Interdigitated Array Electrode as an Alternative to the Rotated Ring

Chem. , 1996, 68 (17), pp 2951–2958 ..... Empirically, this relationship was closely given by the following, for 0 < ε < 1: Equation 24 .... Water ...
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Anal. Chem. 1996, 68, 2951-2958

Interdigitated Array Electrode as an Alternative to the Rotated Ring-Disk Electrode for Determination of the Reaction Products of Dioxygen Reduction Timothy A. Postlethwaite,† James E. Hutchison,‡ and Royce Murray*

Kenan Laboratories of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290 Bruno Fosset and Christian Amatore*

De´ partement de Chimie, Ecole Normale Supe´ rieure, URA CNRS 1679, 24 rue Lhomond, 75231, Paris Cedex 05, France

Electrochemical reduction of dioxygen in aqueous media can proceed to water, hydrogen peroxide, or a mixture of the two. The production of hydrogen peroxide, classically established with the rotated ring-disk electrode, can also be quantitatively assessed at interdigitated array (IDA) electrodes, where dioxygen is reduced at the set of microband generator electrodes and any H2O2 produced is detected by its oxidation (back to O2) at the interdigitated set of microband collector electrodes. The sensitivity of the IDA for H2O2 detection is higher owing to its more complete collection, and to the ensuing regeneration of O2, which leads to an amplification of the generator currents. The production of H2O2 is thus reflected both in the ratio of collector and generator electrode currents [the collection efficiency, coll(τ)] and in the ratio of the generator current with the collector potential on to that with it off [amplification factor, ampl(τ)]. The necessary theory for interpretation of the fraction E of H2O2 produced per dioxygen reduced is presented, based on conformal mapping techniques. Explicit equations are derived for E at long times that are independent of the IDA dimensions and that can be used with any two-product electrochemical reaction analogous to the dioxygen reduction. Experimental data are presented for dioxygen reduction in acidic and basic media to illustrate application of the theory. The electrochemical reduction of dioxygen (O2) in aqueous media has received enormous attention as a result of its importance in fuel cell applications. This reaction has been studied on bare metal1-6 and carbon2,7 electrodes as well as on electrodes † Present address: W. R. Grace & Co., Washington Research Center, 7379 Route 32, Columbia, MD 21044-4098. ‡ Present address: Department of Chemistry, University of Oregon, Eugene, OR 97403-1253. (1) (a) Damjanovic, A.; Genshaw, M. A.; Bockris, J. O’M. J. Electrochem. Soc. 1967, 114, 466. (b) Damjanovic, A.; Genshaw, M. A.; Bockris, J. O’M. J. Electrochem. Soc. 1967, 114, 1107. (c) Genshaw, M. A.; Damajanovic, A.; Bockris, J. O’M. J. Electroanal. Chem. 1967, 15, 163. (d) Genshaw, M. A.; Damajanovic, A.; Bockris, J. O’M. J. Electroanal. Chem. 1967, 15, 173. (e) Genshaw, M. A.; Damjanovic, A.; Bockris, J. O’M. J. Phys. Chem. 1967, 71, 3722. (2) Horrocks, B. R.; Schmidtke, D.; Heller, A.; Bard, A. J. Anal. Chem. 1993, 65, 3605. (3) Striebel, K. A.; McLarnon, F. R.; Cairns, E. J. J. Electrochem. Soc. 1990, 137, 3351. (4) Adzic, R. R.; Strbac, S.; Anastasijevic, N. Mater. Chem. Phys. 1989, 22, 349.

S0003-2700(96)00327-7 CCC: $12.00

© 1996 American Chemical Society

that have been modified with metal adlayers,8 adsorbed and bound metalloporphyrins,2,9-11 metallophthalocyanines,9 and other molecular films12 so as to result in electrocatalytic dioxygen reduction. Dioxygen reduction can proceed along several pathways, namely, the two-electron reduction to hydrogen peroxide and the fourelectron reduction to water (or in basic media, to HO2- and to OH-, respectively). Studies of electrode effects and of the efficacy of a catalytic scheme generally include determining which pathway predominates (they often co-exist). For maximum fuel cell efficiency, the four-electron pathway to water at the reversible electrochemical potential is desired. One of the most convenient and widely used methods of determining the dioxygen reduction pathway is an electrochemical assay of the reduction products (i.e., H2O2 or H2O) using a rotating ring-disk electrode (RRDE).13,14 In this method, dioxygen is reduced at the disk electrode, the reduction products are swept hydrodynamically to the ring electrode, and any hydrogen peroxide in the product(s) is detected by reoxidizing it there to dioxygen. Quantitation of the extent of peroxide production is achieved by comparing the experimental collection efficiency (current measured at ring divided by current measured at disk) of hydrogen peroxide produced during dioxygen reduction at the disk to the theoretical or experimentally calibrated collection efficiency for the RRDE employed. (5) Evans, D. H.; Lingane, J. J. J. Electroanal. Chem. 1963, 6, 283. (6) Zurilla, R. W.; Sen, R. K.; Yeager, E. J. Electrochem. Soc. 1978, 125, 1103. (7) (a) Tarasevich, M. R.; Sabirov, F. Z.; Mersalova, A. P.; Burshtein, R. Kh. Elektrokhimiya 1968, 4, 432. (b) Tarasevich, M. R.; Savirov, F. Z.; Mertsalova, A. P.; Burshtein, R. Kh. Elektrokhimiya 1969, 5, 608. (c) Tarasevich, M. R.; Savirov, F. Z.; Mertsalova, A. P.; Burshtein, R. Kh. Elektrokhimiya 1970, 6, 1130. (8) (a) Adzic, R. R.; Markovic, N. M.; Tripkovic, A. V. Glas. Hem. Drus. Beograd 1980, 45, 399. (b) Adzic, R. R.; Despic, A. R. Z. Phys. Chem. N.F. 1975, 98, 95. (c) Adzic, R. R.; Tripkovic, A. V.; Markovic, N. M. J. Electroanal. Chem. 1980, 114, 37. (d) Adzic, R. Tripkovic, A.; Atanasoski, R. J. Electroanal. Chem. 1978, 94, 231. (9) Vasudevan, P.; Santosh; Mann, N.; Tyagi, S. Trans. Met. Chem. 1990, 15, 81, and references therein. (10) Collman, J. P.; Wagenknecht, P. S.; Hutchison, H. E. Agnew. Chem., Int. Ed. Engl. 1994, 33, 1537, and references therein. (11) (a) Rocklin, R. D.; Murray, R. W. J. Electroanal. Chem. 1979, 100, 271. (b) Takeuchi, E. S.; Murray, R. W. J. Electroanal. Chem. 1985, 188, 49. (c) Bettelheim, A.; White, B. A.; Murray, R. W. J. Electroanal. Chem. 1987, 217, 271. (d) Bettelheim, A.; White, B. A.; Raybuck, S. A.; Murray, R. W. J. Electroanal. Chem. 1988, 246, 139. (12) Katz, E.; Schmidt, H.-L. J. Electroanal. Chem. 1994, 368, 87, and references therein. (13) Albery, W. J.; Hitchman, M. L. Ring-Disk Electrodes; Oxford: London, 1971. (14) Bard, A. J.; Faulkner, L. R. Electrochemical Methods; Wiley: New York, 1980.

Analytical Chemistry, Vol. 68, No. 17, September 1, 1996 2951

Other possible methods include a calculation of the number of electrons passed (n) from currents at a rotated disk electrode (RDE)14,15 or in linear sweep voltammetry14 and coulometry in a thin-layer electrode cell.14 A more recent methodology2 is based on using scanning electrochemical microscopy to detect hydrogen peroxide during mapping of the dioxygen reduction catalytic activity of a electrode surface; this potentially powerful technique has not however yet been reduced to quantitative evaluation of the two- vs four-electron pathways. The interdigitated array electrode (IDA), an outgrowth of lithographic microfabrication technology,16-18 consists of a series of parallel microband electrodes in which alternating microbands are connected together, forming a set of interdigitating electrode fingers. Typical dimensions of an individual microband “finger” are 0.1-0.2 µm in height, 1-10 µm in width, and 5-10 mm in length, and the typical interfinger separation (gap) is 1-10 µm. The potential of each finger set of electrodes can be controlled (independently of the other set) relative to that of a reference electrode, just as with a RRDE. For diffusivities typical of fluid media, the small gap dimensions of the IDA allow, for sufficiently prolonged electrolysis, reaction products to diffuse away from the microbands of one finger (generator) set and to bathe the microbands of the other finger (collector) set. That is, the IDA substitutes a small transport distance for the fast hydrodynamic transport of the RRDE and, with multiple sets of IDA fingers, attains a more quantitative detection of reaction products. A comparison between the behavior of IDAs and the RRDE can be based on the general electrochemical reaction

A + ne- f B + C

(1)

in which the electroactive species A is reduced to a mixture of products B and C, of which B is electroactive and reoxidizable to A and C is not electroactive. The value of “n” represents the average of the two pathways. In the RRDE and IDA experiments, the products B and C generated by reaction 1 at the disk and generator electrode set, respectively, are swept hydrodynamically and diffuse, respectively, to the ring and collector electrode set, which are each set at a potential sufficient to reoxidize B back to A. At the RRDE, for an exclusively A f B disk reaction, the efficiency of the collection of B by the ring as measured by the ratio of ring and disk currents (i.e., the collection efficiency) depends solely on the disk, ring, and ring-disk gap dimensions and is typically 30-40% or less. With an IDA, the small gap dimensions and the use of an array rather than a single generator/ collector electrode pair result in very large (>0.98) collection efficiencies, which gives the IDA an advantage in detecting small amounts of generator electrode products. A more essential difference between the RRDE and IDA experiments is that the A that is regenerated at the collector electrodes of the IDA can diffuse back to generator fingers to be reduced again, whereas with the RRDE, the regenerated A is (15) Bruckenstein, S.; Miller, B. Acc. Chem. Res. 1977, 10, 54. (16) (a) Aoki, K.; Morita, M.; Niwa, O.; Tabei, H. J. Electroanal. Chem. 1988, 256, 269. (b) Niwa, O. Electroanalysis 1995, 7, 606. (c) Tabei, H.; Takahashi, M.; Hoshino, S.; Niwa, O.; Horiuchi, R. Anal. Chem. 1994, 66, 3500. (d) Niwa, O.; Tabei, H. Anal. Chem. 1994, 66, 285. (17) Chidsey, C. E. D.; Feldman, B. J.; Lundgren, C.; Murray, R. W. Anal. Chem. 1986, 58, 601. (18) Hutchison, J. E.; Postlethwaite, T. A.; Murray, R. W. Langmuir 1993, 9, 3277.

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hydrodynamically swept away into the solution. The recycling, or feedback, of the A/B reaction by the IDA has the important effect of amplifying the generator current far above the value it would have were the collector finger set disconnected. In the absence of feedback, A arrives at the generator solely by diffusion from the solution. The amplified generator current also amplifies, thereby, the ensuing collector current. The extent of feedback current amplification at an IDA clearly will depend on the value of n and the fraction of product C in reaction 1. The generator current would not be amplified at all if C were the sole reaction product at the generator electrode finger set. (There is no parallel to this effect with a RRDE). Thus, in an IDA, the generator current amplification and collection efficiency are related to one another and are both affected by the B vs C reaction pathway. With reference to the dioxygen reaction, in reaction 1 clearly A represents O2, B represents H2O2, and C represents H2O. Production of solely B (H2O2) means that n ) 2 whereas production solely of C (H2O) gives n ) 4. Theory that would allow the use of IDA electrodes for deducing reaction pathways in the above manner has not been previously described. In the theoretical section following, we will develop the necessary relationships between n, the IDA collection efficiency [ratio of collector to generator currents, coll(τ)] and the generator current amplification [ratio of generator current with collector finger set potential on, to the generator current with collector finger set off, ampl(τ)]. The theoretical results are stated in terms of the dioxygen reaction, but are general for any reaction 1 and, outside of the equalities noted, any IDA dimensions. Experimental results for IDAs operating under various conditions of dioxygen reduction will then be given. THEORY Formulation of the Time-Dependent System. The theory is developed for an IDA with generator and collector electrodes of length l and width w separated by interfinger gaps g (Figure 1). The number N of generator/collector pairs is taken as sufficiently large that edge effects are negligible. Then, all element cells (i.e., half a generator, one gap, and half a collector, Figure 1a) in the IDA are equivalent with period P ) w + g and because of the symmetry, each element cell communicates only with the slab of solution of width P and length l immediately above it. Also because of the symmetry, all concentration gradients are zero anywhere on the planes defining the sides of the element cells (dashed vertical lines in Figure 1a), and diffusion to the overall array of electrodes is linear at distances that are large compared to P.19 Diffusion at distances from the array that are comparable to the finger width and gap dimensions follows a complex pattern, with infinite current densities at the edges of each electrode.19-22 Therefore a precise calculation of the concentration profiles of electroactive species and of their product(s) as a function of distance and time is complex, requiring large computer facilities23 but which can be greatly simplified with conformal mapping techniques.20-22,24 (19) Amatore, C.; Save´ant, J.-M.; Tessier, D. J. Electroanal. Chem. 1983, 147, 39. (20) Fosset, B.; Amatore, C. A.; Bartelt, J. E.; Michael, A. C.; Wightman, R. M. Anal. Chem. 1991, 63, 306. (21) Fosset, B.; Amatore, C. A.; Bartelt, J. E.; Wightman, R. M. Anal. Chem. 1991, 63, 1403. (22) Aoki, K.; Morita, M.; Niwa, O.; Tabei, H. J. Electroanal. Chem. 1988, 256, 269.

coefficient is introduced to take account of the local space compression/dilation imposed by the transform used.20,21 Several transforms could have been used instead of the above one. The present transforms were selected because they allow analytical expressions to be derived for the diffusion coefficients DΓ,θ in the (Γ, θ) transformed space:

[

]

DΓ,θ (R + β - (1/λ*2))2 + 4β/λ*2 ) ∆Γ,θ ) D (R + β - 1)2 + 4β

1/2

(6)

with

R ) [cosh(πΓ) sin(πθ)]2

(7)

β ) [sinh(πΓ) cos(πθ)]2

(8)

and

where D is the (constant) true diffusion coefficient of the species considered in true space (x, y). This allows the formulation of the present system along the following set of equations:

Figure 1. Schematic representation of the cross section of an interdigitated array of band electrodes in various spaces.: (a) true space (x, y) indicating the geometrical parameters defining the array; (b) transformed space (X, Y) defined by application of eqs 2 and 3 to the element cell shown in (a); (c) transformed space (Γ, θ) obtained by application of eqs 4 and 5 to the space shown in (b).

For the specific problem at hand, a double conformal transformation is used22 as defined in Figure 1b,c. A first transform is applied to transform the true space (x, y) in Figure 1a into an intermediate conformal one (X, Y) resembling a paired band configuration (Figure 1b):20

( ) ( ) πy πx X ) λ cosh( ) sin( ) P P πy πx Y ) λ sinh cos P P

(2) (3)

where λ is an adequate scaling factor. In the following, we use λ ) 1. This second space is next transformed into its conformal space (Γ, θ) in Figure 1c:20

X ) λ* cosh(πΓ) sin(πθ)

(4)

Y ) λ* sinh(πΓ) cos(πθ)

(5)

( (

(9)

δh δ2h δ2h ) d∆Γ,θ + δτ δΓ2 δθ2

(10)

where o ) [O2]/[O2]bulk, h ) [H2O2]/[O2]bulk, d ) DH2O2/DO2, and τ ) DO2t/P 2, where t is the true time. The boundary equations, in which the generator finger set potential is considered to be on the reduction plateau of the dioxygen wave and that of the collector finger set on the oxidation plateau of the H2O2 wave, are:

Γ ) 0, -1/2 e θ e 1/2 (gap):

δo δh ) )0 δΓ δΓ

(11)

Γ > ω, θ ) (1/2 (symmetry plane):

δo δh ) )0 δθ δθ

(12)

0 e Γ e ω, θ ) -1/2 (generator): o ) 0

(13)

0 e Γ e ω, θ ) 1/2 (collector): h ) 0

(14)

where ω the width of each electrode finger in the (Γ, θ) transformed space is given by

ω) where λ* is another adequate scaling factor; we use λ* ) sin(πg/2P). By defining the conformal transforms in this way, the flux of any species through any surface and the transformed flux through the transformed surface are equal. Similarly, the Laplacian operator is conserved by each transform. The only changes introduced to the diffusion equations and boundary conditions are then, that in the transformed space a space-dependent diffusion (23) Varco Shea, T.; Bard, A. J. Anal. Chem. 1987, 59, 2102. (24) Amatore, C. In Physical Electrochemistry: Principles, Methods and Applications; Rubinstein, I., Ed.; M. Dekker: New York, 1995.

) )

δo δ2o δ2o ) ∆Γ,θ + δτ δΓ2 δθ2

1 cosh-1(1/λ*) π

(15)

To complete the theoretical formulation, reaction 1 is written for the dioxygen reaction as

O2 + 2(2 - )(e-) + 2(2 - )(H+) w (H2O2) + 2(1 - )(H2O) (16) where  represents the fractional molecular yield  of H2O2 per dioxygen reduced. For a four-electron process,  ) 0. Oxidation Analytical Chemistry, Vol. 68, No. 17, September 1, 1996

2953

of H2O2 to dioxygen at the collector is considered to be quantitative. Because of the conservation of fluxes by conformal transformations, two additional boundary conditions are needed to express the electron stoichiometries at each electrode:

δh δo 0 e Γ e ω, θ ) -1/2 (generator):  ) -d δθ δθ 0 e Γ e ω, θ ) 1/2 (collector):

(17)

δh δo ) -d δθ δθ

(18)

The currents at each electrode are evaluated from the above formulations using

∫

igenerator ) [2(2 - )] (FNlDO2[O2]bulk)

(δθδo)

ω

o

dΓ

Γ,θ)-1/2

Figure 2. (a) Relationship between simulated collection efficiency coll(τ) and amplification factor ampl(τ) as a function of dimensionless time τ ) Do2t/P 2 (numbers indicated). The slanted dashed line corresponds to the empirical relationship in eq 24 ( ) 0.9), and the filled circle in the top left part of the figure is the value at infinite time (eqs 38 and 39,  ) 0.9). (b) Plot of the data in (a) presented under the form of eq 25. Data in (a and b) were simulated with:  ) 0.9, d ) DH2O2/DO2) 1, and g/P ) 0.4.

(19) icollector ) 2(FNlDO2[O2]bulk)

∫

ω

0

(δθδo)

dΓ

Γ,θ)1/2

(20)

Introducing parameters related to these currents, the collection efficiency20,21 coll relates the collector and generator currents when potentials are applied to both electrodes as above:

δo ∫ (δθ ) δo ∫ (δθ) ω

icollector ) -(2 - )-1 coll ) igenerator

o

dΓ

Γ,θ)1/2

(21)

ω

o

Γ,θ)-1/2

dΓ

and the current amplification ampl relates20,21 the generator current when the collector potential is on to that when it is off:

ampl )

(igenerator)coll,on (igenerator)coll,off

)

∫ (δo/δθ) [∫ (δo/δθ) [

(2 - )

-1

ω

o ω

Γ,θ)-1/2

dΓ]coll,on

o

Γ,θ)-1/2

dΓ]coll,off

(22) 2(2 - )coll(τ) ) 1 +  -

Both coll and ampl are readily measured in the IDA format. They do not depend on the length l of the array electrodes (although the currents themselves do). Equations 9-14 and 17-22 were solved numerically as a function of time for selected values of  using a Hopscotch finite differences procedure. The algorithm used was adapted from that previously employed for a paired microband device operated in a generator/collector mode,20 the significant difference being the presence here of the coefficient  in the flux equation (eq 17) for the generator finger set and of the possibility of allowing different diffusion coefficients for O2 and H2O2 (the factor d in eqs 17 and 18; d was taken as unity in the simulations done). At each time τ, the collection efficiency coll(τ) was determined through the numerical integration of the current densities at each electrode (eq 21). To determine the feedback current amplification, ampl(τ), an independent series of simulations was run, using a new collector boundary condition

0 e Γ e ω, θ ) 1/2 (collector): 2954

δo δh ) )0 δθ δθ

to represent a measurement in which the collector was off (open circuit). This allowed numerical evaluation of the denominator of eq 22. In previous calculations for paired and triple microband assemblies,20,21 we found that specific relationships resulted at long times between coll(τ) and reciprocal ampl(τ) that were more indicative of the feedback process than were the collection efficiency or amplification factors themselves. A similar relationship was found in the present case, as shown by the slanted asymtote between coll(τ) and reciprocal ampl(τ) approached in Figure 2a for τ . 1 (i.e., t . P 2/DO2) for the example value  ) 0.9. As expected, since this limiting relation is determined by the generator/collector feedback process, it depends on the value of . Results like those in Figure 2a for different values of  and different array geometries showed that the coefficients of the linear, long-time relationship between coll(τ) and 1/ampl(τ) depended only on  and were independent of g/P and of w. (Note that w is already included in the dimensionless variable τ ) DO2t/ P 2.) Empirically, this relationship was closely given by the following, for 0 <  < 1:

(23)

Analytical Chemistry, Vol. 68, No. 17, September 1, 1996

1 ampl(τ)

(τ . 1)

(24)

Equation 24 allows extraction of the value of  from simulated values of coll(τ) and ampl(τ):

1 ampl(τ) 1 + 2coll(τ)

4coll(τ) - 1 + computed )

(25)

Application of this procedure to the data in Figure 2a gave the results in Figure 2b, where it is seen that when τ > 1, one has computed )  ) 0.9 with high precision. Since the existence of a simple relation (eq 25) based on parameters that are easily available experimentally is crucial for the determination of  in a real experiment, we tested it over a large range of  values and several array dimensions. The results are given in Figure 3 for two IDA dimensions similar to those used experimentally (vide infra), and computed )  to better than 1% as soon as τ ) DO2t/P 2 > 1. Owing to the importance of the empirical eq 24 for the experimental determination of , its validity was further assessed by the following partly intuitive arguments.

and coll coll,on coll coll,on [φO ] ) - [φH ] 2 2O2

(32)

A combination of eqs 29-32 gives gen coll,on coll coll,on gen coll,off (1 + )[φO ] + 2[φO ] ) [φO ] 2 2 2

(33)

which formulated in terms of currents and considering the electron stoichiometry defined by eq 16 gives Figure 3. Comparison between true  values (true, abscissa) and computed  values (computed, eq 25) based on theoretical collection efficiencies and amplification factors simulated for a series of different times (τ ) DO2t/P 2 ) 10 (4), 102 (2), and 4 × 103 (1) and true values. d ) DH2O2/DO2 ) 1 and g/P ) 0.4 (true ) 0, 0.2, 0.4, 0.6, 0.8, 1) or 0.6 (true ) 0.3, 0.5, 0.7, 0.9).)

Relation between Coll(τ) and Ampl(τ) at Long Times or Large τ. When τ . 1, meaning the diffusion layer is thicker than the period P of the IDA array, diffusion in the near vicinity of the array (i.e., distances ≈P) is nearly conservative.19 Indeed, owing to the small diffusion distances, the flux of each species to each electrode (φgen and φcoll) adjusts to compensate for the slow time variation of linear diffusional fluxes (φdiff) that prevail at longer distances from the array surface.24 With the collector on, then, one has gen coll coll,on diff coll,on [φO + φO ] ) [φO ] 2 2 2

(26)

gen coll coll,on diff coll,on + φH ] ) [φH ] [φH 2O2 2O2 2O2

(27)

2(2 - )[icoll]coll,on ) (1 + )[igen]coll,on - [igen]coll,off

(34)

Based on the definitions of collection efficiency and feedback current amplification, this equation can be shown to be identical to the empirical eq 24 and is valid at large values of τ (i.e., for DO2t/P 2 . 1). This comparison validates the procedure proposed for the determination of experimental  values from collection efficiencies and feedback current amplification factors. Moreover, recasting a combination of eqs 30-32 in terms of currents gives

(2 - )[icoll]coll,on )  [igen]coll,on

(35)

which affords the limiting value of collection efficiency at long times

coll∞ ) /(2 - )

(36)

and with eq 34 gives the amplification factor at long times

ampl∞ ) 1/(1 - )

and when the collector is off gen coll,off diff coll,off [φO ] ) [φO ] 2 2

(28) Equations 36 and 37 thus afford another means of determining , since

The linear diffusional fluxes of dioxygen when the collector potential is on and off are nearly identical (i.e., [φO2diff]coll,on ) [φO2diff]coll,off) because both fluxes are imposed by linear diffusion far from the array and by nearly identical boundary conditions (i.e., [O2] ≈ 0 in the vicinity of the array when the generator potential is on the dioxygen reduction plateau). Then also, when the collector potential is off, since the collector quantitatively oxidizes any arriving H2O2, [φO2diff]coll,on ≈ [φH2O2diff]coll,off, and when the collector potential is on, [φH2O2diff]coll,on ≈ 0 since the strong feedback between the collector and generator ensures that almost no H2O2 escapes from the small solution domain next to the IDA. Introducing the above identities yields gen coll coll,on gen coll,off [φO + φO ] ) [φO ] 2 2 2 gen [φH 2O2

+

coll coll,on φH ] 2O2

)0

(29)

)

(31)

2coll∞ 1 )11 + coll∞ ampl∞

(38)

Figure 2a (solid circles) shows, however, that the limits in eqs 36 and 37 and thus the identities in eq 38 are obtained only at very long (infinite) times, which contrasts with the fact that eq 24 is obeyed with high precision as soon as τ is only somewhat larger than unity (Figure 2a). The deviations of coll(τ) and ampl(τ) from their infinite time limits depend both on time and on . Extremely precise empirical relations can be derived from regression analysis of simulated values of coll(τ) and ampl(τ) for τ > 1 and various  values:

(30)

Finally, the stoichiometry at the generator and collector electrodes imposes that gen coll,on gen coll,on ] ) -[φH ] [φO 2 2O2

(37)

[A + B2] coll(τ) ) coll∞ - (2 - )-1 (πτ)1/2

(39)

2[A + B2] 1 1 + ) ampl(τ) ampl∞ (πτ)1/2

(40)

and

Analytical Chemistry, Vol. 68, No. 17, September 1, 1996

2955

Figure 4. Comparison between simulated collection efficiences (a) and amplification factors (b) and their empirical eqs 39 and 40, respectively, with A ) 0.1447 and B ) 0.6154, for several values of  (0, 0.1, 0.2, ..., 0.9) and τ ) DO2t/P 2 (1, 10, 103). d ) DH2O2/DO2 ) 1 and g/P ) 0.4 or 0.6. Figure 5. Generator/collector voltammograms at a platinized Pt IDA electrode in dioxygen-saturated 0.5 M H2SO4. The potential of the generator microband finger set was scanned at 20 mV/s while that of the collector fingers was held constant at 1.2 V vs SSCE.

with A ) 0.145 and B ) 0.615. The efficacy of these relations for collection efficiency and amplification factors is shown in Figure 4. It is noteworthy that the two terms expressing the deviations of coll(τ) and ampl(τ) from their infinite time limits exactly compensate one another when the coefficients in eq 24 are employed, which explains why eq 25 is almost exact when τ > 1 but does not require τ . 1. The fact that the deviations from limiting values in eqs 39 and 40 depend on (πτ)-1/2, i.e., are Cottrellian, establishes that their origins are related to linear diffusion components that were neglected in the unrefined approximations that allowed the simplifications of eqs 26-28 into eqs 29 and 30. This particular point can be demonstrated exactly by more refined approximations, but this will not be presented here.

the ratio of the generator current with the collector on to that with the collector at open circuit potential. The time-dependent collection efficiency, coll(t), is defined in eq 21 as the ratio of the collector and generator currents. Both measure IDA feedback as influenced by the O2 reaction stoichiometry. The time dependence of the moles of H2O2 produced per O2, (t), is then calculated as in eq 25. Computations. Algorithms used for the simulations, similar to those used previously20 except as noted under Theory, were written in Pascal and run on a PC 486 33 MHz.

EXPERIMENTAL SECTION Chemicals. All reagents used were ACS reagent grade or better and were used as received. Water was purified with a Barnsted Nanopure system (>18 MΩ cm). Electrodes. The Au and Pt IDA electrodes were a generous gift from Osamu Niwa and Masao Morita of NTT Corp. (Japan). Their fabrication has been described.16a The present studies used IDAs with 50 3 µm wide, 0.1 µm high, and 2 mm long finger pairs separated by 2 µm gaps of SiO2. Pt IDAs were used as received, unless otherwise noted. The collector electrode on Au IDAs were platinized as we did before18 (deposition by passing 400 µC charge from 2 mM K2PtCl4/0.1 M K2HPO4) to improve the oxidative collection of H2O2 resulting from O2 reduction at the generator electrode. Electrochemical Measurements. The instrumentation included a Pine Model RDE4 and AFCBP1 bipotentiostat and, for RRDE and IDA generator/collector experiments, a locally constructed triangle wave generator and Yokogawa XYY′ chart recorder. A HP 8116A pulse/function generator and Nicolet 310 digital oscilloscope were used for potential step experiments. Both generator and collector electrode currents were low-pass filtered at 100 Hz. Measurements were carried out in a three-compartment cell with Pt counter and SSCE reference electrodes, in solutions sparged with O2 for at least 10 min before beginning measurements and for at least 30 s between successive measurements. Experiments recording the current response to potential steps at the generator electrode consisted of two measurements: the first with the collector electrode at open circuit; the second with the collector set to a potential oxidizing hydrogen peroxide. The timedependent current amplification, ampl(t), is defined in eq 22 as

RESULTS AND DISCUSSION Dioxygen Reduction at Pt in Acidic Solution. It has been established1a that the reduction of dioxygen at clean Pt electrodes in acidic electrolytes proceeds by four electrons to water, with no detectable hydrogen peroxide intermediate. To test the theory outlined above in this extreme case, we performed dioxygen reduction experiments in 0.5 M H2SO4 at Pt IDA electrodes. Experiments utilizing Pt IDAs as received (without any pretreatment) resulted in a substantial amount of hydrogen peroxide [coll(t) ∼0.4] being detected during dioxygen reduction. Platinization of the generator electrode set of the IDA resulted in a drastic decrease in the amount of hydrogen peroxide produced. A generator/collector voltammogram using a platinized IDA is shown in Figure 5. Setting the collector at a potential sufficiently positive to oxidize H2O2 while sweeping the generator electrode through the dioxygen reduction wave results in a generator current with a peak and subsequent decay, and a collector current that is roughly a mirror image but much smaller. The peak collector current is about 5% of the peak generator current. The above theory is for potential steps not sweeps; the result of a potential step experiment at the platinized IDA is shown in Figure 6A where current-time curves a and b are generator current responses with the collector electrode at open circuit and at a H2O2-oxidizing potential, respectively. The feedback current is clearly quite small since it made little difference in the generator current whether the collector was on or off. Curve c is the collector current for the latter case and, as seen, is very small. Application of eq 25 to values of coll(τ) and ampl(τ) derived from the current-time responses in Figure 6A gives the result shown in Figure 6B for the time dependence of 100 (the molar percentage H2O2 produced per mole of O2 reduced, eq 16). As

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Figure 6. (A) Potential step current-time responses at a platinized Pt IDA electrode in dioxygen-saturated 0.5 M H2SO4. Curve a (dashed line), generator current when the generator electrode potential is stepped from 0.7 to 0.1 V vs SSCE while the collector electrode is at open circuit. Curve b, generator current when the generator electrode potential is stepped from 0.7 to 0.1 V vs SSCE while the collector electrode potential is held at 1.2 V vs SSCE. Curve c, collector electrode potential for experiment of curve b. (B) Hydrogen peroxide detected as a function of time, calculated from eq 25 using the timedependent ratios of currents in curves c and b [i.e., coll(τ)] and of currents in curves b and a [i.e., ampl(τ)]. Figure 8. Potential step current-time responses at a Au IDA electrode in dioxygen-saturated 1 M NaOH. (A) Curve a (dashed line), generator current when the generator electrode potential is stepped from -0.1 to -1.25 V vs SSCE while the collector electrode is at open circuit. Curve b, generator current when the generator electrode potential is stepped from -0.1 to -1.25 V vs SSCE while the collector electrode potential is held at 0.1 V vs SSCE. Curve c, collector current for experiment of curve b. (B) Same as (A) except that the final generator potential is -0.6 V vs SSCE. (C) Hydrogen peroxide detected with generator potential at -0.6 V (upper curve) and -1.25 V vs SSCE (lower curve) as a function of time, calculated from eq 25 using the time-dependent ratios of currents in (A) and (B), curves c and b [i.e., coll(τ)] and of currents in curves b and a [i.e., ampl(τ)].

Figure 7. Generator/collector voltammograms at a Au IDA electrode in dioxygen-saturated 1 M NaOH. The potential of the generator microband finger set was scanned at 20 mV/s while that of the collector fingers was held constant at 0.1 V vs SSCE.

seen, the amount of H2O2 produced is quite small (5% and less), but it is a detectable amount. Such small amounts of H2O2 would be difficult to detect by RRDE; that they are quantitatively measurable in Figure 6 reflects the inherent sensitivity of the IDA,

based on the overlap of diffusional transport distance from the generator electrode with the collector electrode. It has been reported1a that small amounts of organic impurities in the electrolyte can cause H2O2 to be produced during dioxygen reduction in acidic media at Pt, which may be the origin of the result in Figure 6B. Whether the small time variation of the amount of peroxide detected in Figure 6B is mechanistically significant was not pursued. The decrease in H2O2 production as a result of platinizing the IDA, relative to the as-received IDA surface, may reflect organic impurities on the surface or, alterAnalytical Chemistry, Vol. 68, No. 17, September 1, 1996

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Figure 9. Percentage hydrogen peroxide (100) detected in experiments as in Figure 8 with various generator potentials, an initial generator potential of -0.1 V, and a collector potential of 0.1 V vs SSCE.

natively, may involve a poisoning of the native Pt IDA surface by Cr from the IDA adhesion layer (either at the microband electrode edges or from migration or diffusion through the Pt film to its surface). Dioxygen Reduction at Au in Basic Solution. The number of electrons for dioxygen reduction at Au electrodes from basic electrolytes has been found to be potential dependent.2,25,26 At low negative overpotentials, dioxygen is reduced quantitatively to H2O2. At more negative potentials, the H2O2 is further reduced to water, resulting in no oxidation of H2O2 detected at the ring electrode in RRDE experiments. These features serve as a convenient test for the IDA theory. Figure 7 presents a generator/collector voltammogram for the reduction of dioxygen at a Au IDA (with a platinized collector electrode for efficient H2O2 oxidation) in 1 M NaOH. As is evident from the nearly equal generator and collector currents, between -0.4 and -0.9 V vs SSCE, dioxygen reduction proceeds largely to H2O2 at those potentials. At more negative potentials, smaller amounts of H2O2 are produced which causes both the collector and generator electrode currents to fall (the latter owing to the diminution of feedback). However, the collector current does not fall entirely to zero at potentials negative of -0.9 V. Potential step experiments were performed in which the generator electrode potential was stepped to various reducing (25) Frumkin, A.; Nekrasov, L.; Levich, B.; Ivanov, J. J. Electroanal. Chem. 1959/ 60, 1, 85. (26) Vilambi, N. R. K.; Taylor, E. J. J. Electroanal. Chem. 1989, 270, 61.

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potentials negative of -0.5 V vs SSCE; current-time responses for steps to -1.25 V (the potential for the minimum in the generator current seen in Figure 7) and to -0.6 V vs SSCE are shown in Figure 8A,B. The generator currents at -0.6 V exhibit a larger feedback amplification (compare curves a and b, Figure 8B) and come to steady state values much more quickly than is the case for the currents resulting from the -1.25 V step in Figure 8A. Calculating values of coll(τ) and ampl(τ) from these currenttime results gives values for 100 or percent H2O2 as shown in Figure 8C. The upper curve in Figure 8C, for a -0.6 V generator potential, shows essentially quantitative H2O2 production, whereas the lower one shows that about 45% H2O2 results at -1.25 V vs SSCE. It is notable (as predicted from the theory above) that, although the values of coll(τ) and ampl(τ) from Figure 8A are time dependent (i.e., the currents do not reach steady state and give linear plots according to eqs 39 and 40), the value of 100 is constant for all times larger than DO2t/P 2 > 1. Figure 9 shows in more detail how the 100 or percent H2O2 production depends on the stepped generator electrode potential. Clearly at about -1.3 V vs SSCE, further reduction of H2O2 begins, but its complete reduction is not consummated within the available potential windows on these electrodes. The reason for such a large residual H2O2 production at negative potentials is not clear but again may reside in exposure of the Cr underlayer on the generator electrode microband. This is a present limitation of these electrodes as used for detection of H2O2 production on Au IDA electrodes chemically modified as with chemisorbed Co porphryins (which will be described elsewhere), but drawing from the effects of platinizination, as noted above, may possibly be solved by deposition of a further layer of Au on the generator electrode. This was not explored in the present study. ACKNOWLEDGMENT This research was supported by grants from the National Science Foundation and the Office of Naval Research (R.M.) and from CNRS and ENS (C.A.). We thank Dr. Osamu Niwa and Masao Morita of NTT (Japan) for providing us with the IDA electrodes used in this work. J.E.H. is the recipient of a National Science Foundation Postdoctoral Fellowship (CHE-9203585).

Received for review April 2, 1996. Accepted June 17, 1996.X AC960327B X

Abstract published in Advance ACS Abstracts, August 1, 1996.