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Determination of the kinetic parameters of the oxygen reduction reaction using the rotating ring-disk electrode
305
Chem., 229 (1987) 305-316 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
J. Electroanal.
DETERMINATION OF THE KIN-ETIC PARAME TERS OF THE OXYGEN REDUCTION REACTION USING THE ROTATING RING-DISK ELECTRODE PART I. THEORY *
N.A. ANASTASIJEVIC, V. VESOVIC and RR. ADiIC Institute of Electrochemistry, ZCTM und Center For Multidisciplinoty P.O. Box 815, Belgrade (Yugoslavia)
Studies. University of Belgrade,
(Received 5th January 1987)
ABSTRACT A general scheme of oxygen reduction is given and analysis of the disk-ring measurements is performed. Expressions for the diagnostic criteria for such a scheme have been derived and their implications are discussed. The existence of superoxide and oxygen ions and the interaction of the series and direct paths have been assumed in postulating the scheme. Also, all the electrochemical reactions involved only one-electron exchange. The possibilities and limitations of the disk-ring measurements in the mechanistic study of oxygen reduction are discussed together with a reevaluation of some wellaccepted criteria which are shown to be misleading. New definitions and terminology for different pathways of 0, reduction are proposed.
INTRODUCTION
Oxygen reduction is one of the most investigated electrochemical reactions because of its paramount importance for electrochemical energy conversion (see ref. 1 and refs. cited therein). One of the most commonly used experimental setups to elucidate the mechanism of this reaction has been the rotating ring-disk electrode, because it enables the quantitative detection of some of the intermediates [2]. In order to analyse the ring-disk results it is necessary to postulate the reaction scheme. Since the first proposition by Damjanovic et al. [3], several reaction schemes have been analysed [4-81. The merits of various schemes have been considered by Hsueh et al. [9]. One of the difficulties in analysing the correct scheme is that the number
* In honour of Professor H. Gerischer on the occasion of his retirement as Director of the Fritz-Haber Institute. 0022-0728/87/$03.50
8 1987 Elsevier Sequoia S.A.
306
of experimentally obtained quantities from the disk-ring measurements is usually not sufficient to determine all the parameters of the model. Consequently, simple schemes have been considered in the past. Unfortunately, oversimplification in some schemes had undesirable effects. For instance, the failure to consider the adsorption/desorption equilibrium of hydrogen peroxide [3] led to insufficient diagnostic criteria regarding the series and direct paths for O2 reduction [5]. In this work we have tried to construct a reaction scheme which includes nearly all the possible intermediates discussed in the literature. In doing so, the direct four-electron path has been further analysed in terms of strongly adsorbed intermediates. Also, the possibility has been allowed for interaction between a series and a direct path which has not been considered before. Further analysis of ring-disk currents based on this scheme allowed a critical comparison with the conclusions drawn from previous schemes. The further aim of this work is two-fold. Firstly, to elucidate the reaction mechanism of oxygen reduction as far as possible in terms of particular reaction steps and rate constants. Secondly, to analyse the electrochemical data in the light of this new scheme and to assess how much detailed information about the particular reaction steps electrochemical measurements can furnish. THE REACTION SCHEME
Consider the following scheme of oxygen reduction (Fig. 1). The k, are overall rate constants for the ith step and subscripts sa, a, b and * denote strongly adsorbed, weakly adsorbed, bulk and the vicinity of the disk electrode, respectively. The scheme has been written for alkaline soiutions, but it can easily be transformed, mutatis mutandis, into an analogous scheme for acidic solutions. The following electrochemical reaction steps have been postulated:
Fig. 1. General scheme of oxygen reduction.
kl Oca+ H,O + e- .z HO,,+
OH-
k-2
o,+e-
k,\ 0;
(Cl
O,+e-
S
(Cl
O&,+
0:
H,O + e- k,\ H02$+
OH-
(D)
HO& + e- k! O;+OH5 OS; +e-+HzO
k,\ 20H-
(F)
It is worth pointing out that eqn. (E) is very irreversible in acid media [lo]. The following chemical reactions have been taken into an account on the basis of the behaviour of adsorbed intermediates in aqueous [ll] and non-aqueous solutions
[W 2 O&+ H,O %
O,,a + HOz+ + OH-
k
2H0,,+20H-+Oz,a HO,, o,,
k,,\ OH- + 0, k,,\ o,+oi
(G) (H) (I)
(J)
Some of these intermediates have been considered in Vetter’s classic book [13]. Most of these reaction steps are not single-step processes but can actually involve a few reaction steps themselves. No attempt has been made to probe these reaction steps further, because the electrochemical data up to now are unlikely to be able to distinguish among them. A special feature of the above scheme is that no reaction step involves the exchange of more than one electron. It has been postulated that oxygen reduction proceeds through the adsorption of 0, and its intermediates on the electrode surface. Sufficient evidence for this is the strong electrocatalytic behaviour of this reaction which can be illustrated by different reaction rates on the basal plane of pyrolytic graphite with and without cobalt tetrasulphonated phthalocyanines [14] and on single-crystal gold electrodes of different orientations [15,16]. Also, the scheme of Fig. 1 is a generalization of the schemes proposed so far [3-81 and, as before, it consists of two major paths by which the oxygen reduction can proceed. It is postulated that the direct path involves strongly adsorbed species, while the first step in a series path is the formation of a weakly adsorbed oxygen molecule. On the strongly adsorbed sites,
308
reactions proceed mainly as irreversible processes (k3, k,, k12, k,,) where the strongly adsorbed species are chemisorbed. It is postulated that such strongly adsorbed species cannot desorb directly and go into solution. The series path, on the other hand, proceeds through weakly adsorbed species, where the energy of adsorption is of the same order of magnitude as kT. These species are most likely to be physisorbed. In this case, some kind of adsorption-desorption equilibrium with corresponding species in solution (k,, k_, and kz5, k_25) is established. In addition, it has been assumed that the reaction constants for the same reaction will differ depending on whether the reactant is weakly or strongly adsorbed (k2 and W In previous work [3-91, the series path has been treated in much more detail compared with the direct path. The major difference in the series path of the scheme of Fig. 1 is in the explicit inclusion of a superoxide ion O$. The formation of this ion is a logical consequence of the oxygen molecule receiving an electron (k,). Even though the superoxide ion O,,- is very unstable in aqueous solution [ll], its existence has been reported in a number of studies [11,12,17]. It seems that the adsorption of superoxide ion on electron donor sites stabilizes the adsorbed particle due to electron occupation of the unoccupied nz* antibonding orbital (Table 1). The implicit assumption made when constructing the scheme of Fig. 1 was that Oz$ superoxide ion is not in equilibrium with the solution. This appears to be a reasonable assumption since the O,TBsp ecies is unstable in aqueous solution and undergoes rapid chemical and electrochemical transformations. In addition it would show up in the ring-disk measurements, whose analysis implies that only one intermediate species is discharged on the ring. This second point will be discussed in more detail when the ring-disk equations are developed. The weakly bound superoxide ion can react with a proton and an electron (k,) to form HOz,, or it can decompose chemically into HOzVaand oxygen (k,,) [12]. It has been shown 1191 that most of the chemical d~mposition takes place on the electrode and not in solution. The formation of hydrogen peroxide as an intermediate in oxygen reduction is well established and its presence is incorporated in nearly every proposed scheme [3-81. Here, the standard practice of assuming hydrogen peroxide to be in equilibrium with its counterpart in the bulk is followed. Also, the chemical decomposition of HO,Ta (k,,) [ZO]has been included. TABLE 1 Influen~ of the numberof a&bonding &xtrons (9: ) on the characteristicsof the O-O bond in O$’*P WI Species
Numberof vz* electrons
0: 02 0; 0;-
1 2 3 4
O-O distance /m 0.112 0.121 0.133 0.149
PO-0 /cm-’ 1860 1556 1145 770
309
A further difference between this scheme and previous schemes is that the possibility has been allowed that the weakly adsorbed intermediates from the series path can undergo surface diffusion and form their strongly adsorbed counterparts in the direct path. The effects of surface diffusion of intermediates in oxygen reduction have been mentioned by McIntyre and Peck [Zl]. Therefore, it is no longer possible to represent the direct path as one overall process with a specific rate constant, since there is now an interaction between a series and a direct path. It has been assumed that surface diffusion of the strongly adsorbed species is not energetically favourable. In the previous schemes [3-g] the direct path was treated as a black box and only the overall rate constant for a four-electron exchange was quoted. Even though some suggestions have been made about the nature of the direct process [1,4-g], no analysis of the disk and ring currents has been made. In the scheme of Fig. 1, it has been postulated that the first step in a direct four-electron transfer is the formation and immediate dissociation of a chemisorbed oxygen molecule (kzl or k,,) which cannot desorb back to the bulk. According to the gas-phase literature 1221, the strongly adsorbed oxygen molecule is very unstable and it dissociated immediately into atoms. Once it is formed, the chemisorbed oxygen molecule exchanges an electron (k3) and forms an oxygen ion OS;. This in turn can, by exchanging a further electron, either be reduced to OH- (k6) or be oxidized to a strongly adsorbed peroxide HO& (k_,). On the other hand, the formation of strongly bound superoxide ion proceeds through k,,. O& is less stable than the physisorbed superoxide ion owing to the nature of the bonding to the surface, and therefore it undergoes a relatively fast transformation. It is either transformed electrochemically into a strongly bound hydrogen peroxide (k4) or it undergoes chemical d~mposition (k& into OS; and 0,. The existence and chemical identification of the adsorbed intermediates can only be proven conclusively by the use of spectroscopic techniques. Fortunately, the existence of a strongly bound peroxide can be inferred from electrochemical me~urements. Dubrovina and Nekrasov obtained [23] three plateaus of the disk diffusion limiting current which correspond to one, two and four electrons exchanged, respectively. No increase of the ring current corresponding to the second plateau, i.e. 0, reduction to H,O,, was observed. This implies that a species which has exchanged two electrons has not left the disk electrode. The species in question is most likely strongly adsorbed hydrogen peroxide. Once HO;= has been formed, it can either exchange an electron and form OS; or it can d&so&ate chemically (k,,) into OH- and OS,. The reaction constant k12 and the similar reaction constants klO, k,, and k13, which are defined by purely chemical reactions, can be related to the dismutation reaction constants discussed in ref. 1. Even though some of these reactions are found to be second order when they take place in solution (k,,) [If], we will follow the common practice [l-19] and assume them to be practically first order when proceeding through adsorbed states. The justification for such a choice
310
lies in the fact that the assumption of the reactions being second order is inconsistent with the behaviour of the experimentally measured ring and disk currents. THE N&,/Z,
VS.
w-O5 PLOT
~~j~o~~ et al. [3] were the first to use this plot to obtain a distinguishing between the direct and the series path. Postulating reaction steps follow first-order kinetics and by performing material each component for steady-state conditions, the followiug equations for the scheme of Fig. 1: 0 2. *
:
ZPO%,b
0 2,a
1
bocl,.
QG
:
kcx.a
OzTsa
:
k23C2,a = 0%
HO,,
:
k25c3,a
HO<,
:
(kz+k,o/2)c,,,+k-,,c,,.
HO<,,
:
k2ec3.a
0,
:
2ksx,.
0,;;
:
kc3,sa
-
Cl,* 1 + k-2OCl,a
+ 0.5h0e2,~
=
Oh
+ hh,* + k-20
+ huh,,
+ k2 + k,,)c,,,
+ k3ha
= (k-25
+ Z,W”.~)C~,
+ bc2,sa
f
w = (~-2+k2~+k~+k~~)c3,~
+ k-se,
+ =22cl,a + k,c,
+ 0.%lc3,a
= ko
+ k-s3,a
= &I
criterion for that all the balances on are obtained
= @a
+ kdc3,sa
+ k13~2,sa + k12C3,sa = be
k13C2,sa = (k,
+ k-dc,
For clarity, the subscripts 1, 2, 3, 4 and 5 have been used for the oxygen molecule, superoxide ion, hydrogen peroxide, oxygen atom and oxygen ion, respectively, and Z, = 0.62 D2/3/~‘/6, where D is the diffusion coefficient and Y is the kinematic viscosity. The disk current is given by
while the ring current is given by I R = n RANFZ 3w”-‘c3,*
09
where A is the disk area, N is the collection efficiency, w is the rotation frequency and rra is the number of electrons exchauged on the ring electrode. nR is not necessarily a whole number but can in fact vary with the potential [24]. By dividing eqn. (10) by eqn. (11) and using eqns. (2)~(9) to eliminate the concentration ratios, one obtains NID/IR = 2(1+ A, + A,k_25/Z3w0.s)/nR
(12)
where A, and A, are ~rnp~cat~ dimensionless functions of the reaction constants which are given in Appendix 1. The most interesting feature about eqn. (12) is the linear relationship between AVo,/IR and W-O.‘. This behaviour has also been observed in earlier and much
311
simpler schemes of oxygen reduction [3-91 which among other things do not include the possibility of interactions between the direct and series paths. Thus, the electrochemical evidence alone, based on investigation of the disk and ring currents, does not allow us to assume independence of the two paths. This in turn makes the whole concept of the series and the parallel path slightly doubtful. Furthermore, the same linear function dependence of NZr,/Za on W-O.’ will be observed if one neglects the back reactions (k_,,, k_,, k_,). In fact, any system whose elementary path reactions are first order with respect to the reactants and which has only one process taking place on the ring would give a linear dependence of NZ,/Z, on w-o.s The conclusion of their scheme, which equilibrium for H,O, does Wroblowa et adsorption-desorption
Wroblowa et al. [7] was that no criterion could be made, for would distinguish whether or not the adsorption/desorption existed. However, eqn. (12) contains this information and so al’s [7] scheme. For k_,, = 0, implying the lack of equilibrium eqn. (12) simplifies to
NZD/ZR = 2/n,(1+
A,)
(13)
Therefore, if the ratio of the disk current to the ring current is independent of the speed of rotation at each potential, no equilibrium is established. If two intermediates react on the ring, the following behaviour should be observed [25]: NZr)/ZR = (Do + D,wO.S + D*w)/( D,w”.s + Z&w)
04)
where the 0, are the ratios of the reaction rate constants. Hence, the non-linearity of the plot Zr,/ZR vs. W-O.’ implies either the possibility of the existence of more than one process on the ring or that some of the reactions involved are not first order with respect to the reactant. THE J-S
PLOT
A further diagnostic criterion, as suggested by Wroblowa et al. [7], was to compare the dependence of the intercept, J, on the slope, S, of equations equivalent to eqn. (12). For the scheme of Fig. 1, the following J-S dependence is obtained: J = 2(1-t A&n,
+ 2$/k_,,
05)
where A, is given by 4
= (kxAs
+ k,,A,/k,
+ kd/(k,
+ k,o/2)
(16)
and A, and A, are given in Appendix 1. So far, this criterion has been used to distinguish between the series and the parallel paths [7]. Specifically, the experimentally obtained linearity of the J-S function has been explained by the same potential dependence of the reaction rate constants defining the series and the direct path [7]. Also, the unity intercept of the linear J-S plot has been taken to imply non-existence of the direct path. It is obvious from eqn. (15) that the J-S function is not in general linear but a strong
312
function of the potential. There are in fact three characteristic shapes of the J-S plot: (1) A non-linear J-S plot is obtained when a reaction goes through both strongly and weakly adsorbed intermediates. (2) A linear J-S plot, which has been observed experimentally in some cases, arises under the following conditions: the diffusion of weakly adsorbed oxygen molecules and superoxide ions is slow and can be neglected ( kz2 = k,, = 0); the first electrochemical step is much faster than the desorption of oxygen molecules (k, z+ k_,); the second electrochemical step is much faster than the catalytic decomposition of weakly adsorbed superoxide ions (k2 B k,,). Then the intercept with the J-axis, J’, of the linear J-S plot eqn. (15) is given by
J’ = 2/n, 0 + k,,/k,o)
(17) Therefore, from the value of J’ it is possible to evaluate the ratio of the direct to the series path. This equation differs considerably from the expression for J’ given by Wroblowa et al. [7]. A condition of the linearity and J’ > 1 in their expression is the same potential dependence of the rate constants for the exchange of four and two electrons in the direct and series paths, respectively. It is difficult to verify this assumption. For the rate constants k,, and k,,, representing adsorption of O2 and 0, it is easier to envisage the same potential dependence. Further implications of eqn. (17) will be discussed in Part II of this work. (3) It is interesting to note that if there is no formation of strongly bound oxygen (k,, = 0) and the diffusion of the weakly bound oxygen species is slow (k,, = k,, = 0), eqn. (15) reads
J = 2/n,
+ Z,S/k_,,
(18)
where S is given by S = 2k-,,(ki, + &,)/nnZ&,s 09) Assuming that the rate constants used in eqns. (16) and (19) are not functions of the potential, J and S are also independent of the potential. The J-S diagram is therefore given for such a case as a point. Further implications of eqns. (18) and (19) will be discussed in Part II of this work. THE &,/(I‘,,
- I) vs. w-O5 PLOT
This plot has been used by Hsueh et al. [9] as an additional equation for the determination of some constants in the simpler schemes [26]. In deriving the above relationship, they have assumed, as in all the cases so far for O2 and H202 reduction [l-9], that in the diffusion limiting current region the number of electrons exchanged per 0, and H,O, molecules is four and two, respectively. Since 0, reduction is a complex reaction involving a large number of paths each exchanging a different number of electrons, it is not possible to take the number of electrons as a constant independent of the potential [24]. Therefore the diffusion limiting current is given by Zdl = n D FAZ 1 w’,~
(20)
313
where no is the average number of electrons per molecule of the reactant exchanged on the disk at each potential. Using eqns. (10) and (20) together with the mass balance equations, one obtains after long and tedious algebra the following expression: Z&Z,,
- I) = (B, - Z~W’.~)/( B, + B,/n, /n,n,NFAZ,w”~5c,,,
+ (B,Z,w’.’
- Z,W’.~)
- B,)I, (21)
where B, to B4 are complicated expressions involving rate constants and are given in Appendix 2. Equation (21) is in a form very similar to the corresponding equation in Hsueh et al.‘s work [9] which has been derived for a much simpler scheme. It is obvious that eqn. (21) in its present form does not show a linear relationship between Z&Id, - I) and w -o.5 On the other hand, some experimental results [9,26] show a linear behaviour between these two quantities. It is therefore interesting to determine under what conditions eqn. (21) will be reduced to a linear one. It will be valuable at this point to digress slightly from eqn. (21) and to consider an overall problem of the type 0, + products
(K)
where the reactant 0, diffuses to the electrode and there reacts with an overall rate constant k, exchanging in the process n,, electrons. The solution to this overall problem in terms of the diffusion limiting current is easily obtained [2,24,27] and the expression for Z&Id, - Z) reads I,,/( Z,, - I) = 1 + k/Z,w0.5
(22)
Equation (22) has been derived under the assumption that only one reactant, namely O,, diffuses to the electrode and there undergoes a first-order overall reaction which takes place on the surface and not in the solution. Under these conditions, Zd,/(Zd, - I), vs. w -OS shows the desired linear form. On the other hand, when deriving eqn. (21) it has been assumed that some of the peroxide diffuses back from the solution (k_25); hence the overall process cannot be given by eqn. (22). Therefore, for situations where the flux of hydrogen peroxide from the solution, k_,,c,, . , is negligibly small, both models are identical and eqns. (21) and (22) should be equivalent. In other words the non-linearity of eqn. (21) can be ascribed solely to the non-negligible hydrogen peroxide flux from the solution rather than, as some workers have previous thought [9] to non-existence of the catalytic reaction. If the flux is small, eqn. (21) reads I,,/( Id, - I) = (B, - Z,W’.~)/(
B, + B,/n,
- Z,W’.~)
(23)
Since eqns. (22) and (23) are identical, n D = - B,/B,
(24)
which gives us an expression for the average number of electrons exchanged per molecule of oxygen reacted as a function of the potential.
314 EXPRESSIONS
FOR nD AND
k
The explicit dependence of the number of electrons exchanged on the potential has already been discussed for a simple scheme [24]. For our model, the equivalence of eqns. (22) and (23) allows us to obtain easily the explicit dependence of the number of electrons exchanged and the overall rate constant on the specific rate constants and therefore the potential as well. By using the expressions for B, and B, given in Appendix 2 in eqn. (24), one obtains n D = 4 - (2k, + ‘h + 4 ( b(2k, + k20 - 2k,2 )/b - k,,)/A9 (25) where A, and A, are given in Appendix 1. Also, by further comparing eqns. (22) and (23) one obtains the explicit expression for the overall rate constant k in terms of the specific rate constants: k=
-B,
(26) - k-,&)/k,(4 -&4,/2) (27) to note that expressions (25) and (27) have been derived under the IdJ(ldl - 1) vs. w-0.5 is linear. In situations where this is not the of electrons exchanged and the overall rate constants are given by and (27), only as a first approximation.
k = km + k,, + (A,k-,k,
It is important assumption that case, the number expressions (25) CONCLUSIONS
A general scheme of the reduction of oxygen is given. All the electrochemical processes are represented as at most one-electron exchanges. The existence of superoxide and oxygen ions is assumed. Analysis of the ratio of the disk current to the ring current for this scheme shows that some of the well-accepted criteria used in analysing the results of oxygen reduction can be misleading. The concept of two independent pathways, namely series and parallel, is doubtful since there are no physical reasons why a weakly adsorbed intermediate cannot diffuse along the surface and become more strongly adsorbed. The linearity of the NID/IR vs. w -‘s function is a general characteristic of any scheme whose reactants are first order with respect to the corresponding reacting species and where only one intermediate is discharged on the ring. The J-S plot in general is not linear but is a function of the potential. A non-linear plot is obtained when a reaction goes through both strongly and weakly adsorbed intermediates. Under specific conditions, a linear J-S plot is obtained in which case the ratio of the direct to the series path can be evaluated. Surprisingly enough, the J-S plot is represented by a point when only a series path is operational, if the catalytic decomposition of hydrogen peroxide is not potential-dependent. The explicit dependence of the number of electrons exchanged and the overall rate constant in terms of specific rate constants on the potential are given. Thus it would seem that in general it is not possible using electrochemical measurements alone to decide on the correct scheme of oxygen reduction. However,
315
with some simplifications a considerable amount of information can be obtained. The use of spectroscopic methods able to detect the adsorbed intermediates is therefore highly desirable if a complete elucidation of the oxygen reduction mechanism is to be performed. There is considerable non-uniformity in the terminology for the reaction schemes for Oz reduction [7-91; in particular, the term “series” lacks precision. We propose somewhat modified terms with a new one resulting from the scheme in Fig. 1 for which a criterion has been obtained. The following pathways can be defined: (1) “direct” four-electron reduction without hydrogen peroxide detected on the ring; (2) a two-electron “series” pathway involving reduction to hydrogen peroxide; (3) a “series” pathway with two- and four-electron reduction. In the case of only four-electron reduction without hydrogen peroxide detected on the ring, the case is indistinguishable from a “direct” four-electron reduction; (4) a “parallel” pathway which is a combination of (l), (2) and (3); and (5) an “interactive” pathway in which diffusion of species from a “series” path into a “direct” path is possible. ACKNOWLEDGEMENTS
This work was financed by the Yugoslav-American Fund for Scientific and Technological Cooperation in cooperation with the National Science Foundation, Contract No. 471 U.S.A., and by the Research Fund of SR Serbia, Yugoslavia. APPENDIX I
Expressions for A’s in eqn. (12) Ao=A,+A3 A, =A,@
640) +A,)/kz
(Al)
-A,
A,=k,,+k_,+k,
(A21
kuA,/kl + kzd/(k,
A, = (k,,A,
+
A, = (k,,A,
- k,
A, = ((kz A, = (2(k,
+ k-,(k,
+ k-zo + k,)A,
+ 2k,d/k,)/k,,
644) 645)
- k,ok&/k,k,
+ k-zo + kdk-,
A, = (k, + k,o)/(k,,
(A3)
+ k,o/2)
+ k,,k,)/k,ok,
bw (A71
+ Ad
A, = k,, + k, + k,, A,
= Adk,
A,, = Mk,,
+ k,,Vk,
w3) + k,dA,o
+ k-20 + kd(k,o
- ATA&) + k, + kd
- A,k-
z (kl
- klk,o)Pk,kzo
+ km
I/k,
- k,o/2
(A91 (AlO)
316 APPENDIX 2
B, = -@*o
+ k21) + @,k-,k*
B2 = B,(4 - ((2k, B, = B,B,
-k-,0&)/(&
+ km) + B,(k-2(2k,
(Bl)
- &4,/2)/k,
+ km - 2k,,)/k,
-k&A,)
+ (2kzA,)/A,
B4 = ((4B1k21-
Bdkm
(B3) + kdAd2
+
-2B,(k,,-k-2(2k22-kl+B*k20/4Bl)/kl)/A2) B, = ((nk,,
+ k&n
Bs = -2k,,A4/A2 B, = (kz + k&A,
032)
- 4))A,/2 - nkA,
- 2k-,(2kz,
(B4) - k, + nk,,/4Vkd/A,
VW (W (B7)
REFERENCES 1 M.R. Tarasevich, A. Sadkowski and E. Yeager in B.E. Conway, J.O’M. Bockris, E. Yeager, S.U.M. Khan and R.E. White (Eds.), Comprehensive Treatise of Electrochemistry, Vol. 7, 1983, Plenum Press, New York, p. 301. 2 Yu. V. Pleskov and V.Yu. Filinovskii, The Rotating Disc Electrode, Consultants Bureau, New York, 1976. 3 A. Damjanovic, M.A. Genshaw and J.G’M. Bock&, J. Chem. Phys., 45 (1964) 4057. 4 M.R. Tarasevich, Elektrokhimiya, 4 (1968) 210. 5 R.W. Zurilla and E.B. Yeager, Technical Report No. 23, Case Western University, 1969. 6 V.S. Bagotskii, M.R. Tarasevich and V.Yu. Filinovskii, Elektrokhimiya, 5 (1969) 1216; 8 (1972) 84. 7 H.S. Wroblowa, Yen-&i-Pan and G. Razumney, J. Electroanal. Chem., 69 (1976) 195. 8 R.W. Zurilla, R.K. Sen and E. Yeager, J. Electrochem. Sot., 125 (1978) 1103. 9 K.L. Hsueh, D.T. Chin and S. Srinivasan, J. Electroanal. Chem., 153 (1983) 79. 10 M.R. Tarasevich, Elektrokhimiya Uglerodnyh Materialov, Izd. Nauka, Moscow, 1984, p. 143. 11 J.T. Lu, D. Tryk and E. Yeager, Electrochemical Society Meeting, Montreal, 9-14 May 1982, Electrochem. Sot., Princeton, NJ, 1983, Ext. Abstr. 82-l. 12 D.T. Sawyer, E.J. Nanni and J.L. Roberts, Paper 24, American Chem. Sot., 1982, 585. 13 K.J. Vetter, Electrochemische Kinetik, Springer, Berlin, Goettingen, Heidelberg, 1961, p. 673. 14 R.K. Sen, J. Zagal and E. Yeager, Inorg. Chem., 16 (1977) 12. 15 N.M. Markovic, R.R. Adxic and V.B. Vesovic, J. Electroanal. Chem., 165 (1984) 105. 16 R.R. Adzic, N.M. Markovic and V.B. Vesovic, J. Electroanal. Chem., 165 (1984) 121. 17 E. Yeager, D. Scherson and B. Simic-Glavacki in G.D.E. McIntyre, J. Weaver and E.B. Yeager (Eds.), The Chemistry and Physics of Electrocatalysis, Vol. 84-12, Electrochemical Sot. Princeton, NJ, 1984. 18 F.A. Cotton and G. Wilkinson, Advanced Inorganic Chemistry, Interscience, London, 1972. 19 J. Divisek and B. Kastening, J. Electroanal. Chem., 65 (1975) 603. 20 F. van den Brink, E. Barendrecht and W. Visscher, J. Electrochem. Sot., 127 (1980) 2003. 21 J.D.E. McIntyre and W.F. Peck in ref. 17. 22 (a) J.L. Gland, B.A. Sexton and G.B. Fisher, Surf. Sci., 95 (1980) 587; (b) R.B. Grant, R.M. Lambert, ibid., 146 (1984) 256 and refs. cited therein. 23 N.I. Dubrovina and L.N. Nekrasov, Elektrokhimiya, 8 (1972) 1503. 24 V. Vesovic, N.A. Anastasijevic and R.R. Adxic, J. Electroanal. Chem., 218 (1987) 53. 25 V. Vesovic and N.A. Anastasijevic, unpublished results. 26 N.A. Anastasijevic, Z.M. Dimitrijevic and R.R. Adxic, J. Electroanal. Chem., 199 (1986) 351. 27 V.G. Levich, Physicochemical Hydrodynamics, Prentice-Hall, Englewcod Cliffs, NJ, 1%2.
Chem., 229 (1987) 305-316 Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands
J. Electroanal.
DETERMINATION OF THE KIN-ETIC PARAME TERS OF THE OXYGEN REDUCTION REACTION USING THE ROTATING RING-DISK ELECTRODE PART I. THEORY *
N.A. ANASTASIJEVIC, V. VESOVIC and RR. ADiIC Institute of Electrochemistry, ZCTM und Center For Multidisciplinoty P.O. Box 815, Belgrade (Yugoslavia)
Studies. University of Belgrade,
(Received 5th January 1987)
ABSTRACT A general scheme of oxygen reduction is given and analysis of the disk-ring measurements is performed. Expressions for the diagnostic criteria for such a scheme have been derived and their implications are discussed. The existence of superoxide and oxygen ions and the interaction of the series and direct paths have been assumed in postulating the scheme. Also, all the electrochemical reactions involved only one-electron exchange. The possibilities and limitations of the disk-ring measurements in the mechanistic study of oxygen reduction are discussed together with a reevaluation of some wellaccepted criteria which are shown to be misleading. New definitions and terminology for different pathways of 0, reduction are proposed.
INTRODUCTION
Oxygen reduction is one of the most investigated electrochemical reactions because of its paramount importance for electrochemical energy conversion (see ref. 1 and refs. cited therein). One of the most commonly used experimental setups to elucidate the mechanism of this reaction has been the rotating ring-disk electrode, because it enables the quantitative detection of some of the intermediates [2]. In order to analyse the ring-disk results it is necessary to postulate the reaction scheme. Since the first proposition by Damjanovic et al. [3], several reaction schemes have been analysed [4-81. The merits of various schemes have been considered by Hsueh et al. [9]. One of the difficulties in analysing the correct scheme is that the number
* In honour of Professor H. Gerischer on the occasion of his retirement as Director of the Fritz-Haber Institute. 0022-0728/87/$03.50
8 1987 Elsevier Sequoia S.A.
306
of experimentally obtained quantities from the disk-ring measurements is usually not sufficient to determine all the parameters of the model. Consequently, simple schemes have been considered in the past. Unfortunately, oversimplification in some schemes had undesirable effects. For instance, the failure to consider the adsorption/desorption equilibrium of hydrogen peroxide [3] led to insufficient diagnostic criteria regarding the series and direct paths for O2 reduction [5]. In this work we have tried to construct a reaction scheme which includes nearly all the possible intermediates discussed in the literature. In doing so, the direct four-electron path has been further analysed in terms of strongly adsorbed intermediates. Also, the possibility has been allowed for interaction between a series and a direct path which has not been considered before. Further analysis of ring-disk currents based on this scheme allowed a critical comparison with the conclusions drawn from previous schemes. The further aim of this work is two-fold. Firstly, to elucidate the reaction mechanism of oxygen reduction as far as possible in terms of particular reaction steps and rate constants. Secondly, to analyse the electrochemical data in the light of this new scheme and to assess how much detailed information about the particular reaction steps electrochemical measurements can furnish. THE REACTION SCHEME
Consider the following scheme of oxygen reduction (Fig. 1). The k, are overall rate constants for the ith step and subscripts sa, a, b and * denote strongly adsorbed, weakly adsorbed, bulk and the vicinity of the disk electrode, respectively. The scheme has been written for alkaline soiutions, but it can easily be transformed, mutatis mutandis, into an analogous scheme for acidic solutions. The following electrochemical reaction steps have been postulated:
Fig. 1. General scheme of oxygen reduction.
kl Oca+ H,O + e- .z HO,,+
OH-
k-2
o,+e-
k,\ 0;
(Cl
O,+e-
S
(Cl
O&,+
0:
H,O + e- k,\ H02$+
OH-
(D)
HO& + e- k! O;+OH5 OS; +e-+HzO
k,\ 20H-
(F)
It is worth pointing out that eqn. (E) is very irreversible in acid media [lo]. The following chemical reactions have been taken into an account on the basis of the behaviour of adsorbed intermediates in aqueous [ll] and non-aqueous solutions
[W 2 O&+ H,O %
O,,a + HOz+ + OH-
k
2H0,,+20H-+Oz,a HO,, o,,
k,,\ OH- + 0, k,,\ o,+oi
(G) (H) (I)
(J)
Some of these intermediates have been considered in Vetter’s classic book [13]. Most of these reaction steps are not single-step processes but can actually involve a few reaction steps themselves. No attempt has been made to probe these reaction steps further, because the electrochemical data up to now are unlikely to be able to distinguish among them. A special feature of the above scheme is that no reaction step involves the exchange of more than one electron. It has been postulated that oxygen reduction proceeds through the adsorption of 0, and its intermediates on the electrode surface. Sufficient evidence for this is the strong electrocatalytic behaviour of this reaction which can be illustrated by different reaction rates on the basal plane of pyrolytic graphite with and without cobalt tetrasulphonated phthalocyanines [14] and on single-crystal gold electrodes of different orientations [15,16]. Also, the scheme of Fig. 1 is a generalization of the schemes proposed so far [3-81 and, as before, it consists of two major paths by which the oxygen reduction can proceed. It is postulated that the direct path involves strongly adsorbed species, while the first step in a series path is the formation of a weakly adsorbed oxygen molecule. On the strongly adsorbed sites,
308
reactions proceed mainly as irreversible processes (k3, k,, k12, k,,) where the strongly adsorbed species are chemisorbed. It is postulated that such strongly adsorbed species cannot desorb directly and go into solution. The series path, on the other hand, proceeds through weakly adsorbed species, where the energy of adsorption is of the same order of magnitude as kT. These species are most likely to be physisorbed. In this case, some kind of adsorption-desorption equilibrium with corresponding species in solution (k,, k_, and kz5, k_25) is established. In addition, it has been assumed that the reaction constants for the same reaction will differ depending on whether the reactant is weakly or strongly adsorbed (k2 and W In previous work [3-91, the series path has been treated in much more detail compared with the direct path. The major difference in the series path of the scheme of Fig. 1 is in the explicit inclusion of a superoxide ion O$. The formation of this ion is a logical consequence of the oxygen molecule receiving an electron (k,). Even though the superoxide ion O,,- is very unstable in aqueous solution [ll], its existence has been reported in a number of studies [11,12,17]. It seems that the adsorption of superoxide ion on electron donor sites stabilizes the adsorbed particle due to electron occupation of the unoccupied nz* antibonding orbital (Table 1). The implicit assumption made when constructing the scheme of Fig. 1 was that Oz$ superoxide ion is not in equilibrium with the solution. This appears to be a reasonable assumption since the O,TBsp ecies is unstable in aqueous solution and undergoes rapid chemical and electrochemical transformations. In addition it would show up in the ring-disk measurements, whose analysis implies that only one intermediate species is discharged on the ring. This second point will be discussed in more detail when the ring-disk equations are developed. The weakly bound superoxide ion can react with a proton and an electron (k,) to form HOz,, or it can decompose chemically into HOzVaand oxygen (k,,) [12]. It has been shown 1191 that most of the chemical d~mposition takes place on the electrode and not in solution. The formation of hydrogen peroxide as an intermediate in oxygen reduction is well established and its presence is incorporated in nearly every proposed scheme [3-81. Here, the standard practice of assuming hydrogen peroxide to be in equilibrium with its counterpart in the bulk is followed. Also, the chemical decomposition of HO,Ta (k,,) [ZO]has been included. TABLE 1 Influen~ of the numberof a&bonding &xtrons (9: ) on the characteristicsof the O-O bond in O$’*P WI Species
Numberof vz* electrons
0: 02 0; 0;-
1 2 3 4
O-O distance /m 0.112 0.121 0.133 0.149
PO-0 /cm-’ 1860 1556 1145 770
309
A further difference between this scheme and previous schemes is that the possibility has been allowed that the weakly adsorbed intermediates from the series path can undergo surface diffusion and form their strongly adsorbed counterparts in the direct path. The effects of surface diffusion of intermediates in oxygen reduction have been mentioned by McIntyre and Peck [Zl]. Therefore, it is no longer possible to represent the direct path as one overall process with a specific rate constant, since there is now an interaction between a series and a direct path. It has been assumed that surface diffusion of the strongly adsorbed species is not energetically favourable. In the previous schemes [3-g] the direct path was treated as a black box and only the overall rate constant for a four-electron exchange was quoted. Even though some suggestions have been made about the nature of the direct process [1,4-g], no analysis of the disk and ring currents has been made. In the scheme of Fig. 1, it has been postulated that the first step in a direct four-electron transfer is the formation and immediate dissociation of a chemisorbed oxygen molecule (kzl or k,,) which cannot desorb back to the bulk. According to the gas-phase literature 1221, the strongly adsorbed oxygen molecule is very unstable and it dissociated immediately into atoms. Once it is formed, the chemisorbed oxygen molecule exchanges an electron (k3) and forms an oxygen ion OS;. This in turn can, by exchanging a further electron, either be reduced to OH- (k6) or be oxidized to a strongly adsorbed peroxide HO& (k_,). On the other hand, the formation of strongly bound superoxide ion proceeds through k,,. O& is less stable than the physisorbed superoxide ion owing to the nature of the bonding to the surface, and therefore it undergoes a relatively fast transformation. It is either transformed electrochemically into a strongly bound hydrogen peroxide (k4) or it undergoes chemical d~mposition (k& into OS; and 0,. The existence and chemical identification of the adsorbed intermediates can only be proven conclusively by the use of spectroscopic techniques. Fortunately, the existence of a strongly bound peroxide can be inferred from electrochemical me~urements. Dubrovina and Nekrasov obtained [23] three plateaus of the disk diffusion limiting current which correspond to one, two and four electrons exchanged, respectively. No increase of the ring current corresponding to the second plateau, i.e. 0, reduction to H,O,, was observed. This implies that a species which has exchanged two electrons has not left the disk electrode. The species in question is most likely strongly adsorbed hydrogen peroxide. Once HO;= has been formed, it can either exchange an electron and form OS; or it can d&so&ate chemically (k,,) into OH- and OS,. The reaction constant k12 and the similar reaction constants klO, k,, and k13, which are defined by purely chemical reactions, can be related to the dismutation reaction constants discussed in ref. 1. Even though some of these reactions are found to be second order when they take place in solution (k,,) [If], we will follow the common practice [l-19] and assume them to be practically first order when proceeding through adsorbed states. The justification for such a choice
310
lies in the fact that the assumption of the reactions being second order is inconsistent with the behaviour of the experimentally measured ring and disk currents. THE N&,/Z,
VS.
w-O5 PLOT
~~j~o~~ et al. [3] were the first to use this plot to obtain a distinguishing between the direct and the series path. Postulating reaction steps follow first-order kinetics and by performing material each component for steady-state conditions, the followiug equations for the scheme of Fig. 1: 0 2. *
:
ZPO%,b
0 2,a
1
bocl,.
QG
:
kcx.a
OzTsa
:
k23C2,a = 0%
HO,,
:
k25c3,a
HO<,
:
(kz+k,o/2)c,,,+k-,,c,,.
HO<,,
:
k2ec3.a
0,
:
2ksx,.
0,;;
:
kc3,sa
-
Cl,* 1 + k-2OCl,a
+ 0.5h0e2,~
=
Oh
+ hh,* + k-20
+ huh,,
+ k2 + k,,)c,,,
+ k3ha
= (k-25
+ Z,W”.~)C~,
+ bc2,sa
f
w = (~-2+k2~+k~+k~~)c3,~
+ k-se,
+ =22cl,a + k,c,
+ 0.%lc3,a
= ko
+ k-s3,a
= &I
criterion for that all the balances on are obtained
= @a
+ kdc3,sa
+ k13~2,sa + k12C3,sa = be
k13C2,sa = (k,
+ k-dc,
For clarity, the subscripts 1, 2, 3, 4 and 5 have been used for the oxygen molecule, superoxide ion, hydrogen peroxide, oxygen atom and oxygen ion, respectively, and Z, = 0.62 D2/3/~‘/6, where D is the diffusion coefficient and Y is the kinematic viscosity. The disk current is given by
while the ring current is given by I R = n RANFZ 3w”-‘c3,*
09
where A is the disk area, N is the collection efficiency, w is the rotation frequency and rra is the number of electrons exchauged on the ring electrode. nR is not necessarily a whole number but can in fact vary with the potential [24]. By dividing eqn. (10) by eqn. (11) and using eqns. (2)~(9) to eliminate the concentration ratios, one obtains NID/IR = 2(1+ A, + A,k_25/Z3w0.s)/nR
(12)
where A, and A, are ~rnp~cat~ dimensionless functions of the reaction constants which are given in Appendix 1. The most interesting feature about eqn. (12) is the linear relationship between AVo,/IR and W-O.‘. This behaviour has also been observed in earlier and much
311
simpler schemes of oxygen reduction [3-91 which among other things do not include the possibility of interactions between the direct and series paths. Thus, the electrochemical evidence alone, based on investigation of the disk and ring currents, does not allow us to assume independence of the two paths. This in turn makes the whole concept of the series and the parallel path slightly doubtful. Furthermore, the same linear function dependence of NZr,/Za on W-O.’ will be observed if one neglects the back reactions (k_,,, k_,, k_,). In fact, any system whose elementary path reactions are first order with respect to the reactants and which has only one process taking place on the ring would give a linear dependence of NZ,/Z, on w-o.s The conclusion of their scheme, which equilibrium for H,O, does Wroblowa et adsorption-desorption
Wroblowa et al. [7] was that no criterion could be made, for would distinguish whether or not the adsorption/desorption existed. However, eqn. (12) contains this information and so al’s [7] scheme. For k_,, = 0, implying the lack of equilibrium eqn. (12) simplifies to
NZD/ZR = 2/n,(1+
A,)
(13)
Therefore, if the ratio of the disk current to the ring current is independent of the speed of rotation at each potential, no equilibrium is established. If two intermediates react on the ring, the following behaviour should be observed [25]: NZr)/ZR = (Do + D,wO.S + D*w)/( D,w”.s + Z&w)
04)
where the 0, are the ratios of the reaction rate constants. Hence, the non-linearity of the plot Zr,/ZR vs. W-O.’ implies either the possibility of the existence of more than one process on the ring or that some of the reactions involved are not first order with respect to the reactant. THE J-S
PLOT
A further diagnostic criterion, as suggested by Wroblowa et al. [7], was to compare the dependence of the intercept, J, on the slope, S, of equations equivalent to eqn. (12). For the scheme of Fig. 1, the following J-S dependence is obtained: J = 2(1-t A&n,
+ 2$/k_,,
05)
where A, is given by 4
= (kxAs
+ k,,A,/k,
+ kd/(k,
+ k,o/2)
(16)
and A, and A, are given in Appendix 1. So far, this criterion has been used to distinguish between the series and the parallel paths [7]. Specifically, the experimentally obtained linearity of the J-S function has been explained by the same potential dependence of the reaction rate constants defining the series and the direct path [7]. Also, the unity intercept of the linear J-S plot has been taken to imply non-existence of the direct path. It is obvious from eqn. (15) that the J-S function is not in general linear but a strong
312
function of the potential. There are in fact three characteristic shapes of the J-S plot: (1) A non-linear J-S plot is obtained when a reaction goes through both strongly and weakly adsorbed intermediates. (2) A linear J-S plot, which has been observed experimentally in some cases, arises under the following conditions: the diffusion of weakly adsorbed oxygen molecules and superoxide ions is slow and can be neglected ( kz2 = k,, = 0); the first electrochemical step is much faster than the desorption of oxygen molecules (k, z+ k_,); the second electrochemical step is much faster than the catalytic decomposition of weakly adsorbed superoxide ions (k2 B k,,). Then the intercept with the J-axis, J’, of the linear J-S plot eqn. (15) is given by
J’ = 2/n, 0 + k,,/k,o)
(17) Therefore, from the value of J’ it is possible to evaluate the ratio of the direct to the series path. This equation differs considerably from the expression for J’ given by Wroblowa et al. [7]. A condition of the linearity and J’ > 1 in their expression is the same potential dependence of the rate constants for the exchange of four and two electrons in the direct and series paths, respectively. It is difficult to verify this assumption. For the rate constants k,, and k,,, representing adsorption of O2 and 0, it is easier to envisage the same potential dependence. Further implications of eqn. (17) will be discussed in Part II of this work. (3) It is interesting to note that if there is no formation of strongly bound oxygen (k,, = 0) and the diffusion of the weakly bound oxygen species is slow (k,, = k,, = 0), eqn. (15) reads
J = 2/n,
+ Z,S/k_,,
(18)
where S is given by S = 2k-,,(ki, + &,)/nnZ&,s 09) Assuming that the rate constants used in eqns. (16) and (19) are not functions of the potential, J and S are also independent of the potential. The J-S diagram is therefore given for such a case as a point. Further implications of eqns. (18) and (19) will be discussed in Part II of this work. THE &,/(I‘,,
- I) vs. w-O5 PLOT
This plot has been used by Hsueh et al. [9] as an additional equation for the determination of some constants in the simpler schemes [26]. In deriving the above relationship, they have assumed, as in all the cases so far for O2 and H202 reduction [l-9], that in the diffusion limiting current region the number of electrons exchanged per 0, and H,O, molecules is four and two, respectively. Since 0, reduction is a complex reaction involving a large number of paths each exchanging a different number of electrons, it is not possible to take the number of electrons as a constant independent of the potential [24]. Therefore the diffusion limiting current is given by Zdl = n D FAZ 1 w’,~
(20)
313
where no is the average number of electrons per molecule of the reactant exchanged on the disk at each potential. Using eqns. (10) and (20) together with the mass balance equations, one obtains after long and tedious algebra the following expression: Z&Z,,
- I) = (B, - Z~W’.~)/( B, + B,/n, /n,n,NFAZ,w”~5c,,,
+ (B,Z,w’.’
- Z,W’.~)
- B,)I, (21)
where B, to B4 are complicated expressions involving rate constants and are given in Appendix 2. Equation (21) is in a form very similar to the corresponding equation in Hsueh et al.‘s work [9] which has been derived for a much simpler scheme. It is obvious that eqn. (21) in its present form does not show a linear relationship between Z&Id, - I) and w -o.5 On the other hand, some experimental results [9,26] show a linear behaviour between these two quantities. It is therefore interesting to determine under what conditions eqn. (21) will be reduced to a linear one. It will be valuable at this point to digress slightly from eqn. (21) and to consider an overall problem of the type 0, + products
(K)
where the reactant 0, diffuses to the electrode and there reacts with an overall rate constant k, exchanging in the process n,, electrons. The solution to this overall problem in terms of the diffusion limiting current is easily obtained [2,24,27] and the expression for Z&Id, - Z) reads I,,/( Z,, - I) = 1 + k/Z,w0.5
(22)
Equation (22) has been derived under the assumption that only one reactant, namely O,, diffuses to the electrode and there undergoes a first-order overall reaction which takes place on the surface and not in the solution. Under these conditions, Zd,/(Zd, - I), vs. w -OS shows the desired linear form. On the other hand, when deriving eqn. (21) it has been assumed that some of the peroxide diffuses back from the solution (k_25); hence the overall process cannot be given by eqn. (22). Therefore, for situations where the flux of hydrogen peroxide from the solution, k_,,c,, . , is negligibly small, both models are identical and eqns. (21) and (22) should be equivalent. In other words the non-linearity of eqn. (21) can be ascribed solely to the non-negligible hydrogen peroxide flux from the solution rather than, as some workers have previous thought [9] to non-existence of the catalytic reaction. If the flux is small, eqn. (21) reads I,,/( Id, - I) = (B, - Z,W’.~)/(
B, + B,/n,
- Z,W’.~)
(23)
Since eqns. (22) and (23) are identical, n D = - B,/B,
(24)
which gives us an expression for the average number of electrons exchanged per molecule of oxygen reacted as a function of the potential.
314 EXPRESSIONS
FOR nD AND
k
The explicit dependence of the number of electrons exchanged on the potential has already been discussed for a simple scheme [24]. For our model, the equivalence of eqns. (22) and (23) allows us to obtain easily the explicit dependence of the number of electrons exchanged and the overall rate constant on the specific rate constants and therefore the potential as well. By using the expressions for B, and B, given in Appendix 2 in eqn. (24), one obtains n D = 4 - (2k, + ‘h + 4 ( b(2k, + k20 - 2k,2 )/b - k,,)/A9 (25) where A, and A, are given in Appendix 1. Also, by further comparing eqns. (22) and (23) one obtains the explicit expression for the overall rate constant k in terms of the specific rate constants: k=
-B,
(26) - k-,&)/k,(4 -&4,/2) (27) to note that expressions (25) and (27) have been derived under the IdJ(ldl - 1) vs. w-0.5 is linear. In situations where this is not the of electrons exchanged and the overall rate constants are given by and (27), only as a first approximation.
k = km + k,, + (A,k-,k,
It is important assumption that case, the number expressions (25) CONCLUSIONS
A general scheme of the reduction of oxygen is given. All the electrochemical processes are represented as at most one-electron exchanges. The existence of superoxide and oxygen ions is assumed. Analysis of the ratio of the disk current to the ring current for this scheme shows that some of the well-accepted criteria used in analysing the results of oxygen reduction can be misleading. The concept of two independent pathways, namely series and parallel, is doubtful since there are no physical reasons why a weakly adsorbed intermediate cannot diffuse along the surface and become more strongly adsorbed. The linearity of the NID/IR vs. w -‘s function is a general characteristic of any scheme whose reactants are first order with respect to the corresponding reacting species and where only one intermediate is discharged on the ring. The J-S plot in general is not linear but is a function of the potential. A non-linear plot is obtained when a reaction goes through both strongly and weakly adsorbed intermediates. Under specific conditions, a linear J-S plot is obtained in which case the ratio of the direct to the series path can be evaluated. Surprisingly enough, the J-S plot is represented by a point when only a series path is operational, if the catalytic decomposition of hydrogen peroxide is not potential-dependent. The explicit dependence of the number of electrons exchanged and the overall rate constant in terms of specific rate constants on the potential are given. Thus it would seem that in general it is not possible using electrochemical measurements alone to decide on the correct scheme of oxygen reduction. However,
315
with some simplifications a considerable amount of information can be obtained. The use of spectroscopic methods able to detect the adsorbed intermediates is therefore highly desirable if a complete elucidation of the oxygen reduction mechanism is to be performed. There is considerable non-uniformity in the terminology for the reaction schemes for Oz reduction [7-91; in particular, the term “series” lacks precision. We propose somewhat modified terms with a new one resulting from the scheme in Fig. 1 for which a criterion has been obtained. The following pathways can be defined: (1) “direct” four-electron reduction without hydrogen peroxide detected on the ring; (2) a two-electron “series” pathway involving reduction to hydrogen peroxide; (3) a “series” pathway with two- and four-electron reduction. In the case of only four-electron reduction without hydrogen peroxide detected on the ring, the case is indistinguishable from a “direct” four-electron reduction; (4) a “parallel” pathway which is a combination of (l), (2) and (3); and (5) an “interactive” pathway in which diffusion of species from a “series” path into a “direct” path is possible. ACKNOWLEDGEMENTS
This work was financed by the Yugoslav-American Fund for Scientific and Technological Cooperation in cooperation with the National Science Foundation, Contract No. 471 U.S.A., and by the Research Fund of SR Serbia, Yugoslavia. APPENDIX I
Expressions for A’s in eqn. (12) Ao=A,+A3 A, =A,@
640) +A,)/kz
(Al)
-A,
A,=k,,+k_,+k,
(A21
kuA,/kl + kzd/(k,
A, = (k,,A,
+
A, = (k,,A,
- k,
A, = ((kz A, = (2(k,
+ k-,(k,
+ k-zo + k,)A,
+ 2k,d/k,)/k,,
644) 645)
- k,ok&/k,k,
+ k-zo + kdk-,
A, = (k, + k,o)/(k,,
(A3)
+ k,o/2)
+ k,,k,)/k,ok,
bw (A71
+ Ad
A, = k,, + k, + k,, A,
= Adk,
A,, = Mk,,
+ k,,Vk,
w3) + k,dA,o
+ k-20 + kd(k,o
- ATA&) + k, + kd
- A,k-
z (kl
- klk,o)Pk,kzo
+ km
I/k,
- k,o/2
(A91 (AlO)
316 APPENDIX 2
B, = -@*o
+ k21) + @,k-,k*
B2 = B,(4 - ((2k, B, = B,B,
-k-,0&)/(&
+ km) + B,(k-2(2k,
(Bl)
- &4,/2)/k,
+ km - 2k,,)/k,
-k&A,)
+ (2kzA,)/A,
B4 = ((4B1k21-
Bdkm
(B3) + kdAd2
+
-2B,(k,,-k-2(2k22-kl+B*k20/4Bl)/kl)/A2) B, = ((nk,,
+ k&n
Bs = -2k,,A4/A2 B, = (kz + k&A,
032)
- 4))A,/2 - nkA,
- 2k-,(2kz,
(B4) - k, + nk,,/4Vkd/A,
VW (W (B7)
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