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J. Phys. Chem. B 2006, 110, 11912-11917
Potential Oscillations in Galvanostatic Electrooxidation of Formic Acid on Platinum: A Mathematical Modeling and Simulation Yoshiharu Mukouyama,*,†,‡ Mitsunobu Kikuchi,†,‡ Gabor Samjeske´ ,§,| Masatoshi Osawa,§ and Hiroshi Okamoto†,‡ College of Science and Engineering, Tokyo Denki UniVersity, Hatoyama, Saitama 350-0394, Japan, Research Institute for Science and Technology, Tokyo Denki UniVersity, Tokyo, 101-8457, Japan, Catalysis Research Center, Hokkaido UniVersity, Sapporo 001-0021, Japan, and CREST, Japan Science and Technology Agency, Kawaguchi, Saitama 332-0012, Japan ReceiVed: February 22, 2006; In Final Form: April 25, 2006
We have modeled temporal potential oscillations during the electrooxidation of formic acid on platinum on the basis of the experimental results obtained by time-resolved surface-enhanced infrared absorption spectroscopy (J. Phys. Chem. B 2005, 109, 23509). The model was constructed within the framework of the so-called dual-path mechanism; a direct path via a reactive intermediate and an indirect path via strongly bonded CO formed by dehydration of formic acid. The model differs from earlier ones in the intermediate in the direct path. The reactive intermediate in this model is formate, and the oxidation of formate to CO2 is rate-detemining. The reaction rate of the latter process is represented by a second-order rate equation. Simulations using this model well reproduce the experimentally observed oscillation patterns and the temporal changes in the coverages of the adsorbed formate and CO. Most properties of the voltammetric behavior of formic acid, including the potential dependence of adsorbate coverages and a negative differential resistance, are also reproduced.
Introduction Electrochemical oscillations have been reported for a variety of systems and have been summarized in recent reviews.1-5 In potentiostatic (i.e., constant potential) systems the current can oscillate, and in galvanostatic (i.e., constant current) systems the potential can oscillate. In the past decade, the mechanisms of electrochemical oscillations have been studied by mathematical modeling as well as by experiments.3-18 Mathematical modeling can give some information about the electrode dynamics that is not easily accessible by experiments.13-14 The study of the electrooxidation of small organic compounds, such as formic acid, formaldehyde, and methanol, is quite important due to their potentials to be used as fuels for fuel cells. The electrooxidation of formic acid on platinum is generally thought to proceed via a dual-path mechanism.19,20 One is a direct path through an adsorbed reactive intermediate, and the other is an indirect path through strongly adsorbed carbon monoxide, CO. A carboxylic species, COOH, has long been speculated as the reactive intermediate in the direct path. The electrooxidation of formic acid produces temporal oscillations under both potentiostatic and galvanostatic conditions.16-18,21-34 The oscillations have been simulated mathematically based on the dual-path mechanism.16-18 Albahadily and Schell constructed two models for the potential oscillation under galvanostatic conditions with as many as 9 or 10 possible surface reaction steps with six intermediates.16 Okamoto et al. modeled the potential oscillation with five reaction steps with * Corresponding author e-mail:
[email protected]. † College of Science and Engineering, Tokyo Denki University. ‡ Research Institute for Science and Technology, Tokyo Denki University. § Catalysis Research Center, Hokkaido University. | CREST, Japan Science and Technology Agency.
two intermediates, which requires only three coupled differential equations.17 Strasser et al. constructed a model for the current oscillation with complex waveforms such as mixed-mode oscillation, by considering not only surface reaction steps but also the change in the surface concentration of formic acid.18 All these models successfully simulate experimentally observed oscillations, but the simplest model by Okamoto et al. suggests that, even if many reaction steps are involved in formic acid oxidation, a limited number of reaction steps plays essential roles in the oscillations. The earlier models assume that COOH is the reactive intermediate and that the formation of COOH is rate-determining. Recently we found that the reactive intermediate is formate (HCOO) adsorbed in a bridging configuration (bonded via both oxygen atoms to two platinum atoms) by using time-resolved surface-enhanced infrared absorption spectroscopy (SEIRAS).33-35 It was also found that the coverage of the adsorbed HCOO oscillates synchronously with the oscillating potential34 and that the oxidation of the adsorbed HCOO to CO2 is rate-determining.33,34 These new experimental findings have forced us to revise the existing models. For modeling the oscillation, a proposed model must reproduce not only the oscillatory behavior but also the voltammetric behavior because the dynamic behavior prerequisite for the occurrence of oscillations appears in voltammograms.1-5 The voltammograms for formic acid electrooxidation show a negative differential resistance (NDR) at 0.6-0.8 V (RHE), that is, a decrease in the oxidation current with increasing potential.33,34,36,37 It is well established that the NDR plays a decisive role in electrochemical oscillations.1-5 To explain the NDR, as well as the oscillatory behavior, we proposed a new concept that the oxidation of adsorbed HCOO to CO2 requires an adjacent vacant reaction site, which leads to a second-order
10.1021/jp061129j CCC: $33.50 © 2006 American Chemical Society Published on Web 06/01/2006
Electrooxidation of Formic Acid on Platinum
Figure 1. Potential oscillations observed at a current density, j ) (a) 1.3, (b) 1.7, and (c) 2.5 mA cm-2 in a 0.5 M H2SO4 + 1 M HCOOH (M ) mol dm-3) solution at 43 °C. The working electrode was a polycrystalline Pt, and the reference electrode was a standard hydrogen electrode (SHE).
reaction model for the direct path.33,34 The newly proposed model was successfully used to qualitatively explain the appearance of the NDR in the voltammograms33,34 and both the appearance of the current oscillation33 and the potential one.34 In this paper, we quantitatively show how the proposed model reproduces most of the experimental results.
J. Phys. Chem. B, Vol. 110, No. 24, 2006 11913
Figure 2. Observed oscillation patterns of (a) the electrode potential, E, (b) the coverage of HCOO(a), θformate, and (c) that of COL(a), θCO_L, at j ) 0.30 mA cm-2 in a 0.5 M H2SO4 + 1 M HCOOH solution at 25 °C (data taken from Figure 2 in [34] and the IR band intensities were converted to coverages).
formate. The oxidation current is not a simple function of either the coverage of CO-free sites () 1-θCO_L-2θCO_B) or θformate. By the analogy with formate decomposition on metal surfaces in UHV, we proposed that the oxidation of adsorbed formate (the rate-determining step) requires a vacant reaction site. These findings lead us to the following reaction formulas for the direct path: k1
HCOOH + 2* y\ z HCOO(a) + H+ + ek -1
(1)
Modeling To facilitate the later discussion, the results obtained in our previous experimental work are summarized in the following. Typical oscillation patterns are shown in Figure 1 for applied current densities of 1.3, 1.7, and 2.5 mA cm-1. The frequency and amplitude of the oscillations increase as the applied current density increases. Time-resolved SEIRAS experimentals revealed that linearlybonded CO (COL), bridge-bonded CO (COB), and formate are adsorbed on the electrode and that the coverages of COL (θCO_L), and formate (θformate) oscillate synchronously with the potential oscillations.34 The coverage of COB (θCO_B) is constant (∼ 0.1) during the oscillations. Here, the coverage of the adsorbed species is defined as the ratio of the number of the adsorbed species to that of surface Pt atoms. As shown in Figure 2 (which is a re-plot of Figure 2 in ref 34 after converting the band intensities of these species to their coverages), θformate increases and θCO_L decreases at high potentials. After the drop in the potential to the low limiting value, θformate decreases quickly to the low value, while θCO_L recovers quickly first and then gradually. A time-resolved SEIRAS measurement using isotope-labeled formic acids (H12COOH and H13COOH) showed that adsorbed formate is replaced by formate newly supplied from HCOOH in the solution at a rate of >5 s-1 at 0.6 V, while the substitutions of adsorbed COL and COB are negligibly slow. The rate of the isotopic exchange for formate is fast enough to explain the observed current by assuming formate to be the reaction intermediate in the direct path and the decomposition (oxidation) of formate to CO2 to be rate-determining. Additional SEIRAS measurements under linear potential sweep conditions at different COL coverages revealed that adsorbed CO (both COL and COB) suppresses formic acid oxidation by blocking the adsorption and also the oxidation of
k2
HCOO(a) + * 98 CO2 + H+ + e- + 3 *
(2)
where the asterisk and (a) represent a surface reaction site and an adsorbed state, respectively. k1 and k-1 are the rate constants of the forward and backward reactions of reaction 1, respectively. Equation 1 indicates that the adsorption of HCOO requires two reaction sites because HCOO is adsorbed in a bridging configuration.33-35 Equation 2 expresses the rate of HCOO(a) oxidation by the second-order rate equation, k2θformateθvacant, where θvacant is the coverage of free sites () 1-θCO_L-2θCO_B-2θformate). It was also found that the dehydration of formic acid to yield COL(a) requires two vacant sites as k3
HCOOH + 2 * 98 COL(a) + H2O + *.
(3)
The rate of COL accumulation is potential-dependent and decreases as the potential increases. The CO accumulation (both COL and COB) was not observed at potentials more positive than 0.6 V. COL(a) is oxidized slowly at 0.4-0.8 V and quickly at 0.8-0.9 V, while COB(a) is oxidized at potentials more positive than 0.9 V at a sweep rate of 0.1 V s-1. We can assume that COL(a) is oxidized to CO2 via the reaction with water adsorbed at a vacant site, H2O(a), because the potential oscillations occur in the double-layer potential region: k4
COL(a) + H2O(a) 98 CO2 + 2H+ + 2e- + 3 *.
(4)
We additionally make the following three assumptions: (i) The concentration of HCOOH near the surface is constant, (ii) the adsorption and desorption of H2O is so fast that H2O(a) is in
11914 J. Phys. Chem. B, Vol. 110, No. 24, 2006
Mukouyama et al.
equilibrium with H2O in the bulk solution, and (iii) the solution resistance, RΩ, between the Pt working and reference electrodes is ignored because the experimental conditions are galvanostatic and the potential difference due to ohmic drop is constant. The ohmic drop merely shifts the potential-time curves in the positive direction (by about 15 mV ()3 mA x 5 Ω) in the case of Figure 1). On the basis of the observations and under the assumptions mentioned above, we can derive the following differential equations by using three variables of θformate, θCO_L and the electrode potential, E:
TABLE 1: Parameter Values Used in This Papera
a
a1
a-1
a2
a3
a4
16
-24
6.1
-5
39
E1
E-1
E2
E3
E4
0.33
0.33
0.01
0.00
0.72
The units of ai and Ei are, respectively, V
-1
and V.
dθformate/dt ) k1 θvacant2 - k-1 θformate - k2 θformate θvacant (5) dθCO_L/dt ) k3 θvacant2 - k4 θCO_L θvacant
(6)
dE/dt ) j/C - (F h/C) {k1 θvacant2 - k-1 θformate + k2 θformate θvacant + 2 k4 θCO_L θvacant}, (7) where j is the current density applied to the working electrode, C is the electrode capacity (8.0 × 10-5 C V-1 cm-2, measured), F is the Faraday constant (96500 C mol-1), and h is the total amount of surface sites per unit area (2.2 × 10-9 mol cm-2 for a polycrystalline Pt electrode). Equations 5 and 6 are mass balance equations, and eq 7 is a charge balance equation derived from an equivalent circuit for electrochemical systems.1,3-5 The rate constants k1 and k3 include the near-surface concentration of HCOOH (1 M). The rate constant of an electrochemical reaction at E is given by
ki ) ki0 exp[RnF(E-Ei0′)/RT]
(8)
in the Bulter-Volmer model, where ki0 is the standard rate constant, R is the transfer coefficient, n is the number of electrons transferred, Ei0′ is the formal potential, R is the gas constant (8.31 J mol-1 K-1), and T is the temperature (K). We assume that this equation holds also for nonelectrochemical reaction steps such as the COL formation (reaction 3) because the chemical adsorption also depends on the electrode potential.17 For the convenience of parameter change on the same order of magnitude, we rewrite the rate constant ki (i ) 1, -1, 2, 3, 4) in the following form:17
ki ) exp[ai (E-Ei)],
(9)
where ai ) RnF/RT and Ei ) E° ′ + ln(1/ki0)/ai. For the desorption of formate, the reverse reaction of reaction 1, a-1 is given by -(1-R)nF/RT. The differential equations were numerically integrated with the Runge-Kutta method using commercially available software, MATLAB for MS-Windows (MathWorks). Results and Discussion For most electrochemical steps, R is around 0.5 and ai is close to 20 V-1 for n ) 1 and 39 V-1 for n ) 2 at T ) 298 K. Because the oxidation of COL(a) is an electrochemical 2ereaction, we first set a4 at 39 V-1.17 On the other hand, we optimized other parameter values to reproduce the observed oscillations under the following constraints, which are found from experimental data or thought to be reasonable: (i) 0.3 < R < 0.7 for a1 and a-1, (ii) E1 ) E-1, (iii) k2 > 5 s-1 at E ) 0.6 V,34 (iv) k3 ∼ 0.11 s-1 at E ) 0.4 V,34 (v) k3 ) k4 at a potential between 0.55 and 0.70 V,17,34 and (iv) θCO_B ) 0.1.34
Figure 3. Calculated time courses of E, θformate and θCO_L at j ) (a) 0.22, (b) 0.23, (c) 0.28, (d) 0.34, (e) 0.40, and (f) 0.46 mA cm-2. The parameter values used are shown in Table 1 and θCO_B was set at 0.1.
The best-fit parameter values obtained are shown in Table 1. It is noted that a2 () 6.1 V-1) is much smaller than the value expected for ordinary electrochemical 1e- reactions (∼ 20 V-1). This small a2 may suggest that the oxidation of HCOO(a) is a catalytic reaction rather than an electrochemical one, although such an interpretation is inconsistent with those on other electrochemical reaction steps. Figure 3 shows the time courses of E, θformate and θCO_L calculated at several current densities. The oscillation occurs for 0.22 < j < 0.46 mA cm-2 (the data for j > 0.46 mA cm-2 is not shown in Figure 3), and E oscillates between ca. 0.5 and 0.8 V. The potential E increases gradually and then sharply with time, which is followed by a sudden drop to the minimum value. The amplitude of E increases with an increasing j. The oscillation period ranges between 40 and 60 s and becomes shorter with an increasing j. Synchronizing with the E oscillation, θformate and θCO_L oscillate. At the potential spikes, θformate increases and θCO_L decreases sharply, which are followed by a sudden decrease in θformate and a gradual increase in θCO_L. The amplitudes of the θformate and θCO_L oscillations increase
Electrooxidation of Formic Acid on Platinum
Figure 4. Expanded time courses of E, θformate and θCO_L at j ) 0.23 mA cm-2 calculated with the same parameter values as in Figure 3.
with an increasing j. The time-average of θformate increases and that of θCO_L decreases with an increasing j. The calculated results are essentially in good accordance with the experimental results (Figures 1 and 2, and also the figures in ref 34). To see the potential oscillations in more detail and to find the correlation with the coverage oscillations of the adsorbates, the result at 0.23 mA cm-2 is replotted in Figure 4 by expanding the time-scale. In the time region where E increases gradually from its minimum value of 0.49 V to 0.64 V, both θformate and θCO_L increase gradually, associated with the gradual increase in E. Because the rate of COL(a) formation is faster at lower potentials as is evident from the negative potential dependence of a3 () -5 V-1) and COL(a) oxidation is negligible at 0.490.64 V ( ca. 0.62 V is ascribed to the decrease in Vads and Vox. Although the rate constants k1 and k2 increase exponentially as shown in Figure 6c, Vads and Vox themselves decrease at U > ca. 0.62 V due to the decrease in θvacant, as shown in Figure 6d. This is the essence of the second-order rate equation we introduced in the present work.
A mathematical model that simulates potential oscillations in formic acid oxidation was proposed on the basis of SEIRAS experiments. A significant difference from earlier models is that formate is the reactive intermediate in the reaction and the oxidation of formate to CO2 is the rate-determining step. To express the necessity of an adjacent vacant site for the oxidation of adsorbed formate, a second-order rate equation was introduced in the model. Adsorbed CO (both COL and COB) produced by dehydration of HCOOH affects the adsorption and oxidation of formate. Five elementary reaction steps (adsorption/ desorption and oxidation of formate, and adsorption and oxidation of COL) were incorporated into a set of coupled differential equations. The model successfully simulated the experimentally observed potential oscillations (oscillation current range, waveform, amplitude, and period), the oscillations of the coverages of the adsorbates (waveform and amplitude), their dependences on the current density, and also the voltammetric behavior of HCOOH oxidation (the appearance of the NDR and the potential dependence of the coverage of adsorbed formate), although some small discrepancies with the experiments still remain. Acknowledgment. This work was partially supported by the Research Institute for Science and Technology of Tokyo Denki University Science under grants Q03M-01 and Q04M-06, the Ministry of Education, Culture, Sports, Science and Technology of Japan (Grant-in-Aid for Basic Research no. 14205121 and for Scientific Research on Priority Areas 417), and Japan Science and Technology Agency. References and Notes (1) Hudson, J. L.; Tsotsis, T. T. Chem. Eng. Sci. 1994, 49, 1493. (2) Fahidy, T. Z.; Gu, Z. H. In Modern Aspects of Electrochemistry; White, R. E.; Bockris, J. O.; Conway, B. E., Eds.; Plenum: New York, 1995; Vol. 27; p 383. (3) Koper, M. T. M. In AdVances in Chemical Physics; Prigogine, I.; Rice, S. A., Eds.; John Wiley & Sons: New York, 1996; Vol. 92, p 161. (4) Krischer, K. In Modern Aspects of Electrochemistry; Conway, B. E.; Bockris, J. O.; White, R. E., Eds.; Plenum: New York, 1999; Vol. 32, p 1. (5) Krischer, K. In AdVances in Electrochemical Science and Engineering; Alkire, R. C.; Kolb, D. M., Eds.; WILEY-VCH: Weinheim, 2003; Vol. 8, p 89. (6) Koper, M. T. M. J. Electroanal. Chem. 1996, 409, 175. (7) Strasser, P.; Eiswirth, M.; Koper, M. T. M. J. Electroanal. Chem. 1999, 478, 50. (8) Mukouyama, Y.; Nakanishi, S.; Chiba, T.; Murakoshi, K.; Nakato, Y.; J. Phys. Chem. B 2001, 105, 7246. (9) Mukouyama, Y.; Nakanishi, S.; Konishi, H.; Ikeshima, Y.; Nakato, Y. J. Phys. Chem. B 2001, 105, 10905. (10) Wolf, W.; Krischer, K.; Lu¨bke, M.; Eiswirth, M.; Ertl, G. J. Electroanal. Chem. 1995, 385, 85. (11) Mukouyama, Y.; Nakanishi, S.; Nakato, Y. Bull. Chem. Soc, Jpn. 1999, 72, 2573. (12) Mukouyama, Y.; Nakanishi, S.; Konishi, H.; Nakato, Y. J. Electroanal. Chem. 1999, 473, 156. (13) Nakanishi, S.; Mukouyama, Y.; Karasumi, K.; Imanishi, A.; Furuya, N.; Nakato, Y. J. Phys. Chem. B 2000, 104, 4181. (14) Nakanishi, S.; Sakai, S.; Hatou, M.; Mukouyama, Y.; Nakato, Y. J. Phys. Chem. B 2002, 106, 2287. (15) Okamoto, H.; Tanaka, N.; Naito, M.Electrochim. Acta 1994, 39, 2471. (16) Albahadily, F. N.; Schell, M. J. Electroanal. Chem. 1991, 308, 151. (17) Okamoto, H.; Tanaka, N.; Naito, M. Chem. Phys. Lett. 1996, 248, 289.
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