VOLTAGE TRANSIENTS OF FRESHLY PRODUCED NOBLEMETALSURFACES
3329
Voltage Transients of Freshly Produced Noble Metal Electrode Surfaces
by R. S. Perkins, R. C. Livingston,' T. N. Andersen, and H. Eyring Rate Processes Institute, University of Utah, Salt Lake City, Utah (Received M a y 1 1 , 1566)
The faces of Pt, Pd, Au, Cu, and Ag electrodes were scraped off in Nz-saturated solutions of varying ion types, ion concentrations, and pH. The accompanying potential transients show peak potentials which vary with anion type and concentration in a manner qualitatively similar to the variance of zero charge potential (z.c.P.) or electrocapillary maximum of mercury in the same solutions. The peak potentials, however, are also more negative in solutions of higher pH. The mechanism of establishing the peak potentials is discussed, as well as the relationship of these potentials to zero charge potentials. In the case of all metals studied, reactions spontaneously drive the potential positive from the Z.C.P.
Introduction I n a previous communication2 we introduced a method for determining zero charge potentials (z.c.P.) of solid electrodes. The method consists of generating a completely new electrode surface by rapidly scrap,ing or cutting off the existent surface (with its charge and double layer) and measuring the accompanying opencircuit t r a n ~ i e n t . ~If certain criteria are satisfied, the resulting potential transient peak, Vpk, is the zero charge potential. These criteria are: (1) that adsorption must approach equilibrium before appreciable reaction occurs to change the electrode charge4; (2) that the experimental scraping and recording times must be sufficiently rapid to separate the adsorption and reaction processes; and (3) that a sufficient number of scrapes be performed that charge redistribution from the departing metal shaving onto the fresh surface be negligible. In the present paper, the method is applied to several systems in order to determine to what extent the above criteria are experimentally satisfied. Criterion 1 can best be satisfied by dealing with noble metals in nondilute simple ionic solutions. From such solutions the time for specific adsorption of ions would be expected to be less than sec. (as it is onto m e r c ~ r y )provided ~~~ that the adsorption is of the nonhomopolar type (as evidence indicates is the case for Hg),' and providing the metal electrodes do not contain deep pores. By studying noble metal electrodes the reaction should be limited to solvent reduction or oxidation which are slow compared to
many metal dissolution reactions. Criterion 3 can be determined experimentally by comparing the size of transients for different numbers of successive scrapes of the electrode. Whether criterion 2 is satisfied in a given experiment cannot be simply determined, but rather all evidence for the separation of adsorption and charge-transfer reactions must be considered. Such a separation is apparently feasible for some systems as evidenced by results of the dip m e t h ~ d . ~ In the present case, the peak potential should reach a limit with increase in the rate at which fresh metal surface is exposed. This condition does not alone satisfy criterion 2 since a very fast reaction may be over in a time too short for us to measure. To eliminate the possibility that such fast reactions are occurring, other evidence such as Vpk trends with variation of ion types, ion concentrations, pH, and electrode composition must be considered. This paper considers the (1) Summer N.S.F. Undergraduate Research Fellow, 1964. (2) T. N. Andersen, R. S. Perkins, and H. Eyring, J. A m . Chem. SOC., 86, 4496 (1964). (3) The present method has little relationship to the Billiter scrape method [J. Billiter, Trans. A m . Electrochem. SOC.,5 7 , 351 (1930); 2.Elektrochem., 14, 624 (1908)l. (4) The "dip" method [B. Jakuszewski and 2. Kozlowski, Rocrniki Chem., 36, 1873 (1962)l utilizes the separation of double-layer
formation and Faradaic processes but involves the uncertainty of the predip environment of the electrode and hence differs from the present method. (5) V. I. Melik-Gaikazyan and P. I. Dolin, Dokl. Akad. S a u k SSSR, 64, 409 (1949).
(6) V. I. Melik-Gaikazyan and P. I. D o h , Tr. Inst. Fiz. Khim., Akud. Nauk SSSR, No. 1, 115 (1950). (7) T. N. Andersen and J. O'M. Bockris, Electrochim. Acta, 9, 347 (1964).
Volunae 69,Number 10 October 1566
3330
R. 8. PERKINS, R. c. LIVINGSTON, T. N. ANDERSEN, AND H.EYRING
above-mentioned effects on Vpk, as well as the rate of the transient decay a t the same potential, relevant to the judging of the suitability of the present method for determining Z.C.P. values. Comparisons of V p k values wit,h 2.c.p. values obtained by independent methods is also made.
Experimental Section Apparatus and Material. The Pyrex electrolytic cell is shown in Figure 1. The test electrode was inserted into the solution through the side of the center compartment of the cell. This electrode consisted of a length of metal wire tightly fitted in a cylindrical Teflon tube in such a way that only the face of one end of the wire was exposed to the solution. The wirecontaining tube was inserted into the cell through another Teflon connection. The reference electrode used throughout the work was a saturated calomel electrode connected to compartment 2 of the test cell by an agar-KC1 salt bridge. Extending into the solution through a Teflon stopper and a mercury seal was an alumina rod attached to a variable speed motor capable of 17,000 r.p.m. The end of the alumina rod was shaped into a cutting form which was used to remove the entire surface of the electrode, thus exposing a new surface. Another cell, similar in design to that described above, was also used for hand scraping of the electrodes and differed in appearance from the above cell only in the manner of sealing. Hand or manual scraping was accomplished by vertical motion of a n alumina or Pyrex rod (with identical results in either case). This system was kept gas tight with an inflated inverted polyethylene bag covering the top of the cell and attached securely to the scraper. The hand-scraping device was more convenient and faster to use than the powered scraper, and when comparison of the peak potential values obtained from the two types of scraping showed that they were in close agreement, the hand scraper was used to complete studies of anion and concentration effects. Potential measurements were made with an Offner Type P dynograph assembly containing a Type 9405 cathode follower coupler which provides log ohms input impedance. This instrument amplified the voltage output and recorded it on a strip chart recorder. The maximum chart speed was 100 mm./sec., and the full scale balance time of the needle did not exceed 0.005 sec. The internal input impedance of the dynograph was high enough to not influence the results as was shown by comparing the results with those obtained by feeding the input first through a Keithley Model 6108 electrometer, of 1014 ohms internal imThe Journal of Phyaical Chemistry
-
compartment 2
L-y-------)
compartment I
-
compartment 3
Figure 1. Schematic diagram of electrolytic cell: (1) electrode; (2) Teflon tubing and connections; (3) salt bridge; (4) Teflon stoppers; (5) mercury seal; (6) aluminum oxide scraping rod; (7) variable speed motor; (8) mercury seal stopcock (no grease); and (9) auxiliary electrode.
pedance. The response time of the dynograph was fast enough to follow the potential as was shown by comparing transients recorded on it to those recorded on an oscilloscope. The test electrodes used were wires of 0.020-in. diameter (supplied by A. D. Mackay Co.) and of the following minimum purities: Cu, Ag, and Au, 99.95%; Pt and Pd, 99.990/,. The solutions used were prepared with reagent grade chemicals and water twice distilled from a basic permanganate solution.* Experiments were run with prepurified (99.997%) nitrogen bubbling through the cell. The peak potentials in solutions open to the atmosphere were 0 to 50 mv. more positive than those in N2-saturated solutions, indicating that O2leakage in the latter case could be neglected. Procedure. After cleaning and assembling the cell, the powdered scraper was begun rotating a t some arbitrary speed, and the electrode was moved against it. The electrode was scraped approximately 20 or 30 times before being withdrawn. The above procedure was repeated four to five times, and then the scraper was set a t a higher speed. Repetition of this procedure usually initially produced a larger voltage transient, but the size of the transient, or the value of V p k , soon became constant with increase in scraping speed. A typical result is shown in Figure 2 in which the time scale is the order of several seconds. (8) This degree of purity has been found sufficient to give satisfactory zero charge potentials in the case of the streaming mercury electrode.
VOLTAGE TRANSIENTS OF FRESHLY PRODUCED NOBLEMETALSURFACES
3331
values were obtained in many of the experiments in order to estimate the error in the electrode charge caused by the finite scraping time and also in order to estimate the order of net reaction rate which the scraping process can “outrun.”
ipk
Experimental Results
TIME Figure 2. Appearance of experimental data as obtained. Curve 1 is for a single scrape and curve 2 for multiple scrapes.
I n the case of manual scraping, one pass over the metal produced a smaller transient than did many successive scrapes. Since it was considered that this was due to incomplete removal of the old surface or incomplete removal of the charge, due to charge redistribution, the more reproducible “many-scrape” Vpk was the peak potential which was recorded. The peak potential, Vpk, was independent of the prescrape potential, V’,,, as shown by varying the latter, in several experiments, from the stable steady-state potential to values several hundred millivolts negative of the peak potential. Such experiments were executed by cathodically polarizing the electrode to the desired prescrape potential, whereupon the polarization was stopped and the electrode was scraped while its potential decayed. A marked difference in the natural decay rate and the scrape-induced potential shift from these negative prescrape potentials was noted for most systems. The net rate, 2 i c a t h - 2 i a n o d , at which Faradaic reactions occur at Vpk, and hence add charge to the electrode, can be measured as follows. Under open circuit conditions and a t all decay potentials
where dqdL/dt is the rate of change of charge on the electrode, and Zicath and z i a n o d are the summations of the currents produced by all cathodic and anodic reactions, respectively. If the electrode is potentiostatted at v p k by passing through it external current i p k (under steady-state conditions), then dqdL/dt = 0 and
The peak potentials, steady-state potentials, i p k , and comparison of manually and power-scraped peaks are given in Tables I through V. The Z.C.P. and amount of specific adsorption for mercury in corresponding solutions given in Table VI were determined by Grahame and co-worker~~-’~ and by Wroblowa, Kovac, and Bockris.13 The reproducibility of Vpk values as determined from repetitive experiments (ie., different solutions, days, etc.) is given in the results as a value following the Vpk value. Detailed comparison between manual and power scraping is made later. Junction potentials were omitted since they were smaller than the experimental deviation. The potentials are recorded relative to a normal hydrogen electrode with the potential of the saturated calomel electrode being taken as +0.242 v. (European sign convention). The potentiostat experiments (ipk) were run in the manually operated cell. After the tables are also given qualitative observations concerning the transient decays, which are relevant to the explanation of the data in the tables.
Table I: Experimental Results for Gold [Potentials in volts i p k in amp. cm.-2 (Geometrical Area)]
us. N.h.e. and
Vpk
Solution 0.1 N KF 1.ONKF 0 . 1 N &SO4 0 . 0 1 N KCl 0.1 NKCI 1.ONKCl 0.1 N KC104 0 . 1 N KNOa 0 . 1 N KBr 0 . 1 N KSCN 0.1 N KI 0 . 1 N KzSO4 (pH 12) 0 . 1 N KzSO4 (PH 3) a
VB B +0.17 +0.17 +0.17 +0.17 +0.17 +0.17 +0.17 4-0.17 +0.17 +0.17 $0.17 +0.20
+0.41
f 0.17 f 0.17 f 0.17
f 0.17 i 0.17 f 0.17 f 0.17 f 0.17 f 0.17 f 0.17 f 0.17
(manual scraper)
-0.06 -0.06 -0.06 -0.05 -0.11 -0.19 -0.18 -0.04 -0.26 -0.44 -0.47 -0.00
* 0.02
ipk
2 . 5 X 10-0
f 0.02
f 0.02 zk 0.02
* 0.OP f 0.02 f 0.02 j.
3.5
x
10-0
7.5 x 10-0 1 . 0 x 10-0 2 . 2 x 10-5
0.02
f 0.02 f 0.02
* 0.02
3 . 0 X 10-6
1.5
x
10-5
f 0.OP + 0 . 1 4 f 0.02
Potential also measured with power scraper.
(9) D. C. Grahame and B. A. Soderberg, J. Chem. Phys., 2 2 , 449 (1954). (10) D.C. Grahame, J. Am. Chem. Soc., 80,4201 (1958). (11) D.C.Grahame, J. Electrochem. SOC.,98, 343 (1951). (12) D.C.Grahame, E. M. Coffin, J. I. Cummings, and M. A. Poth, J . Am. Chem. Soc., 74, 1207 (1952). (13) H.Wroblowa, Z.Kovac, and J. O’M. Bockris, unpublished.
VoEume 69,Number 10 October 1966
R. S. PERKINS, R. C. LIVINGSTON, T. N. ANDERSEN, AND H. EYRING
3332
Table 11: Experimental Results for Copper [k'.. and Solution
0.1 N 0.1 N 0.1 N 0.1 N 0.1 N Vpk
Vpk
us. N.h.e. (in volts) and
Vsa
KF KC1 KBr KI KCl (pH 2 . 3 )
-0.12 -0.12 -0.12 -0.12 $0.06
f 0.07 zk 0 . 0 7 f 0.07 i 0.07
in amp. cm.-l (Geometrical Area)]
ipk
Vpk
vpk
(power scraper)
(manual scraper)
- 0 . 5 0 f 0.02 -0.64 f 0.02 -0.70" -0.71" -0.36"
-0.30 -0.36 -0.49
1.0 X
( a t -0.64 v.)
had not leveled out at maximum scraping speed.
Table 111: Experimental Results for Platinum (Potentials Are Given in volts us. N.h.e. and Solution
vas
0 . 1 .V K F 1 . 0 .V K F 0 . 1 r\a 0 . 1 .V KC1 1 . 0 -V KC1 0 . 1 ,V KC104 0 . 1 ,V KBr 0 . 1 iV KSCN 0 . 1 i V KI O . l , V K C l ( p H 11.5) 0.1 iV KCl ( p H 2 . 7 ) 0 . 1 iV &So4 (PH 2 . 3 )
$0.34 $0.34 $0.34 +0.34 $0.34 +0.34 $0.34 +0.34 +0.34 +0.27 $0.60 0.48
f 0.10 f 0.10 f 0.10 f 0.10 f 0.10 f 0.10 f 0.10 f 0.10 f 0.10
vpk
(manual scraper)
Solution
0.1 N KSCN 0.1 N K I 0.1 N K2804 (pH 12)
Va B
(manual scraper)
$0.35 f 0.12 4-0.35f 0.12 +0.35 f 0.12 +0.35 f 0.12 +0.35 f 0.12 +0.35 i 0.12 +0.35 i 0.12 10.35 f 0.12 $0.35 f 0.12 +0.35 f 0.12 +0.35 f 0.12
-0.18 f 0.05 -0.18 i 0.05 -0.16 f 0.05
-0.14 -0.16 -0.21 -0.21 -0.23 -0.33 -0.33 -0.41
i 0.05 f 0.05 f 0.05 i 0.05 i 0.05 i 0.05 i 0.05 i 0.02'
ipk
2.0 X 10-6 2.5 X 10-6
Value also obtained with power scraper.
-0.19 -0.19 -0.16 -0.17 -0.21 -0.23 -0.26 -0.43 -0.43 -0.40
A 0.05
ipk
5
x
10-6
f 0.05
zk 0 . 0 3 f 0.05
5 x 10-6 1.1 x 10-4 4 . 7 x 10-4
i 0.05 f 0.03 f 0.02
3.0
5
-0.04
x
x
10-4
10-6
Table VI: Zero Charge Potentials for Mercury
Solution
2.c.p. (volts us. N.h.e.)
Amount of anion specifically adsorbed in rcoulombs om.-'
0.1 N K F 1.0 N KF 0 . 1 N &SO4 0 . 1 N KC1 1. O N KC1 0 . 1 N KNOa 0 . 1 N KC104 0 . 1 N KBr 0.1 NKSCN 0.1 N K I 0.1 N KOH 0 . 1 N HC1
-0.19 -0.19 -0.20 -0.23 -0.28 -0.24 -0.24 -0.30 -0.35 -0.45 -0.19 -0.28
0.0 0.0 0.1 2.7 7.3 2.3 3.7 5.2 9.6 11.1 0.3 3.0
Vpk
0.1 N K F 1.0 N K F 0.1 N KpSOi 0.01 N KC1 0.1 N KC1 1.0 N KC1 0.1 N KC104 0.1 N KBr
in amp. cm.-2)
Vpk
-0.40 f 0.02 $0.05 f 0.02 + O . 13
+
ipk
(power scraper)
-0.06 f 0.02
Table IV : Experimental Results for Palladium (Potentials Are Given in volts us. N.h.e. and i p k in amp. cm.-2)
a
ipk
Table V : Experimental Results for Silver (Potentiah Are Given in volts us. N.h.e.) vpk
Solution
Vas
(power scraper)
0 . 1 N KC1
+0.28
-0.82 f 0.02
Decay Data. A . General. The transient decays lasted from about a second up to several minutes. The Journal of Physical Chemietry
Limited work indicates that vigorous stirring facilitates a faster decay rate for all metals studied. Decay rates in general paralleled the i p k values, i.e., the decay rate (as studied by means of the manual-scraping assembly) increased in the order: Au < Pd, Pt < Cu, as did ipk. With the manual scraper, the decay was much more rapid following a single scrape (at the same potential) than it was after multiple successive scrapes.
VOLTAGE TRANSIENTS OF FRESHLY PRODUCED NOBLEMETALSURFACES
B. Gold and Copper. The decay rate increased with a decrease in pH and increased slightly with an increase in anion adsorption (interpreting the varying values of V p k as a measure of adsorbability). C. Platinum and Palladium. Decay rates for these metals were very nonreproducible, but within the experimental uncertainty no trends in decay rates as a function of solution were observed.
Discussion Comparison of Results with Manual and Power Scraper. Before the experimental results are discussed in relationship to the meaning of V p k , the difference in V p k values between the power and manual scraping must be considered. Both methods produce identical results for Au and for Pt and Pd in basic solutions; a more negative V p k is produced with the power scraper for Cu and with the manual scraper for Pt in neutral and slightly acidic solutions. Two effects are responsible for these differences: (1) because of the rapid H 3 0 + reduction, the local pH a t an electrode is increased, and the effect is more pronounced for the manual scraping assembly since it does not effect mass transfer of solution to and from the electrode as rapidly as the mechanical scraper; and (2) the manual scraper operates more slowly than the mechanical one and hence cannot “outrun” the cathodic reactions when the latter are rapid. I n the case of copper, the results indicate the latter effect is dominant. In the case of Pt and Pd, both methods of scraping remove the charge from the electrode so that the pH effect is the dominant one. At pH 12, for Pt and Pd, there is no mass-transfer problem since the solution is self-buffered, and thus there is no difference in V p k between the two scraping methods. In the case of gold, H30+ reduction is slow enough that neither of the effects 1 or 2 is significant. Although the trends in v p k for manual scraping are qualitatively correct (cf. the results on Cu for both methods), the absolute values obtained with the mechanical scraper must be considered the more reliable, Interpretation of V p k . The following experimental facts are in accord with V p k values being the zero charge potential: (a) V p k is independent of V’BB; (b) v p k comes to a limiting value with increased scraping speed; (c) v p k increasingly becomes more negative with anion variation in the order F-, S042- < C1- < C104- < Br- < SCN- :< I- (‘Ompare ‘I with I-IV); (d) there is a greater difference between V p k for 0.1 N KC1 and 1.0 N KCl than between V p k for 0.1 N K F and 1.0N K F (compare Table VI with Tables I, 111, and IV); (e) in a given solution (0.1 N KCl), is more negative for with lower work tiOnS,’4915i.e., l’pkPt > V p k A U > Z.C.p.Hg > Vpkcu.
3333
Ag does not fit this trend if one uses its “usually accepted” work function. The pH dependence of V p k cannot be explained with the theory that V p k is the Z.C.P. If the following model is assumed, all of the experimental facts can be explained, however. Scraping removes the metal charge and double layer which results in the metal achieving its z.c.p., but immediate discharge of nearby H 3 0 + and HzO drives the potential positive before V p k is measured. Immediately following this the reduction rate decreases rapidly since the rate-controlling step changes from rapid discharge onto an empty surface to the slower H-atom desorption (electrochemical or recombination) and slow mass transfer of H30+to the surface. These latter processes control the observed transient decay and i p k . v p k is recorded between the rapid discharge reaction and the slower (desorption- and mass transfer-controlled) reduction, and faster scraping outruns the latter process (except in cases such as Cu in K I where V p k did not level out with an increase in scraping speeds). It follows from this model that the peak potential in acidic solutions is positive of that in basic solutions because of the additional H 3 0+ and HzO reduction occurring in the initial prerecorded time, and the Z.C.P. is at least as negative as V p k in basic solution. Discussion of 2.c.p. Values Obtained by Other Investigators. Kheifets and Krasikovl‘j have done extensive capacitance measurements on a series of metals. Their 2.c.p. results for Pt are in excellent agreement with our v p k in neutral and basic solutions and show the same general trend with pH. Our peak potential in acid solution corresponds quite closely to other reported values of 2.c.p. for Pt.17-24 The reported potentials (+0.1 to 0.3 v.) were usually measured in
(14)P.Ruetschi and P. Delahay, J. Chem. Phys., 23, 697 (1955). (15)B. Jakuszewski, Bull. Acad. Polon. Sei., Ser. Sci. Chim.,9, No. 1, 11 (1961). (16) V. L. Kheifets and B. S. Krasikov, Z h . Fir. Khim., 31, 1992 (1957).
(17) T. N. Voropaeva, B. V. Deryagin, and B. N. Kabanov, Izv. A k a d . N a u k SSSR, Otd. K h i m . N a u k , N o . 2,257 (1963). (18) L. Young, Ph.D. Dissertation, Cambridge University, 1949. (19)A. N. Frumkin, A. W. Gorodetakaya, B. Kabanov, and N. Nekrassov, Physik. 2.Sowjetunion, 1, 225 (1932). (20) T. Voropajeva, B. Derjaguin, and B. Kabanov, DokE. Akad. N a u k SSSR, 128,981 (1959). (21) N. Balashowa and A. N. Frumkin, ibid., 20, 449 (1938). (22) N. A. Balashowa, ibid., 103, 639 (1955). (23)A. Frumkin and B. Kabanov, Physik. 2. Sowjetunion, 5, 418 (1934). (24)E. K. Wenstrom, V. I. Lichtman, and P. A. Rehbinder, Dokl. A k a d . N a u k SSSR, 107, 105 (1956).
Volume 69,Number 10 October 1966
3334
R. S. PERKINS, R. C. LIVINGSTON, T. N. ANDERSEN, AND H. EYRING
acidic solutions containing salts which are not strongly adsorbed on mercury. Two 2.c.p. values have been given for Au in the literature. A recent determination by the method of doublelayer repulsion gives a value of 0.05 v. in very dilute C1- and YO3- solution^.^^ A value of 0.2-0.3 v. has been obtained by the adsorption-shift method25 and by the capacity method in HC10, solutions.261n The present experimental transient peaks, V p k , in acid solution (about +0.1 v. for solutions of slightly adsorbing ions) are in better agreement with the above values26-27than is the v p k in basic solutions. A variety of values has been given for the Z.C.P. of silver. These are well reviewed by LeikkZ8 The values fall roughly into two classes. One class consists of values that are in the vicinity of the normal hydrogen electrode potential. The other class consists of two values: -0.6 v., the result of electrocapillary measurements on molten silver,29and -0.7 v., found by capacity measurements2* in dilute sulfate solutions. Leikis performed a detailed study of concentration, anion, and organic adsorbant effects, and Frumkin30 considers Leikis’ values to be correct. The present v p k values agree quite well with the latter two values. Z.C.P. values reported for Cu in the literature are quite inconsistent. A review of these has been given by Bockris, Green, and SwinkeW who consider the Z.C.P.of Cu to be -0.2 v. with an uncertainty of +0.2 and -0.1 v.; this value is positive of the present V p k values except in acidic solutions.
.
Summary From the present experiments, our proposed model predicts 2.c.p. values near the peak voltage, V p k , in
The J O U Tof ~Physical Chemistry
basic solutions. The V p k values in acid solutions more nearly agree with results and interpretations of other investigators. This difference requires further consideration. In addition to the H30+ and water reduction reactions occurring at z.c.P., reactions such as M 20H- + M(OH)2 2e- should become more important in basic solution and should shift the peak potential in the negative direction. Even in neutral solutions, due to the HsO+ reduction producing a more basic solution near the electrode, this result may still be observed. Also, OH- adsorption may be important in neutral solutions since its local concentration is high. A detailed pH study of the scrape transients, which would show leveling out of v p k with pH if it existed, would be valuable in testing such considerations. Also, it would be valuable to study metals exhibiting high hydrogen overvoltage since for them H 3 0 + and H 2 0 reduction reactions would be negligibly slow a t the z.c.P., as is the case with mercury.
+
+
AcknowEedgment. The authors gratefully acknowledge financial support from the Atomic Energy Commission under Contract No. AT(11-1)1144. R. C. L. wishes to thank the National Science Foundation for a summer undergraduate research fellowship. (25) M. Green and H. Dahms, J. Electrochem. SOC.,110, 466 (1963). (26) G. M. Schmid and N. Hackerman, ibid., 109, 243 (1962). (27) G. M. Schmid and N. Hackerman, ibid., 110, 440 (1963). (28) D. I. Leikis, Dokl. Alcad. Nauk SSSR, 135, 429 (1960). (29) S. Karpachev and A. Stromberg, J. Phy8. Chem. USSR, 18, 47 (1944). (30) A. N. Frumkin, J. Electrochem. Soc., 107, 461 (1960). (31) J. O’M. Bockris, M. Green, and D. A. J. Swinkels, ibid., 111, 743 (1963).
