Electrode kinetics of oxygen reduction

J. Electroanal. Chem., 153 (1983) 79-95 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

79

E L E C T R O D E KINETICS OF OXYGEN R E D U C T I O N A THEORETICAL A N D E X P E R I M E N T A L A N A L Y S I S OF T H E R O T A T I N G RING-DISC E L E C T R O D E M E T H O D

K.-L. HSUEH and D.-T. CHIN

Department of Chemical Engineering, Clarkson College of Technology, Potsdam, N Y 13676 (U.S.A.) S. SRINIVASAN

Electronics Division, E-11, MSD429, Los Alamos National Laboratory, Los Alamos, N M 87545 (U.S.A.) (Received 15th November 1982; in revised form 26th January 1983)

ABSTRACT The previous theoretical treatments of the rotating ring-disc electrode method to distinguish between the mechanisms of electroreduction of O 2 to H 2 0 with and without the formation of H202 as an intermediate, were examined. A new expression was derived for l a l / ( l a l - Id) as a function of ~0 l/~_ (where lal is the disc limiting current, I d is the disc current and ~0 is the rotational speed of electrode) for five possible reaction models. This, along with the corresponding expressions for I d / l r vs. w I/2 (it is the ring current), enables the calculations of the individual rate constants for the intermediate steps of 02 reduction. The experimental data of I a and I r were obtained for O 2 reduction on platinum in 0.55 M HzSO 4 at 25°C. By use of these experimental results in the present theoretical treatment, it is shown that: (1) the most applicable model over the entire potential region was the one suggested by Damjanovic, Genshaw and Bockris; (2) the models involving the adsorption/desorption of H202 were applicable only over a narrow region of potential; and (3) the models involving the chemical decomposition of H 202 were inconsistent with the dependence of I d t / ( l a l -- I d ) VS. w-1/2

INTRODUCTION

The rotating ring-disc electrode (RRDE) technique has been extensively used for the investigation of the mechanism of the O 2 reduction reaction in which H 2 0 2 is formed as an intermediate [1-5,9]. In this method, the reduction of 02 takes place on a central disc electrode and the generated H 2 0 2 is detected at a concentric ring electrode with a larger radius. Damjanovic et al. [2] proposed a criterion to distinguish two possible reaction mechanisms of O 2 reduction from the plot of the ratio of the disc (Id) to the ring (It) currents vs. the reciprocal of the square root of the electrode rotating speed (co). The first mechanism is a direct reduction path which reduces O 2 to H 2 0 through a four-electron transfer step. The second mechanism is a series reaction path where O 2 is first reduced to H 2 0 2 followed by the 0022-0728/83/$03.00

© 1983 Elsevier Sequoia S.A.

80 (a) 02,b ~

k1 02,a ~

(b)

H202,Q~

1"420

k1

02 b ~

lk 4

'

02 = ~

H202,a

H20

E k~42j/k{t Ik6 H202 ' ,

H202 ,b

i H202 ,b

(¢)

k1

I 02, b ~

k2

02,e ~

(e) 02, b ~ 0 2 ,

(d)

k3 H202,o~

I H20

k2 02, b "---~" 02, a ~

k3 H202, a ~

H202,* k5

H202,

H202, b

H20 2 b

H20

kl

I

k2

o.

k-2

k3

~ H202,(a ~ H 2 0

i

I H202, b

Fig. 1. Models for the electroreduction of O 2 proposed by (a) Damjanovic et al. [3], (c) Appleby and SaW [4], (d) Zurilla et al. [5], and (e) Bagotskii et al. [10].

[2], (b)

Wroblowa et al.

reduction of H202 to H20. These two reaction paths are presented in Fig. la. Wroblowa et al. [3] considered the adsorption-desorption step of H202 at the disc electrode (Fig. lb) and developed a method to determine the mechanism of 02 reduction from the plots of I d / I r VS. ~0-t/2 and of the intercept vs. slope of the former plot at different potentials. The theory was extended by Appleby and Sa W [4] to porous electrodes to include the catalytical decomposition of HzO 2 to O 2 and H 2 0 (Fig. lc). Zurilla et al. [5] proposed a reaction model for 02 reduction on Au in alkaline solution where only the series reaction path was considered (Fig. ld). For a given set of experimental data, the use of different models leads to different conclusions as was first pointed out by Zurilla et al. [5]. For example, if the intercept of the plot of I a / I r vs. ~0-1/2 is greater than the reciprocal of collection efficiency of the R R D E ( l / N ) , then according to Zurilla's model the conclusion will be that 02 reduction is only via the series reaction path. However, if one uses the model by Damjanovic et al. [2], the same result would suggest that O 2 is reduced to H 2 0 via

81 both the series reaction path and the direct reduction path. A quantitative understanding of the kinetics of 02 reduction is as important as the qualitative determination of the mechanism of 02 reduction. Several papers were devoted to the evaluation of the rate constants of the intermediate steps for the 02 reduction reaction. On the basis of the equations derived by Damjanovic et al. [2,6,7], the rate constant k 3 and the ratio of k~ to k 2 (see Fig. la for the definition of symbols) can be obtained from the intercepts and slopes of a plot of I a / I , vs. ~0 1/2 Bagotskii et al. [8-14] derived two sets to equations: one for an electrolyte saturated with 02 and the other for an electrolyte containing only H202. From the set of equations, a procedure was developed to calculated the rate constants k~, k 2, k z, k 3 and k 4 (Fig. le). Huang et al. [15] used the same method as Wroblowa et al. [3] to calculate k l / k 2 and k 6 (Fig. lb) for oxygen reduction on Pt in 85% phosphoric acid. Appleby and Savy [4] derived two equations for N I d / I , as a function of ~0- 1/2. One equation was concerned with the reduction of O 2 with H202 as a reaction intermediate and the other equation was concerned with the reduction of H202. The rate constants were obtained from the intercept and the slope of the plot of N I a / I r vs. kl Model

1

I

O2,b " ' ' 0 2 ,

~

k2

H202, ,

k3

t

~ H20

i H202,b

k1 I

Model

2

O2,b-~"~" O2,~ ~

k2

H202,*

k3 a..-H!20

i

H202,b

kl Model

3

02 b ~ O 2

I

k2

*

I

k4

I

k2

~H202 a

k3

""-H20

/ kl

Model

4

O2 b ~ O 2 , ,

: H202, a

k3

|

~ H20

k~ ~tk~ H202 *

t

H202,b kl

I

Model

5

O2,b- ~ " (~2,*

k2

a J/ k 6~--, 1H202, I k5 k4 H202,*

k3

|

-~--H20

i

H202,b

Fig. 2. Reaction schemes for the electroreductionof Oz considered in the present work.

82

~0-1/2 at different potentials. Based on a reaction model proposed by Bagotskii et al. (Fig. le), Van den Brink et al. [16] calculated the value of k 4 by measuring the ring current in a solution containing only H202, while the disc was kept at the open-circuit potential. The purpose of this work is to modify previous theoretical treatments of Damjanovic et al., Bagotskii et al. and Wroblowa et al., in order to calculate most of the rate constants for the intermediate steps of the models in Fig. 2. The rotating ring-disc electrode experimental data obtained for 02 reduction in Pt in 0.55 M H2SO 4 are used to illustrate the calculations of rate constants according to the present theoretical treatments. An analysis of the applicability of the various models is also made in this paper. A knowledge of the rate constants is essential in elucidating the role of electrocatalysts, electrolytes and anion adsorption on oxygen reduction kinetics and should lead to a rational basis for the selection of electrodes and electrolytes for oxygen reduction in fuel cells and metal-air batteries. MODIFICATION OF THEORETICAL TREATMENTS FOR THE CALCULATION OF RATE CONSTANTS

The main aim of the present theoretical work is to derive mathematical expressions which would permit the calculations of the rate constants of the intermediate steps for the O z reduction reaction from the rotating ring-disc electrode experimental data. For this purpose, each of the reaction models depicted in Fig. 2 will be used. It is assumed that oxygen reduction is taking place in the Tafel regime for both direct and series reduction paths such that the values of k 1, k 2 and k_ 3 are small and can be neglected in the analysis. In this section, the mathematical expressions are derived in detail for I d l / ( I d l - Id) and I d / I r as a function of ~0 for the model suggested by Damjanovic et al. (Model 1, Fig. 2). For the sake of brevity of this article, only the final expressions for I d l / ( I d l - Id) and I J I r are presented for the other four models (see the Appendix). Consideration of material balances for 0 2 . and H202. species in the model proposed by Damjanovic et al. (Model 1, Fig. 2) yields the following equations: Z , ~ ' / 2 ( C , b -- C,.) -- ( k 1 + k2)c,. =O(for 0 2 . )

(1)

k2C 1. -- ( k 3 -~ Z2¢a)l/2)c2. = 0 ( f o r H 2 0 2 , , )

(2)

where Z1 ~- 0 . 6 2 D ~ / 3 v Z2 =

1/6

0.62D~_/3v-1/6

(3)

(4)

The disc (Id) and ring currents (It) are given by: I a = 2SDF[(2k

1 + k 2 ) c ,. + k3c2. ]

I~ = 2 S D F N Z 2 c 2 . c f l / 2

(5) (6)

From eqns. (1), (2), (5) and (6), the relation between the concentration of 02. and

83

that of 02, b c a n be expressed by:

[ Ir/N+Id ] ct. = clb 1 irl/N + id l

(7)

It has been observed [6,7] that the ring current is much smaller than the disc current for O 2 reduction ( I r << I d and Irl << Idl)" Therefore, eqn. (7) can be simplified to: c,. = C,b[I -

Id/Idl ]

(7a)

Rearranging eqns. (2), (5) and (6), yields:

II dr

[ k']2 N1 1 + 2 ~_~

+

[ 2 ( k ' / k 2 2+ l )

]

k 3 to

(8)

which is the same equation derived by Damjanovic et al. [2]. Combining eqns. (1), (5) and (7a), gives: Idl kl + k 2 Id,--l~--l+~t°

1/2

(9)

This simple equation, which in combination with eqn. (8) is most valuable for calculating k 1 and k 2 independently, has not been derived in any of the previous theoretical treatments. The rate constants kl, k 2 and k 3 are calculated from the intercepts and slopes of the plot of Id/I r VS. to 1/2 and from the slopes of the plot of Idl/(Idl -- Id) VS. to 1/2 at different disc potentials. These rate constants are given by the expressions:

k, = S2Z,( I , N - 1)/( I,N +

1)

(10)

k 2 = 2Z,Sz/(I,N + 1)

(ll)

k 3 = Z2NS1/(I,N +

(12)

1)

By utilizing a similar procedure, the rate constants for the other four models (Models 2-5, Fig. 2) can also be calculated. The details are summarized in the Appendix. EXPERIMENTAL

A glass cell with one compartment for the test and auxiliary electrodes and another for the reference electrode was used in the electrode kinetics experiment. A platinum ring-disc electrode (Pine Instrument) with a collection efficiency of 0.176 served as the working electrode. It was mechanically polished with 25 /~m and 5/~m polishing powder and then with 1 /~m and 0.25 /~m diamond paste before the experiment. Potentials were measured against a dynamic hydrogen electrode (DHE) and the readings were converted to a reversible hydrogen electrode (RHE) scale. A large platinum gauze was used as the counter electrode. The potentials of the disc and the ring electrodes were controlled by a potentiostat (Pine Instrument RDE 3) and the rotational speed of the electrode was controlled by an analytical rotator

84 (Pine Instrument ASR 2). The currents at the disc and ring electrodes were recorded on a dual pen X - Y - Y ' recorder (Soltec 6431). The cell, the electrodes and the other glassware were cleaned with chromic acid (0.1 mol K2Cr207 dissolved into 1 1 H2SO4) followed by soaking in a 1:1 HzSO4/HNO3 solution for 8 h and then in double distilled water for another 8 h. The 0.55 M H2SO 4 solution was prepared by diluting concentrated H2SO 4 (ultra pure, Alfa, Ventron Div.) with double distilled water. The purity of the solutions was ascertained by the cyclic voltammetry. The cyclic voltammograms at a scanning rate of 50 m V / s between 0.05 and 1.45 V vs. DHE, were recorded after the solution had been deaerated N 2 gas. Before starting the R R D E experiments, 02 (99.999% pure) was bubbled through the electrolyte for 1 h. During the R R D E experiments, the potential of the disc electrode was scanned from 1.0 to 0.3 V vs. D H E at a scan rate of 5 m V / s , while the potential of the ring electrode was maintained at 1.1 V vs. D H E (this is a limiting current potential for the oxidation of H202 to 02). Experiments were carried out for a range of rotational speed from 400 to 4900 rpm at 25°C. Both N 2 and 02 gas were purified by passing the gases through three columns of molecular sieves (Alumina-Silicate basis, Union Carbide, Linde Div.). The first column of molecular sieve was heated to 200-300°C and the other two columns were at room temperature. RESULTS AND DISCUSSION M a s s transfer corrected Tafel behavior

From the R R D E experimental data, a plot of 1 / i a vs. 0~ 1/2 (Fig. 3) was made over the potential region from 0.7 to 0.4 V vs. RHE. In order to obtain i a from I a, the surface area of the disc electrode was calculated from the total charge of H-adsorption in the cyclic voltammogram of Pt in 0.55 M HzSO 4. The average solubility-diffusivity factor, D?/3Clbas calculated from the slopes of the plot of 1 / i a vs. ¢0-~/2 (for the potential range from 0.6 to 0.4 V vs. RHE) is 6.4 × 10 10 (cm2/s) 2/3 (mol/cm3). From this value, the limiting current densities (iaj) at different rotating speeds of electrode were calculated. The mass transfer corrected Tafel equation is given by: E = 2 . Rv 3 a n ~ logi0

RT

log[[

iali d ]

]

(13)

Fig. 4 shows a mass transfer corrected Tafel plot ( E vs. log idliJ[id~ -- id]) for 02 reduction on Pt in 0.55 M H2SO 4 (pH = 0). Within an accuracy of + 5%, this Tafel behavior is independent of ~ which covers the range of rotational speeds from 400 to 4900 rpm. The apparent limiting current density which is also independent of ~ is in all probability caused by a chemical reaction control prior to the first electron transfer step. The indication is that the adsorption of 02 is probably the rate determining step in the potential region more negative than 0.5 V vs. RHE; further

85

800

ELECTROLYTE : H2SO4 (0.55 M)

A

~

40C

/

I 11 ~ I i

//~,7/ 20C

~OT~N71~AL/V vs

//0 ~. ~/

/ ~

0 0.55 @ 050 D 0.40

//

0.'05

0

0110

0,115

o)-1/2,/ s 1/2

Fig. 3. 1 / i d vs. o~ ]/2 at various disc potentials.

r

I

i

I

I

0.8

hi :I: PC

x~t~ 0.7

> > d

0.6-

_< tz I.d I-0 n

05-

+ 400

rpm

A 900

rpm

X

0

1 600

rpm

°

2 500 3600

rpm rpm

x

\ q~

0.4

\

1

10-4

1

i

1

1

i

I i I 10-3

CURRENT

l

l

I

I

I

I

I

~ I

10-2

DENSITY/

A c m -2

Fig. 4. Mass transfer corrected Tafel plot for O 2 reduction on Pt in 0.55 M H 2 S O 4 at 25°C. The scale in the h o r i z o n t a l axis is for the m a s s transfer corrected current density, i d ] i d / ( i d l -- ia)-

86 study within this potential region should give more insight into the oxygen adsorption phenomenon. Evaluation o f the rate constants

The two critical expressions for the calculation of the rate constants are: (1) Id) as a function of ~ 1/2; and (2) I d / I r as a function of w 1/2 (except for Model 3 where it is assumed that there is no ring current). Figure 5 shows that the plot of I d l / ( I d l -- Id) VS. ~O-1/2 at different electrode potentials exhibits a linear behavior with an intercept equal to 1. This linear relation between Idl/(Id~ -- I d ) and ~0 1/2 indicates that k 4 is relatively small. For the models involving k4, this plot will not be linear (see Models 2, 3 and 5 in the Appendix). The plots of I d / I r VS. ~0-~/2 at various electrode potentials are given in Fig. 6 (from 0.75 to 0.55 V vs. RHE) and in Fig. 7 (from 0.55 to 0.35 V vs. RHE). From the plots of I d / I ~ vs. ~0- l/z, it can be concluded that the reaction mechanism undergoes a change as the electrode potential is shifted toward the negative direction. This becomes obvious if one examines the potential dependence of the intercepts and of the slopes of the straight lines of I d / I r vs. ~0-1/2 as shown in Fig. 8. The slope decreases as the potential becomes more negative in the potential region I (0.8 >/E >/ 0.7 V vs. RHE). In the potential region II (0.7 >/E >/0.5 V vs. RHE), the slope remains constant and the intercept decreases with decreasing potentials. In region III (0.5 >~ E , V vs. RHE), the slope increases and the intercept decreases as the potential decreases. Idl/(Idl-

16 POTENTIAL / V vs. RHE ---0'--- 0 . 5 0

ELECTROLYTE : H2S04 ( 0 . 5 5 M )

---£3-- 0.55 12

~

060 065 0.70

~ 8 L o

4

°o

0105

o'Io

0'15

to 1/2/S 1/2

Fig. 5. loll(

Idl

--

ld) as a function of co- 1/2 at various disc potentials.

87

150

,

i

POTENTIAL/ V vs. RHE ---0-- 0.75 0.70 0.65 ---A-- 0.60 ~ 0 - - O55

I0C

i

ELECTROLYTE: H2SO4 (0.55M)

5C

, 0.05

O0

! 01

, 0.15

e/-1/2/ sl/2 F i g . 6. l d / l r vs. o~ 1/2 in the p o t e n t i a l region 0 . 7 5 - 0 . 5 5 V vs. R H E .

Using Model 1, it is possible to calculate the rate constants over the entire potential range (from 0.8 to 0.4 V vs. RHE); the rate constants as a function of electrode potential are presented in Fig. 9. The potential dependence of k~ is nearly the same as the mass transfer corrected Tafel behavior. The ratio of k~ to k2 is about 5 - 1 2 and is potential dependent. Since k~ is larger than k2, 02 is mainly reduced to H20 via the direct four-electron transfer reaction path and only trace amounts of O~

150

POTENTIAL/ Vvs. RNE ---o--

/

~ ~

lOO~ - - 0 - -

/

ELECTROLYTE H2SO4 (0.55 M)

0.35

o.4o o45

/0/ / /

0.50

/

/

5

0

0.05

0.10

0.15

~o- 1/2/ 51/2 F i g . 7. I d / l r vs. w - 1 / 2

in the p o t e n t i a l region 0 . 5 5 - 0 . 3 5 V vs. R H E .

88

Intercepts [3 Slope

8OO

60£ z~

ELECTROLYTE : H2SO4 (0.55M)

O

4C

2C0

O

~

3

m,400

20C

REGION I ~{~ - 20

o.8

0'.7

REGION II

= [~

i

o.6 POTENTIAL

REGIONIII i

o'.5

/

V

0.4

vs. RHE

Fig. 8. Potential d e p e n d e n c e of the intercepts and the slopes obtained from the plot of l d / 1 ~ vs. ~

1/2.

are reduced to H 2 0 via the series reaction path which involves H202 as an intermediate. The rate constant k 3 is greater than k 2. This indicates that H202 is reduced to H 2 0 at a relatively rapid rate. Therefore, only a little amount of H202 diffuses into the bulk electrolyte as evidenced by the small ring currents. The faradaic efficiency for O 2 reduction is about 97%.

I

[

0.7

---O--O.e

>

L~

ELECTROLYTE:

~o

I~.

%

2_ o

i

10-4

I

10-3

I

10-2

10-I

RATE C O N S T A N T / c m s -I

Fig. 9. Rate c o n s t a n t s of i n t e r m e d i a t e steps for 0 2 r e d u c t i o n on IPI in 0.55 M H 2 S O 4. These c o n s t a n t s were calculated based on M o d e l 1.

89

Inapplicability of some of the proposed models

The linear behavior of Ial/(Id, -- Id) VS. ~0 1/2 for Pt in H 2 S O 4, suggests that k 4 is negligibly small. An attempt has been made to evaluate the values of k4 from the present experimental data according to Model 2 for which the expression of Ia,/(Id, -- Id) VS. ~0 1/2 is not linear (see the Appendix). The accumulated errors in the non-linear curve fitting procedure were quite large, and because of the small values of k 4 s o m e calculations even resulted in a negative value for k 4. Since a ring current was observed for the 02 reduction on Pt in 0.55 M HzSO 4, Model 3 can be excluded. The sum of the rate constant (k I + k2) calculated using this model is higher than the value based on Model 1. In order to calculate the rate constants k,, k 2, k 6 and k 3 / k 5 according to Model 4, it is necessary to have a linear relationship between the intercepts and the slopes (obtained from the plot of I d / I r VS. ~0- 1/2 at different potentials). In a previous work [17] such plots have been found to be linear only over a limited range of potential. A plot of intercept vs. slope from the present experimental data is given in Fig. 10. The non-linear behavior of the data points indicate that the assumption of k l / k 2 being independent of potential is not correct as evidenced by the results shown in Fig. 9. The same problems were also encountered with Model 5. Only over a narrow

I

r

POTENTIAL/V vs. RHE 0.725

20

°~ )/e~ e ~°.75 Q65-~) 0 / 0 . 6 7 5 Q 6 0 ~ I - 0-625

~o~ o5o'~ F-

10

g _z

0.40-

0

0

I 200

SLOPE

x 400

600

Fig. 10. Intercepts vs. slopes obtained from the plot of I d / l r VS. to-1/2 (Figs. 6 and 7).

90 potential region was it possible to obtain acceptable values of rate constants. The calculations sometimes even led to negative values of rate constants. It should be noted that Model 5 is the most complete reaction scheme for 02 reduction. The fact that it did not fit the present data is probably caused by too many unknowns (nine) and insufficient number of independent equations (five) as shown in Appendix (E). Additional experiments, such as oxidation or reduction of H202 in the electrolyte without the presence of O 2 will be needed to evaluate all the rate constants in the model. CONCLUSIONS A theoretical and experimental study has been carried out for the 0 2 reduction reaction on a platinum rotating ring-disc electrode in 0.55 M HzSO4. The analytical procedures for the calculation of the intermediate reaction rate constants were developed for various reaction models. It was found that a simple reaction model as proposed by Damjanovic et al. is consistent with the present experimental data. The results indicate that O 2 (97%) reduces to H 2 0 via a direct four-electron transfer reaction. At potentials more negative than 0.5 V vs. RHE, a chemical reaction step or an adsorption process prior to the charge transfer reaction becomes the rate controlling step. ACKNOWLEDGMENTS This work was carried out under the auspicies of the U.S. Department of Energy. Helpful discussions with Dr. S. Feldberg of Brookhaven National Laboratory and Professor E. R. Gonzalez of the Instituto de Fisica e Quimica de Sao Carlos, USP are gratefully acknowledged. The experimental work and part of the theoretical work reported in this paper were carried out by K.-L. Hsueh at Los Alamos during the period May 1981-August 1982. The contribution of K.-L. Hsueh is in partial fulfillment of the requirements for his Ph.D. degree in Chemical Engineering from Clarkson College of Technology, Potsdam, NY. NOTATIONS

Symbol Description

Unit

Clb cl, c2, Dl DR E F Id Ir

mol/cm3 mol/cm3 mol/cm3 cm2/s cm2/s V vs. R H E C/mol A A

concentration of oxygen in the bulk solution concentration of oxygen near the electrode concentration of H202 near the electrode diffusivity of oxygen diffusivity of H202 electrode potential Faraday's constant disc current ring current

91 I 1 id

idj irl

ki N n

R SD $1

S2 T OL

¢0

intercept of the plot of I a / I ~ vs. w-1/2 disc current density ring current density disc limiting current density ring current density at disc limiting current condition rate constants of step i collection efficiency charge n u m b e r of electron transfer per mole of O 2 gas constant surface area of disc electrode slope of the plot of I d / I r VS. oa I / 2 slope of the plot of I d l / / ( I d l -- Ia) vs. w -1/2 temperature transfer coefficient kinematic viscosity rotational speed of electrode

A/cm A/cm A/cm A/cm cm/s

2 2 2 2

J/mol • K cm 2 S

I/2

s -1/2 K cm2/s s- 1

APPENDIX

(A) Model 1 (reaction scheme proposed by Damjanovic et aL [2]) kl

Reaction scheme

O2,b~ O 2 ,

~ H202, .

" H20

H202,b

Assumptions

Material balance Expressions for current Expression for the calculation of rate constants Expressions for rate constants

(1) N o catalytical decomposition of H202. (2) The adsorption and desorption reactions of H 2 0 2 a r e fast and in equilibrium. (3) Rate constant for electrochemical oxidation of H 2 0 2 is negligible. For 02.,: Zlogl/2(Clb -- Cl. ) -- (k 1 -~- k 2 ) c l . = 0 For H202: k2Cl, - (k 3 + Zzwl/2)c2, = 0 Disc current: I d = 2 S D F [ ( 2 k 1 + k2)cl. + k3c2, ] Ring current: I r = 2 S o F N Z 2 w l / 2 c 2 , Id/Ir

1 + 2 k J k 2 2(1 + k l / k 2 ) N + NZ 2 k3 w - 1/2

_ Idl -- 1 + -kl - + wk 2 ldl - ld Z, IIN- 1 _

= s

z,/-7V71 2ZIS 2

k2= I,N + 1

- 1/2

92 Z 2 NS 1

k3-

I1N+ l where 11 and S 1 are the intercept and slope of the plot of I o / I r vs. ~0-1/2 respectively. S 2 is the slope of the plot of I d , / ( I d , - Id) VS. CO-1/2.

(B) Model 2 (reaction scheme proposed by Bagotskii et al. [9])

Reaction scheme

.I

02, b -~l-- 02,~

k2

k3

~ H202,*

!

~H20

H202,b

Assumptions

(1) The adsorption and desorption reactions of H202 are fast and in equilibrium. (2) Rate constant for electrochemical oxidation of H202 is negligible.

Material balance

For 02.: Z l o D l / Z ( C l b - - C l . ) - F k 4 c 2 . - - (k I + k2)Cl. = 0 For H202,.: kzcl. - (k 3 -F k 4 4- Z2~1/2)c2 . = 0

Expressions for current

Disc current: I d = 2 S D F [ ( 2 k ~ + k2)cl. 4- k3c2. ] Ring current: I r = 2 S D F N Z 2 w l / 2 c 2 .

Expressions for the calculation of rate constants

I d - 1 ( 1 + 2 k l ] + (k3 + k4)(1 + 2 k , / k 2 ) + k 3 o _ , / 2 I, N k2 ] NZ2

Idl

1 + ~

,dl-,d (

o

Zl

-1/2

1 + 2SDFNZ1Zzq b

Expressions for rate constants

k~ = A 2 ( I z N 1 ) / ( h N + 1) k 2 = 2 A z / ( 1 2 N + 1) k 3 = ( S 3 N Z 2 - I 2 N A 3 ) / ( L N + 1) k 4 =-,4 3 where 12 and S 3 are the intercept and slope of the plot of I d / I , VS. oa-1/2. A 2 and A 3 are obtained by least square fitting of the equation: r 1

I d l - Id

- - 1 + ( k 1 + k 2 ) oa

I/2

Z1

where A 2 = k~ + k 2 and A 3 = k 4

Irldl k 4 2 S D F N Z I ZzClb ( Idl -- 1a ) Oa

93 (C) Model 3 (reaction scheme for oxygen reduction in which no ring current can be detected) kl I

k2

k3

Reaction scheme

02 b ~ O 2

Assumptions

(1) N o H202 diffuses into the bulk. (2) Rate constant for electrochemical oxidation of H202 is negligible. F o r 0 2 . : Zffol/2(Clb -- Cl. ) + k4c2. - ( k 1 + k2)cl. = 0 For H202,.: k2Cl. - ( k 3 + k4)c2. = 0 Disc current: I d = 2SDF[(2kl + k2)Cl. + k3c2.]

Material balance

Expressions for current Expressions for the calculation of rate constants

Expressions for rate constant

,

f

~ H 2 0 2 ca

~ H20

k4 /

Idjld kzk3 2 S D F C , b ( I d , - Id) = 2k, + k 2 + k3 + k~ Id~ = 1 + 1 Ial - la ~ (kl + k2

k4k2 )~o 1/2 [<3 4- k 4

kl + k2 = 2 S D F c l b ( I d l - - l,a) -- Z1S4 where S 4 is the slope of Idy(Idl -- Ia) vs. w - l / z

(D) Model 4 (reaction scheme proposed by Wroblowa et al. [3] with

k 4

neglected)

kl

Reaction scheme

o2 b - - o2,.

k2

= H2O2,o

k3

"1

~ H2o

k~ 4Ik~

14202 *

t

N202,b

Assumptions

(1) No catalytical decomposition of H202.

Material balance

(2) Rate constant for electrochemical oxidation of H zO z is negligible. (3) k I and k 2 have the same potential dependence. For 0 2 . . : Z I ~ O 1 / 2 ( C l b - - Cl. ) -- (k I + k2)Cl* = 0 F o r H 2 0 2 , . : k2Cl. q- k 6 c 2 . - ( k 3 4- k 5 ) c 2 a = 0 F o r H2O2.a: k5c2a - ( k 6 + Z 2 0 2 1 / 2 ) c 2 . = 0

Expressions for current

Disc current: I~ = 2SDF[(skl + k2)cl. + k3c2~] Ring current: I r = 2SDFNZzc2.~ 1/2

Expressions for the calculation

Idl Idl _ Id

of rate constants

id

1

I~-

N

1+

k~ + k= ~/2 Z1 ~0

1+

+ 2k-2z

~k ~

+2~

94 Expressions for rate constants

k, = S ~ Z , ( I 4 - 1 ) / ( I 4 + l)

k: = 2 S 2 Z , / ( I 4 + 1) k 6 = Z2/S 6 k 3 / k 5 = S s & / ( I 4 + 1) where S 2 is the slope of the plot of I a l / ( l a l - Ia) vs. ~ 1/2 I s and S 5 are the intercept and slope of the plot of I a / I r vs. ~o-1/2, respectively. 14 and S 6 are the intercept and slope of the plot of N/s vs. NSs, respectively.

(E) Model 5 (reaction scheme proposed by Wroblowa et al. [3])

kl Reaction scheme

O2,b~O2,*

I

k2

~ H202, o

k3

~ H20

H202,*

I H202,b

Assumption Material balance

Expressions for current Expressions for the calculation of rate constants

(1) Rate constant for electrochemical oxidation of H202 is negligible. For 02,.: ZlOal/2(Clb -- cl. ) + k4c2a - (k~ + k2)c~. = 0 For H202,a: k2c~. + k6c2. - (k 3 + k 4 + ks)c2a = 0 For H202,,: k5c2a - (k 6 + ZIODI/2)C2. = 0 Disc current: I d = 2 S D F [ ( 2 k 1 + k2)cl. + k3c2. ] Ring current: I. = 2SDFNZ2wl/2c2.

Ial

( k , + k 2 - Z,w ' / z )

Id~ - Ia

( k4k6

\

+ k4

1/2

)I, --

Zl~l/2

2SDFNZzool/Zclb Id 1 2 k, (k3+k4) I r - N 1 + k2 + [2 kl k2k5

2k3+k4]

+

k~

1 k l ( k 3 + k4) 2k3 + k4 k6 1/2 + -~2 k2ks + k5 Z2 w Expressions of rate constants

kl=

A3[IsN-

1 - (Z2AxSv/A,) ]

IsN + 1 -(ZzA2SvN/A,)

k2=

2A3

IsX + 1 - ( ZzA2SvN/A1) k 6 =ALIA 2 k3 (ZzAzSvN/A~) - [NI 5 - (Z2AzS7N/A,)]A2 ks k 4/k 5 = A z

2[I5N + 1 - (ZzAzSvN/A,) ]

where 15 and S v are the intercept and slope of the plot of I J I r vs. w-1/2. A1 ' A2 and A 3 are obtained from the least

95

square fitting of equation: ,/2 _

2SDFNZ2ool/2Clb

,/2

Id~I7 (,d_,d,)l 'd'-'d Ia

where A 1 = kak6/k

5

A 2 = k4/k 5 A 3= k 1+ k 2

REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14

L. Muller and L.N. Nekrasov, Electrochim. Acta, 9 (1964) 1015. A. Damjanovic, M.A. Genshaw and J.O.'M. Bockris, J. Chem. Phys., 45 (1966) 4057. H.S. Wroblowa, Y.C. Pan and G. Razumney, J. Electroanal. Chem., 69 (1976) 195. A.J. Appleby and M. Savy, J. Electroanal. Chem., 92 (1978) 15. R.W. Zurilla, R.K. Sen and E. Yeager, J. Electrochem. Soc., 125 (1978) 1123. A. Damjanovic, MIA. Genshaw and J.O'M. Bockris, J. Electrochem. Soc., 114 (1967) 446. A. Damjanovic, M.A. Genshaw and J.O'M. Bockris, J. Electrochem. Soc., 114 (1967) 1107. M.R. Tarasevich, Elektrokhimiya, 4 (1968) 210. V.S. BagotskiL V.Yu. Filinovskii and N.A. Shumilova, Elektrokhimiya, 4 (1968) 1247. V.S. Bagotskii, M.R. Tarasevich and V.Yu. Filinovskii, Elektrokhimiya, 5 (1969) 1218. M.R. Tarasevich, R.Kh. Burshtein and K.A. Radyushkina, Elektrokhimiya, 5 (1969) 372. M.R. Tarasevich and K.A. Radyushkina, Elektrokhimiya, 6 (1970) 376. K.A. Radyushkina, M.R. Tarasevich and R.Kh. Burshtein, Elektrokhimiya, 6 (1970) 1352. M.R. Tarasevich, K.A. Radyushkina, V.Yu. Filinovskii and R.Kh. Burshtein, Elektrokhimiya, 6 (1970) 1522. 15 J.C. Huang, R.K. Sen and E. Yeager, J. Electrochem. Soc., 126 (1979) 786. 16 F. van den Brink, E. Barendrecht and W. Visscher, J. Electrochem. Soc., 127 (1980) 2003. 17 W.E. O'Grady, E.J. Taylor and S. Srinivasan, J. Electroanal. Chem., 132 (1982) 137.