Synergistic effect in the electrocatalytic oxidation of methanol on platinum+palladium alloy electrodes

J. Electroanal. Chem., 125 (1981) 89--103 Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands

89

SYNERGISTIC EFFECT IN THE ELECTROCATALYTIC OXIDATION OF METHANOL ON PLATINUM+PALLADIUM ALLOY ELECTRODES

F. KADIRGAN *, B. BEDEN, J.M. LEGER and C. LAMY ** Universit~ de Poitiers, Laboratoire de Chimie I "Electrochimie et Interactions", 40, avenue du Recteur Pineau, 86022 Poitiers Cddex (France) (Received 14th November 1980; in revised form 4th February 1981)

ABSTRACT The electrocatalytic oxidation of methanol has been investigated on platinum+palladium alloy electrodes of different compositions in acid, neutral and alkaline aqueous solutions. The surface characteristics (composition and roughness factor) of the alloys and the stability of the electrodes in contact with different electrolytic solutions have been studied using cyclic voltammetry. In particular, a surface enrichment in platinum due to a preferential dissolution of palladium and an increase of the roughness factor with an increase of the palladium content has been shown. The electrocatalytic activity of different alloys for methanol oxidation has been characterized by exchange current densities obtained from extrapolation of Tafel lines to calculated equilibrium potential. The plot of these current densities vs. the surface composition leads to a synergistic effect, particularly important in alkaline medium. A reasonable explanation of this enhanced electroactivity at about 15 at. % in Pd is given on the basis of a decrease of electrode poisoning.

INTRODUCTION

The electrooxidation of methanol in aqueous solution has been thoroughly studied during the last two decades, mainly for its use in fuel cells [1,2]. Nevertheless an increasing number of fundamental studies have been undertaken recently in order better to understand the oxidation mechanism and the catalytic role played by metal electrodes [3,4]. Most of the studies were carried out with platinum electrodes either in acid or in alkaline medium. Although a large number of other single electrodes were investigated, among these, platinum appears to be the best electrocatalyst chiefly in acid medium [5]. The reaction mechanism of the overall reaction has not yet been completely ascertained, particularly the nature of the adsorbed intermediate, which blocks the electrode surface in acid medium -- (COH)ads assumed by Bagotzky and co-workers [6], or (CO)ads assumed by Biegler [7]. Moreover, if the electrocatalytic activity seems to be better in alkaline medium since an adsorbed species such as (CO-)ads is more easily oxidized to carbon dioxide, a new problem arises because of the carbonate formation which strongly modifies the conduc-

* Permanent address: I.T.I.A. Eczacilik Bilimleri Fakiiltesi, Nisantasi]Istanbul, Turkey. ** To whom correspondence should be addressed. 0022-0728/81/0000--0000/$02.50 © 1981 Elsevier Sequoia S.A.

90

tivity of the electrolyte. To circumvent these difficulties a large number of electrocatalytic tests were made in acid medium using a binary catalyst consisting of platinum and a second metal which improves the oxidation rate of the adsorbed residues [8]. However, only a few systematic studies have been made on the electrocatalytic behaviour of a given binary system [9--11]. In this paper, platinum+palladium alloy electrodes have been investigated because both metals are of considerable interest for their electrocatalytic activity. Moreover, these alloys constitute a continuous series of solid solutions which allows us to vary continuously the bulk composition, and therefore the surface composition in the whole composition range. Although Pt and Pd have very similar properties (same group of the periodic table, same fcc crystal structure, similar atomic size), they have a different electrochemical behaviour. In particular, Pd is completely inactive for the electrooxidation of methanol in acid solutions [ 12]. Therefore, a systematic study of these alloys may bring new light to the knowledge of the electrocatalytic mechanism of methanol oxidation [13]. Only a very few investigations o f these alloys have as y e t been made. Methanol electrooxidation has been studied mainly by Indian scientists [ 14,15], b u t they only use one alloy composition. In particular, R o y et al. [14] found a higher electroactivity for alloys than for pure platinum electrodes. Finally, another electrocatalytic reaction, namely the oxidation of formic acid, has been studied on platinum--palladium alloy electrodes by Capon and Parsons [ 16], w h o also found an enhanced activity for the alloys compared to pure metals. EXPERIMENTAL

Cyclic voltammetry has been used for determining both the electrode surface characteristics and their electrocatalytic activities. Cyclic voltammograms were recorded using a Wenking 68 FR 0.5 potentiostat, a P.A.R. 175 universal programmer and a Hewlett Packard 7000 AM X--Y plotter. The experiments were carried out in a three-electrode electrochemical cell with a platinum counter electrode and a mercurous sulphate reference electrode (MSE). The temperature was maintained constant within 0.2°C by circulation of thermostated water through the double wall of the cell. The aqueous solutions (CH3OH either in 0.5 M H2SO4 or 0.25 M K2SO4 or 0.5 M KOH) were prepared from triply distilled water and Merck "Suprapur" reagents. The electrolyte was deoxygenated by bubbling pure argon through the cell. Before each experiment the impurity level of the complete system was checked by recording the voltammogram of a smooth platinum working electrode [17]. Alloy electrodes were prepared by electrolytic codeposition of Pt and Pd from hydrochloric solutions of their soluble salts, H2PtC16 and PdC12 respectively, in a determined ratio to obtain the desired alloy bulk composition. The electroplating was carried o u t at controlled potential (0.05 V vs. SCE) on a small platinum bead (about 1.5 mm diameter) obtained by melting a platinum wire of 0.5 mm diameter (Pt 99.998% from Johnson-Matthey). To decrease the roughness factor, the alloy electrodes were then annealed by warming them to red heat in a hydrogen flame. Finally, the electrode wire was m o u n t e d in a spe-

91

cial electrode holder which prevents any solution leakage, particularly when the electrolyte temperature is changed from room temperature to higher temperature [18]. The surface characteristics of the alloys (surface area, surface composition) were determined before and after each electrocatalytic measurement in another electrochemical cell similar to the first one, except for the absence of methanol in the supporting electrolyte. The measurements were made at the same temperature as the main cell, usually at 50 ° C. Surface areas of pure metals and alloyed metals were evaluated from the quantity of electricity involved in the reduction of the oxygen layer previously adsorbed during the anodic sweep. In this determination, it was assumed, as usual, that the completion of an oxide monolayer (at a b o u t 1.5 V vs. SHE) corresponds to M--O formation, i.e. to 420 #°C cm -2 for both metals [19]. The alloy surface composition was also determined from the cyclic voltammograms recorded in exactly the same experimental conditions. The surface composition was estimated from the peak potential of the oxide reduction during the cathodic sweep, assuming that there is a linear relation between this peak potential and the surface composition [ 16,20]. The alloy bulk composition was calculated from the lattice parameters determined by X-ray diffraction diagrams according to Vegard's linear law. The geometric area of the electrodes was measured using a metallographic microscope with a micrometric screw. RESULTS

Before studying the electrocatalytic activity of Pt+Pd electrodes for methanol oxidation, it is essential to know their surface characteristics (surface area and composition) and to determine their stability in contact with the electrolytic medium.

The surface behaviour o f the alloy-electrodes in contact with supporting electrolyte Cyclic voltammograms for pure metals and for alloys in supporting electrolytes of different pH (acid, neutral, alkaline) are given in Figs. 1--3 respectively. They were recorded at 50°C and 50 mV s -~, since these experimental conditions were usually used for determining the alloy electroactivity for methanol oxidation. For palladium and Pt--Pd electrodes, the cathodic potential limit of the sweep has been chosen to be more anadic than the hydrogen adsorption region in order to avoid any hydrogen absorption which would change the electrode structure. In neutral medium it is very important to stir the electrolyte solution vigorously to avoid local variations of pH. On the other hand, stirring may introduce Current fluctuations due to mass transfer limitations. To circumvent these two difficulties the voltammograms are recorded immediately after stopping the stirring of the solution at the end of the anodic sweep. On these voltammograms, one can see that the reduction peak potential of

92

0.2 :x

E

0

U

............. ' i

:---

I I

/z-.~ i/

1

-0.2

-0.4

-0%8

-o'.~

;

0'.4

o'.~

E/V(HSE)

Fig. 1. Cyclic v o l t a m m o g r a m s of platinum (-- -- --), palladium ( . . . . . ) and platinum+palladium alloy ( ) electrodes in acid m e d i u m 0.5 M H2SO4 (temperature 50°C, sweep rate 50 m V s -1 , no stirring).

c,,,0'2I i

u

~0

r.

.

.

.

.

.

"

"

T

T

~

............ "

~

-0.2

!/

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-o'.8

-o.'~

'

6

d.4 E/V(MSE)

Fig. 2. Cyclic v o l t a m m o g r a m s of platinum ( - - - - - - ) , palladium ( . . . . . . ) and platinum+palladium alloy ( ) electrodes in neutral m e d i u m 0.25 M K2SO 4 (temperature 50°C, sweep rate 50 m V s -1 , no stirring).

93 0.1 u

E

0

!/ ,,/

~ ,,

-1.2

-O.g

..~

-0.1

-0.2

k

r

-0.4

0

'

E/V(MSE)

Fig. 3. Cyclic voltammograms of platinum (-- -- -- ), palladium ( . . . . . . ) and platinum+palladium alloy ( ) electrodes in alkaline medium 0.5 M KOH (temperature 50°C, sweep rate 50 mV s -1 , no stirring).

t h e o x y g e n l a y e r a d s o r b e d o n a l l o y e l e c t r o d e s is i n t e r m e d i a t e b e t w e e n t h o s e o f p u r e m e t a l s , t h u s l e a d i n g t o a n e s t i m a t e o f t h e s u r f a c e c o m p o s i t i o n . T h i s surf a c e c o m p o s i t i o n d e t e r m i n a t i o n is n o t so a c c u r a t e b e c a u s e t h e o x y g e n r e d u c -

TABLE 1 Surface composition of the Pt+Pd alloys (in Pt at.%) Bulk composition according to the composition of the electrolyte bath

Surface composition after working in usual electrochemical conditions In acid medium

In neutral medium

In alkaline medium

5 10 12 15 20 25 30 40 50 80 85 90 99.5

22 41 50 56.5 69 75 87.5

20

23 46 54

50

77 -69

59 61.5 73 89 90

84.5

92

94

tion peaks of pure metals are t o o close to each other (potential separation of a b o u t 80 mV). Nevertheless, this is the only method which can give in situ the composition of the first layer, in contrast to the electron spectroscopic techniques which require a vacuum and give mean information on more than one monolayer. The results obtained (Table 1) clearly show that the surface composition of the alloy codeposits is very often far from the bulk composition. The initial atomic Pd content is usually higher for the surface than the bulk alloy because Pd is more easily electrodeposited than Pt. However, the surface composition changes during repetitive cycling of potential between the hydrogen and oxygen regions (Fig. 4). After a few thousand cycles, the surface composition tends 2100 1400 20

3600

E u E 20

-0.2

_~3600

(b)

-0.

200

220 I~ 7oo

(c) -0.1 '

. . . . . . .

d.4'

'.

'o'.8

E/V(HSE1

Fig. 4. Evolution of the alloy electrodes in base electrolyte during repetitive potential cycling (temperature 50°C, sweep rate 50 mV s -1 , no stirring) (the number of cycles is given for each curve) (a) Acid medium 0.5 M H2SO4; (b) neutral medium 0.25 M K2SO4; (c) alkaline medium 0.5 M KOH.

95

5O

o []

o

o

20

J

20

I

~o

I

60

8'o

i0o A t % Pd

Fig. 5. E l e c t r o d e r o u g h n e s s f a c t o r p as a f u n c t i o n of surface composition (atomic palladium c o n t e n t ) for n o n - a n n e a l e d e l e c t r o d e p o s i t e d e l e c t r o d e s . T h e d i f f e r e n t s y m b o l s c o r r e s p o n d t o

different inital bulk alloy compositions, the surface composition of which was modified by preferential Pd dissolution: (A) 20 at.% Pd; (X) 50 at.% Pd; (D) 70 at.% Pd.

to stabilize. For the three electrolyte media used in this work (acid, neutral and alkaline media), this evolution is quite similar, except for the rate of evolution which is higher in acid medium, and leads to an electrode surface enriched in platinum. This can be due to a preferential chemical or electrochemical dissolution of palladium, the presence of which in the solution was checked by atomic absorption spectrophotometry. Furthermore, the surface roughness increases continuously during the potential cycling, particularly in acid and alkaline media. The surface areas are obtained from the oxygen layer by measuring the quantity of electricity for the cathodic reduction of the adsorbed oxygen. By comparing these data for the real active area to the geometric area, one obtains rnughness factors which, for unannealed electrodes, vary regularly with the surface composition (Fig. 5). This figure shows a monotonic increase of the roughness factor with the surface content in atomic palladium.

The electrocatalytic activity o f Pt ÷Pd alloy electrodes for the electrochemical oxidation o f methanol The electrocatalytic activity of pure metal electrodes and of alloy electrodes has been systematically investigated by recording cyclic voltammograms (at a sweep rate of 50 mV s -~) of the different electrodes in 0.1 M CH3OH aqueous solutions of different pH at a controlled temperature of 50°C. The results are shown in Figs. 6--8, for acid, neutral and alkaline solutions respectively. The behaviour of both metals is obviously different since palladium elec-

96

'7 (a)

f

(b)

0.2

(c)

-0.2

-0.8

-0.6

-0.4

-0.2

0.2

0.4

0.6

0.8

EIv(MsE)

Fig. 6. Cyclic voltammograms of methanol electrooxidation on: (a) platinum; (b) platinum+ 25% palladmm; (c) palladmm electrodes, in acid medmm 0.5 M H2SO4 (50 C, 50 mV s- , 0.1 M CH3OH). •

.

.

o

1

trodes are completely inactive in acid medium, whereas platinum electrodes are reasonably electroactive in the same medium. This is at variance with the results for formic acid oxidation, for which both metals are electroactive in the same potential range [16,21]. On the other hand, the electroactivity of platinum for methanol oxidation reaches a maximum in neutral medium (about 7 mA cm -~ of true active area for 0.1 M CH3OH at 50°C). The electrocatalytic activity of alloy electrodes is higher than the weighted activity of pure metals regardless of the solution pH, leading thus to a synergistic effect. In the cases of active alloy electrodes in neutral medium, and of all electrodes in alkaline medium, the methanol oxidation curves i(E) are similar for the anodic sweep and for the cathodic sweep at the relatively negative potentials where the methanol oxidation takes place on electrodes free of any blocking species (adsorbed oxygen or OH, methanol adsorption residues, ...).

97

(a) 2.

/

(b)

03

(c) 0.1

0

-~.¢

-1:2

-o.'e

-0:6

-o.'~

-ok

~

o'.z

0'.4

o:6 E/v(MsE)

Fig. 7. Cyclic voltammograms of methanol electrooxidation on: (a) platinum; (b) platinum+ 27.5% palladium; (c) palladium electrodes, m neutral medmm 0.25 M K2SO4 (50 C, 50 mV s -1, 0.1 M CHsOH). .

.

O

This may be a p r o o f of the lack of formation of the strongly b o u n d poisoning species (COH)aas either in neutral medium for the most active alloy electrode, or in alkaline medium where {CO-)ads is more weakly adsorbed. Since the voltammograms are nearly independent of the sweep rate (in a certain range from 10 to 500 mV s-l), they may be considered as quasi-stationary current--potential curves. Thus Tafel plot analysis of the most negative part of the i(E) curves has been carried out, for the cathodic sweep in acid (Fig. 9), or in neutral (Fig. 10) media, and for the anodic sweep in alkaline medium (Fig. 11), since in this last case the anodic and cathodic sweeps are superimposed, and the anodic sweep may be analysed to higher positive potentials. These Tafel plots lead to relatively good straight lines, the extrapolation of which to equilibrium potential gives an exchange current density. This quantity may be chosen as a good test of electroactivity of alloy electrodes since the methanol concentration is kept constant, and the transfer coefficients obtained from the slope of Tafel plots are nearly constant (Tables 2--4). Because the methanol

98

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E I 0

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\ (c)

-1.4

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0'.2 Ely MSE)

Fig. 8. Cyclic voltammograms of methanol electrooxidation on: (a) platinum; (b) platinum-23% palladium; (c) palladium electrodes, in alkaline medium 0.5 M KOH (50°C, 50 mV s -1 , 0.1 M CH3OH).

oxidation reaction is highly irreversible, it is impossible to measure an equilibrium potential. Therefore this potential must be calculated from thermodynamic data and the following estimated values were obtained for the three pH used in this work [13]: Electrolyte medium

Acid

Neutral

Alkaline

Eeq/V(MSE)

--0.618

--0.938

--1.588

For neutral and alkaline media, the extrapolation of the Tafel lines (dashed lines on the plots) have been carried o u t with the same slope corresponding to approximatively 128 mV decade -1 at 50°C, i.e. to the same an ~ 0.5 (see Tables 3 and 4) in order to avoid rough errors on the current exchange densities arising from slope errors. But for acid medium, due to a monotonic increase of

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Fig. 9. Tafel plots of the quasi-stationary current density--potential curves for the electroo x i d a t i o n o f m e t h a n o l in acid m e d i u m on d i f f e r e n t alloy e l e c t r o d e s [ c a t h o d i c s w e e p in the same c o n d i t i o n s as in Fig. 6; ( - - - - - - ) e x t r a p o l a t e d Tafel l i n e ] .

~-~

~

~

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l Ol Z

•

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BB

Pt

l 0~

E/V(MSE)

Fig. 10. Tafel plots of the quasi-stationazy current density--potential curves for the electrooxidation of methanol in neutra] medium on different Mloy electrodes [cathodic sweep (except for Pd) in the same conditions as in Fig. 7; (-- - - - - ) extrapolated Tafel line ].

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<~ :=

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9

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~

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Pd

P't,

-4.

'

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-o'.9

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-d.7

Fig. 11. Tafel p l o t s of t h e q u a s i - s t a t i o n a r y c u r r e n t d e n s i t y - - p o t e n t i a l curves for t h e electroo x i d a t i o n o f m e t h a n o l in alkaline m e d i u m o n d i f f e r e n t alloy e l e c t r o d e s [ a n o d i c sweep in t h e same c o n d i t i o n s as in Fig. 8; ( - - - - - - ) e x t r a p o l a t e d Tafel line ].

TABLE 2 T r a n s f e r c o e f f i c i e n t s for t h e e l e c t r o o x i d a t i o n o f m e t h a n o l o n P t + P d alloys in acid m e d i u m (surface c o m p o s i t i o n given in at.% Pd) At.% Pd

0

an

0.52

12.5

16

0.56

25

0.57

31

0.58

43.5

0.58

50

0.58

59

0.62

78

0.67

100

0.78

--

TABLE 3 T r a n s f e r c o e f f i c i e n t s for t h e e l e c t r o o x i d a t i o n o f m e t h a n o l o n P t + P d alloys in n e u t r a l mediu m (surface c o m p o s i t i o n given in at.% Pd) A t .% Pd o~n

0

5.5

0.42

0.41

11 0.42

16.5 0.42

27.5 0.43

33 0.48

38.5 0.46

41 0.40

50 0.39

80 0.42

100 0.42

101 TABLE 4 Transfer coefficients for the electrooxidation of methanol on Pt+Pd alloys in alkaline medium (surface composition given in at.% Pd) At.% Pd 0in

0 0.48

7.5 --

15.5 --

23 0.49

31 0.48

46 0.49

54 0.50

77 0.52

100 --

the Tafel slopes for alloys with Pd surface contents higher than 50 at. %, the extrapolation was made taking this slope variation into account. DISCUSSION

The exchange current densities obtained as explained above may be plotted vs. the alloy surface composition (Fig. 12). In alkaline solution, this curve (Fig.

(a)

.2" -g -10

(b)

-7

i

,

I

(c)

-8

-g(

'

2b'

'

'

loo

At % Pd (sup.compn) Fig. 12. D e p e n d e n c e of the exchange current density i0 for m e t h a n o l electrocatalytic oxidation with the surface c o m p o s i t i o n (at.% Pd) of p l a t i n u m - - p a l l a d i u m electrodes (50°C, 0.1 M CH3OH): (a) in 0.5 M H2SO4; (b) in 0.25 M K2SO4; (c) in 0.5 M KOH.

102

12c) displays a pronounced maximum for a surface composition of a b o u t 15 at. % in palladium. This synergistic effect is relatively important, since the exchange current densities are up to 10 times greater than for platinum, the most active pure metal. Conversely, in acid (Fig. 12a) and neutral media (Fig. 12b), there is no such maximum and the exchange current densities decrease monotonically from pure platinum to pure palladium. Nevertheless this corresponds to a synergistic effect, since the activity of alloys is higher than the weighted activity of the two metals. I n the present state of our knowledge and investigations, it is hard to explain quantitatively the origin of this synergistic effect. Such effects are also observed in heterogeneous catalysis [22], and in electrocatalysis [23], either for other electrodes [9] or other reactions [ 16,24]. Three types of explanations may be invoked to interpret such effects: (1) Modification of the electronic properties and collective surface properties by alloying two metals. (2) Modification of the activity through bifunctional electrocatalysis mechanism. (3) Enhancement of the overall reaction rate by decreasing the electrode poisoning. The first explanation is difficult to take into account since platinum and palladium have very similar electronic properties [25], and the Fermi level does not change very much in the alloys. The second one has been proposed by M o t o o and Watanabe [9], each atom playing a definite role in the overall oxidation process. For example, platinum atoms adsorb methanol leading to an adsorbed residue (HCO)ads, or (COH)aas. Then the other metal, such as ruthenium, adsorbs OH radicals at more negative potentials (from 0.35 V vs. RHE in this case) than platinum, which leads to an increase of the oxidation rate by increasing the rate of the chemical surface reaction between methanol residue and OH radicals through an increase of the OH concentrations. In our case this explanation does not work because Pt and Pd, having very similar properties, the coverage by OH radicals occurs in the same potential range, although Pd is slightly more easily oxidizable than Pt. The third explanation may interpret our results in acid medium, because Pd is completely inactive in this medium. As previously stated, the platinum electrode is blocked by the formation of a strongly b o u n d species, such as (~COH)ads , which requires three neighbouring Pt sites to be adsorbed. As far as this requirement is fulfilled, the electrode surface is slowly covered with this poison, and the electrocatalytic activity decreases according to the rough mechanism [6] for the overall oxidation process: CH3OH -+ (COH)~d~ + 3 H ÷ + 3e: (at potential above 0.35 V vs. RHE)

(Ia)

(COH)ads + H20 mow CO2 + 3 H ÷ + 3 e-

(Ib)

Alloying platinum with palladium, which is inactive in acid medium, results in diluting the platinum sites, which prevents the presence of the three adjacent sites necessary for the formation of the strongly b o u n d intermediate. For alloy electrodes of surface composition > 33 at. % Pd, it is statistically difficult to find three adjacent Pt sites. Only two neighbouring Pt sites are n o w available

103

for CH3OH adsorption, which favours the adsorbed species ( : C O ) a d s . This leads to the other methanol oxidation path, according to the rough mechanism [ 7]: CH3OH -* (CO)ad s + 4 H ÷ + 4e-

(IIa)

( C O ) a d s -b H 2 O

(IIb)

relatively slo T C O 2 "b 2 H ÷ + 2 e -

The rate of reaction (IIa) is smaller than that of reaction (Ia), b u t the rate of reaction (IIb) is greater than that of reaction (Ib). Consequently, the overall reaction rate is increased. F o r higher content of palladium, the electroactivity of the alloy electrode decreases because of the inactivity of the palladium sites. Thus, the electrocatalytic activity must be enhanced for a surface Composition comprised between 0 and 33 at.% Pd. ACKNOWLEDGEMENTS

The authors are very grateful to the C.N.R.S. for financial support through the A.T.P. Utilisations Physique et Chimique de l'Electricit~, and to the D.R.E.T. for a scientist position granted under contracts Nos. 78/1128 and 79/ 1138. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

K.R. Williams, An I n t r o d u c t i o n to Fuel Cells, Elsevier, A ms t e rda m, 1966, p. 111. J.O'M. Bockris and S, Srinivasan, Fuel Cells: Their Electrochemistry, McGraw-Hill, New York, 1969. V.S. Bagotzky, Yu.B. Vassiliev and O.A. Khazova, J. Eleetroanal.'Chem., 81 (1977) 229. N.A. Hampson, M.J. Willars and B.D. McNicol, Trans. Faraday Soc., 75 (1979) 2535. A.K. Vijh, J. Catal., 37 (1975) 410. V.S. Bag otzky and Yu.B. Vassiliev, Electrochim. Acta, 12 (1967) 1323. T. Biegler, J. Phys. Chem,, 7 (1968) 1571. M.M.P. Janssen and J. Moolhuysen, Electrochim. Acta, 21 (1976) 869. M. Watanabe and S. Motoo, J. Electroanal. Chem., 60 (1975) 2 5 9 , 2 6 7 . D.F.A. Koch, D.A.J. Rand and R. Woods, J. Electroanal. Chem., 70 (1976) 73. Yu.B. Vassiliev, V.S. Bagotzky, N.V. Osetrova and A.A. Mikllailova, J. Electroanal. Chem., 97 (1979) 63. A. Capon and R. Parsons, J. Electroanal. Chem., 44 (1973) 239. F. Kadirgan, Th~se de D o c t o r a t de 3~me Cycle, Universit~ de Poitiers, June 1980. C.B. Ro y, S.C. Das and H.R. Kundu, Ind. J. Chem., 14A (1976) 315. V.L. Murugkar and H. Lal, Trans. S.A.E.S.T., 12 (1977) 255. A. Capon and R. Parsons, J. Electroanal. Chem., 65 (1975) 285. B.E. Conway, H. Angerstein-Kozlowska, W.B.A. Sharp and E.E. Crlddle, Anal. Chem., 45 (1973) 1331. B. Beden, C. L a m y and J.M. Leger, J. Electroanal. Chem., 99 (1979) 251. R. Woods in A~I. Bard (Ed.), Electroanalytical Chemistry, Vol. 9, Marcel Dekker, New York, 1976, p. 1. D.A.J. Ran d and R. Woods, J. Electroanal. Chem., 36 (1972) 57, J.M. Leger, Th~se de D o c t o r a t de 3~me Cycle, Universit~ de Poitiers, November 1978. D.W. McKee, Trans. Faraday Soc., 64 (1968) 2200. R.R. Adzic, Israel J. Chem., 18 (1979) 166. B. Beden, C. Lamy and J.M. Leger, Electrochim. Acta, 24 (1979) 1157. N.F. Mott and H. Jones, The Theory of the Properties of Metals and Alloys, Dover, New York, 1958.