Palladium and platinum hydrogen electrodes I: Hydrogen chemical potentials, molecular hydrogen diffusion and local cell hydrogen transfer effects at palladium and platinum electrodes under open-circuit conditions and during constant current and pulsed current electrolysis in hydrogen-saturated solutions

Surface Technology, 18 (1983) 147 - 166

147

PALLADIUM AND PLATINUM H Y D R O G E N ELECTRODES I: H Y D R O G E N CHEMICAL POTENTIALS, M O L E C U L A R H Y D R O G E N D I F F U S I O N AND LOCAL CELL H Y D R O G E N T R A N S F E R EFFECTS AT PALLADIUM AND PLATINUM ELECTRODES U N D E R OPENCIRCUIT CONDITIONS AND D U R I N G CONSTANT C U R R E N T AND PULSED C U R R E N T ELECTROLYSIS IN H Y D R O G E N - S A T U R A T E D SOLUTIONS F. A. LEWIS, R. C. JOHNSTON, M. C. WITHERSPOON and A. OBERMANN

Chemistry Department, Queen's University, Belfast BT9 5A G (Northern Ireland) (Received October 8, 1982)

Summary Measurements at 25 °C are reported of open-circuit electrode potentials and hydrogen overpotentials at both static and rotating palladized palladium electrodes in hydrogen-saturated catholytes, and of the potential responses of platinum black and palladium black electrode surfaces to square wave current pulses. The results are consistent with governing influences of rates of diffusive transport of molecular hydrogen through the Brunner-Nernst interfacial solution layer, and of local cell hydrogen transfer processes, in controlling hydrogen chemical potentials at the electrode surfaces.

1. Introduction The open-circuit electrode potentials and/or hydrogen overpotentials of platinum group metal electrodes (as. functions, for example, of hydrogen content or electrolytic current density) can exhibit large differences related to their catalytic activities for dissociations of hydrogen molecules and complementary recombinations of hydrogen adatoms [ 1, 2]. Electrode surfaces of these metals, however, can be prepared of such high general catalytic activities that overall processes of gain or loss of hydrogen are dominated by rates of transport of hydrogen molecules up to and away from the electrode surfaces through the Brunner-Nernst interfacial layer of solution. Under these conditions measurements of electrode potentials can be reliably correlated with hydrogen chemical potentials [1, 2]. Such an overall control of the gain and loss of hydrogen by transport processes in the solution, however, can largely conceal an underlying wide range of differing surface activities, including the probable existence and 0376-4583/83/0000-0000/$03.00

© Elsevier Sequoia/Printed in The Netherlands

148 influences of a " s p e c t r u m " of surface sites, considered for example with respect to their relative catalytic activities or their relative likelihoods of being preferred points of initial hydrogen ion discharge [ 1, 2]. Much of the evidence for these conclusions has been obtained from studies with electrodes of palladium and palladium alloys. These materials can absorb substantial contents of hydrogen under conveniently obtainable experimental conditions and this has proved to be an advantage in studying kinetics of both hydrogen gains and losses. A general experimental procedure has been to employ static electrodes and to record measurements of electrode potential and electrical resistivities in conjunction with one another, in well-stirred hydrogen-saturated solutions and with continuous constant current electrolysis [ 1, 2]. Results are reported here and in the following paper of further such experiments with a wide range of concentrations of various electrolytic solutions and over a substantial range of current densities. Although "bright" palladium and platinum surfaces of high catalytic activity may be obtained by means of either aerial or anodic oxidation [ 1, 2], the present comparative studies have been limited to surfaces produced by electrodeposition of palladium and platinum black layers, at which measurements of electrode potentials generally are more consistently equatable with hydrogen chemical potential, and with which there generally are reduced likelihoods of substantial alterations in surface conditions over a series of electrolytic discharge experiments extending to relatively high current densities. Since rates of diffusive transport through the Brunner-Nernst layer can be expected to be increased by reduction in its effective thickness, it has been of interest to carry o u t some comparative studies with a rotating palladium electrode. Again, measurements have been made of rates of hydrogen absorption from hydrogen-saturated solutions and also of the relationships between the current density and the hydrogen chemical potential components 773 of hydrogen overpotential during subsequent electrolysis, after equilibrium had been established with the hydrogen-saturated solutions before electrolysis. Preliminary measurements also have been reported [1, 2], following establishment of equilibria of cathodes in hydrogen-saturated solutions, of overpotential responses to square wave current pulses. As an extension to studies of single-pulse effects [2 - 4] measurements are reported here of the effects of repeated pulsing at various pulse lengths and frequencies up to conditions approaching almost continuous currents. Electrolytic pulse studies also have been carried out with platinized platinum electrodes under similar conditions to those for palladium, for which estimates of rate constants governing diffusive transport of hydrogen molecules within the interfacial solution layer can be accurately estimated. Correlations have been made between shifts in the position of oscillographicaUy recorded voltage responses to pulsing from their initial baselines and

149 components of the overpotential associated with surface hydrogen chemical potentials.

2. Experimental

procedure

Specimens were wires of platinum 0.0122 and 0.0457 cm in diameter and palladium 0.0122 cm in diameter. Lengths varied from about 0.5 cm in rotating electrode experiments to about 1.0 cm in most experiments with palladium and about 3.5 cm in pulsed electrolysis experiments with the finer gauge platinum. These relatively short lengths allowed measurements to be extended up to quite high current densities under controlled current conditions in even the most dilute solutions, both for the pulsed current experiments and for those described in the following paper. Specimens were spot welded to platinum leads sealed into soda glass electrode holders, and the junction was afterwards also covered with soda glass. Lengths of specimens exposed to the solution were measured with a travelling microscope. For most experiments specimen holders were constructed in a way similar to that of previous studies. This allowed measurements of electrical resistance to be made either potentiometrically or with an a.c. bridge network [5]. However, for rotating electrode experiments, the specimen was a single length of wire which extended horizontally from its junction with the electrode holder. It could be rotated at up to 600 rev min -1 and electrical connection was made by a looped lead through a concentric " t u b e " of mercury which also was arranged to act as a gas seal. In addition to the single-pulse facility, square wave current pulses were obtainable at 10, 100 and 1000 pulses s-1 with pulse durations ranging from 100 las to times sufficient to give m a x i m u m pulse:pause ratios of 90% at each pulse frequency. Electrode potential responses were displayed on an Advance type OS 2200 storage oscilloscope. Electrodes were electroplated wth platinum black from a 1% solution of PtCI4 in 0.1 N HCI containing 0.2% lead acetate and with palladium black from a 2% solution of PdC12 in 0.1 N HC1 containing 0.1% lead acetate. Depositions were preceded by heating the specimens in air to red heat and brief pr¢anodizations. Platinum and palladium platings were usually at 200 mA cm -2 for 10 s. This was generally just sufficient to produce a m a t t black surface. Acids employed were BDH Aristar grade solutions prepared from water with conductivity of less than 1 0 -6 ~-1 cm purified by distillation and deionization in a Permutit mark 7 unit. During experiments all solutions were continuously saturated and stirred by streams of hydrogen gas bubbles that were purified by passage through Pd-Ag membranes [6]. Electrode potentials were recorded with respect to a PtJH2 reference electrode immersed beside the specimen. Pressures P of hydrogen at the reference electrode were adjusted for water vapour and immersion depth effects [6]. All measurements were made at 25 + 0.I °C.

150 3. Results o f constant c u r r e n t e l e c t r o l y s i s

3.1. Absorption of hydrogen by palladium electrodes before electrolysis Figure 1 illustrates examples of changes in the open-circuit electrode potential E with time in hydrogen-saturated and stirred HC1 solutions of initially hydrogen-free, static and rotating palladium electrodes which had been b o th quite thinly and more thickly electroplated with palladium black. It m ay be seen that specimens have a d o p t e d potential E ~ 0 after periods of 1-2h. 70

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m

10

0 0

(a)

20

40

60

80

100

0 20 Time ( min )

40

60

80

100

120

(b)

Fig. I. Time-dependent changes in electrode potentials at 25 °C during absorption of hydrogen from hydrogen-saturated HCI solutions of various concentrations by static (©, O, ~:~, ~F ) and rotating (==, A, v ) palladium wires 0.0122 cm in diameter (a) thinly coated

and (b) thickly coated with palladium black: o, 1.0 N HCI; m, 1.0 N HCI; 4, 0.01 N HCI; ~, 0.001 N HCI; m, 1.0 N HCI;ZX,0.01 N HCI;~r, 0.001 N HCI.

3.2. Decays of hydrogen overpotential after interruption of electrolysis After their adoptions of E ~ 0, electrodes were cathodized at various current densities in the same hydrogen-saturated and stirred HC1 solutions, and measurements were made o f the time-dependent increases in their total apparent h y d r o g en overpotentials 77 until these had assumed constant values (after a b o u t 10 - 15 min). Electrolysis was then interrupted and decays in the open-circuit potential (which was now o f a reverse sign to that shown in Fig. 1) were recorded back to E ~ 0. Examples of plots o f such decays in E are shown in Fig. 2(a). Figure 2(b) shows c o m p l e m e n t a r y plots [7] of the function log~p/(p --P}} where P is the corrected pressure of the saturating hydrogen gas. Values of

151

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1

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3

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T i m e ( rain )

(a)

(b)

Fig. 2. Time dependences of (a) open-circuit electrode potential E and (b) the function log{p/(p --P)} derived from values of E in (a) for thickly palladized static (o, $, -o-, +, ×, A) and rotating (o, A) palladium electrodes 0.0122 cm in diameter after interruption of catholysis in hydrogen-saturated and stirred H2SO4 at various concentrations: e, 1.0 N, 2.2 mA cm-2; $, 1.0 N, 7.8 mA cm-2; * , 1.0 N, 251 mA cm-2; +, 0.01 N, 251 mA cm-2; x, 0.005 N, 251 mA cm-2; A, 0.001 N, 251 mA cm-2; o, 0.1 N, 1.9 mA cm-2; z~, 0.1 N, 8.2 mA cm -2.

p have each been calculated from corresponding values of E (see discussion) by the relation E (mV) = 29.5 l o g ( p - - P )

(1)

Extrapolated values of the plots in Fig. 2(b) at t = 0 were equated with log{p0](P0-- P)} where p0 is the value o f p at t = 0 [7 - 9]. The c o m p o n e n t of overpotential 772 was defined as the value of electrode potential calculated by inserting values of P0 in eqn. (1). Figure 3 shows examples of plots of the so-defined 772 c o m p o n e n t of the overpotential plotted against the logarithm of the current density i, to which has been added the term 2PFko/Nwhere F and N are the Faraday and Avogadro constants respectively and k 0 (see discussion) had been determined from measurements of open-circuit potentials before electrolysis in each case. It may be seen from Fig. 3 that, at low current densities for either static or rotating electrodes in all acid concentrations, values of ~72 fall closely on lines drawn with a slope of 0.0295 V through appropriate values of log(2PFko/N) at ~72 = 0.

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Fig. 3. Values (derived from extrapolations of plots of the function log~v/(p --P))) of the reversible hydrogen chemical potential component 172 of the hydrogen overpotential plotted against the function log(/+ 2PFko/N) for static (a) and rotating (o) palladized palladium electrodes 0.0122 cm in diameter in various concentrations of H2SO4: (solid lines in each figure have been drawn with a slope of 0.0295 V through values of log(2PFko/N) represented by • and A): (a) 1.0 N; (b) 0.1 N; (c) 0.01 N; (d) 0.005 N; (e) 0.002 N; (f) 0.001 N.

T e n d e n c i e s f o r ~2 values to deviate t o w a r d s u p p e r limits at higher curr e n t densities m a y b e seen t o o c c u r a t increasingly l o w e r values o f 77~ a n d i w i t h decreasing acid c a t h o l y t i c c o n c e n t r a t i o n . This l a t t e r f e a t u r e is a m a i n s u b j e c t o f t h e f o l l o w i n g paper. T h e results in Figs. 1 - 3 are quite t y p i c a l o f m e a s u r e m e n t s r e c o r d e d w i t h b o t h static a n d r o t a t i n g p a l l a d i u m e l e c t r o d e s o v e r similar ranges o f c o n c e n t r a t i o n o f H : S O 4 , HC1 a n d HC1Oa solutions. T h e y are also, w h e r e a p p r o p r i a t e , t y p i c a l o f results o b t a i n e d w i t h static e l e c t r o d e s in K O H in general c o n f i r m a t i o n o f r e l a t e d a s p e c t s o f earlier studies [8, 9 ] .

153 4. Overpotentials produced b y square wave current pulse electrolysis

4.1. General features For palladium and palladium alloy electrodes the technique of electrolysis in short single square wave pulses of current has been of interest for studying components, such as the W1 c o m p o n e n t [3, 4 ] , of the overpotential developed over very short times of electrolysis. An additional feature which has been observed [2, 4] in the course of such measurements has been that continuous pulse repetitions produce displacements in oscillographically displayed potential responses to the current pulses from initial potential baselines. A diagrammatic representation of overpotential components defined with reference to this displacement is shown in Fig. 4.

>~

0

~

~(b.p.) ~(a.p.) i(m.d.p.) Time

Fig. 4. Diagrammatic representation of steady state potential responses to repetitive square wave current pulses (increases from open-circuit reversible values represented by ~7(b.p.) at the beginning of each successive pulse, ~7(m.d.p.) at its maximum value during the pulse and ~?(a.p.) immediately after the pulse. For the experiments reported here, the initial potential baseline again corresponds to a value of E ~ 0 with respect to a Pt]H: electrode in the same hydrogen-saturated and stirred solution. The overpotential c o m p o n e n t ~ (a.p.) represents the maximum value of the open-circuit electrode potentials which exhibit time-dependent decays after interruption of each pulse. The component ~(b.p.) represents values to which this open-circuit potential has decayed before c o m m e n c e m e n t of a further current pulse. Finally, ~(m.d.p.) represents the maximum overpotential developed during the course of the pulse. Values of these parameters reported here have been recorded after pulsing has been sufficiently prolonged for steady state values to have been established at the cited combinations of pulse durations {lengths) and repetition rates {frequencies).

4.2. Results o f pulsed current electrolysis Figure 5 shows plots of ~?(a.p.), ~?(b.p.) and ~(m.d.p.) recorded with platinized platinum electrodes at the same current density in 0.1 N H2SO4 with variations in pulse length at three different pulse frequencies. A similar general pattern of results may be seen to have been obtained at each pulse frequency. However, for the lower pulse frequencies, the values of 1?(a.p.) obtained after the shorter pulse lengths have decayed back to values of ~?(b.p.) ~ 0 before application of the next pulse. When, however,

154

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Fig. 5. Steady state values o f the parameters o f potential responses to square wave current pulses at a pulse current density of 5.8 m A cm -2 with platinized p l a t i n u m electrodes

in hydrogen-saturated and stirred 0.1 N H2SO4 solutions for pulse repetition rates of (a) 1000 pulses s - l ; (b) 100 pulses s - l ; (c) 10 pulses s -1 (©, ~7(b.p.); I , ~(a.p.); ×, ~7(m.d.p.)).

combinations of pulse length and frequency correspond to c o m m o n upper limits of current flow of about 80% of overall times of continuous pulsing then, at all three pulse frequencies, ~?(b.p.) is only slightly less than ~(a.p.) at almost c o m m o n values near 20 mV, and ~?(m.d.p.) has almost c o m m o n values near 40 mV. Figure 6 shows comparisons of the three overpotential parameters at platinized platinum electrodes in experiments at 100 pulses s-I at a c o m m o n (slightly lower) current density in differing concentrations of hydrogensaturated H2SO4. Again, at the highest pulse lengths, which approach conditions of continuous current flow, values of ~(b.p.) are only slightly less than values of ~?(a.p.), and both have attained closely similar values of a b o u t 14 mV in each acid concentration. However, corresponding values of ~(m.d.p.) in Fig. 6 exhibit marked increases with decreasing acid concentration. This dependence of ~?(m.d.p.) on acid concentration is also further illustrated in Fig. 7 in comparison with values recorded at maximum available pulse:pause ratios as a logarithmic function of pulse current density plus the constant term 2PFko/N (see below). Although in Fig. 7 only values o f ~?(b.p.) in 0.01 N H2SO4 have been included for comparison purposes, values of either ~?(a.p.) or ~?(b.p.) in the other acid concentrations would show an almost equal correspondence as may be appreciated from considerations of results plotted in Fig. 6 or Figs. 8-12. It may be noted that no Luggin capillary arrangement was employed in the present studies, so that it would seem probable from the marked

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dependences of 7?(m.d.p.) on acid strength (and accompanying reductions in electrolyte conductivity) that the larger part of the differences between ~(m.d.p.) and ~(a.p.) or ~(b.p.) could be attributable to "solution I R d r o p " effects. It may, however, also be noted that, in 1.0 N H2SO4, ~(a.p.) still constitutes the major part of ~?(m.d.p.); this has a counterpart in findings in allied studies of the hydrogen overpotential with comparably surface-active electrodes that a major part of total apparent overpotentials at relatively low current densities consists of a c o m p o n e n t representative of the surface hydrogen chemical potential [10 - 12]. Figure 8 illustrates comparisons, analogous to those of Fig. 6, of measurements obtained with a platinum electrode thinly coated with palladium black. The features are quite similar to those of Fig. 6 in that 7?(m.d.p.) is markedly dependent on acid strength and that 7?(a.p.) and ~?(b.p.) are both virtually independent of acid strength and are in generally close agreement with one another, although values of ~(a.p.) may be slightly higher in comparison with results for platinized platinum in Fig. 6.

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In Figs. 9 and 10 results are recorded of measurements, with platinum black and palladium black surfaces respectively, of 7?(a.p.) and 7?(b.p.) in three different acid concentrations at 100 pulses s-~ and at a series of current densities. Figures 11 and 12 show values of 7?(a.p.) and ~?(b.p.) recorded for the longest pulses (8.6 ms) in Figs. 9 and 10 respectively and corresponding

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Fig. 9. Comparisons for a platinized platinum electrode as a function of pulse length at a pulse repetition rate of 100 pulses s-1 of the open-circuit potential at pulse conclusion ~?(a.p.) (e, 4~, ~ ) and the potential to which it has decayed before the next pulse 17(b.p.) (o, ~>, ~ ) in hydrogen-saturated and stirred H2SO4 solutions at various concentrations and current densities (mA cm -2) (e, o, 1.0 N; O , ~ , 0.01 N; i , ~ , 0.01 N): (a) 0.735 mA cm-2; (b) 1.46 m A c m -~, (c) 2.94 mA cm-2; (d) 4.40 mA cm-2; (e) 7.34 m A cm -2.

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Fig. 10. A n a l o g o u s comparisons t o those o f Fig. 9 o f / / ( a . p . ) (e, ~ , ~ ) and l?(b.p.) ( 0 ~ ,

~ ) for a palladized platinum electrode in hydrogen-saturated and stirred H2SO 4 solutions of various concentrations and current densities (symbols as for Fig. 9): (a) 0.58 mA cm-2; (b) 1.16 m A cm-~; (c) 2.22 mA cm--2; (d) 3.47 m A cm--2; (e) 5.80 m A c m -2.

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Fig. 11. Values forplatinized platinum electrodes of fi(a.p.) (e), fi(b.p.) (o) and r/(m.d.p.) (x) at the maximum pulse durations (about 8.6 ms) at 100 pulses s- l , shown in Fig. 9 plotted against the logarithm of the pulse current density i ((a) - (c)) and also against the function l o g ( / + 2PFko/N) ((d) - (f)) where 2PFko/N again has been taken as equal to 3.0 mA cm -2 (cf. Fig. 7) (0, log 2PFko/N at zero-voltage responses, and the line through again has been drawn with a slope of 0.0295 V): (a), (d) 1.0 N H2SO4; (b), (e) 0.1 N H2SO4; (c), (f) 0.01 N H2SO4.

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Fig. 12. Analogous plots for paUadized platinum electrodes to those of Fig. 11 (these should also be compared with Fig. 8): (a) - (f) as for Fig. 11.

159

values of ~(m.d.p.), plotted in Figs. l l ( a ) - 11(c) and 12(a) - 12(c) against the logarithm of pulse current density i. In Figs. l l ( d ) - l l ( f ) and 12(d) - 12(f) the same values of ~?(n.b.), ~(b.p.) and w(m.d.p.) have been replotted against the function log(i + 2PFko]N) where (as for Fig. 7), in an additional experiment with a paUadized palladium electrode under similar conditions of hydrogen saturation and stirring, the value k0 = 9.3 × 10 is molecules c m - : s-1 bar -l was derived from which 2PFko/N was calculated to be 2.5 mA cm -2. In the lower plots of Figs. 11 and 12 the values of ~?(a.p.) and ~/(b.p.) may be seen to fall close to lines drawn with a gradient of 29.5 through values of log 2.5 on each abscissa.

5. Discussion

5.1. Open-circuit electrode potential measurements and rates o f hydrogen absorption before electrolysis The overall forms of changes in open-circuit electrode potentials E with time in Fig. 1 are similar to those reported in earlier studies [ 7 , 9, 1 3 - 18] of rates of hydrogen absorption by palladium electrodes from solutions saturated and stirred with hydrogen gas at 25 °C. Thus an initial region of steadily declining E, corresponding to absorption of hydrogen in the solid solution ~ phase concentration range, is succeeded by a region of relative potential invariance corresponding to an ~ ~ ~ phase transition and lastly by a range corresponding to absorption in the ~ phase over which the electrode potential decreases steadily with time until finally exhibiting an exponentialtype approach to values of E ~ 0, at which point the hydrogen content n expressed as the atomic ratio H:Pd was about 0.7 [19, 20]. For experiments with static electrodes in Fig. 1, the times taken for each of the above stages were also quite similar to those recorded in earlier studies [7, 18] with wire specimens 0.0122 cm in diameter in aqueous solutions in which rates of absorption and desorption of hydrogen have been shown to be governed b y diffusion of dissolved hydrogen molecules up to and away from the electrode surface with a diffusive flux J = DH2(C1-- C2)

5

(2)

where C1 and C 2 are the concentrations of hydrogen molecules dissolved in the bulk of the solution and dissolved in the layer of solution adjacent to the electrode surface respectively, 5 is the effective thickness of the BrunnerNernst diffusion layer and DH2 is the diffusion coefficient of the dissolved hydrogen molecules in the solution. Complementarily, the rates of change in the hydrogen contents n of the electrodes could be represented [1, 6 - 9, 14, 18, 20] by the equation dn - koko'(P--P) (3) dt

160 Here, with the rate constant k 0 expressed as molecules c m - : s-1 bar -1, the constant for adjustment of units, ko' = 4 M p d / r p p d N (where Mpd and PPd are the molar mass and the density of palladium respectively, r is the wire radius and N the Avogadro number). P is the suitably corrected pressure of hydrogen dissolved in solution at the surface of the Pt[H2 reference electrode and p is the vapour pressure of hydrogen at the palladium electrode, which for electrodes sufficiently active catalytically for kinetics of hydrogen gain and loss to be governed by eqn. (2) has been shown [1, 6 - 9, 14, 17, 18, 20] to be equatable with E by the relation RT ln(p/P) = 2RE

(4)

which at 25 °C simplifies to eqn. (1). Provided that eqn. (3) is applicable it is possible, in principle, to derive relationships between equilibrium hydrogen pressures p and hydrogen content n from relationships derived between E and n. Good agreement has indeed been found both for the Pd]H: system [1, 2, 7 - 9, 13 - 17, 20] and for palladium alloy[H2 systems [21] between p - n relationships and also relationships between p and physical properties related to n, such as electrical resistivity [22 - 2 4 ] , that have been determined in direct equilibration studies, and p - n relationships derived from electrode potential measurements. This has been the case even when hydrogen contents were being continually increased (or decreased) under similar conditions to those of the experiments of the present study, i.e. in solutions saturated with hydrogen gas at atmospheric pressure. A simplifying assumption which generally has been made in such indirect derivations is that surface hydrogen pressures derived from the electrode potentials are characteristic of the hydrogen chemical potentials of the entire substrate of the electrode. The fact that this can be so closely the case is a consequence of the high values of the diffusion coefficient of hydrogen D H w i t h i n palladium and its alloys. In the Pd[H2 system at 25 °C, DH. has values of about 10 -7 cm: s:~ in the a phase and about 10 -6 cm 2 s-1 in the fl phase concentration ranges respectively [19, 25]. Despite these high values of Dm some gradients of hydrogen concentration must be expected to occur from the surface to the interior during the course of experiments where E is being recorded for continuous absorption (or desorption) of hydrogen. The magnitudes of such concentration gradients will be dependent on rates of supply or removal of hydrogen to the electrode surface, and they can be expected to be more especially significant in ranges of hydrogen content where p (or E) is a more sensitive function of small changes in n, e.g. for the ~ phase concentration range of the PdIH 2 system, where differences between surface hydrogen concentrations estimated from electrode potential measurements and overall internal hydrogen contents have been employed to determine the hydrogen diffusion coefficients [26]. Even in regions of less potential variation with n corresponding to ~ ~ fi phase transitions, increasing rates of overall hydrogen absorption can be expected to lead to some increases in the extent to which the surface chemical potential can exceed that of the substrate, either in cases where the

161

surface may be entirely o f an c~ or ~ phase composition or in cases where it consists o f a mixture o f ~ and ~ phase regions [ 2 7 ] . Nevertheless, such substrate c o n c e n t r a t i o n gradients will n o t alter the fact that, when overall gain or loss of hydr ogen is governed by diffusion of molecular h y d r o g e n through the B r u n n e r - N e r n s t layer, the electrode surface and interfacial h y dr oge n concentrations represented by C2 in eqn. (2) and p in eqn. (3) will be the factors governing c o n c u r r e n t rates of desorption of h y d r o g e n during the course of experimental runs such as those represented in Fig. 1. Some previous experiments were carried out with static palladium electrodes where an analysis has shown t ha t the kinetics of absorption of hydrogen are governed by diffusive transport of dissolved hydrogen molecules through the B r u n n e r - N e r n s t layer. Values of the rate constant k0 in eqn. (3) in solutions saturated with hydrogen gas at pressures P ~ 1 bar have been estimated f r o m overall rates of absorption calculated from conjoint measurements o f changes in the electrical resistance of specimens [7, 8, 14, 15, 18] over ranges of hydrogen c o n t e n t which included the region of the ~ ~ phase transition where E ~ 50 mV at 25 °C, which corresponds to only effective desorption pressures p ~ 0.025 bar. F o r more precise measurements of k0 considerations of the c o n c u r r e n t desorptive effects of p have to be taken into account, and an alternative m e t h o d has been [6, 9, 14, 20, 21, 28 - 30] to integrate k o k o ' ( P - - p ) dt over the time intervals up t o a know n value of hydrogen c o n t e n t n to which the integration result is then equated. F o r the experimental runs in Fig. 1, k o k o ' ( P - - p ) dt has been integrated over t he total time up to E ~ 0 and equated to n = 0.7 [19, 20] after derivations of appropriate values o f p from experimental values of E using eqn. (1). Calculated values o f k0 are given in Table 1 where it m a y be seen that values for rotating electrode experiments are a p p r o x i m a t e l y twice those for static electrodes. TABLE 1 Values of the rate constant k0 and the related constant i0 derived from results (25 °C) plotted in Fig. 1 HCI solution normality

Electrode condition

k~ x 10 -16 (molecules cm-2 s-1 bar-1)

io = 2PFko/N (mA cm-2)

1.11

3,55

2.20 2.57 2.47

7,05 8,24 7,92

1.24 1.06 1.21 2.23 2.59 2.19

3.97 3.39 3.88 7.15 8.32 7.01

Thinly paUadized surfaces 1.0

Static

1.0 Rotating 0.01 Rotating 0.001 Rotating Thickly paUadized surfaces 1.0 Static 0.01 Static 0.001 Static 1.0 Rotating 0.01 Rotating 0.001 Rotating

162

However, these values of k0 for the rotating electrodes are still n o t as high as k0 values derived in experiments with static palladized palladium electrodes in hydrogen-stirred acidified (0.1 N H2SO4) methanol, ethanol and other alcohols [18]. Also, the values of E over the potential plateau region for the thinly palladized rotating electrodes in Fig. l ( b ) have not been decreased as much from the corresponding values for the static electrodes as the corresponding values for the experiments with static electrodes in alcoholic solutions [18]. The results of the experiments in the alcoholic solutions [18] have nevertheless still been found to be consistent with a control of hydrogen absorption by diffusion of molecules through the B r u n n e r - N e m s t layer with the higher values of the rate constant k0 equivalent to the diffusion flux J in eqn. (2) accountable in terms of a correspondingly higher solubility of hydrogen in the alcoholic solutions compared with the aqueous solutions and correspondingly higher values of C2 in eqn. (2). It would seem reasonable to conclude from these comparisons that the kinetics of hydrogen absorption by the rotating electrodes were also governed by molecular diffusion through the Brunner--Nernst layer, with the higher values of the rate constants corresponding to a reduction in the effective Brunner-Nernst layer thickness 6 in eqn. (2).

5.2. Local cell hydrogen transfer effects The values in Table 1 show that increasing depositions of palladium black have not produced marked alterations in the rate constant k0. However, Fig. 1 illustrates that they have led to substantial reductions in values of electrode potential E over the relatively time-invariant regions corresponding to the ~-~ fl phase transition and to marked further reductions in these values of E with decreasing acid concentration, even for static electrodes and particularly for rotating electrodes. Additional depositions of palladium black can be observed to produce increasingly pronounced dendritic growth. With the accompanying development of longer internal diffusion paths, from geometrical considerations the hydrogen contents of such dendritic regions can be expected to increase substantially faster in the hydrogen-saturated solutions than in the main substrate, so that electrode potentials at their surfaces can complementarily be expected to decrease more rapidly towards E ~ 0. In highly conducting electrolyte solutions, however, corresponding local cell differences in electrode potential between the "end regions" of dendrites and other parts of the surface can be supplementarily reduced by electrolytic hydrogen transfer [1, 2, 4, 5, 22, 31 - 35]. Such external local cell hydrogen transfer equalizations of the hydrogen chemical potential will be increasingly less effective with decreases in the conductivity of the surrounding electrolyte; this would probably account for the spread of divergences of E over the regions of the -~ ~ phase transition in Fig. 1, from values which should characterize hydrogen chemical potentials corresponding to the hydrogen contents of interior substrates [20]. Such considerations of local cell effects have a

163 general importance for employing palladium black depositions as a combined electrode surface activating and hydrogen transmitting medium [25]. The results in Fig. 1 serve to emphasize that, commensurate with a required surface activity, the depositions should be as thin as possible and contact the substrate as homogeneously as possible, particularly when carrying out experiments in electrolytes of low conductivity. Studies in the subsequent paper of the electrical resistivities of cathodes provide an example of a case where measurements in lower conductivity electrolytes may otherwise reduce problems arising from parallel conduction paths through the electrolyte, including the low interface impedances at surfaces with high catalytic activities [1, 2, 5, 31 - 35].

5.3. Overpotential studies with constant current electrolysis and measurements o f open-circuit potential decays after electrolysis The argument for deriving values of I?2 from plots of the function log (p/(p --P)} against time as in Fig. 2(b) stems from a supposition [7] that, if the overall rate of desorption of hydrogen from the electrode surface after interruption of electrolysis can again be governed by molecular diffusion of dissolved hydrogen through the Brunner--Nernst layer, an equality koko'blPt = l n ( pP - ~ ) -

In (p0P~_° p)

(5)

may be derived by making use of the finding in the ~ phase of the PdIH2 system, near values of hydrogen content n ~ 0.7 corresponding to p -- P ~ 1 bar (E ~ 0), that n is a linear function of In p. In deriving eqn. (5) this relationship has been expressed [7] as 1 n = 0.7 + - - l n p bl

(6)

The excellent linearity of the plots in Fig. 2(b) for both the static and the rotating palladium electrodes can therefore be regarded as evidence in both cases that the overall rates of desorption of hydrogen during the period of open-circuit electrode potential decay back to E ~ 0 are again governed by the overall rate of loss of hydrogen molecules by diffusion out through the Brunner--Nernst layer as again represented by eqn. (3). In addition, the values of k0, derived from the slopes in Fig. 2(b) by taking [7] bl = 35, are consistently of the same magnitudes as the values of k 0 in Table 1 derived from measurements of open-circuit potentials in experiments in HC1 solutions before c o m m e n c e m e n t of electrolysis, giving values of 1.3 X 1016 - 1.6 × 1016 molecules cm -2 s -1 bar -1 for the static electrodes and 2.8 × 1016 molecules cm -2 s-1 bar -1 for the rotating electrode. It also then follows from the form of definition of the 772 c o m p o n e n t of overpotential that these results support a conclusion that, for the rotating electrodes, 72 is again still equatable [7] with the chemical potential of the electrode substrate in equilibrium with the concentration o f hydrogen molecules dissolved in the solution

164

layer adjacent to the cathode surface under steady state conditions of electrolysis. These concentrations of dissolved molecules are again in turn governed by the limitations of their rate of release to the bulk of the solution by the diffusion barrier of the Brunner-Nernst layer. These conclusions also are consistent with the close agreement, shown by characteristic examples in Fig. 3, between the derived values of rh and the relationship

_ RT ln(.i + 2PFko/N t r~2

2F

~ 3 ~

/

(7)

which also has been derived [7, 9] by combination with eqn. (1) on the assumption that at a current density i the additional electrolytically discharging hydrogen (corresponding to Ni/2F molecules cm -2 s-1) raises the hydrogen chemical potential to corresponding values of P0 > P by amounts which again are governed by the rate of diffusion of the evolved molecules o u t through the Brunner-Nernst layer. The comparative effects of rotation of the electrodes have merely been to shift the position of the linear relationship along the abscissa, b y extents representative of higher values of log (2PFko/N) corresponding to the higher values of k 0. It seems important to point out that, from its definition and the analyses of the kinetics, values of ~72 derived in these studies represent components of overpotential corresponding to the hydrogen chemical potentials of the surface of the electrode as well as to the substrate. However, since it is governed by diffusion of molecules in the Brunner-Nernst layer, r~2 gives no information concerning intermediate surface reactions such as the dissociation of the hydrogen molecules and the recombination of the hydrogen atoms which should by implication be occurring very rapidly in comparison with the diffusion processes. It is noteworthy, however, that in strongly acid solutions, as found previously [1, 11, 12] and again in both constant current and pulsed current experiments reported here, how dominating the c o m p o n e n t rl2 of the total apparent overpotential can be, even without reducing the resistive drop components of the total apparent overpotential by Luggin capillary arrangements. Taken in conjunction with difficulties found in identifying electrode potentials with hydrogen chemical potentials at less catalytically active surfaces [1, 2 ] , this consideration seems to continue to impose limitations on attempts to use overpotential-current relationships as diagnostic of surface kinetics [1, 7 - 10, 3 6 ] . It should also be stressed, however, that in more dilute catholytes or at higher current densities or with alternative conditions of electrode activation such as thicker deposits of palladium black, other components may contribute significantly to the total apparent overpotentials, such as hydrogen ion concentration terms or a term due to high localized hydrogen atom concentrations at the ends of dendrites which, it has been suggested, contribute to the less easily defined rll c o m p o n e n t of the overpotential at palladium surfaces [4].

165

5.4. P o t e n t i a l responses to p u l s e d c u r r e n t electrolysis

In Figs. 7, 11 and 12, the measures of agreement at the highest pulse: pause ratios of ~(a.p.) and ~(b.p.) with the theoretical lines equating overpotential to the function 0.0295 log{{/+ 2 P F k o / N ) / ( 2 P F k o / N ) } with reasonably estimated values of k0 provide sound evidence t h a t both of the components representative of the overall pulse displacement are essentially representative of hydrogen chemical potentials and are again governed in magnitude by the rates of diffusion of evolving hydrogen molecules through the BrunnerNernst layer. This conclusion is supported by the close similarity between relationships obtained with either platinum black or palladium black and by their independence of alterations in catholyte acid concentrations. For the experimental surfaces of very high catalytic activity presently employed, this conclusion is also consistent with the interpretations of the form of relationships between the ~/2 component of the overpotential and the current density shown in Fig. 3. It can be appreciated that, in other experimental conditions where open-circuit potentials can be reliably correlated with surface hydrogen chemical potentials, measurements of overall pulse displacements can provide a very useful source of information concerning these hydrogen chemical potentials supplementary or alternative to information obtainable by singlepulse or continuous-current techniques.

Acknowledgments R.C.J. and M.C.W. acknowledge awards of Research Studentships by the Ministry of Education for Northern Ireland. A.O. acknowledges the award of a Leverhulme European Visiting Research Fellowship. Thanks also are due to the Science Research Council and J o h n s o n - M a t t h e y and Co. for financial support.

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