Hydrogen evolution reaction on sodium-tungsten bronzes

~~~~~~~~~~~~~~Arta. 1975, Vol. 20, pp 37-43. Pergamon

Press. Printed

in Great

Bntam

HYDROGEN EVOLUTION ON SODIUM-TUNGSTEN

REACTTON BRONZES

J. P. RANDIN and A. K. VIJH Hydro-Quebec

Institute of Research. Varcnnes. P.Q.. Canada

hydrogen evolution reaction has been investigated on sodium-tungsten bronzes (Na,WO,) stoichiometrles (0.34 < Y < 0.89) in sulfuric acid solutions. Steady-state current-potential relationships and capacity-potential profiles were examined The fil-si cathodic skady-stale currenpotential curve in the ascending direction indicates the presence of two distinct Tafel lines with slopes ofabout -2RT/F and -RT/2F. This behavior is interpreted in termsof alternative reactions. At low overvoltages the mechanism is fast discharge-slow clcctrochcmical desorption. while at higher overvoltagcs a fast discharge-slow recombination mechanism is indicated. The change of the rate-determining step Abshact-The

of various

from one potential range to the other is attributed to a change in the crystallographic structure of the electrode surface, eg, a lattice dimensional change of the hydrogen tungsten bronze. The Tafel slope for an electrode pre-polarized cathodically is close lo - RT/F. In this case the rate-determining step is proposed to be the surface diffusion of adsorbed hydrogen atoms to recombination sites. The u-value in Na,WO, and the platinum content of the electrode were found to have no significant effect on the rate of the hydrogen evolution reaction.

INTRODUCTION

Recently, the electrochemical behavior of sodiumtungsten bronze electrodes has been extensively studiedtl-81, undoubtedly owing to their possible use as cathodes in fuel cells. The hydrogen evolution reaction (her) has been examined on these materials by Bockris. Damjanovic and Mannan[9] and Sepa, Ovcin and Vojnovic[ 101. In the course of a recent iavestigation[X] of the oxygen reduction reaction at sodium-tungsten bronze electrodes, it was found that this reaction occurs at a potential close to the hydrogen reversible potential. The “background” current in the potential range close to that of interest for the oxygen reduction reaction corresponded to the her. An extension ul’ the study of the electrochemical behavior of Na,WO, to cathodic potentials was, therefore, of interest. The results of this investigation are prescntcd here.

EXPERIMENTAL Sodium-tungsten bronzes with an s-value between @34 and 089, and a platinum content from 1 up to 12OU ppm were investigated. The preparation and analysis of these samples were described elsewhere[ll]. Three compartment all-Pyrex cells were used with some runs performed with a rotating disc electrode. Unless otherwise indicated the measurements were carried out with a stationary electrode. The gas outlets from the cell had water-filled bubblers in order to eli-

minate the diffusion of atmospheric oxygen into the cell. The stopcocks separating the three compartments of the cell had long necks and were solution-sealed. The hydrogen bubbled in the working and the reference compartments was purified by a palladium diffusion processor (Model HPD 050, Engelhard Industries, Newark, N.J.). The helium bubbled in the counter compartment was purified as described previously[6]. Both gases were led into the cell by means of glass-to-glass connections. All solutions were made from sulfuric acid (Ultrex, J. T. Baker Chemical), sodium sulfate (J. T. Baker, certified) and conductivity water. No pre-electrolysis was conducted in the present work since it was previously noted that this pretreatment tends to produce impurities from the anode[6]. Steady-state current-potential curves were automatically recorded using 10 mV potential step per 5 min. Preliminary tests were conducted to ascertain that the true steady-state was reached with the chosen potential step program. The same current-potential relationships were obtained with programs involving much longer polarization times. The lack of hysteresis between the ascending (potentials acquiring more cathodic values) and descending values for the low potential section of the Tafel line is an indication that the equilibrium values were indeed reached with the chosen program. The instruments and the details on the electrode mounting were described previously[5-

81.

A hydrogen reference electrode in the same solution or a Hg/HgzSO, (1 N HISOb) electrode was used as

J. P.

3x

-OS-

=yz/--B

-0.5 w h4 9

-

z-o.3

-

/--

_/_/I_

/ /

/

RANDIN

-7 ,

-

w

/J’

9

G :

,-< 1’

w ---

A. K. VIJH

AND

1’

z

w-05-

-0-Z -

-0-l -

06

5

I

I

I

I

4

3

2

1

-Log

01

1

I

I

I

I

6

5

4

3

2

1

LlA.cm-21

-Logi(A

Fig. I. Steady-state

(point-by-point) current-potential relationship!, with increasingly cathodic scanning potential in I N H,SO,at Na, szW03. The curves were recorded III the order ,4. R and C. The scanning direction is indicated by

the I-&I-ence electrode. All electrode potentials are given with respect to a standard hydrogen electrode. Experiments were carried out at room temperature unless otherwlse specified.

KESULTS

Strndy-state

currunt-potrntid

rrlatiorrships

Typical steady-state (point-by-point) current-potential curves in 1 N H2S0, are shown in Fig. 1. Three main Tafel lines can be distinguished. At low overpotentials (line A), ie, for -0.45 < E < -03 V, the Tafel plot is free of hysteresis between the ascending and descending curves with a slope between - 120 and - 180 mV/dccade. When the potential is further increased in the cathodic direction, a Tafel line with a slope of about -30 to -45 mV/decade is observed (line B). Further scanning of potentials between about -0.2 and -0.6 V gave a current-potential curve (line C) with a slope around - 70 mV/decade. After pre-polarization at potentials more cathodic than about -0.5 V the current potential curve in the ascending direction did not exhibit lines A and B unless the bronze electrode was slightly oxidized (prior to cathodic polariza-

cm-‘)

current-potential curves at an Fig. 2. Steady-state electrode polarized at highly cathodic potenNa ,, ,,WO, tials in 05 M sulfate solutions of different pH values. pH = 0.3 (m), I.8 ( x 1.2.4 (O), 2.8 (0). 3.4 (A), 4,3 (A) and 115 (El). A stationary electrode was used for these measurements. lower than about 5 mA cm-l was negligibly small. At higher current densities it appears that the ohmicpotential drop associated with line C is much greater than that of line B. The analysis of the current-potential curve at the high current densities for line C indicates that the curvature at high current densities originates primarily from the ohmic drop, a part of which probably resides in the semiconducting surface layer. The data in Fig. 1 have, however, not beeti corrected for this factor because of the apparent change of this value from line B to line C. In the discussion part of I

I 0

tion).

When the maximum cathodic potential of the scan was progressively made more cathodic in region B between -0.5 and - ti6 V, the resulting scan exhibited a slope which decreased in value as the maximum cathodic potential increased. The slope of line C did not decrease further by applying potentials more cathodic than - 0.6 V. III 1 N H,SO, solution and under the experimental conditions in Fig. 1, rotation of the electrode had no significant effect on either one of the potential regions studied. The ohmic drop between the tip of the Luggin capillary and the working electrode at current densities

I

I

1

2 PH

Fig. 3. Plots of log i DSpH for the Tafel region -0.45 region

A ( x ) at E = V. Tafel region R (0) at E = -0-55 V, and T&l C(A) at E = -0.4OV. A Na,.,,WO, electrode was used at 9CQrpm in 0.5 M sulfate solutions.

Hydrogen

evolution

Fig. 4. Plot of 9 (V US rht*) ~i.7pH for the Tafel region A ( x ) at I’= -0-05 mA/ctYZ, Tafel region B (0) at i = - 5 mA/ cm-‘. and Tale1 region C (A) at i = -@05 mAjcm_ ‘. A Na,,.,,WO, electrode was used at 900 rpm in 06 M sulfate

stllulions. this paper only the current-potential curves in potential ranges where the ohmic-potential negligible will be considered. pH-drpende~zcr

ofthe current-potential

recorded drop is

relationships

curves for the her at in Fig. 2. The curves correspond to an electrode polarized at highly cathodic potentials (line C in Fig. 1). The relationships did not exhibit a significant hysteresis between the ascending and descending (on the potential scale) measurements. The first scan giving the two separate relationships A and B was not taken into consideration in Fig. 2; this will be considered later on (Fig. 5). Three main regions can he distinguished in Fig. 2: (i) at low cathodic potentials where Tafel lines correspond to the her by H,O’ discharge; (ii) at intermeSteady-state

current-potential

various pH values are depicted

-04

1

6

39

reaction

diate potentrals where a limiting current density indicates that the rate of the reaction is limited by the diffusion of H,O*, as will be shown later on by means of the rotating disc technique (Fig. 6): and (iii) at highly cathodic potentials where Tafel lines are associated with the hur proceeding by the dlschargc of H20. The reaction order for the lower Tafel region in Fig. 2 (corresponding to region C) can be extracted from Fig. 3, in which log i at a given electrode potential has been plotted GSpH. The chemically significant reaction order[12], (2 log i/c’ PH)~,~~,.~is found to be P9 and the pseudo-reaction order (?q/ii pH),,,, .r is 0.00 V (Fig. 4). The data in Figs. 3 and 4 were restricted to values measured at pH lower than 3 because of the lack of buffering power of the electrolytes with higher pH values that make its proton concentration too unstable to permit reliable measurements. It is evident from l-‘ig. 2 that ‘rhe reaction order is zero for the upper I‘afcl lines because the Ilcr proceeds by the discharge of H20. The first ascending steady-state current--potentin relationships for the Irrr. at various pH values are given in Fig. 5 The rotating disc assembly has been used for these measurements to minimize problems associated with the diffusion in the electrolyte and to extend the potential region B. The two Tafel lines with different slopes corresponding to lines A and B are found for all pH-values studied [Fig. 5). The rotation ofthe electrode had no significant effect on the current density in either of the two regions A and B. The current density in the diffusion limiting region (Figs. 2 and 5) was a function of the rotation rate as shown in Fig. 6. The linear plot of l/Y r:s,f’- I shows that the hrr is first-order with respect to H,O* and is purely diffusion-controlled at E = -08 V and at pH 1 2.9. since the extrapolation LoJ- : = 0 yields a zero intercepl. The reaction orders for lines A and B can be derived from Figs. 3 and 4. The values are collected in Table I. The dispersion in the results obtained for the region

I

I

I

I

5

4

3

2

- Log

I 1

I

L t A cm-‘)

steady-state current-potential relationship in @5 M sulfate solutions of different pH values; pH = 0.3 (o), 1,7(O) and 2.7 (A). The disc electrode was rotated at 900 rpm.

Fig. 5. First ascending

J. P.

40 Table

RANDIN

AND

A. K. VIJH

I. Reaction orders observed in the different lower Tafel lines before diffusion control takes over (see Fig. I ) m

O-7 ._ 0.9

A

5 C

-

I

r

I

I

4

1

1/,/’

0 0

~(*~)~1;7;;h T

[(3 log i)i(c’PH)I,,,T

Relationship

1

J

DO2

,

-I

I

004 ,-I12 (rpmlY2

006

Fig. 6. A plot of I,‘i USf‘ i for the hydrogen evolution reaction on Na,, n5W03 in 0.01 N H2S0, + 0,495 M Na2S0, (pH 2 2.9) at E = -0.X V.

52 0 0

with I/WC. indicating that the process is completely reversible and purely controlled by diffusion.

The rate of the hrr was found not to depend (within the experimental scatter) either on the u-value in Na,WOx (for x between @34 and @89), or on the platinum content of the bronze electrode (from a few up to 1200 ppm). A bronze electrode preoxidized at IO mA/cmm2 for 30 min exhibited a current-potential curve similar to that reported in Fig. I for a non-oxidized electrode but with current densities higher by almost one order of magnitude over the entire potential range studied. Similar, although less pronounced effects, were found for the oxygen reduction reaction[S]. Part of the effect may he attributed to an increased specific area of the electrode[7] and possibly a part to some sort of a catalytic effect. Hydrogen oxidation

B (Fig. 3) does not allow a precise i) ,‘? pH, however.

value for the i (log

Galvanostatic charging curves performed on Na,WO, in He-saturated I N H2S0, were previously ruporled[6]. The capacity-potential profiles calculated from them showed very high pseudo-capacitances. Ac impedance measurements were also reported previously[7] and confirmed the presence of a high pseudo-capacitance. The series capacitance and resistance components of the QC impedance measured at about -0.4 V were found to give two parallel straight lines when plotted t’s (I)~ ‘173, In this previous study the real and imaginary components of the impedance were not corrected for the ohmic resistance of the electrolytc and for the double layer capacitance. In the present work further impedance measurements were performed at potentials more cathodic than those in the previous investigation. Furthermore, the ohmic resistance of the electrolyte was subtracted from the real part of the impedance and the double layer capacitance separated from the imaginary part of the admittance.Thc resultsgiven in Fig. 7 show that straight lines for R and I/WC (series configuration) c‘s w-j are obtained. Within the experimental error R coincides

Steady-state current-potential relationships carried out in hydrogen or helium saturated I N H,SO, showed no significant difference in the anodic potential range, indicating that sodium tungsten bronzes of the composition investigated in the present work have no activity toward the oxidation of hydrogen. This result confirms findings by Armstrong et U&Z].

0

002

004

006 "-VP

008

010

Fig. 7. Frequency dependence of the ohmic (open symbols) and capacitive (solid symbols) components (series configuration) of the fardaic impedance of Na, ,,WO, in Hz-saturated I N H,SO, at -0.35 V (circles), -0.52 V (triangles) and -058 V (squares), in the order indicated.

41

Hydrogen evolution reaction DISCUSSION

Previous studies[il, 673 on the electrochemical behaviour of sodium-tungsten bronzes have postulated the formation of hydrogen tungsten bronze at potentials as anodic as about 0.2 V. The same conclusion has been reached recently from the electrochemical reduction of Na,WO,[13] and WO,[t4] in acidic media. On the basis of these findings, it will be assumed in the following discussion that the surface layers of the sodium tungsten bronze electrode are saturated with hydrogen. The surface composition may be represented by Na,H,WO,, where x -+ z is likely to be one. or even greater than one, at high cathodic potentials. Under these conditions the coverage of the electrode surface by adsorbed hydrogen or a hydride layer is expected to be high. The discrepancy between this assumption and the results from the gas phase adsorption of hydrogen at bronzes (maximum coverage 0.05[13, 151) is apparent only. During the electrochemical evolution of hydrogen, the presence of an overpotential gives rise to a situation comparable to an astronomically high gas pressure with the result that the application of the gas phase adsorption data obtained under atmospheric pressures to the electrochemical situation is misleading. For example, Kita[ 161 pointed out that a cathodic overpotential of 0+4 V corresponds to a pressure of about IO’ ’ mm Hg of hydrogen. Vermilyea[ 171 and Van R ysselberghe[ 181 discussed the possible formation of surface phases (which are thermodynamically and kinetically unlikely under ordinary conditions) on electrode surfaces at moderate Vdhes of overvoltage. equivalent to enormously high gas pressures. Hence high coverage by H under conditions of cathodic polarization is not inconsistent with low coverage observed in the gas phase adsorption studies. On solid electrodes the first scan of a potentiostatic curve is often found to differ from the subsequent ones, owing to various surface transformations occurring during the first polarization. For this reason the first scan is usually disregarded in the mechanistic interpretation of the results. In the present investigation, however. the current-potential relationship obtained at low potentials (tine A) is reproducible and free of hysteresis. It seems justified, therefore, to take the entire potential range into consideration in order to explain the different processes occurring in the various potential regions. The first steady-state current-potential curve (Figs. 1 and 5) indicates the presence of two distinct Tafel relationships (A and R) with slopes h, - - 120 mV/ decade and hs = - 30 mV/decade. For a given change of potential a smaller change of the electrochemical rate constant arises for process A than that for reaction B for the same change of potential, since h,, is greater than h,. The behavior obtained in Fig. 5 is typical of alternative pathways for regions A and 81191. This occurs because in alternative reactions (parallel) the faster path predominates in determining the rate and the reaction route.

In acidic solutions the 1tcr usually proceeds through the discharge of H30i : H,O+ followed path :

by

+ cm + M-+M-H either

the

electrochemical

M-H+H,O++r~-iM+HL+H1O or the recombination

+ II,0

(1) desorption

(2)

path:

2MH+

2M + HZ.

(3)

Rriurior~ship A (Figs. I and 5) The slope of the steady-state current-potential curve in region d is between - 120 and - 180 mV. The high Tafet slope may qualitatively be attributed to the fact that part of the potential drop occurs across a semiconducting surface layer of some sort of hydride. It has. indeed, been observed that the surface film of the sudium-tungsten bronze is depleted of sodium[7]. Furthermore, at cathodic potentials a proton space charge is most likely to be present within the electrode (see below) giving rise to an additional potential drop. Therefore the Tafel slope greater than lZRT/fl as well as its variation from one experiment to the other and from one sample to the other may be attributed to some variations of the surface film. For the simplicity of the discussion, it will be assumed that the transfer coeflicient is 05 and, therefore, that the Tafel slope is - ZRTF. A Tafel slope of - 2RT/F and reaction orders (C log i/i; pH),,.,= 0.7 (which may be approximated by the theoretical value of t), and (&I/? pH),,,,, -- - 60 mV/ decade indicate that the rate determining step (r&) of the hrr is reaction (2)_ assuming a high hydrogen surface coverage of the electrode. It may be mentioned that the stoichiometric number is not accessible. owing to the solid-state reactions occurring near to the reversible potential.

The slope of the Tafel line 5 is between -35 and 45 mV/decade and the reaction order (?~/?(PH))~,$.~ 1 0. The reaction order (L1log i/C PH)~,~,~- is not clearly defined (Fig. 3) but is between 1 and 2. The experimental Tafet slopes foi- lines A and C are always found to he greater than the theoretical ones because of some potential drop occurring across the semiconducting oxide surface layer. Therefore, the significant slope of line R is believed to be -30 mV/decade. Also a slope of -40 mV/decade would be incompatible with the reaction order indicated by the experiments. From the foregoing data it is proposed that the Irer occurs through a fast discharge-slow recombination mechanism in region B. The data obtained imply that hydrogen coverage of the electrode surface is a function of the electrode potential since one has not yet reached the potential region in which a recombinationcontrolled limiting current might be observed. The

42

J. P.

RANDIN AND A. K. VIJH

potential-dependence of “electrode coverage” at higher cathodic potentials, when the surfice coverage by adsorbed hydrogen has already been indicated to bc unity at lower cathodic potentials, can arise if one assumes the potential-dependent formation of a multilayered hydrogen bronze (or a change of lattice composition) at the higher cathodic potentials. The change ofrds from region A to B possibly arises from a change in the crystallographic structure of the electrode surface, “9, a lattice dimensional change of the hydride at high cathodic potentials. The parameter of the electrode lattice is known to be of great importance in the case of reactions involving a rds of the recombination of atoms adsorbed on adjacent clectrode sites[9, 201. The occurrence of such a reaction depends on the stretching of two M-H bonds and an optimum M-M distance. This latter is expected to decrease the energy of activation and, hence. increase the rate of reaction. Relatioizship

c (Figs. 1 und 2)

The Tafel slope for an electrode previously polarized cathodically is close to --RT/F and the reaction orders ((7log i,‘a pH),,, - 0.9 and (?v/S pH),,,, 1 0. These data are in agreement with a rds involving the surface diffusion of adsorbed hydrogen atoms to recombination sites. This recombination mechanism. in which one hydrogen atom is adsorbed and the other is not. was formulated by Pentland, Bockris and SheIdon[21]. The mechanism is comparable to that known at a catalytic surface in the gas phase, ic: M--H

it H (y) -t- M

(4)

M--H

t H (9) $ H,

(5)

Hiyhll, cuthodic putrrr/iuls In this potential range a Tafel slope of about - I20 mV/decade and a reaction order of one were found (Fig. 2). These facts would indicate that the electrochemical desorption is the rds, as was suggested for the relationship A, with the reaction occurring at these highly cathodic potentials by the discharge of H,O instead of that of H30C: M + H,O M-H lrnprdamr

+ H,O

+ cm F?M-H+OH+ e- 3

M + H, + OH-

(6) (7)

at highly cathodic potrntirtls

The impedance measurements carried out at high cathodic potentials did not reveal the complex frequency dependence expected for a faradaic process involving adsorption such as the her. No significant differences were found between the results obtained at low and high cathodic potentials (Fig. 7). The behavior of the impedance components (Fig. 7) is characteristic of a process controlled by diffusion with a negligibly small activation ovcrpotcntial, it, the reaction is complctcly rcversible[ 131. As no diffusion was observed in the electrolyte. the diffusion occurs in the solid-state.

The process may be the result of protons entering the oxide from the electrode surface as the potential is made cathodic, thus creating a proton space charge within the oxide electrode[22]. The data in Fig. 7 are, therefore, best interpreted as resulting mainly from the diffusion of protons within the electrode. The diffusion components of the impedance are so large that the charge-transfer resistance and the components from the desorption process subsequent to the discharge step have no significant influence on the total impedance values. The difference between the impedance values obtained at low and high cathodic potentials may be attributed to a roughening effect which increases the electrode surface, as shnwn previously by scamling electron microscopy[7]. The impedance data support further the mechanismx proposed for the IILJI.since the initial proton discharge is shown to be a fast process and the hydrogen content of the surf’dce should, consequently, bz high. E,ficr ~$ll~r x-value i/l Nu,WO,. Bockris, Damjanovie and Mannan[9] claimed that the i, values for the Ivr on Na,WO, pass through a minimum at .X = 0.65. whereas Sepa. Ovcin and Vojnovic [ 101 found a maximum at approximately the same s-value. In the present study the rate of the I?er was found not to depend (within the limits of experimental error) on the r-value of the bronze electrode. According to Frumkin et u1[20] the electrocatalytic properties of an electrode depend mainly on the chemical composition of its surface and not on its bulk electronic properties. In view of the hydride formation occurring at the surface of the bronze electrode, and the large proton space charge present at cathodic potentials (see above), it is unlikely that the bulk .Yvalue of Na,WO, will have a significant effect on the rate of the /ICY.The results of the influence of the .Yvalue on the rate of the hi obtained by Bockris et u&9] and Sepa YI a![ lo] are in contradiction with each other and are believed to he due only to the scattering of the measurements. The lack of an unambiguous dependence of the rate of the IICYon the s-value found in the present study is in agreement with the abovementioned interpretation of the elcctrocatalytic effect. E,flticr c$tmcrs ~f’platitu~~~~. On platinum the IIL’I.proceeds by a recombination step similar to the rds proposed on Na,YWO, in the region I% The adsorption of hydrogen on platinum is determined hy the parameters of the platinum lattice rather than by those of an isolated platinum atom. The recombination step will consequently not he favored by a low concentration of active metal in the surface layer. The rate of the hrr on bronzes is therefore not expected to change significantly in the presence of traces of platinum in the bronze. This hypothesis has recently been confirmed in a study of the effect of platinum crystallite Ge on the kinetic parameters for the elrctro-oxidation and deposition of adsorbed hydrogen. Stonehart and Lunduist[23] have shown that a platinum size ofabout 300 II was needed to confer “bulk” properties to platinum.

Hydrogen

evolution

Although the crystallite size of platinum in bronzes is not known, it is not expected to be greater than a few hundred AngstrGms. Consequently the conclusions reached by Stonehart and Lundquist are probably also valid for the case of bronzes containing platinum. The results of the present study are in agreement with the above-mentioned interpretation since no significant effect of the traces of platinum was found. The same lack of catalytic effect of platinum in Na,WO, has also been found for the oxygen reduction reaction[X]. This latter result is in conflict with the findings by Bockris ~‘r ~431 who found a large increase in the rate or the oxygen reduction reaction when platinum was introduced into the Na,WO,. Ackrion,i~dycrnc~f~s~The assistance

of Mr. R. Bellemarc is gratefully acknowledged Thanks are also due to Dr. G. G. Clouticr, Director of Research. IREQ. for his interest and encouragement. with

the experimental

work

4. 5. h.

8. 9.

Ii). I I. 17.

13. REFERENCES I. D. B. Sepa. A. Damjanovic and J. O’M. Bockris. EIecrrochirll. Acru 12. 746 (1967); A. Damjanovic. D. Sepa and J. O’M. Bockrls, d. Rss. Ifrst. Catuljsis Hokkaido Cnitl. 16, 1 (1968): B. Rroyde, J. Cmtolysis 10, 13 (I 968): J. M. Fishman, J. F. Henry and S. Tessorc, Elucrmchi,n. At*rtr 14, 1314 (1969); J. O’M. Bockris, A. Damjanovic and J. McHardy. Proc. 3rd Irlf. S~,/?tp. Fur( Cells, Brussels, Belgium, I&20 June, 1969, p. 15. Press Acad. Europiennes. Brussels. (1969): R. A. Fredlein and J. McHardy, 24th Power Sources Symp. p. 175. P.S.C. Pub. Committee. Red Bank. N.J. (1970): J. McHardy and J. O’M. Bockris, in Frvnt E lectrocntcrlvsis to Fwl Cells (Edited by G. Sandstede). p. 109, Univ. Washington Press Scattlc. Washington (1972): J. HctHer and H. Bohm, M~rtrfoharfiarcile .411{/rw. Electrolhertl. 27, 77 (1973). 2. R. D. Armstrong, A. F. Douglas and 0. E. Williams. ulil,r:/ri? Corlrrrsiorl Il. 7 ( 197 I ).

14. 15. 16. 17.

IX. 19. 70. ?I.

22. 23.

reaction

43

I. O’M. Bockris and J. McHardy, d. &crroche,n. Scic. 120. 61 (1973). 1. McHardy and J. O’M. Bockris. J. clucrrochrrn. 120, 53 (1973). 1. P. Randin, .f. &crrdm. Sm. 120, 378 (1973). J. P. Ran&n. A. K. VlJh and A. B. Chughtai. J. elrctro&r,1. sot 120, I I74 (1973). J. P. Randin, Eluctrochim. Acfa 19, 87 (1974). J. P. Randin, /. ~lectroannl. Chem. 51. 471 (1974): J. ~&ctrochem. Sot. 121, 1029 (1974). J. O’M. Bockris. A. Damjanovic and R. Mannan, J. c~l~~ctroumrl. Chw. 18, 349 (196X); R. Mannan, Ph.D. Thesis. University of Pennsylvania (1967), Un~v. Microfilms. Ann Arbor, Mich. No. 68-4595. D. B. Sepa. D. S. Ovcin and M. V. VoJnovlc. d. clrctroc/1r,n. SOCK.119, 1285 ( 1972). J. P. Randin, J. &crr*ochern. Sot. 120. 1325 (1973). E. Gileacli and B. E. Conway, in Modc)rrl Aspects of C/~,c~r,.oc~heririsrr~(Edited by J. O’M. Bockris and B. E. Conwavl. Vol. 3, D. 347. Butterworths. London. (I 964). J. Vonhrak and j, Balej. Elrcfrocllir,!. Actu 18; lOI? (1973). G. Siclet. J. Chewier. J. Lenoir and C. Eyraud, C. R. khd. Sram Ad. Sci. Puris. 277 C, 227 ( 1973). F. T. Jones and E. M. Loebl. J. plr_vs. C&m. 73, 894 (1969). H. Kita. J. efcctroclleril. Sot. 113, lOY5 (1966). D A. Vermilyea. in [email protected] in Electmciwrnisrry anti EI~ctroche,,ticct/ E~~giwrring (Edited by P. Dclahay), Vol. 3. D 21 I. Interscience Pub.. New York (1963). P. van kyssclberghe, J. cll~rtl. Phl~. 20, I522‘( 1952). B. E. Conway. Theory und Pririciplvs of Electrode Pro~~~w~~.s. p. I IO. The Ronald Press Co.. New York (1965). A. Frumkin. N. Polianovskaya. I. Bagotskaya and N. Grigorycv. J. ulertrounal. Chum. 33, 3 19 (1971). N. Pcntland, J. O’M. Bockris and E. Sheldon. J. &crrnchf~,w. SOL.. 104, I x2 (1957). D. A. Vermilyea. J. Phw. Chrm. Solids 26, 133 (1965); J. c,/ccrrnchrrrr. Sot. 115, 177 ( 1968). P. Stonehart and J. Lundquist, Electrochi!,l. Acta 18, 907 (1973).