Determination of hydrogen absorption isotherm and diffusion coefficient in Pd81Pt19 alloy

Journal of

Electroanalytical Chemistry Journal of Electroanalytical Chemistry 588 (2006) 32–43 www.elsevier.com/locate/jelechem

Determination of hydrogen absorption isotherm and diffusion coefficient in Pd81Pt19 alloy F. Vigier, R. Jurczakowski 1, A. Lasia

*

De´partement de chimie, Universite´ de Sherbrooke, Sherbrooke, Que´., Canada J1K 2R1 Received 10 May 2005; received in revised form 15 November 2005; accepted 25 November 2005 Available online 18 January 2006

Abstract In the present paper, hydrogen absorption into Pd81Pt19 foil was studied using the permeation and impedance techniques. Pd81Pt19 is an interesting alloy in which the a-phase is extended to high hydrogen concentrations. The total amount of hydrogen absorbed is smaller than that in pure palladium and the absorption plateau is obtained at negative overpotentials. An important error in the absorbed hydrogen amount can be made if the measurements are performed in a stagnant solution because of the dissolved hydrogen formation; its charge adds to the absorbed hydrogen oxidation charge.The hydrogen diffusion coefficient was determined by various permeation and impedance techniques. They gave similar values with the exception of the small differential step permeation technique and EIS in the transmissive mode. Hydrogen induced stress might be at origin of the deviations observed in the permeation studies.
2005 Elsevier B.V. All rights reserved. Keywords: Hydrogen absorption isotherms; Hydrogen permeation; EIS; Transfer functions; Hydrogen diffusion coefficient; Pd81Pt19

1. Introduction Palladium and its alloys – hydrogen systems may be considered as models for other metal–hydrogen systems. At ambient temperatures hydrogen in Pd forms a-phase at low concentrations (atomic ratio H/M < 0.025) whereas at high concentrations (H/M > 0.6) it forms b-phase. High H solubility and diffusion coefficient allow application of Pd alloys for hydrogen storage and purification [1,2]. Recently, we have studied hydrogen absorption in thin Pd layers [3–7]. Although Pd is the most studied hydrogen absorbing metal its alloys e.g. with Pt have also attracted a lot of attention for hydrogen absorption [8–17], electrocatalysis [18,19] or catalysis [20], and D2–H2 separation [21]. Pd– *

Corresponding author. Tel.: +1 819 821 7097; fax: +1 819 821 8017. E-mail address: [email protected] (A. Lasia). 1 On leave from the Department of Chemistry, University of Warsaw, ul. Pasteura 1, PL-02-093 Warsaw, Poland. 0022-0728/$ - see front matter
2005 Elsevier B.V. All rights reserved. doi:10.1016/j.jelechem.2005.11.035

Pt alloys form the f.c.c. solid solutions. As the atomic radius of Pt is similar to that of Pd (0.138 and 0.137 nm, respectively) the substitution of Pd by Pt atoms expands the lattice only slightly, however, the lattice parameter does not vary linearly with the Pt content [13,22]. Pd–Pt alloys containing more than 12 at.% of Pt behave differently with regard to hydrogen solubility. Although the quantity of hydrogen dissolved in Pd81Pt19 alloy is lower than in Pd its concentration in the a-phase is ten times higher (at the pressure studied) and the critical temperature of the a–b transition is below 298 K [8,10–12]. For absorption from the gas phase there is no absorption plateau but higher pressures than accessible in typical electrochemical experiments are necessary to increase the hydrogen content [8,10,11,14]. The decrease of the hydrogen solubility in the Pd–Pt alloys was explained by the filling up of the palladium conduction band by the valence electrons of platinum [22]. The anomalous decrease of the stability of the alloy–hydrogen was explained by the large broadening of the valence

F. Vigier et al. / Journal of Electroanalytical Chemistry 588 (2006) 32–43

33

Nomenclature A Ag Cdl Cp CH(x) CH,max

DH Eeq Ei f ji j2(1) Dj2 1 K K4 L

real electrode surface area, cm2 geometric surface area, cm2 double layer capacity, F cm2 hydrogen adsorption pseudocapacitance, F cm2 hydrogen concentration at the distance x, mol cm3 maximal concentration of hydrogen in the alloy obtained at negative overpotentials at given experimental conditions hydrogen diffusion coefficient, cm2 s1 potential of the reversible hydrogen electrode, RHE, in the same solution entry i = 1 and exit i = 2 potentials F/RT, V1 current density at the entry i = 1 and exit i = 2 side, A cm2 steady state current density at the exit side, A cm2 variation of current at the output side, A cm2 potential dependent equilibrium constant for the hydrogen adsorption reaction (2) equilibrium constant for absorption reaction (3) thickness of the Pd–Pt foil (50 lm)

band upon substitution [22]. Phase separation was observed after hydriding at high temperatures [23,24]. Zoltowski and Makowska [15] have studied the Pd81Pt19 alloy under reflective boundary conditions by the EIS. They found that the diffusion coefficient of hydrogen in that alloy (
1 · 107 cm2 s1) is lower than that in pure Pd (
3 · 107 cm2 s1). Two mechanisms are generally considered in electrochemical hydrogen absorption: (i) one-step or direct absorption mechanism in which the proton is reduced and transferred (absorbed) into the metal [25–30] M þ Hþ þ e ¢ M  Habs;0

ð1Þ

where Habs,0 denotes hydrogen atom just below the first atomic plane (subsurface, x = 0). In parallel hydrogen adsorption, Eq. (2), may occur on the metal surface, but it does not lead to the hydrogen absorption; (ii) two-step or indirect absorption mechanisms in which the proton is reduced and adsorbed on the metal surface, and next it is transferred from the adsorbed to absorbed state [28,31,32]: M þ Hþ þ e ¢ M  Hads

ð2Þ

M  Hads ¢ M  Habs;0

ð3Þ

H/M nH Q0H;i Q0H Rct R Rab Rp t bW Z V X /W g r1 rX r0 s h x

atomic ratio of sorbed hydrogen and metals (Pd + Pt) in the alloy the same as H/M potential dependent specific charge for hydrogen adsorption (i = ads) or absorption (i = abs), C cm2 and C cm3, respectively total (adsorption and absorption) specific charge of hydrogen per unit volume of the alloy charge transfer resistance, X cm2 =A/Ag, surface roughness factor absorption resistance, X cm2 hydrogen evolution resistance, X cm2 time, s mass transfer (Warburg) impedance, X cm2 =AgL, electrode volume, cm3 absorbed hydrogen fraction, CH/CH,max, between 0 and 1 constant phase coefficient for diffusion hydrogen overpotential g = E  Eeq, V maximal hydrogen adsorption charge, C cm2 maximal hydrogen absorption charge, C cm3 mass transfer coefficient, X cm3 s1 dimensionless coefficient, s = DHt/L2 hydrogen surface coverage fraction ac signal angular frequency, rad s1

The subsurface hydrogen diffuses in the bulk of metal: M  Habs;0 ¢ M  Habs;x

ð4Þ

where M  Habs,x denotes hydrogen absorbed in the bulk at the distance x from the interface. The consequence of the entry of hydrogen into metal is the lattice expansion. At more negative potentials hydrogen evolution reaction may proceed in two processes: (i) Tafel reaction (chemical recombination) 2M  Hads ¢ 2M þ H2ðgÞ

ð5Þ

(ii) Heyrovsky reaction (electrochemical recombination) M  Hads þ Hþ þ e ¢ M þ H2ðgÞ

ð6Þ

Electrochemical impedance spectroscopy (EIS) is a very sensitive technique for studying hydrogen reactions [33,34]. It may be applied to determine electrode and process parameters such as double layer capacitance, Cdl, charge transfer resistance, Rct, diffusion coefficient, DH, etc. The aim of this work was to determine the hydrogen absorption isotherm and to compare different methods of determination of the diffusion coefficient, DH, in Pd81Pt19: ac (impedance in the reflective and transmissive mode)

34

F. Vigier et al. / Journal of Electroanalytical Chemistry 588 (2006) 32–43

and dc permeation techniques under potentiostatic and galvanostatic conditions. 2. Experimental 2.1. Equipment and chemicals Pd81Pt19 foils (25 · 25 mm, thickness of 50 lm) were supplied by Goodfellow (USA). They were heated for 2 h in air at 300 C to remove the carbon containing species (e.g. adsorbed hydrocarbons) [35]. Next, the samples were reduced under hydrogen atmosphere (5%H2–N2) during 2 h at the same temperature. After this treatment, the sample was annealed in the inert atmosphere (Ar 99.99% purity) at 650 C and cooled slowly to room temperature. The electrolyte used was 0.1 M H2SO4 prepared from concentrated H2SO4 (Merck, 99.999%) with ultra-pure water (Millipore MilliQ 18.2 MX cm). Oxygen was removed with the ultrahigh purity argon (Ar UHP 5.0, Praxair). All the experiments were performed at room temperature (
23 C). Two electrochemical cells were used for the experiments. A two-compartment cell was used for the determination of the isotherms and EIS experiments in the reflective boundary conditions. The working electrode was a piece of the Pd81Pt19 foil of 0.56 cm2 (weight 31 mg) attached to a gold wire. The second cell, used for permeation, EIS and for the transfer function experiments, was similar to that described by Devanathan and Stachurski [36] and the surface area of the foil exposed to the solution was 1 cm2. The counter electrode was a platinized platinum separated by sintered glass. The reference electrode was Hg/ Hg2SO4 in 0.1 M H2SO4 but all the potentials are referred to the reversible hydrogen electrode in the same solution (RHE) and expressed as overpotentials. It was assumed, that at room temperature hydrogen fugacity is equal to one. The hydrogen equilibrium potential versus HgjHg2SO4j0.1 M H2SO4 electrode is 0.732 V. For all the electrochemical experiments Solartron SI 1260 and SI 1287 or PAR 273A and 5210 lock-in amplifier were used. Under EIS conditions frequencies ranged from 1 mHz to 20 kHz and the ac amplitude was 5 mV r.m.s. For the transfer function techniques Bank POS2 potentiostat/galvanostat was used in a floating configuration and the data acquisition was carried out using computer controlled data acquisition card (PD2-MF-16-1M, United Electronics) controlled by a PC. 2.2. Determination of the hydrogen absorption isotherms

hydrogen present in the metal matrix. At higher hydrogen concentrations, the potential was kept at 0.535 V until the current dropped to zero. Integration of the current versus time gave the total amount of hydrogen adsorbed at the electrode surface and absorbed in the metal matrix. The experiments were preformed with and without bubbling with argon. The hydrogen absorption isotherms were expressed in terms of atomic ratio H/M. The experimental setup for the permeation experiments was described in details elsewhere [3]. 3. Theory 3.1. Permeation Permeation experiments were carried out by imposing a potential or current steps at the entry side 1 (x = 0) and monitoring hydrogen oxidation at the exit side 2 (x = L) under potentiostatic control. Under these conditions, it is possible to determine the diffusion coefficient of hydrogen [37–39]. Classical approach to the analysis of the diffusion coefficient uses the time-lag methods [40]. However, these methods use only one parameter to determine the diffusion coefficient. It is much better to analyze the whole transient of current vs. time to determine this parameter. The current at the exit side vs. time transients may be approximated using the so-called fast or slow absorption models [39]. The fast model assumes that the absorption reaction is fast. The current at the exit side is described by the equations [39]:   j2 ðtÞ 2 1 ¼ pffiffiffiffiffi exp  for 0 < s < 0:23 ð7Þ j2 ð1Þ 4s ps and j2 ðtÞ ¼ 1  2 expðp2 sÞ j2 ð1Þ

for

s > 0:23

ð8Þ

where s = DHt/L2, j2 is the exit current, indices t and 1 refer to the time t and the steady-state current, respectively, DH is the diffusion coefficient, and L the membrane thickness. However, assuming that the hydrogen entry is limited by surface process on the entry side, the so-called slow absorption model is obtained [39]: " # n 2 1 j2 ðtÞ 4X ð1Þ ð2n þ 1Þ p2 s ¼1 exp  ð9Þ j2 ð1Þ p n¼0 2n þ 1 4 Finally, for the galvanostatic step the current transients are described by [39]:   j2 ðtÞ 1 ¼ 2erfc pffiffiffi for 0 < s < 0:32 ð10Þ j2 ð1Þ 2 s and

To determine hydrogen absorption isotherms a constant potential was applied until the equilibrium conditions of hydrogen absorption were obtained. Then, a single scan at 5 mV s1 from the absorption potential to 0.535 V vs. RHE (double layer region) was applied to oxidize all the

 2  j2 ðtÞ 4 ps ¼ 1  exp  for j2 ð1Þ p 4

s P 0:32

ð11Þ

In the above conditions, it is assumed that at the end of the experiment a linear concentration gradient is reached in the

F. Vigier et al. / Journal of Electroanalytical Chemistry 588 (2006) 32–43

a

Cp

b

CH (E2 )

35

CH (E2 ) CH (E1 )

CH (E0 )

CH (E0 )

c

d CH (E2 )

CH (E2 ) CH (E1 )

ZW β

CH (E1 )

α

L

Rab

Fig. 2. Equivalent electrical model for the faradaic impedance in presence of hydrogen absorption.

E1 0

Rp

Rct

CH (E0 )

CH (E0 ) 0

L

Fig. 1. Hydrogen concentration profiles in different permeation methods: (a) method 1 or 4, (b) method 2, (c) method 3, (d) possible concentration profile in the presence of the phase transition.

membrane. Nevertheless, if there is a phase transition the concentration gradient is discontinuous, see Fig. 1d, the model becomes much more complex. The permeation experiments were carried in four ways: (1) Keeping initially the same potential at 535 mV (in the double layer zone) at both sides of the membrane followed by the step to a more negative potential at the entry side (large step method), Fig. 1a. (2) Keeping initially the membrane in the double layer zone (no hydrogen absorbed) at the exit side and more negative potential at the entry side (hydrogen absorption and transfer occurs). When a steady-state is reached, another small steps (20 mV) at the entry side is applied, keeping the exit side at g = 535 mV (small step method), Fig. 1b. (3) Saturating the membrane by applying the same potential in the hydrogen absorption zone at the two sides (no initial concentration gradient) followed by a small (20 mV) step at the entry side (small differential step), Fig. 1c. (4) Keeping initially the membrane in the double layer zone (no hydrogen absorbed) followed by the galvanostatic step at the entry side, Fig. 1a.

The equivalent model for the indirect or adsorption– absorption mechanism used is shown in Fig. 2; this is the most common model used for the hydrogen absorption mechanism [7,34]. It consists of the charge-transfer resistance, Rct, adsorption pseudocapacitance, Cp, hydrogen evolution resistance, Rp, hydrogen absorption resistance, b W [34]: Rab, and mass transfer impedance, Z b f ¼ Rct þ Z

1 jxC p þ R1p þ

1

ð12Þ

Rab þb ZW

pffiffiffiffiffiffiffiffiffiffiffiffi b W ¼ r0 = jxDH The mass transfer impedance equals Z ffi pffiffiffiffiffiffiffiffiffiffiffiffiffi  coth ð jx=DH LÞ for the reflective boundary and coth is replaced by tanh for transmissive boundary, and r 0 is the Warburg coefficient depending on the thermodynamic parameters of hydrogen adsorption and absorption [7,34]. In the H UPD region Rp equals zero. Taking into account distribution of diffusion paths the generalized Warburg element was used [7]: sffiffiffiffiffiffiffi !/W 0 r L jx bW ¼ Z ð13Þ L qffiffiffiffiffi /W coth D H jx L DH DH where /W is the constant phase coefficient for diffusion. It should be noticed that the Warburg impedance being the bulk property is independent of the absorption model chosen. The impedances were analyzed using a modified version of the complex non-linear least squares fitting program (CNLS) of Macdonald et al. [41], from which the experimental parameters were determined. 4. Results

3.2. EIS 4.1. Cyclic voltammetry EIS was used in the reflective and transmissive modes [33,34]: (i) Impermeable (reflective) mode: Hydrogen enters the electrode from both sides up to x = L/2. (ii) Permeable (transmissive) mode: Hydrogen enters the electrode at one side (x = 0), diffuses through the membrane and is oxidized at the other side (x = L), the potential at the exit side is 0.535 V.

The cyclic voltammogram (CV) of Pd81Pd19 foil is displayed in Fig. 3. The obtained voltammogram is similar to that of Pd [6] with exception of the shoulder at 0.27 V on the hydrogen oxidation peak. The surface oxidation begins at 0.9 V during the positive scan and the reduction peak appears at 0.74 V during the negative scan. The hydrogen adsorption/absorption begins at 0.33 V.

36

F. Vigier et al. / Journal of Electroanalytical Chemistry 588 (2006) 32–43

the saturation and oxidation steps. Under such conditions, the obtained saturation value is H/M = 0.16, the isotherms are presented in Fig. 4. This value corresponds to rX = 1730 C cm3 or CH,max = 0.0179 mol cm3. It is evident that hydrogen dissolved in the solution around the electrode affects strongly the results. It is also interesting to note that the total isotherm presented contains contribution form the hydrogen adsorption and absorption. The total hydrogen oxidation charge may be written as:

1.0 0.27 V

I / mA cm

-2

0.5 0.0 -0.5 -1.0

QH ðgÞ ¼ AQ0H;ads ðgÞ þ VQ0H;abs ðgÞ

-1.5 0.0

¼ Ar1 hðgÞ þ V rX X ðgÞ 0.5

1.0

1.5

E / mV(RHE) Fig. 3. CV of the hanging Pd81Pt19 foil (thickness 50 lm) recorded in 0.1 M H2SO4 at 50 mV s1.

4.2. Hydrogen absorption isotherms Absorption isotherms were initially determined by applying a constant potential in the absorption region and waiting long enough to obtain a constant hydrogen oxidation charge while argon was passed above the solution surface. The obtained saturation values of H/M were equal to 0.35 or 0.46 depending on the absorption time, see Fig. 4. This value is larger than that found earlier for this alloy [15,16]. However, it is obvious that at slightly positive overpotentials hydrogen is generated in the solution around the electrode, according to the Nernst equation: aH2 ¼ expð2f gÞ, reaching the saturation value at g = 0, i.e. at the reversible hydrogen electrode equilibrium potential. At longer times, a quasi-equilibrium hydrogen concentration is reached around the electrode, but during the anodic sweep, hydrogen from the solution, as well as hydrogen from the foil, are oxidized, increasing the total charge. For this reason in determination of hydrogen isotherms argon was bubbled through the solution during 1

0.5

ð14Þ

where Q0H;i are potential dependent specific H adsorption and absorption charges, A and V are the real surface area and the volume of the foil, r1 and rX are the maximal adsorption and absorption charges, h is the surface coverage, and X is the dimensionless hydrogen concentration. Dividing by the apparent surface (geometric) area, Ag, and the total volume leads to: ðH=MÞF =V m ¼ QH ðgÞ=V ¼ Q0H ðgÞ ¼ ðR=LÞQ0H;ads ðgÞ þ Q0H;abs ðgÞ

ð15Þ

where Vm is the molar volume of the alloy, R is the surface roughness and L is the absorbing foil thickness. At the potentials more positive than 0.1 V the influence of the adsorption is visible, i.e. the first term in Eq. (15) is important. At the potentials between 0.16 and 0.04 V the logarithmic slope dE/dlog nH = 0.063 ± 0.002 V dec1 indicating nernstian character of the absorption isotherm. It should be stressed that the zone in which linear relation can be observed is quite limited: at more positive potentials there is an influence of H adsorption and at more negative potentials influence of the hydrogen evolution. The fast increase in hydrogen content occurs around
 0.05 V. It is shifted to more negative potentials in comparison with palladium (+0.05 V) and the hydrogen solubility is much lower. It should be stressed that the quasi-plateau observed on the electrochemically measured isotherms is due to the

0.1 0.01 1E-3 H/M

H/M

0.4

1E-4 1E-5

1

1E-6

0.3

-0.2

0.0

0.2

0.4

E / V vs. RHE

with Ar bubbling, 1.5 h Ar above solution, 2 h Ar above solution, 8 h

0.1

I2 / mA cm

1E-8

0.2

-2

1E-7

0.1

0.0 -0.2 -0.1

0.0

0.1

0.2

0.3

0.4

0.5

0.01

E / V vs. RHE Fig. 4. Hydrogen absorption isotherms, expressed as an atomic ratio H/M in 50 lm Pd81Pt19 foil in 0.1 M H2SO4 without (open symbols) and with (black circles) bubbling with argon. Maximal equilibration times are indicated in the legend; with Ar bubbling there was no difference for longer times.

-50

0

50 100 150 E1 / mV(RHE)

200

Fig. 5. Current density I2 recorded at the exit face of a Pd81Pt19 membrane (E2 = 0.53 V) as a function of the entry potential in 0.1 M H2SO4.

F. Vigier et al. / Journal of Electroanalytical Chemistry 588 (2006) 32–43

insufficient apparent hydrogen pressure applied to the alloy as in the gas phase experiments there is no plateau on the absorption isotherms. 4.3. Permeation experiments Dependence of the steady-state permeation current on the applied entry potential is illustrated in Fig. 5. The logarithmic plot is linear with the slope dE1/dlog j2 = 0.061 ± 0.002 V dec1 but at more negative potentials a limiting current is observed. The permeation experiments were carried out by cycling the applied potential between two values selected for each experiment and the reproducible curves were quickly obtained. The first experiment consisted of the application of a large potential step into the hydrogen absorption zone (method 1). The fast absorption model was used to approximate the experimental transients [39], Eqs. (7) and (8), and the diffusion coefficient DH was evaluated with a good precision (relative errors below 1%) to be around 0.9 · 107 cm2 s1. Fig. 6 shows both, the experimental and the approximated data to confirm the precision of the fitting technique. The results obtained by using small step method 2 are illustrated in Fig. 7. In this method, the entry potential was changed by 20 mV in the hydrogen adsorption zone while the exit potential was always kept at 0.535 V. In this case, a change in the current Dj2 was registered. For relatively low hydrogen concentration the DH around

600

800

500

600 400

400

300 200

0 0

50 100 150 200 250 300 350 t/s

350

100

200 t/s

300

ð16Þ

400

E1 = 40 mV DH = 0.90 x 10-7 cm2 s-1

100

DH = 0.80 x 10-7 cm2 s-1

0 0

E1 =20 mV

200

E1 = 0 mV DH = 0.72 x 10-7 cm2 s-1

200

dC H C H ð0Þ ¼ FDH L dx

600

j2 / µA cm-2

j2 / µA cm-2

800

j2 ¼ FDH

1000

1200 1000

1 · 107 cm2 s1 was found and the approximation with the fast model was good. At higher hydrogen concentration, the value of DH dropped to 0.72 · 107 cm2 s1 and a small deviation from the approximation was observed (at g = 0). The use of the slow absorption model, Eq. (9), did not improve the approximation. In the third protocol, Fig. 8, a small differential step was applied. At low hydrogen concentrations, the fast absorption model gives good approximations and the values of the diffusion coefficient obtained are similar to those found using methods 1 and 2. However, at the most negative overpotentials, some deviation is observed and the slow absorption model gave better, although not adequate approximations. Current transient at the exit side, obtained using the galvanostatic step method, are reported in Fig. 9. At lower currents, the entry and exit currents were identical while at higher entry currents the exit current was lower, which indicated that the hydrogen evolution reaction took place at the entry side. The approximation was good even at high currents. DH evaluated is between 0.75 and 0.97 · 107 cm2 s1. From the permeation currents determined in mode 1, known diffusion coefficient and the membrane thickness it is possible to estimate the surface hydrogen concentration at the entry side assuming linear gradient in the membrane:

j2 / µA cm-2

1400

37

0

400

0

100

5

80

4

50

100 150 t/s

200

250

j2 / µA cm-2

j2 / µA cm-2

250 200 150 100

E1 = 60 mV DH = 1.0 x 10-7 cm2 s-1

50

j2 / µA cm -2

300

60 40

E1 = 100 mV DH = 0.85 x 10-7 cm2 s-1

20

0

0

0

50

100 t/s

150

200

3 2

E1 =160 mV DH = 0.90 x 10-7 cm2 s-1

1 0

0

50

100 150 t/s

200

250

0

50

100 t/s

150

200

Fig. 6. Current transients during the permeation experiments in 0.1 M H2SO4, 50 lm Pd89Pt19 membrane, large step method 1, E2 = 0.535 V/RHE, experimental (  ) and fit (—–).

38

F. Vigier et al. / Journal of Electroanalytical Chemistry 588 (2006) 32–43 140

400

500

120

400 300 200

200

E1 = 0 mV DH = 0.72 x 10-7 cm2 s-1

100

100

E1 = 20 mV DH = 0.82 x 10-7 cm2 s-1

0 80

100

200 t/s

2.5

1.0

2.0

0.8 ∆j2 / µA cm-2

1.0

20

E1 = 80 mV DH = 1.14 x 10-7 cm2 s-1

E1 = 160 mV DH = 0.98 x 10-7 cm2 s-1

0.5

0

50

100 150 t/s

200

50 100 150 200 250 300 t/s

0.6 0.4

E1 = 180 mV DH = 1.01 x 10-7 cm2 s-1

0.2

0.0

0

E1 = 60 mV DH = 1.05 x 10-7 cm2 s-1 0

1.5

40

40

300

∆j2 / µA cm-2

60

60

0 0

50 100 150 200 250 300 t/s

80

20

0

0

∆j2 / µA cm-2

100

∆j2 / µA cm -2

-2 ∆j2 / µA cm

∆j2 / µA cm

-2

300

0.0 0

250

25

50

75 100 125 150 t/s

0

25 50 75 100 125 150 175 t/s

Fig. 7. Current transients during permeation experiment, small step method 2, E2 = 0.535 mV; experimental (  ) and fit to the fast (—–) model. 250 300

300 200

E1 = 0 V DH = 0.23 x 10-7 cm2 s-1 (f)

100

200

j2 / µA cm -2

j2 / µA cm-2

j2 / µA cm-2

400

150

200

100

100

E1 = 20 mV DH = 0.42 x 10-7 cm2 s-1 (f)

DH = 0.82 x 10-7 cm2 s-1 (s)

DH = 1.05 x 10-7 cm2 s-1 (s)

0

0 0

0

150 300 450 600 750 900 t/s

100

200 t/s

300

400

0

4

0.8

40

E1 = 60 mV DH = 0.7 x 10-7 cm2 s-1 (f)

20

DH = 1.9 x 10-7 cm2 s-1 (s)

0 0

50 100 150 200 250 300 t/s

j2 / µA cm-2

80

j2 / µA cm -2

1.0

j2 / µA cm -2

5

3 2 1

E1 = 140 mV DH = 1.1 x 10-7 cm2 s-1 (f)

0 0

50

100

t/s

150

DH = 1.57 x 10-7 cm2 s-1 (s)

0

100

60

E1 = 40 mV DH = 0.59 x 10-7 cm2 s-1 (f)

50

100

200 t/s

300

400

0.6 0.4 0.2

E1 = 180 mV DH = 1.1 x 10-7 cm2 s-1 (f)

0.0 0

50

100

150

t/s

Fig. 8. Current transients during permeation experiment, small differential step method 3, around a steady-state value, E2 = E1 + 20 mV; experimental (  ) and fit to the fast (f) (—–) and slow (s) ( - - -) models.

These values may be compared with those determined from the total hydrogen isotherm. Comparison of the obtained values is presented in Fig. 10. At very positive potentials,

CH values obtained from the isotherm are larger because of the influence of the hydrogen adsorption to the total isotherm. In the middle range, both values are similar but at

F. Vigier et al. / Journal of Electroanalytical Chemistry 588 (2006) 32–43 35

120

500

30

100

400

20 15 10

j1 = -30 µA cm-2

5

-7

2

DH = 0.7 x 10 cm s

80

j2 / µA cm-2

j2 / µA.cm -2

j2 / µA cm-2

25

300

60

200

40

j1 = -100 µA cm-2

20

-1

-7

500

DH = 0.97 x 10-7 cm2 s-1

-1

0

0

0

j1 = -600 µA cm-2

100 2

DH = 0.89 x 10 cm s

0

0

1000

39

t/s

500

1000

0

t/s

100 200 300 400 500 600

t/s

Fig. 9. Permeation experiments performed by applied a galvanostatic step at the entry side of the membrane, experimental (  ) and fit (—–).

from j2

-2 -3

-3

log (CH / mol cm )

from isotherm

-4 -5 -6

-50

0

50

100

150

4.4.1. Transmissive mode Fig. 11 illustrates examples of the complex plane plots obtained under the transmissive conditions at various entry potentials with the diffusion coefficient DH (the relative errors were 0.7–3%). The complex plane plots display high frequency straight line at 45 followed by a skewed semicircle corresponding to the finite length Warburg impedance [34]. The radius of this semicircle decreases as the potential becomes more negative which is related to the decrease of r 0 parameter [34]. The value of log r 0 is a linear function of the applied potential, Fig. 12. In fact, this value is described as [7]:

200

E / mV Fig. 10. Dependence of the logarithm of hydrogen concentrations, determined from the absorption isotherm and the permeation current, on potential.

more negative potentials values obtained from the isotherm are larger. This suggests that either the permeation limiting current, measured right after its stabilization, Fig. 6, does not correspond to the full equilibrium conditions (much longer times (hours) were used to fully saturate the foil) or the concentration gradient is nonlinear. 4.4. EIS spectroscopy The kinetic high frequency semicircle related to Rct  Cdl coupling was not observed on Pd81Pt19 under transmissive or reflective conditions, although on palladium it is well measurable [7]. This indicates that the kinetics of the adsorption/absorption reactions is very fast. Therefore, the double layer capacitance could only be determined in the double layer potential range (400– 530 mV), it was equal Cdl = 65 lF cm2. Zoltowski and Makowska [15] found 30–40 lF cm2 and the value found on 10 ML Pd on Au(1 1 1) is Cdl = 28 lF cm2. This suggests a surface roughness factor of the order of two. Diffusion coefficient was determined using the EIS in the transmissive and reflective mode.

r0 ¼

 1 K 4 Þ2 r1 1 ð1 þ K  1 Þ2 rX C p K 4 ð1 þ K

where the adsorption pseudocapacitance, Cp, is: 1 K f r1 Cp ¼  1 Þ2 2 ð1 þ K

ð17Þ

ð18Þ

then r0 ¼

 1 K 4 Þ2 1 ð1 þ K  1K 4 f rX K

ð19Þ

where r1 and rX are the maximal adsorption and absorp 1 and K4 are the equilibrium constants tion charges, and K of the hydrogen adsorption (potential dependent) and absorption reactions. The value of r 0 has a minimum  1 K 4 ¼ 1. However, when K  1 K 4  1, Eq. r 0 = 4/frX at K  1 K 4 Þ, with K  1 ¼ ðk 1 = (19) simplifies to r0 ¼ 2=ðf rX K k 1 Þef g , and log r 0 increases linearly with overpotential. The slope of dlog r 0 /dg is 77 mV dec1 including all the overpotentials, but becoming closer to the theoretically predicted value of 60 mV dec1 after exclusion of the most negative value. At overpotentials close to zero some production of hydrogen in the solution must occur and this may influence the observed impedance results. Similar dependence was also found for Pd foils [7]. 4.4.2. Reflective mode In the reflective mode, a pseudocapacitive behavior is observed at low frequencies. Examples of the complex-plane

40

F. Vigier et al. / Journal of Electroanalytical Chemistry 588 (2006) 32–43 600

250

120 mV -7 2 -1 DH=1.67 x 10 cm s

100 mV -7 2 -1 DH = 1.63 x 10 cm s

-2

200

-Z ' / Ω cm

400

-Z ' / Ω cm

-2

500

150

2.51

300 200

10

100

2.51

100

1

10 1

50

0

0

0

100

200

300

400

500

-2

600

0

50

Z ' / Ω cm

150

200

250

30

50

40 mV -7 2 -1 DH = 1.4 x 10 cm s -Z " / Ω cm

30

2.51

20

20 15 10

2.51

10

10

1 10

20

30

Z ' / Ω cm

-2

40

50

10

5 0

0

0V -7 2 -1 DH = 1.4 x 10 cm s

25 -2

-Z ' / Ω cm

-2

40

0

100

-2 Z ' / Ω cm

0

5

10

15

1 20

Z ' / Ω cm

25

30

-2

Fig. 11. Complex plane curves registered on Pd81Pt19 membrane in the transmissive conditions, entry potential E1 indicated in the figures, exit potential E2 = 535 mV; points – experimental, lines – approximations; numbers – frequencies in mHz.

The average values of DH determined by the CNLS is (0.99 ± 0.07) · 107 cm2 s1, however, it was not possible to approximate DH at more negative potentials.

-1.5

3

-1

log (σ ' / Ω cm s )

-1.0

-2.0

5. Discussion

transmissive -1 68 mV dec

-2.5 reflective -1 60 mV dec

-3.0 -3.5 0

20 40 60 80 100 120 140 160

E / mV Fig. 12. Dependence of the logarithm of r 0 on potential for the transmissive conditions.

plots in the reflective conditions are displayed in Fig. 13. The relative errors of the diffusion coefficient were 0.7–5%. The straight lines at
45 at high frequency were followed by almost vertical line at low frequencies. Because the low frequency line was not at 90 a constant phase element was used in the Warburg impedance, Eq. (13). The high frequency kinetic loop is not observed, similarly to the transmissive mode. The slope of dlog r 0 /dg = 60 mV dec1, which is the theoretical value.

The cyclic voltammogram of Pd81Pt19, Fig. 3, is similar to those published earlier [15,16] and to that of Pd [6]. A small hump is observed at
0.27 V that is at the potential, where the hydrogen adsorption peak occurs [16]. Processes of hydrogen adsorption and absorption are not separated and the absorption peak is larger in comparison with those obtained on the thin alloy layers [16]. The hydrogen total isotherm is very sensitive to the solution forced mixing because of the equilibrium hydrogen formation in solution even at positive overpotentials. In a stagnant solution, the oxidation charge is much larger because of the additional oxidation charge of hydrogen dissolved around the electrode. The maximal value of H/M is similar to that found by Grden´ et al. [16] on thin alloy layers. In contrast to the gas phase measurements [8,10–12], where the hydrogen content increases with the hydrogen pressure, a plateau on the isotherm was obtained. This may be related to the hydrogen nonelectrochemical desorption during potential sweep in the

F. Vigier et al. / Journal of Electroanalytical Chemistry 588 (2006) 32–43 150

2

750 3.16

500 10 250

0

100 mV

1.58 -2

250

3.98

50

20

1 15 10

10

150 mV -7 2 -1 DH = 1.08x10 cm s 0

100 75

40 mV -7 2 -1 DH = 1.00x10 cm s

25

-1

2

-7

DH = 0.96x10 cm s -Z "/ Ω cm

2

-Z '' / Ω cm

125

30

-Z '' / Ω cm

1.26

1000

41

500

750

Z '/ Ω cm

1000

25 0

0

25

2

50

75

100

Z '/ Ω cm

125

0

150

3.16

10

5

0

5

10

2

15

20

Z ' / Ω cm

25

30

2

Fig. 13. Complex plane curves registered on Pd81Pt19 foil under the reflective conditions, potential indicated in the figures; points – experimental, lines – approximations; numbers – frequencies in mHz.

Fig. 1c, i.e. initially there is no concentration gradient in the foil, the approximations are poorer. The ac impedance curves could be well approximated using the distributed diffusion model, Eq. (13), and the parameters Rct, Cp, Rp, and Rab in Eq. (12) were negligible. The values of the Warburg coefficient r 0 , Eq. (19), depend on the surface equilibrium parameters and the maximal absorption charge. Similar although not identical values were obtained in the transmissive and reflective modes, which may be related to not identical values of the constant phase parameter /W found in both experiments, Eq.(13). The logarithm of the Warburg coefficient is a linear function of the applied potential, Fig. 12, confirming that  1 K 4  1. The values of the diffusion coefficient obtained K under reflective conditions are similar to those found using other techniques while those found using the transmissive conditions are larger.

2.00 model 3 (slow)

-1

1.75

DH x 10 cm² s

1.50

-7

positive direction or the impossibility of applying very high relative hydrogen pressure electrochemically. It should also be noticed that the hydrogen absorption isotherm is shifted to more negative potentials with respect to Pd [6], which indicates, that absorption is less favorable. This is in agreement with the gas-phase measurements [8,10]. The obtained isotherm looks like that for the a–b phase transition although formation of b-phase was not found in the gas-phase experiments, probably because sufficient equivalent hydrogen pressure could not be applied electrochemically. The logarithmic slope dE/dlog nH of the isotherm in the hydrogen absorption zone is 0.063 V dec1 in agreement with the predictions of the indirect and direct absorption mechanisms. Similar slope was obtained for the permeation current dE1/dlog j2 = 0.061 V dec1. However, the permeation current reaches plateau at 0.02 V while the isotherm reaches it at the potentials more negatives than 0.06 V. Such difference may be related to the influence of the stress on the hydrogen concentration gradient inside the foil [12,17]. The permeation curves were well approximated in the whole time range for large step (mode 1, Fig. 1a), small step (mode 2, Fig. 1b) and the galvanostatic step (mode 4). Deviations were observed for the small differential step technique (mode 3, Fig. 1c) in which the uniform hydrogen concentration in the membrane was perturbed on the entry side. In this case, the use of the fast absorption model (which was used for all the other permeation techniques) gave much smaller values of DH at more negative potentials but approximation was not good, Fig. 8. Better, but still not adequate fit was obtained using so-called slow absorption model, but the obtained values were much higher than those obtained using other methods. In fact, the use of the slow model is not fundamentally supported in these conditions. It is interesting to note that when large hydrogen concentration gradient exists, i.e. when the hydrogen concentration at the exit side is zero, Fig. 1a,b, the approximations are good and while a very small gradient exists,

1 2 3 4 EIS t EIS r ZM1 ZM2

1.25 1.00 0.75 0.50 0.25

model 3 (fast)

-50

0

50

100

150

200

E / mV(RHE) Fig. 14. Comparison of the values of the hydrogen diffusion coefficient obtained by different methods; 1–4 permeation experiments (see text, method 3 using slow and fast absorption models), EIS t – transmissive and r – reflective modes, ZM1 and 2 Zoltowski and Makowska [15] results from hydrogen stripping (1) and impedance in the reflective mode (2), respectively.

42

F. Vigier et al. / Journal of Electroanalytical Chemistry 588 (2006) 32–43

Comparison of the values of the diffusion coefficient found using different method are illustrated in Fig. 14 and compared with those from the literature [15]. All the methods used with exception of the permeation technique using small differential step and EIS in the transmissive mode gave similar results. It should be stressed that Zoltowski and Makowska [15] have used the EIS under the reflective conditions. However, the hydrogen stripping method displayed large dispersion of the results at high positive overpotentials [15]. 6. Conclusions The electrochemical behavior of Pd–Pt foil is different from that of Pd. It absorbs less hydrogen than Pd and its diffusion coefficient is also lower; however, the a-phase zone is extended. Hydrogen concentrations in foil, obtained from the isotherm and the permeation current are similar to about 0 V and at more negative potentials the values from the isotherm are much larger, Fig. 10. This confirms that at positive potentials a linear concentration gradient develops in the foil. However, at more negative potentials either there is slow absorption kinetics or a nonlinear concentration gradient, similar to that in Fig. 1d, is present. It is interesting to note that the absorption isotherm (and the permeation current) reaches a plateau which is not observed in the gas-phase experiments, where there is no a–b phase transition [8,10,14,22]. Results of the determination of the hydrogen diffusion coefficient using permeation techniques indicate that an analysis of the whole i–t permeation curve should be performed because sometimes deviations from the theoretical shape appear and the use of the time-lag methods may lead to serious errors. The values of the diffusion coefficient determined from the gas phase permeation experiments are similar to these obtained in this paper [42]. The rate of hydrogen adsorption and absorption is very fast and no kinetic effects were observed on the impedance plots. It is also known that the hydrogen adsorption on Pt is very fast [43,44] and its presence on the alloy surface accelerates adsorption kinetics. The potential range available for the determination of the hydrogen diffusion kinetics using impedance methods is limited to the positive overpotentials while there is no such limitation for the permeation method. Linear relation with close to the theoretical slope was obtained for the isotherm and permeation current. Similar relation was also obtained for the Warburg r 0 parameter. They all indicate the nernstian character of the adsorption process. However, from these experiments it is not possible to distinguish between the direct and indirect absorption mechanisms as they display the same behavior. It is not clear why the deviations were observed for small the differential step permeation technique and EIS in the transmissive mode. The hydrogen gradient conditions for EIS in the transmissive mode are the same as for the permeation experiments in the modes 1, 2 and 4, which gave sim-

ilar results. Deviations observed for the small differential step permeation technique, Fig. 1c, cannot be related to the kinetics of hydrogen oxidation/reduction at the exit side as no kinetic effects were observed in the impedance measurements (no Rct on the complex plane plots). The hydrogen gradient conditions for the permeation experiments in the small gradient mode 3 and the EIS in the reflective conditions are similar, however, in the permeation experiments the potential perturbation was larger (20 mV) while in the EIS experiments it was only 5 mV. It is known that the hydrogen induced stress diffusion is observed when initial hydrogen concentration in the alloy is larger than zero, which could explain the problems with the approximation of the permeation curves in the mode 3. However, the gas phase experiments in which this effect was observed were conducted with much thicker foil [17,42,45]. It should be added that theoretically predicted effects of self stress on the measured impedances [46–49] were observed neither for Pd91Pt19 nor for Pd [7] for the experiments with the foil suspended in the solution and in the Devanathan–Stachursky cell. The effect of the hydrogen induced segregation [23,24] may be excluded at our experimental conditions as it appears only at high temperatures. References [1] G. Alefeld, J. Vo¨lkl (Eds.), Hydrogen in Metals I, Springer-Verlag, Berlin, 1978. [2] G. Alefeld, J. Vo¨lkl (Eds.), Hydrogen in Metals II, Springer-Verlag, Berlin, 1978. [3] C. Gabrielli, P.P. Grand, A. Lasia, H. Perrot, J. Electroanal. Chem. 532 (2002) 121. [4] C. Gabrielli, P.P. Grand, A. Lasia, H. Perrot, Electrochim. Acta 47 (2002) 2199. [5] C. Gabrielli, P.P. Grand, A. Lasia, H. Perrot, J. Electrochem. Soc. 151 (2004) A1919. [6] C. Gabrielli, P.P. Grand, A. Lasia, H. Perrot, J. Electrochem. Soc. 151 (2004) A1937. [7] C. Gabrielli, P.P. Grand, A. Lasia, H. Perrot, J. Electrochem. Soc. 151 (2004) A1943. [8] B. Baranowski, F.A. Lewis, S. Majchrzak, R. Wioniewski, J. Chem. Soc., Faraday Trans. I 62 (1972) 824. [9] J.D. Clewley, J.F. Lynch, T.B. Flanagan, J. Chem. Soc., Faraday Trans. I 73 (1977) 494. [10] B. Baranowski, F.A. Lewis, W.D. McFall, S. Filipek, T.C. Witherspoon, Proc. Roy. Soc. London Ser. A 386 (1983) 309. [11] A. Lewis, J.P. Magennis, S.G. McKee, P.J.M. Ssebuwufu, Nature 306 (1983) 673. [12] B. Baranowski, F.A. Lewis, Ber. Bunsen Phys. Chem. 93 (1989) 1225. [13] Y. Sakamoto, U. Miyagawa, E. Hamamoto, F. Chen, T. Flanagan, R.-A. McNicholl, Ber. Bunsen Phys. Chem. 94 (1990) 1457. [14] H. Noh, T.B. Flanagan, T. Sonoda, Y. Sakamoto, J. Alloy. Compd. 228 (1995) 164. [15] P. Zoltowski, E. Makowska, Phys. Chem. Chem. Phys. 3 (2001) 2935. [16] M. Grden´, A. Pias´cik, Z. Koczorowski, A. Czerwin´ski, J. Electroanal. Chem. 532 (2002) 35. [17] D. Dudek, Collect. Czech. Chem. Commun. 68 (2003) 1046. [18] F. Kadirgan, B. Beden, J.M. Leger, C. Lamy, J. Electroanal. Chem. 125 (1981) 89. [19] A. Capon, R. Parsons, J. Electroanal. Chem. 65 (1975) 285. [20] A. Renouprez, J.-L. Rousset, A.-M. Cadrot, Y. Soldo, L. Stievano, J. Alloy. Compd. 328 (2001) 50.

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