these points crossover points. The location of a crossover point is not governed by any universal law. It is determined by the system’s deterministic laws (the kinetics). The locations of the crossover points, denoted with arrows in Figure 2, relative to the peak currents, are approximately the same for all three processes. Variation of the scan rate or the upl causes a shift in the range of values for other constraints (e.g., concentration) where crossover points are found. However, the location of the crossover points in the i/E plane, with respect to the peak current, remains approximately the same. 5. Nonuniversal Forms of the i/E Curves The sequence of periodic states observed in the oxidations of glycerol, ethylene glycol, and methanol is universal. However, the form of the i/E curve corresponding to each state is not governed by universal laws. The forms are sufficiently complex that it is consequential when they are matched by more than one process. Period-two and period-three i/E curves are shown in Figure 3. The i/E curves for each process have essentially the same forms as those of the other two processes. 6. Nonuniversal Changes on Approaching Instability and the Dominant Reactions Next, we present results on nonuniversal changes that occur while increasing the concentration to values just beyond critical concentrations. These changes are directly related to the reactions that dominate the oxidation processes. Results presented in ref 10 on methanol oxidation provide additional support for these relations. The changes are the same for the oxidations of methanol, ethylene glycol, and glycerol. Limiting i/E curves for different solute concentrations are shown in Figure 4; i/E curves for methanol are on the far left, those for glycerol are on the far right, and curves for ethylene glycol are in the middle. The lowest amplitude i/E curve in Figure 4a is for the supporting electrolyte solution. Although
Schell et al.
Figure 3. Period-two and period-three i/E curves for methanol (far left), ethylene glycol (middle), and glycerol (far right). (a) Methanol, [CH3OH] ) 0.143 M, upl ) 1230 mV; ethylene glycol, [C2H4(OH)2] ) 0.013 M, upl ) 1230 mV; glycerol, [C3H5(OH)3] ) 0.050 M, upl ) 1280 mV. (b) Methanol, [CH3OH] ) 1.00 M, S ) 50 mV/s, lpl ) 380 mV, upl ) 1270 mV; ethylene glycol, [C2H4(OH)2] ) 0.10 M, S ) 150 mV/s, upl ) 1350 mV; glycerol, [C3H5(OH)3] ) 0.25 M, upl ) 1180 mV. (c) Methanol, [CH3OH] ) 1.00 M, lpl ) 330 mV, upl ) 1280 mV; ethylene glycol, [C2H4(OH)2] ) 0.05 M, upl ) 1330 mV; glycerol, [C3H5(OH)3] ) 0.10 M, upl ) 1410 mV.
the original theory16 for this class of i/E curves requires modification, for example, to account for anion adsorption in acid solution,17,18 it remains the best theory for polycrystalline Pt in NaOH solutions. The peaks labeled OI, OII, and OIII originate from the formation of PtOH on three different sublattices through the discharge of OH-. The flat region following the peak OIII on the forward potential scan originates from the conversion of PtOH to platinum oxides. The broad cathodic peak on the reverse scan arises from the reduction of oxygen containing species. A current peak located at the same potential as that of the OI peak is exhibited by i/E curves for each oxidation process, Figure 4a. This location is where peaks occur for the oxidation of CO.19 A study using UV spectroscopy provides evidence that strongly bonded carbon monoxide, PtCO, is the major surface intermediate that forms during the oxidation of methanol.20 An in situ IR study21 furnishes evidence that PtCO is the major intermediate that forms during the oxidation of ethylene glycol. It is generally accepted that PtCO reacts with PtOH.19,22,23 Therefore, we conclude that the location of this current peak for the oxidations of methanol and ethylene glycol as well as glycerol is caused by the reaction of PtCO with PtOH. Other parts of the i/E curves in Figure 4a are essentially the same for the three processes. A peak or shoulder is at the same location as that of the OII peak, indicating that PtOH of the second sublattice reacts with PtCO. At large potentials, forward scans are superimposed with the i/E curve for the electrolyte solution, which reveals that the oxidation processes are all inhibited by platinum oxides. Increasing the solute concentration causes the i/E curves for the three processes to smoothly change to the same form; see
Mechanism Deduced from Instabilities
J. Phys. Chem., Vol. 100, No. 49, 1996 18965 that possess no characteristics of oxide formation or reduction (the cycles with relatively little hysteresis). The other cycles in Figure 3b contain the characteristics of oxide formation (the drop in current near the end of the forward scan) and oxide reduction (the sharp rise in current on the reverse scan). The stated reactions explain these behaviors:10 The behaviors originate from the dual role played by PtOH, which either reacts with PtCO or is transformed to platinum oxides. At sufficiently large solute concentrations, cycles occur in which most of the PtOH reacts with PtCO. The system switches between these cycles and cycles with oxide formation. This switching between cycles with and without oxide formation, and supporting experimental results, are described in detail in ref 10. 7. Conclusions and Conjectures Dominant Reactions. The matching of universal behavior (a forward and reverse U-sequence) and nonuniversal behaviors (location of crossover points, the form of i/E curves for different periodic states and the changes observed on approaching the first instability) provides strong evidence that the reactions that dominate the oxidation of glycerol are the same as those that dominate the oxidation of methanol. The dominant reactions were delineated in the previous section and begin with the formation of PtCO.10,25 At sufficiently large potentials, PtCO reacts with PtOH to produce carbonate:22
Figure 4. Limiting i/E curves for methanol (far left), ethylene glycol (middle), and glycerol (far right) recorded at different concentrations; upl ) 1230 mV. (a) The lowest amplitude i/E curves are for the electrolyte solution (no solute). [CH3OH]: (2) 5.0 × 10-5 M, (3) 3.0 × 10-4 M, (4) 1.0 × 10-3 M, (5) 3.0 × 10-3 M, (6) 6.0 × 10-3 M. [C2H4(OH)2]: (2) 1.0 × 10-5 M, (3) 5.0 × 10-5 M, (4) 1.5 × 10-4 M, (5) 3.0 × 10-4 M, (6) 5.0 × 10-4 M. [Glycerol]: (2) 1.0 × 10-5 M, (3) 5.0 × 10-5 M, (4) 1.5 × 10-4 M, (5) 3.0 × 10-4 M, (6) 5.0 × 10-4 M. (b) [CH3OH] ) 1.9 × 10-3 M, [C2H4(OH)2] ) 2.0 × 10-3 M, [glycerol] ) 1.0 × 10-3 M. (c) [CH3OH] ) 1.2 × 10-1 M, [C2H4(OH)2] ) 1.0 × 10-2 M, [glycerol] ) 6.0 × 10-3 M. (d) [CH3OH] ) 1.3 × 10-1 M, [C2H4(OH)2] ) 1.2 × 10-2 M, [glycerol] ) 1.0 × 10-2 M.
Figure 4 b. Because the i/E curves deform without drastic changes, the causes of their characteristics are assumed to be retained. The increase in current on the forward scan is due to the oxidation of the solute, and the decrease is caused by the formation of inhibiting oxides. The sharp rise in current on the reverse scan is caused by the reduction of oxides and the resumption of the oxidation of the solute.10,24 A comparison of Figure 4b with Figure 4c shows that additional increases in concentration lead to the same changes in all three oxidation processes. The sharp rise in current on the reverse scan in Figure 4c is located at a potential more positive than that in Figure 4b for each process. Results on methanol oxidation show that when fewer oxides form, the sharp rise in current shifts to a more positive potential.10 The result implies that increasing the solute concentration causes more PtOH to react with PtCO and less PtOH to be transformed to platinum oxides. The currents in Figure 4b descend to low values near the end of the forward scan, whereas in Figure 4c this descent is delayed until the reverse scan. The delay in the descent of the current is also caused by more PtOH reacting with PtCO. Oxides take longer to form which delays the inhibition of the oxidation of the solute. Eventually, a period-two response occurs in all three processes, Figure 4d. The bifurcation is consistent with the trend of decreasing oxide formation; small increases in concentration cause the i/E curves in Figure 4d to rapidly change to the form of the curves in Figure 3b. The latter i/E curves contain cycles
PtzCO + PtOH + OH- f (z + 1)Pt + CO2 + H2O + e(1a) CO2 + 2OH- f CO3-2 + H2O
(1b)
where z ) 1 for linearly bonded CO and z ) 2 or 3 for bridge bonded CO,23 Pt represents one vacant site, and letters in italics denote atoms chemically bonded to Pt. Preceding the reactions that produce carbonate, PtOH forms through the discharge of hydroxide ions:
Pt + OH- ) PtOH + e-, Erev ≈ 630 mV for the OI peak (2) Besides reacting with PtCO, PtOH can be converted to platinum oxides,26
PtOH + OH- ) PtO- + H2O
(3a)
PtO- ) PtO + e-
(3b)
Preceding Rapid Reactions. The results on the dominant reactions imply that the elementary reactions preceding the formation of PtCO are relatively fast and, in the case of glycerol, involve cleavage of at least one C-C bond. A possible representation of the overall reaction for the production of PtCO is written as
hzPt + [CnH(n+2)(OH)n] + (2n + 2)OH- f nPtzCO + (2n + 2)H2O + (2n + 2)e- (4) where n ) 1 for methanol, n ) 2 for ethylene glycol, and n ) 3 for glycerol. Equations 1, 2, and 4 imply that the overall reaction for the three oxidation processes can be written as
CnH(n+2)(OH)n + (6n + 2)OH- f nCO3-2 + (4n + 2)H2O + (4n + 2)e- (5)
18966 J. Phys. Chem., Vol. 100, No. 49, 1996
Schell et al.
Figure 5. Phase diagrams and plots of peak currents. (a) Phase diagram for methanol, log(concentration) is plotted against upl. Circles represent measured boundary points for the region of period-two states, which is labeled with a “2”; rectangles represent measured boundary points for the region of period-three states, which is labeled with a “3”; and the region of period-one states is labeled with a “1”. About one-third of the experimental points are shown. (b) Same as a but for ethylene glycol. (c) Same as a but for glycerol. (d) Plots of peak current (Ip) Vs concentration. Circles ) methanol, triangles ) ethylene glycol, rectangles ) glycerol, upl ) 1230 mV.
For methanol, a mechanism for producing PtCO is written as follows:25,27
CH3OH + xPt f Ptx[CH3OHads]
(6)
Ptx[CH3OHads] + OH- f Pty[PtCH2OH] + H2O + (x - y - 1)Pt + e- (7) -
Pty[PtCH2OH] + 3OH f PtzCO + 3H2O + (y + 1 - z)Pt + 3e- (8) where Ptn on the left side of the brackets represents n Pt sites occupied through weak interactions. The reaction in eq 7 is faster than the set of dominant reactions but slower than the three dehydrogenation steps represented by eq 8.25,27 Strong evidence exists only for the reaction in eq 7.27 We make the conjecture that the most probable sequence of reactions that precedes formation of PtCO in the oxidation of glycerol satisfies eq 4, n ) 3. Sequences producing zero, one, or two PtCO complexes have a small probability of occurrence. We also make the analogous conjecture for ethylene glycol. The conjecture is based on the following argument: It is known that PtCO forms at low potentials.23 At low potentials, the favored position for glycerol in the electrode boundary layer is one in which the hydrogen atoms of a purely hydrophobic side of the molecule point toward the electrode surface. The other side, the hydrophilic side, includes the three hydroxyl groups that point toward the bulk solution. Once glycerol is adsorbed on the surface in a hydrophobic-hydrophilic configuration, initial dehydrogenation should occur rapidly at all carbon centers in the same way as it does for methanol. In the hydrophobic-hydrophilic configuration, the precise orientation of glycerol determines which hydrogen atoms touch as it approaches a surface. For all orientations maintaining this
configuration, and with the carbon backbone in a plane parallel to the surface, models28 predict that one hydrogen atom from each of the C1 and C3 carbon atoms always touches the surface; the hydrogen atom of the C2 carbon atom does not always touch. Assuming a hydrophobic-hydrophilic configuration is favored at all potentials, these considerations lead to the following mechanism:
Ptw{[CH2(OH)CH(OH)CH2(OH)]ads} + 2OH- f Ptx{[PtCH(OH)][CH(OH)][PtCH(OH)]} + 2H2O + (w - x - 2)Pt + 2e- (9) Ptx{[PtCH(OH)][CH(OH)][PtCH(OH)]} + 3OH- f Pty{[PtC(OH)][PtC(OH)][PtC(OH)]} + 3H2O + (x - y - 1)Pt + 3e- (10) Pty{[PtC(OH)][PtC(OH)][PtC(OH)]} + 3OH- f 3PtCO + 3H2O + yPt + 3e- (11) Only linear bonded CO is considered. The step represented in eq 11 includes cleavage of the C-C bonds. The positive potential causes an electron from the bond to migrate to each of the adjacent carbon atoms and partake in the bonding with Pt. Bond cleavage does not directly contribute to electron transfer. In the next section, we present evidence in support of the conjecture, eq 4, which provides the basis for the mechanism in eqs 9-11. 8. Phase Diagrams The diagrams in Figure 5, parts a-c, depict the boundaries of the region of period-two states (lines joining circles) and the region of period-three states (lines joining rectangles) for the
Mechanism Deduced from Instabilities three oxidation processes. Only period-one states occupy the area that surrounds the outer period-two boundary. The boundaries are in the plane, the logarithm of the concentration (base 10) Vs the upl. The phase diagrams show that for methanol, Figure 5a, the smallest value for the concentration at which a period-one response becomes unstable is more than an order of magnitude larger than that for ethylene glycol, Figure 5b. The smallest critical concentration for ethylene glycol is slightly larger than that for glycerol, Figure 5c. Over the concentration range examined, the interval between the small and large upl segments of each boundary curve increases with the concentration of methanol, Figure 5a. The complete forward and reverse U-sequence is traversed for a 1.0 M methanol solution.7 The number of instabilities for ethylene glycol and glycerol increases and then decreases with respect to increases in concentration. At 1.0 M, only period-one and period-two states exist for ethylene glycol; for glycerol, the interval between the two inner period-two segments contains only period-four states (not indicated). Boundaries for the other high-order periodic states must have an elliptic shape like the period-three boundaries in Figure 5b,c. The stated results are consistent with the conjecture on the reactions that precede the formation of PtCO. According to the conjecture, each ethylene glycol molecule and each glycerol molecule yield, respectively, two and three PtCO complexes. Hence, the rate for the production of PtCO required for instability is achieved with concentrations smaller than that for methanol. Recall that instabilities appear at the threshold where PtCO is produced at a sufficiently large rate that cycles without oxide formation occur. The mechanism for producing PtCO in the hydrophobichydrophilic configuration requires a large number of neighboring vacant surface sites. The maximum surface area occupied by ethylene glycol in a hydrophobic-hydrophilic configuration is approximately28 1.8 times that of methanol and 0.7 times that of glycerol; the area includes area that can be blocked by hydroxyl groups. The number of vacant sites between adsorbed glycerol or ethylene glycol molecules is often too small at high concentrations to accompany other molecules. At large concentrations of ethylene glycol or glycerol, substantial amounts of surface intermediates are present with hydroxyl groups pointed toward the bulk solution. These hydroxyl groups repel molecules approaching the surface with the hydrophobichydrophilic configuration. The inefficient use of surface sites and the repulsive interactions cause glycerol and ethylene glycol to inhibit their own oxidation. At large concentrations, this inhibition decreases the rate of production of PtCO and the number of instabilities. These deductions are consistent with plots of peak current Vs concentration shown in Figure 5d. At small concentrations, the peak currents for ethylene glycol and glycerol are larger than that of methanol. At large concentrations they are less than the peak current for methanol. Differences exist in the location of the large upl segment of the outer period-two boundary among the three processes, Figure 5. Note, the system must return to period-one behavior at large upls. At sufficiently large upls, the rate of oxide formation is so great that a substantial amount of PtOH cannot react with PtCO. Oxide formation occurs on every cycle, and the periodone response is stabilized. The far right outer period-two boundary has the largest upl values for methanol. For a concentration of 1.0 M, the upl value at the outer period-two boundary is 2730 mV for methanol, 2290 mV for ethylene glycol, and 1980 mV for glycerol. For a fixed amount of PtOH
J. Phys. Chem., Vol. 100, No. 49, 1996 18967 and a potential equal to the upl value stated for glycerol, the rate of PtO formation is greater than that at the reversible potential, ErO, by a factor of exp(20) (ErO ) 930 mV, the potential where deposition of a monolayer is completed during the forward scan for the electrolyte solution; the symmetry factor5 is set to 1/2.). Using the stated upl values for ethylene glycol and methanol, this rate is greater than that using the glycerol upl value by the factors exp(6) and exp(15), respectively. The results on the large upl segment of the outer boundary indicate that, at large upls, methanol is more effective than ethylene glycol and glycerol in supplying PtCO for the reaction with PtOH; the oxidation of methanol is more effective in competing with oxide formation. Ethylene glycol and glycerol are less effective due to the large number of sites required for the hydrophobic-hydrophilic configuration. An efficient mechanism that uses the same number of sites as methanol to produce one PtCO complex per molecule, such as one where only the end of the molecule interacts with the surface, does not exist for ethylene glycol and glycerol. If one did exist, then all three large upl segments would be closer together. If an efficient mechanism that uses the same number of sites as ethylene glycol for producing two PtCO complexes per molecule existed for glycerol oxidation, the large upl segments for glycerol and ethylene glycol would be closer together. 9. Effects of Rotation Rate and Uncompensated Resistance Factors beside chemical reactions affect the dynamics. If these factors dominate, then the conclusions of the geometrical analyses may be invalid. We examine the most influential nonFaradaic effects: mass transport and uncompensated resistance. Rotation Rates. Varying the rotation rate (200-3000 rpm) during the oxidation of glycerol reveals the same trends reported for methanol.7 Period-two states remain stable when the rotation rate is changed by over an order of magnitude. Figure 6 a shows the effects of changing the rotation rate on a period-two state. The U-sequence (Figure 1) is still observed upon decreasing the rotation rate to 200 rpm. Small quantitative changes also follow trends found for methanol. A linear relationship is realized on plotting the peak current Vs the square root of rotation rate. The plot has a negative slope. See Figure 6 b. The negative slope is attributed to increases in the activity of OH- in the electrode boundary layer with respect to increases in rotation rate.7 Although PtOH is required for the reaction of PtCO, the conversion of PtOH to platinum oxides inhibits the reaction. Although changes in rotation rate affect the dynamics only small amounts in the convective diffusion regime (>200 rpm), decreasing the rate below 200 rpm causes the domains of the states of the U-sequence to rapidly shrink. At zero rotation rate, where diffusion and migration are the only means of mass transport, only period-one and aperiodic responses were found. Uncompensated Resistance. A large solution resistance (R) and a large ohmic drop (IR) have been associated with instabilities.2 These conditions occur here due to the requirement of a large ratio for the solute concentration to [NaOH] (Figure 5). The following relationship holds for a three-electrode system:5
E ) V + IRu
(12)
where E is the applied potential, V is the interfacial potential, I is the current, and Ru is the uncompensated resistance. By expressing the current as a sum of the contributions from electron-transfer reactions, If, and charging the double layer, C
18968 J. Phys. Chem., Vol. 100, No. 49, 1996
Schell et al. the feedback, eq 12, the part where I is linearly related to E, one can write
V ) RE
(14)
where R ) 1 when Ru has no effect and R ) 0 when Ru has its most influence on the dynamics. By measuring Ru and the slope of the linear part of the i/E curve, R can be determined. See Figure 6c for the part of the i/E curves we use. For [glycerol] ) 1.0 and 0.26 M, R ) 0.56 and 0.43, respectively, at the far left period-two boundary points in Figure 5c, and R ) 0.41 and 0.15, respectively, at the far right boundary points. For the measurements in Figures 6c,d, R is greater than 0.9. From the measurements and arguments, we conclude that If plays a primary role in the observed dynamics and that our geometrical analyses of universal and nonuniversal behaviors are valid. 10. Summary and Generalization Figure 6. Non-Faradaic effects. (a) Period-two i/E curves for a 0.06 M glycerol solution at different rotation rates: solid curve ) 200 rpm, dotted curve ) 500 rpm, dashed curve ) 1000 rpm. The period-two response was stable at 3000 rpm, where it had a form similar to those in Figure 4d. (b) Plot of peak current Vs (rotation rate)1/2, upl ) 1230 mV; circles ) 1.0 × 10-2 M CH3OH, slope ) -2.4 × 10-3 mA/(rpm)1/2; rectangles ) 1.0 × 10-3 M glycerol, slope ) -2.1 × 10-3 mA/(rpm)1/2. (c) i/E curve for [CH3OH] ) 1.0 M, upl ) 1125 mV, rotation rate ) 4000 rpm, S ) 200 mV/s, r ) 0.1 cm, Ru ) 19 Ω, Ru × Ip ) 37 mV. The slope of the dashed curve was used to calculate R in eq 14; see text. (d) i/E curve (solid) and i/V curve (dashed) for [glycerol] ) 0.45 M, upl ) 1125 mV, rotation rate ) 500 rpm, S ) 200 mV/s, r ) 0.1 cm, Ru ) 19 Ω, Ru × Ip ) 53.2 mV.
dV/dt (dV/dt is the time derivative and C is the capacitance), and rearranging eq 12, one can write
C dV/dt ) -V/Ru - If + E/Ru
(13)
Equation 13 is analogous to equations for forced, damped, nonlinear oscillators,29,30 which typically show instabilities when they are underdamped (Ru large).29 However, attributing a large Ohmic drop or resistance as the sole cause of instability is an oversimplification. To see this, set If to a constant in eq 13. For E equal to a constant or a triangular wave, eq 13 remains stable for arbitrarily large (constant) If and Ru. Instabilities involve the temporal evolution of If, which is determined by the electrochemical reactions. Instabilities can arise from the coupling of If to mass transport, but changes in this coupling are unimportant here in the convective diffusion regime. However, since If depends on V, eq 12 represents a feedback mechanism. For a large Ru, it is possible that the feedback has almost complete control over the dynamics and If has only a small influence. If this is the case, behavior caused by instabilities should disappear on substantially decreasing Ru. Experiments were conducted with the reference electrode placed 0.1 cm below the edge of the disk and a distance r from the edge in the radial direction. Period-two states were stabilized for several conditions: Examples are shown in Figure 6c,d; Ru ) 19 Ω. The i/E curves look the same as curves measured under conditions of a large resistance (250 Ω). Furthermore, the period-two state in Figure 6c remained stable until Ru was increased by a factor of 10.2 (Ru × Ip, Ip ) peak current, increased by a factor of 8.2). The period-two state was replaced by a period-one state. The effect of Ru can also be estimated by using i/E curves. For the part of a curve expected to be the most influenced by
By matching universal and nonuniversal behaviors caused by instabilities, we have provided strong evidence that the dominant reactions in the electrochemical oxidations of glycerol and methanol are the same. The nonuniversal behaviors include behavior directly related to the mechanism for the dominant reactions (section 6 and ref 10). The dominant reactions are the formation of PtCO, its subsequent reaction with PtOH to form carbonate, and the conversion of PtOH to platinum oxides which inhibit the formation and reaction of PtCO. Evidence was presented supporting the conjecture that the most probable reaction pathway that precedes the formation of PtCO is one in which each glycerol molecule produces three PtCO complexes. The study was restricted to an NaOH electrolyte solution and the use of a rotating Pt disk for the electrocatalyst. The results are applicable for a wide range of rotation rates (200-3000 rpm) and a wide range of values for the uncompensated resistance. Comparing behaviors caused by chemical instabilities in a complex reaction process with those in a more fundamental process is a general approach. It should be applicable to the study of a wide range of reactions. Thermal reactions are prime candidates. Conditions for inducing instabilities in thermal reactions are well-understood.31 Many examples exist where a complex reaction is related to a more fundamental reaction. For example, the combustion of an alkane can be compared to the combustion of a shorter alkane. A difficulty with thermal reactions may be the stabilization of behavior caused by instabilities. The approach, in principle, can be applied to isothermal reactions where nonlinear behavior is more easily stabilized. A challenge with isothermal reactions may be finding sufficiently simple fundamental reactions that exhibit instabilities. Acknowledgment. With great admiration, we respectfully acknowledge the many contributions John Ross has made to Thermodynamics and Nonlinear Chemical Dynamics. References and Notes (1) Yildiz, G.; Kadirgan, F. J. Electrochem. Soc. 1994, 141, 725. (2) Horanyi, G.; Kazarinov, V. E.; Vassiliev, Y. B.; Andreev, V. N. J. Electroanal. Chem. 1983, 147, 263. Avramov-Ivic, M. L.; Leger, J. M.; Lamy, C.; Jovic, V. D.; Petrovic, S. D. J. Electroanal. Chem. 1991, 308, 309. (3) Chaos in Chemistry and Biochemistry; Field, R. J., Gyorgi, L. Eds.; World Scientific: Singapore, 1993). (4) UniVersality in Chaos, 2nd ed.; Cvitanovic, P. Ed.; Hilger: New York, 1989).
Mechanism Deduced from Instabilities (5) Parker, V. D. In ComprehensiVe Chemical Kinetics; Electrode Kinetics: Principles and Methodology; Bamford, C. H., Compton, R. G. Eds.; Elsevier: New York, 1986; Vol. 26, pp 145-202. (6) Hudson, J. L.; Tsotsis, T. T. Chem. Eng. Sci., 1994, 49, 1493. Koper, M. T. M. Thesis, Utrecht University, Utrecht, The Netherlands, 1994. (7) Xu, Y.; Amini, A.; Schell, M. J. Phys. Chem., 1994, 98, 12759. (8) Metropolis, N.; Stein, M. L.; Stein, P. R. J. Combinatorial Theory A 1973, 15, 25. (9) Two processes with the same dominant reactions may be prevented from exhibiting the same universal behavior by physical constraints. For example, one process may exhibit a U-sequence when the concentration is varied. A solubility limit may prevent the other process from exhibiting all or part of the sequence. (10) Schell, M.; Xu, Y.; Amini, A. J. Phys. Chem., 1994, 98, 12768. (11) Zdraveski, Z.; Xu, Y.; Amini, A.; Schell, M. J. Chem. Soc., Faraday Trans. 1996, 92, 395. (12) Xu, Y.; Zdraveski, Z.; Schell, M. Chem. Phys. Lett. 1995, 247, 589. (13) Mallet-Paret, J.; Yorke, J. A. Ann. N. Y. Acad. Sci. 1980, 357, 300. Manneville, P. DissipatiVe Structures and Weak Turbulence; Academic Press: New York, 1990; pp 198-200 and 208-212. (14) Amini, A.; Xu, Y.; Schell, M. J. Chem. Phys. 1995, 102, 3220. (15) As universal behavior, we include what might be categorized as generic behavior. (16) 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.; Barnett, B.; Angerstein-Kozlowska, H.; Tilak, B. V. J. Chem. Phys. 1990, 93, 8361. (17) Wagner, F. T.; Ross, P. N., Jr. J. Electroanal. Chem. 1988, 250, 301. Markovic, N.; Ross, P. N. Jr. J. Electroanal. Chem. 1992, 330, 499.
J. Phys. Chem., Vol. 100, No. 49, 1996 18969 (18) Angerstein-Kozlowska, H.; Conway, B. E.; Hamelin, A.; Stoicoviciu, L. J. Electroanal. Chem. 1987, 228, 429. (19) Santos, E.; Giordano, M. C. J. Electroanal. Chem. 1984, 172, 201. (20) Caram, J. A.; Gutierrez, C. J. Electroanal. Chem. 1992, 323, 213. (21) Hahn, F.; Beden, B.; Kadirgan, F.; Lamy, C. J. Electroanal. Chem. 1987, 216, 169. (22) Sun, S.-G.; Chen, A.-C. J. Electroanal. Chem. 1992, 323, 319. (23) Parsons, R.; VanderNoot, T. J. Electroanal. Chem., 1989, 257, 9. (24) Buck, R. P.; Griffith, L. R. J. Electrochem. Soc., 1962, 109, 1005. (25) Gasteiger, H. A.; Markovic, N.; Ross, P. N. Jr.; Cairns, E. J. J. Phys. Chem. 1993, 97, 12020. (26) Damjanovic, A.; Genshaw, M. A.; Bockris, J. O’M. J. Electrochem Soc. 1967, 114, 466. (27) Franaszczuk, K.; Herrero, E.; Zelenay, P.; Wieckowski, A.; Wang, J.; Masel, R. I. J. Phys. Chem. 1992, 96, 8509. (28) Fisher-Hirschfelder-Taylor Atom Model Sets, Fisher Scientific. (29) Kapral, R.; Schell, M.; Fraser, S. J. Phys. Chem. 1982, 86, 2205. (30) To see the analogy with the equations for forced, damped oscillators, in ref 29, identify V in eq 13 as the velocity of a particle in a force field, C as the particle’s mass, 1/Ru as the friction coefficient, and E/Ru as the forcing term. A general difference is that the “force,” If, is velocity dependent instead of position dependent. For the ideal case, Ru ) 0, cyclic voltammetry is analogous to parametrically forced oscillators. (31) Aris, R. In Reacting Flows: Combustion and Chemical Reactors; Ludford, G. S. S., Ed.; Lectures in Applied Mathematics 24; American Mathematical Society: Providence, Rhode Island, 1986; pp 75-107.
JP961195T
