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Platinum Metals Rev., 2003, 47, (1), 32

Uphill Effects on Hydrogen Diffusion Coefficients in Pd77Ag23 Alloy Membranes

Influences due to Gorsky Effect and Lattice Strain Gradient Factors

  • By X. Q. Tong a
  • F. A. Lewis a
  • S. E. J. Bell a
  • J. Čermák b
  • a
    School of Chemistry, Queen’s University, Belfast BT9 5AG, N. Ireland
  • b
    Institute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-182 21 Praha 8, Czech Republic

The choice of palladium (Pd) and Pd alloys selected for use in hydrogen permeation mem-branes is determined by the values for hydrogen solubility and hydrogen diffusion coefficients, DH, with high values being preferred (15). Using pure Pd membranes at temperatures ≤ 300°C can be complicated by the possible involvement of the a phase hydride transition regions, with the likely consequent formation of irreversible distortions (110). However, the problems of phase transition and related hysteresis effects can be much reduced by using membranes made of carefully chosen Pd alloys.

For example, Pd-Ag (palladium-silver) alloys in the composition range Pd77Ag23 to pd75Ag25 have been succesfully used as hydrogen purification membranes over a wide range of equilibration conditions with respect to hydrogen pressure, p, hydrogen content, n (n = H/M atomic ratio, where M is metal) and temperature, T, (from p-c(n)-T relations). Relationships between n and DH, have been derived by using both electrochemical and gas-phase equilibration techniques (610).

Representations of DH-n Relations

Figure 1 compares various forms of the DH-n relationship, for catalytically preactivated surfaces, at 50°C (410). It shows satisfactory agreement between results obtained either by gas-phase or electrolytic techniques over the higher, β-phase, range, where DH increases with increasing n. However, over the lower, β-phase ranges of n, studies using the electrochemical technique, have shown an initial opposing trend of decreasing values of DH with increasing values of n (810).

Fig. 1

Representation of the dependence of hydrogen diffusion coefficients in Pd77Ag23 alloys on initial hydrogen contents from work by: Kussner (8); Hickman (9); Kuballa and Baranowski referred to in (4)

Tubular Membrane Studies

Tubular membranes have been used in a more recent series of studies on electrochemical hydrogen permeation in 0.02 N H2So4 at 25 or 50°C (1523, 25, 26). Parameters measured were the inner-tube hydrogen-gas pressures and internal surface electrode potentials. In electrolytic experiments, essentially analogous to those of Kussner (8), further progressive increases in the hydrogen content (n) of membrane surfaces were introduced by a stepwise series of electrolytic cathodisations.

Uphill Hydrogen Transfer Effects

After interruptions made to each additional outer-surface hydrogen-charging process, open- circuit conditions were maintained for both surface and internal hydrogen equilibration processes, during periods of gradual decay to new steady state interim values of internal hydrogen pressure, p, and electrode potential, E. The p and E interim open-circuit values were then adopted as new initial values, p0 and E0, together with the next initial value of hydrogen content, no, determined from available p(E)-c(n)-T relationships (410).

Fig. 2a

Time dependent incremental changes of internal surface electrode potentials at 50°C, for Pd77Ag23 tubular membranes (dia. 8.0 mm, wall 0.4 mm thick) with Pd black coats after cathodisation in 0.02N H2SO4 at 15 mA cm -2, and after establishment of steady state values for E0. Corresponding values for hydrogen content, n0 were derived from p(E)-n-T (15, 25, 30) relationships. Breakthrough times, tl, are indicated interpolations

Fig. 2b

Complementary incremental changes of thermodynamically equivalent values of hydrogen gas pressures within the tubular Pd77Ag23 membranes, calculated via the amended 2FE ∼ RT In p relationships, F and R are the Faraday and gas law constants, respectively

Figure 2a shows an example of time-dependent measurements of inner-surface electrode potential plots for a membrane of 8.0 mm inner diameter, 0.4 mm wall thickness, with inner and outer Pd black coats. This followed the resumption (at 50°C) of cathodisation at 15 mA cm-2. Earlier established equilibration conditions are at the E0 values (23).

In Figure 2b, the values of p have been calcu-lated from the values of E given in Figure 2a, using the thermodynamically equivalent, when corrected, correlation:


F is the Faraday constant and R is the gas constant. The time dependent paths of the AE-t and the derived Δp-t plots (Figures 2a and 2b, respectively) are typical of similar results that have been interpreted in forms of the uphill Gorsky Effect (15, 18, 21). These involve hydrogen interstitial transfer processes which operate in a direction opposite to the hydrogen permeation flux.

The values of the breakthrough times, tL, in Figures 2a and 2b correspond to intersection points between the AE-(Ap)-t axes and the later, more linear, stages of the time plots. Values of DH were then calculated (15, 20) using Relation (ii):


1 is the thickness of the membrane wall (0.4 mm).

Comparison of DH-n Relations

Figure 3 compares results obtained using alternative ways of deriving the relationship between Dh and n at 50°C. The sources used to determine the Dh values are:

  • a set of measurements obtained from direct hydrogen pressure records (26)

  • calculations using Relation (ii) with tL, values from Figure 2b

  • replotting the corresponding diffusion data of Küssner (Fig. 9 in (8))

From Figure 3 it can be seen that there are overall similarities between the results presented by Küssner (8) and more recent analogous data (23, 26, 27). In particular, each DH-n plot has regions of apparent decrease of DH with increasing n over an initial range from n = 0 to ∼ 0.1-0.2.

For the two more recent determinations, [a] and [b], the results are again similar to earlier analogous Pd77Ag23Hn reports (25, 26, 29). In these cases the temporary sign reversal of the incremental changes of permeation rate, when hydriding is restarted, has been identified with periods of elastic strain gradient-induced uphill Gorsky Effect (opposing the permeation direction) (1526, 2834) on internal hydrogen transfer.

Küssner had not considered this explanation when he described the reversed sign (Fig. 7 in (8)) in terms of a transition to a type of plastic viscoelastic state (8, 10). He did not however cite or present physical evidence of any associated structural or defect changes.

Fig. 3

Comparison of catalytic activity in NOx conversion of three catalysts impregnated onto an industrial -Al2O3 support:

  • Vg = velocity of gas mixture

    • catalyst prepared from cluster (1) and phen. containing 0.1% Pd

    • catalyst based on the platinum salt, H2PtCl6. containing 0.1 % Pt

    • industrial catalyst APK-2: this catalyst contains 2% Pd

Figures 2 and 3 also show that Küssner’s results (8) over the lower range of hydrogen contents: n ∼ 0.0—0.2 in Pd77Ag23, could have been interpreted differently in terms of concurrent uphill hydrogen interstitial diffusion effects (Δtmax in Figure 3) without significantly altering the overall elasticity characteristics.


For each example in Figure 3, the apparent decrease in DH with increase in the α-phase hydrogen content, n, can be equated with longer time intervals and corresponding longer periods of uphill opposing-direction hydrogen permeation flux. This leads to longer times for attaining the break- through times, tL, and so, through Relation (ii), causes misleading apparently decreasing values of Dh with increasing n. In a broader context, this survey also seems to support suggestions of a non-Fickian classification of Pd alloy-hydrogen difusion systems, with possibilities for easy control of concentration gradients and boundary conditions (4, 12-15, 29, 30).


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Acknowledgements are due in regard to collaborative support from Johnson Matthey PLC, The Royal Society, London and the Czech Academy of Sciences.

The Authors

Xiu Qiang Tong was a Ph.D. student in the Department of Chemistry at Queen's University, Belfast. At present he is Director of Support and Service, at Molecular Imaging Co., in Arizona, U.S.A. His interests include hydrogen in metals, scanning probe microscopy and its applications in various disciplines, such as materials surfaces (metals, polymers and biomaterials, etc.).

Fred Lewis is retired from Queen’s University, Belfast, after many years of research into hydrogen diffusion in palladium and palladium alloys. These are still his main interests.

Steven Bell is a Lecturer in Physical Chemistry at Queen’s University, Belfast, with interests in excited state porphyrins, redox enzymes, Raman spectroscopy and spectroscopic analysis.

Jan Čermák, while being retired from the Institute of Physics in Prague, is currently a Research Associate with Professor Marian Černanský. His interests are hydrogen in palladium and diffusion coefficients for nickel and platinum.

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