Electrolytic separation factors on palladium

Electroanalytieal Chemistry and lnterjacial Electrochemistry Elsevier Sequoia S.A., Lausanne - Printed in The Netherlands

323

E L E C T R O L Y T I C S E P A R A T I O N FACTORS ON P A L L A D I U M

B. DANDAPANI* and M. FLEISCHMANN Chemistry Department, University of Southampton, Southampton S09 5NH (England) (Received9th September1971; in revised form 24th March 1972)

Electrolytic separation factors, S, for hydrogen and deuterium as well as hydrogen and tritium have been frequently used to study the mechanism of the hydrogen evolution reaction; references to earlier investigations may be found in the recent papers by Bockris and Srinivasan 1 -3 and Conway and Salomon 4. All these investigators have measured the separation factors for the overall hydrogen evolution reaction, that is, the discharge step followed by either the catalytic recombination or electrochemical desorption step. For the separation of hydrogen and deuterium it has been found that the factors fall into two broad groups 5'6 lying in the range 3-4 (e.9. Hg, Sn, Pb (acid)) and 6-8 (e. 9. Pt, Ni, Pb (alkali), W, Fe). Theoretical interpretations of the separation factors have assigned the first group to slow discharge followed by fast electrochemical desorption 4 or to a dual mechanism of discharge and electrochemical desorption with a significant contribution due to proton tunnelling ~. The separation for a number of metals in the second group (Pt (acid), Rh) has been interpreted as being due to fast discharge and slow recombination (Cu, Ni, Pt (alkali)) to fast discharge and slow electrochemical desorption (Ni (in alkali) and W) to slow discharge and fast recombination. These assignments were made on the basis of both conventional kinetic measurements and tritium separation factors. On the other hand, most calculations l's show the limiting separation factor for deuterium for the slow discharge step alone to be in the vicinity of 13. Since the observed separation factors are ~ 3, Horiuti and his group have attributed this value to slow discharge of molecular hydrogen ions while the recombination step is assumed rate determining for the second group. Marked changes in the separation factor with potential 9 have been attributed to changes of mechanism. A difficulty in all these experiments has been the fact that only the overall separation factor has been measured. In the present investigation an attempt has been made to measure the factors for individual steps in the reaction sequence by coupling the discharge to dissolution in the lattice both in the steady and non-steady state. Previous measurements have reported S for dissolved hydrogen to be 6.6 independently of the extent of charge in the lattice 1°. EXPERIMENTAL Palladium foil electrodes were degassed at 300°C in a vacuum line. They were introduced into the solution and anodically activated at 50 mA c m - 2. These electrodes * Presentaddress : ChemistryDepartment,Universityof Ottawa, Ottawa K 1N 6N5, Ontario(Canada). J. Electroanal. Chem., 39 (1972)

(gL6[) 6~ "tuav/o "It~Ur;OaaaalYI"F

'g'g ( ~ ~ ) :sa!l[stlap ltl~dJn3 11~ ~tl!~JP,tlast(I (~)) "~_ma ~ gk ( x - x ) '0g~ ( 0 - 0 ) :sa!][suap luaJ.ma q~!q le ~u!~3P.qz) (~) "~ tu3 yea g'k (V V ) 'g'g ( 0 - 0 ) :satl!suap luaJJna ~aoI le ~u!~J~qo (V) '~OS~H /dr g'0 u! sl!oj tun!pe, llP.d :~a!ql tua I0"0 jo ~u?~Je, qas!p pue ~ u ! ~ e q a 2oJ Slold a ~ e q a - l e ! l u a l o d 'I '~!d e-Lu= D / b 017

0£

o8

o [.

~'0 + ~. <

7

~'0(o)

0~'i

0 L-

Og-

Og-

[

I

}

£'0o X

X

X

X

X

X

X

X

X

X

X

XX

~ ' 0 - ~+ m

/-'0-

L

(8)

i

0 ~-

" - T ~

{

{

O [ l

Ii

0 ~-

I

0 [ --

l

T

I,'0go-

l

V

I, ,I •

~

T v

7

E'O~g'O -

I

! (v) N N V I ~ H D S I 3 " I c I 'IN " I N V d V ( I N V ( I "8[

~7

£

H/D SEPARATION FACTORS ON Pd

325

were then charged either at constant current or constant potential to different extents including high charges so as to establish steady state conditions. After drying, the electrodes were then degassed in the vacuum line at 300°C, the gases being collected with an automatic Toepler pump ~1 and the pressure being measured. The gases were then transferred to a sample loop of a gas chromatograph and H2, H D and D 2 were separately determined using a 9ft chromia coated alumina column 12 at 70° K with helium as carrier gas and a Gaumac Katherometer detector with tungsten filaments. Separate peaks could be recorded at 650 pV full scale. At each pressure and for each experiment, calibrations for each peak were made with known quantities H2, D 2 as well as H D prepared by equilibration. Gas evolved simultaneously during electrolysis was similarly analysed after removing all moisture so as to avoid isotopic exchange during the analytical procedure. Potential-time measurements were made and Tafel plots constructed at different extents of charge both for the charge and ionisation processes. Experiments were carried out in 0.5 M H 2 S O 4 and 1 M K O H which were prepared with pure H 2 0 and D 2 0 to give a final D 2 0 concentration of ~ 70 ~o. Many previous investigators have used low concentrations of D 2 0 . However, the region of 70 ~ is an optimum for accuracy of solution analysis13 and this level was used as both equilibrium and kinetic separation factors are nearly independent of concentration 14. The composition of the solution was measured using pycnometry in a constant temperature roomaS; sulphuric acid solutions were neutralised with N a z C O 3, potassium hydroxide solutions with COz. All glass ware was cleaned in the usual manner using triply distilled water but this was followed by baking at 120°C to remove all films of moisture. Platinum subsidiary electrodes were used and potentials were measured and are reported with respect to saturated calomel electrodes. Constant current polarisations were made using both a suitably modified Wenking potentiostat and, in experiments at high current densities, a Roband Varex 60-1 constant current source. Potentiostatic experiments were made with a Chemical Electronics TR 40/3A potentiostat. Full experimental details are given elsewhere ~4. RESULTS AND DISCUSSION

Two examples of potential-charge plots are given in Fig. 1A and lB. The potential rises rapidly as the ~ palladium-hydrogen phase is fully formed in all cases; at higher current densities in acid solutions and at all current densities in alkaline solutions it is then independent of time as the ~-fl phase transformation takes place and is succeeded by gas evolution at an atomic ratio H / P d of ~ 0.6 (38 C c m - 2 on the Figure). Only at low current densities in acid solution does the potential rise as gas evolution starts. This behaviour can be interpreted only as due to slow discharge ofhydroxonium species in acid and of water in alkaline solutions. This step is then followed by rapid sorption (and phase transformation) in the initial stages and rapid desorption to form gas when the charging is completed. At low potentials in acid solution the desorption step appears to be somewhat retarded. A potential-charge plot for the ionisation of dissolved hydrogen is shown in Fig. 1C. It can be seen that over a subJ. Electroanal. Chem., 39 (1972)

326

B. D:\NDAP.&NI, M. F L E I S C H M A N N 0.5

> Q2~

I

L

I

I

± ......

!

~

i _ _ L _ _ o

~.5

~

~.5 I o g ( / / A cm -2)

Fig. 2. Tafel plots for charging and discharging of palladium foils in 0.fi M

H2SO

4.

stantial part of this process the potential is also relatively constant. In consequence the Tafel plots, Fig. 2, for the dissolution and ionisation of hydrogen are essentially independent of this extent of charge. In both acid and alkaline solution, for both processes, the plot is divided into two parts, a short region close to the reversible potential where 8r//~ log i ~ 4 0 mV and a region at high potentials where 0r//0 log i 180 mV in acid solutions ( > 2 0 0 mV for alkaline solutions). The break in the plots, Fig. 2, is not due to the effect of the reverse reaction and, for example, is still observed if the potential is plotted against log {i/[1 - e x p (~IF/RT)] } so as to correct the observed net current in the cathodic region for the effect of the anodic process in the region close to the reversible potential. The slopes in both regions of potential are difficult to explain and, in particular, it is difficult to see how the lower value can arise. For the simple discharge at higher current densities the slope would be expected to be 118 mV. "High Tafel slopes" have been variously ascribed to tunnelling contributions 16'17 or to adsorption of impurities 7. Changes of slope have also been frequently observed, e. 9. on Pd 18.19 for hydrogen discharge, but it is difficult to see how a change of mechanism could take place for the simple discharge-sorption route. In experiments on the formation of the c~ and [~ phase of Pd/H, Schuldiner attributed an observed 60 mV Tafel slope to absorption of H + ; this slope has not been found in the present investigation. On the fully formed fi phase for gas evolution, Schuldiner and Hoare ~9 observed slopes of 30, 40 and 120 mV in different current density regions which were attributed to the rate controlling recombination, electrochemical desorption and discharge steps respectively. At high current densities a region was found where the potential was independent of current density. The only features observed here are the 40 mV slope at low current density and the change to a higher Tafel slope. It appears, however, that both these regions must be assigned to slow discharge in view of the independence of the potential of the nature of the succeeding step, i.e. sorption or desorption. The separation factor at different current densities was found to depend on the extent of charge, Table 1, in contrast to the observations of Farkas 1°. The variation of S with q at a current density of 50 mA cm 2 is shown in Fig. 3. The lowest charge for which S could be accurately determined was 7.5 C c m - 2 ; extrapolation to zero charge gave the limiting value of S as ~ 13.5. In view of the rapid diffusion of hydrogen d. Electroanal. Chem., 39 (1972)

H/D SEPARATION FACTORS ON Pd I

XN

N

12

I

327 I

I

N

\

N

N

lo

8

-1

~)

i

h

i

-20 -30 -40 ~ / C crn - 2 Fig. 3. The non-steady state separation factor observed on charging palladium foils as a function o f the

extent of charging. Current density 50 mA c m -2. through palladium and the fact that the discharge step is rate determining, this nonsteady state separation factor may be assigned to the discharge step alone. Similar high values have been found previously by Rowland 13 for hydrogen evolution on iron in alkaline solutions. A limiting model for the calculation of S for the discharge step is that initially proposed by Topley and Eyring 21 in which the activated complex is regarded as being unbound and H and D diffuse out of the transition state in the direction of the reaction co-ordinate. Calculations of this limiting value 1'8'13'21 range from 12-19 depending on the assumptions. In our opinion, realistic calculations 1't3 give 12-14. The present experiments, by isolating S for the slow discharge step from the overall reaction mechanism, have shown that slow discharge, at least on Pd, does indeed conform closely to the limiting model. Confirmatory evidence for the high separation factor of the discharge step was obtained by using a palladium membrane 0.1 m m thick polarised at constant currents on the ingoing face, the outgoing face being maintained at + 0.025 V with TABLE 1 DEPENDENCE OF S ON CURRENT DENSITY DURING c~-//TRANSITIONIN 1.0 N ISOTOPIC ACID MIXTURE (Average of five values) Q/C cm 2

7.5 15.0 22.5 30.0 45.0

Current density/mA cm- 2

5

25

50

250

10.5 8.3 8.1 7.4

9.8 8.5 7.6 7.2

11.2 9.6 8.7 7.8 7.2

9.7 8.7 8.6 7.4

J. Electroanal. Chem.,

39 (1972)

TABLE 2 S VALUES FOR THE EVOLVED GASES AT DIFFERENT CURRENT DENSITIES IN 1.0 N ISOTOPIC ACID MIXTURE (Average of four values) Q/C c m - 2

30 45 60

Current density/mA c m - 2

25

50

250

3.4 3.6 3.9

4.3 3.5' 4.3

4.1 3.8 4.0

328

B. DANDAPANI, M. FLEISCHMANN

respect to the c~-fi P d - H reference system (-0.167 V SCE). In this way at least 9 8 ~ of the current on the ingoing interface could be obtained on the diffusion side. Separation factors were determined by the analysis of the solution in contact with the ingoing interface before and after electrolysis so as to avoid the corrections (caused by H/D separation at the auxiliary cathode) which have to be applied to comparable data on the diffusion side. The S values obtained were ~ 10 indicating that the rapid diffusion succeeded in maintaining steep concentration gradients in the lattice, S thereby approaching the limiting value for slow discharge. On the other hand the gas evolved both during the formation of the fi phase and on the fully formed fi phase at different current densities consistently gave S values in the range 3.44.3, Table 2. This value is in the range predicted for the equilibrium 14 : HD20++D2 ~DaO++HD

(1)

using the data of Urey 22 for the equilibria H 2 q- D 2 ~- 2 H D

(2)

H20+D20

(3)

~ 2HDO

and H20+HD

~ HDO+H 2

(4)

It follows therefore from the evidence given by the separation factors that the desorption steps must be rapid electrochemical reactions such as: H a a s + D 3 O+ ~ H D + D 2 0

(5)

which will lead to a re-equilibration of the gas and hydroxonium ions following the high separation in the discharge step. This conclusion is in agreement with those drawn from the potential~ime plots. It would be logical to attribute S values observed by other workers for metals on which discharge is slow to a similar re-equilibration. This could well be facilitated by the low adsorption energy on those metals (Hg, Sn, Pb) of the adsorbed hydrogen atom intermediates. A further separation factor could be obtained from the measurements: namely that in the lattice for the fully formed [3 phase after prolonged electrolysis. In view of the re-equilibration between the gas and the solution species caused by the rapid electrochemical desorption step, this separation factor into the lattice is also an equilibrium value, in this case due to the reaction HD2 O+ + f i - Pd-D ~ f l - P d - H + D 3 O+

(6)

Figure 4A and B shows the data for acid and alkaline solutions at high negative potentials. It is apparent that S varies with potential and approaches a limiting value of 9.5. The separation factor is given by

\QHD20 + / \QD + lattice/

where the Q terms are the relevant partition functions. A limiting high value will be observed when the species in the lattice are so loosely bound that they can be regarded as three-dimensional classical vibrators, in J. Electroanal. Chem., 39 (1972)

329

H/D S E P A R A T I O N F A C T O R S O N Pd J

I

V~

(A) 10.0

S

8.0

i I _0,7

I _0.8 Potential

I _0.9

I

/ V

I

I

I

(B )

10 S

I

~_ -1.25

I 1,5 Potential

~ - 1.75

I - 2.0

/ V

Fig. 4. Equilibrium separation factor at negative potentials for fully formed fl- Pd-H phase. (A) 0.5 M H2804, (B) 1.0 M KOH. which case QH+ lattice/QD+ lattice = 1/23/2. Using data of Swain et al. 23 for the other partition functions, we derive the limiting value of S for "free protons" in the lattice as 9.5. It is of interest that this value is less than that for slow discharge leading to lattice formation; in the latter case S is obtained from the equilibrium value by multiplying by the ratio of the diffusion coefficients of H and D to allow for the motion out of the transition state 21 i.e. ,-~2 ~ giving a separation factor of 13.6. In the limiting model used to predict the separation factor for dissolution in the lattice, a classical vibrator has been assumed in preference to a model of nonlocalised systems as the data in Fig. 4 do show that S diminishes with increasing (positive) potential so that a difference in zero point energy must in general be attributed to the H + and D + in the lattice regarded as "Einstein" oscillators. This difference in zero point energy is small as is indicated by data of the heat of absorption (AH)H2 of H 2 and (AH)o 2 of D 2 by palladium 25'26. For the processes : H2 ~

2 Pd H

(8)

D 2 ~ - 2 Pd D

(9)

we may regard H2 and D 2 as ideal gases in equilibrium with 6N localised oscillators. We can therefore write J. Electroanal. Chem., 39 (1972)

330

B. DANDAPANI, M. FLEISCHMANN (aH0)n 2-(AHo)D2 = 6N (½ hvn - ½ h v o ) - N(½ hvn2- ½ hVD2)

(10)

where the enthalpies of absorption are at absolute zero. Unfortunately, these data are not known; using the values at 273 °K, - 9 6 0 0 and - 8 4 0 0 cal mol 1 for Pd H and P d - D and the zero point energy difference 1790 cal* tool -1 for the gaseous species and also assuming that vD= Vn/~/2, we obtain the zero point energy difference for the species in the lattice as 336 cal mol 1. The sorbed species are therefore loosely bound but not free. This zero point energy difference gives a separation factor of 8.7 which would correspond to the conditions at the potential of the ~-fi phase transformation. In practice lower values are found both here and in the work of Farkas a°. It follows that the zero point energy difference must in fact be larger than that derived from the heats of absorption. This calculation also cannot explain why the separation factor should vary with potential. Such a variation demands that the binding and therefore the difference in zero point energy decreases as the potential goes more negative. The maximum variation of the binding energy may be estimated by considering the equilibrium Ha ° +

~- H + lattice

(11)

By equating the electrochemical potentials of the two phases we obtain #l+ _t_q~lF = uOS + R T In an+ +~bSF

(12)

where the superscripts 1 and s stand for the lattice and solution respectively. If we assume the activity of hydrogen dissolved in the lattice to be nearly constant (fi phase near saturation) we obtain #l+ ~< const. + (q5s - q51)F

(13)

The total binding energy of the absorbed hydrogen ions with respect to hydrogen atoms at rest may be obtained by considering the cell Pt, H 2 ] H2SO4(m)l Pd H

(14)

for which AG= -2.3065 kcal mol-1. Substituting the partition functions

eDo/kT AG = - 6 R T In 1 - - e

-hv/kT +

6RT + R T In QHz/N

(15)

where the partition function of H2 is also taken with respect to atoms at rest at infinity, which is the reference state. With the usual form for QH2, Do is 14.22 kcal m o l - 1 at the c ~ phase potential. At any other potential the relevant binding energy is

D= D o - ½(&-~o~)F

(16)

The variation of S with zero point energy of the absorbed hydrogen can also be directly expressed as

(sinh t QIfD2°+ \sinh hvn]

2kT/

*

1

ca1-=4.184J.

J. Electroanal. Chem.,39 (1972)

,17)

331

H/D SEPARATION FACTORS ON Pd

and assuming, as usual, vD= va/,] 2, the variation of S with X = h v ~ 2 k T is shown in Fig. 5. At a potential of - 0.6 V, using S = 7, the experimental value, we can estimate X from this plot. The relevant binding energy follows from (16). If the absorbed hydrogen is now assumed to behave as an anharmonic oscillator, the zero point and binding energy can be related to a first approximation by D

=

(18)

hv/4X e

where Xe is the anharmonicity constant. It will be apparent that in this way we can make an independent estimate of the shape of the potential energy curve without using empirical relations such as those of Morse and Mulliken z6. Using eqns. (16) and (18) and Fig. 5, other values of S at different potentials can be calculated ; the results are shown in Fig. 6. It is apparent that Fig. 6 qualitatively reproduces the experimental data but that the rise of S with potential is too slow, particularly when it is borne in mind that eqn. (16) gives an upper limit for the variation of D. Thus it can be seen that simple models oflocalised oscillators which have been widely used in theoretical calculations on the hydrogen evolution reaction can at best be expected to give a qualitative interpretation of the processes. 101

~

I

f

0.4

0.8

1.2

'i X ~

2kT ]

Fig. 5. Variation of separation factor with zero point energy. 10,--

I

J

I - -

i

I_

~

--

9 s

I

-0,6

-1,0 Potential / V

_

l

_

_

~

-1.4

Fig. 6. Predicted variation with potential of equilibrium separation factor for fully formed f l - P d - H phase. J. ElectroanaL Chem., 39 (1972)

332

B. DANDAPANI, M. F L E I S C t t M A N N

ACKNOWLEDGEMENTS

The authors thank the United Kingdom Atomic Energy Authority for the financial support of the studies and for the provision of a maintenance grant to one of us (B.D.). In particular, the authors wish to acknowledge with thanks the discussions with Dr. P. R. Rowland. SUMMARY

It is shown that the separation factor for the slow discharge step of hydrogen onto palladium is ~ 13 and that this corresponds to an essentially unbound transition state. The separation factor for the overall hydrogen evolution reaction, due to a fast electrochemical desorption step, is close to the equilibrium value, 4. This assignment of mechanism agrees with that deduced from the kinetic data. The separation factor for diffusion through palladium membranes is 10.5. In addition, it is possible to measure the separation factor for the fully formed p phase and this approaches 9.5 at negative potentials which corresponds to that calculated for free protons in the lattice. The variation of this separation factor with potential cannot be adequately explained in terms of simple models of localised oscillators. 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 26

J. O'M. Bockris and S. Srinivasan. J. Electrochem. Soc., 111 (1964) 844. J. O'M. Bockris and S. Srinivasan, J. Eleetrochem. Soc., 111 (1964) 853. J. O'M, Bockris and S. Srinivasan, J. Electrochem. Soc., 111 (1964) 858. B. E. Conway and M. Salomon, Ber. Bunsenges. Phys. Chem., 68 (1964) 331. J. Horiuti and G. Okamoto, Sci. Pap. lnst. Phys. Chem. Res. (Tokyo), 28 (1936) 231. H. F. Walton and J. H. Wolfenden, Trans. Faraday Soc., 34 (1938) 436 J. O'M. Bockris and S. Srinivasan, Electroehim. Aeta, 9 (1964) 31. T. Keii and T. Kodera, J. Res. Inst. Catal. Hokkaido Univ., 5 (1957) 105. J. Horiuti and M. Fakuda, J. Res. Inst. Catal. Hokkaido Univ., 10 (1962) 43. A. Farkas, Trans, Faraday Soe., 33 (1937) 552. E. L. Wheeler, Scientific Glassblowing, Interscience, New York. 1958. P. P. Hunt and H. A. Smith, d. Phys. Chem., 65 (1961) 87. P.R. Rowland, Nature, 218 (1968) 945. B. Dandapani, Ph.D. Thesis, Southampton University, 1969. P. R. Rowland, C. R. Wright and A. R. Knott, U.K. At. Energy Auth. Rep., AEEW-M746, 1967. S. G. Christov, Electrochim. Act& 4 (1961) 194. B. E. Conway, Can. J. Chem., 37 (1959) 178. A. N. Frumkin and N. A. Aladzhalova, Acta Physicochim. URSS, 9 (1949) 1. S. Schuldiner and J. P. Hoare, J. Electrochem. Soc., 102 (1955) 485. S. Schuldiner, J. Electrochem. Soc., 106 (1959) 440. B. Topley and H. Eyring, J. Chem. Phys., 2 (1934) 217. H. C. Urey, J. Chem. Soc., (1947) 562. C, G. Swain, R. F. W. Bader and E. R. Thornton. Tetrahedron, 10 (1960) 200. D. M. Nace and J. G. Aston, J. Amer. Chem. Soc., 79 (1957) 3619. D. M. Nace and J. G. Aston, J. Amer. Chem. Soc., 79 (1957) 3627. P. M. Morse, Phys. Rev., 34 (1929) 57.

J. Electroanal. Chem., 39 (1972)