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Time and frequency domain analysis of hydrogen permeationacross PdCu metallic membranes for hydrogen purification

C. Decaux a,b, R. Ngameni c, D. Solas c, S. Grigoriev d, P. Millet c,*a Compagnie Europeenne des Technologies de l’Hydrogene, Route de Nozay, Etablissements DATA 4, 91460 Marcoussis cedex, Franceb ADEME, 2, square La Fayette, B.P. 406, 49004 Angers Cedex 01, Francec Institut de Chimie Moleculaire et des Materiaux, UMR CNRS 8182, Universite Paris Sud 11, Batiment 410, 91405 Orsay Cedex, Franced Hydrogen Energy and Plasma Technology Institute, Russian Research Center ‘‘Kurchatov Institute’’, Kurchatov sq. 1, 123182 Moscow,

Russia

a r t i c l e i n f o

Article history:

Received 8 July 2009

Received in revised form

12 August 2009

Accepted 30 August 2009

Available online 14 October 2009

Keywords:

Hydrogen permeation

Purification

Palladium alloys

Kinetics

* Corresponding author. Tel.: þ33 1 6915 481E-mail address: pierre.millet@u-psud.fr (P

0360-3199/$ – see front matter ª 2009 Profesdoi:10.1016/j.ijhydene.2009.08.100

a b s t r a c t

Hydrogen permeation is a process used in the industry for purification purposes. Palladium

alloys (PdAg and PdCu) are commonly used as membrane material. In this communication,

we report on the kinetics of hydrogen permeation across Pd0.47Cu0.53 metallic membranes

which can be used in catalytic crackers of biofuels. The permeation mechanism is a multi-

step process including surface chemisorption of molecular hydrogen (upstream side of the

membrane), hydrogen diffusion across bulk regions, hydrogen recombination (down-

stream side of the membrane) and evolution. The role of different operating parameters

(temperature, surface state, sample microstructure) is analyzed and discussed using both

time and frequency domain experiments. Experimental pneumato-chemical impedance

diagrams show that there is no significant rate-limitation at surfaces, except at low

temperatures close to room temperature. Diffusion-controlled transport of hydrogen

across the membrane is rate-determining. However, the value of the hydrogen diffusion

coefficient does not rise exponentially with operating temperature in the 40–400 �C

temperature range under investigation, as expected for a thermally activated diffusion

process. At temperatures as low as 300 �C, new rate-limitations appear. They can be

attributed to recrystallization and/or phase transformation processes induced by temper-

ature and the presence of hydrogen.

ª 2009 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.

1. Introduction used for the catalytic cracking of biofuels and the production

Metallic membranes made of palladium-alloys are used in the

industry to purify hydrogen by selective permeation at high

temperature (400–800 �C). Whereas palladium-silver (in

particular the composition Pd77Ag23) has been extensively

used for decades, palladium-copper is now more specifically

studied for application in advanced water gas shift membrane

reactors [1–3]. PdCu membranes are found in microreformers

2; fax: þ33 1 6915 4754.. Millet).sor T. Nejat Veziroglu. Pu

of pure hydrogen [4], for example to feed H2/O2 fuel cells. In

such reactors, the membrane helps to shift the dissociation

reaction, but also extracts and purifies hydrogen. PdCu alloys

have revealed a higher activity than PdAg alloys and a signifi-

cantly higher chemical stability, in particular in the presence

of mixtures of pollutants formed by the cracking of biofuels

such as H2S, CO, H2O [2]. The development of cost affordable,

thin (submicron thick), highly selective and chemically stable

blished by Elsevier Ltd. All rights reserved.

Fig. 1 – Phase diagram of the PdCu system reproduced from

Ref. [9]. Pd0.47Cu0.53 refers to the composition used in this

work.

Nomenclature

C concentration in mol.cm�3

DH hydrogen diffusion coefficient in cm2.s-1

f frequency in hertz

j imaginary unit

JH2 atomic hydrogen flow in mol.s�1.cm�2

KS Sieverts constant in mol.cm�3.Pa�1/2

P pressure in Pa

R ideal gas constant (8.314 J.mol�1.K�1)

RD diffusion resistance per unit area in Pa/

(mole.cm�2.s�1)

Rs surface resistance in Pa.mol�1.s

T absolute temperature in K

V volume in m3

ZD diffusion impedance in Pa.mol�1.s

ZM membrane impedance in Pa.mol�1.s

d membrane thickness in cm

u pulsation in rad.s�1

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 8 8 3 – 4 8 9 24884

metallic membranes able to operate at high (400–800 �C)

temperature remains highly challenging and as a result, a lot

of R&D is still performed in this field. Concerning the mass

transport mechanism involved in the permeation process, the

most reasonable approach is to consider a multi-step reaction

in which (i) a molecule of hydrogen is first chemisorbed

(surface physisorption followed by dissociation into atomic

hydrogen) on the upstream side of the membrane; (ii) atomic

hydrogen atoms diffuse across the membrane, the driving

force being the gradient of chemical potential set between up

and downstream sides via a difference of pressure; (iii)

hydrogen atoms recombine into molecular hydrogen at the

surface of the downstream side of the membrane and

a hydrogen molecule is released. When the metallic

membrane is free from microscopic defects, the selectivity of

the process is very high, close to unity. The kinetics of gas

permeation can be analyzed in both time and frequency

domains. The term kinetics usually refers to the overall rate of

gas permeation (in most studies, a mean diffusion coefficient

is obtained from experiments made under stationary condi-

tions of flow, as a function of different operating parameters

such as alloy composition, operating pressure, pressure

difference, gas purity, etc.). But there is an obvious interest at

determining which individual steps (surface and bulk) are

involved in this multi-step process and at measuring indi-

vidual microscopic rate parameters. To do this, the kinetics

should be analyzed in transient conditions of flows, in order to

shift the rate-determining step (rds) from one step to another

along the experiment. Time domain analysis of permeation in

transient conditions of flow provides a first approach, in

particular when one particular step of the permeation process

is rate-determining. For example, hydrogen diffusion is

reported to be rds when thick (>10 mm thick) membranes are

used. When very thin (submicron thick) membranes are used,

surface effects are supposed to come into play. In the time

domain, the global response of such multi-step processes is

a convolution of individual responses associated with each

step. More detailed information on the mechanism can be

obtained by analyzing the kinetics in the frequency domain,

using for example pneumato-chemical impedance spectros-

copy (PIS) [5–7]. In particular, surface and bulk rate contribu-

tions can be measured separately. Whereas surface steps are

directly related to the surface state of the membrane (surface

composition of the alloy, roughness factor defined as the

dimensionless ratio of the true surface area to the geometrical

area), the kinetics of hydrogen transport in bulk region can be

strongly affected by the microstructure of the membrane. A

marked crystalline texture and a large concentration of

various defects which appear inside the materials during the

cold working process used to produce thin (10–50 mm thick)

membranes can significantly impact the kinetics. Annealing

treatments can be used to release dislocations but they also

deeply modify the microstructure of the samples. Finally, the

presence of different poisons in the hydrogen can induce

surface and bulk corrosion effects which in turn can destroy

the membrane [8]. All these parameters play a major role on

the hydrogen diffusion process and can alter the lifetime of

the membrane. In this communication, we report on results

obtained on the permeation kinetics of pure hydrogen across

Pd0.47Cu0.53 membranes. The main objective of this study was

to establish correlations between sample microstructure,

phase composition, grain size distribution and hydrogen

transport properties. The experimental setup and the

numerical tools used to analyze the kinetics in time and

frequency domains are described in detail.

2. Experimental section

2.1. Thermodynamics of the PdCu system

The phase diagram of the palladium-copper binary system

has been reported in the literature [9–15]. As can be seen from

Fig. 2 – XRD spectrum measured on a Pd0.47Cu0.53 foil

annealed for 556 hours at 200 8C under vacuum and then

for 141 hours at 250 8C under 1 bar H2, showing the peaks

characteristics of the B2 structure.

Fig. 3 – Curves 1 and 2: isotherms measured on the bcc-

Pd0.47Cu0.53 at (1) 523 K and (2) 298 K; curves 3 and 4:

isotherms reproduced from Ref. [18] for respectively 30 (3)

and 20 (4) at.% of copper at 303 K.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 8 8 3 – 4 8 9 2 4885

Fig. 1, an ordered body-centred cubic (bcc) B2 phase is formed

at low temperatures (T< 600 �C) and in the composition

domain ranging from 50 to 70 atomic percent of Cu (at. % in

the followings). A two-phase domain is found in the neigh-

bouring composition ranges. Hydrogen diffusivity has been

reported to be significantly larger in the ordered bcc alloys

than in the corresponding disordered fcc alloys [16]. As

already pointed out by Piper in 1966 [17], the fcc lattice

(a¼ 0.375 nm) is less dense than the bcc one (a¼ 0.297 nm)

and the shorter mean distance between diffusion sites could

explain this observation. According to the phase diagram of

Fig. 1, the more stable B2 PdCu composition is obtained for

a Cu content of ca. 60 at.% (for which phase transformation to

the fcc phase takes place at ca. 600 �C). But the highest

hydrogen diffusivity is observed for the slightly lower Cu

content Pd0.47Cu0.53: DH¼ (3.2� 0.2).10�5 cm2.s at 298 K [16].

This is a composition commonly used in applications and

which was chosen for this study.

2.2. Sample treatments and characterization

2.2.1. Characterization toolsKinetic experiments reported in this communication have

been performed using 20 mm thick Pd0.47Cu0.53 foils (Good-

fellow Co.). In the 10–50 mm thick range, commercial metallic

membranes are obtained by cold working of thicker foils. As

a result, their microstructure is strongly textured, presenting

strongly distorted and oriented crystals. Sample texture can

potentially have a large impact on the kinetics of hydrogen

permeation. It can also impact recrystallization processes

which in turn can either deteriorate the membrane leading to

the formation of pinholes or alter permeation properties. XRD

analysis can be used to determine sample structure and phase

composition. However, intensity of diffraction peaks does not

only depend on the bulk fraction of the different phases but

also on the orientation of crystals inside the sample. Thus,

conventional diffractometers (Bragg/Brentano assembly)

cannot be used to characterize strongly textured materials

such as those considered here. In this study, a texture

goniometer has been used and XRD spectra have been recor-

ded by summing several spectra obtained for different sample

orientations.

2.2.2. Sample annealing under vacuumTo identify the role of lattice structure on the kinetics of

hydrogen permeation across PdCu membranes, two types of

samples have been prepared: (i) a bcc-B2 Pd0.47Cu0.53 and (ii)

a fcc Pd0.47Cu0.53. Permeation experiments across fcc struc-

tures were made using as-received samples which were found,

from XRD analysis, to be single-phase fcc. According to the

phase diagram of Fig. 1, a thermal treatment at low tempera-

ture (< ca. 450 �C) is required to obtain the bcc structure. This is

a first indication since phase boundaries differ from one

reference to the other. According to Piper [17], at 350 �C (in the

absence of hydrogen) different phase domains are observed as

a function of alloy composition. For Cu contents <43 at.% and

>75 at.%, a single-phase fcc domain is observed. The bcc phase

is obtained in the composition domain ranging from ca. 54 at.%

to 68 at.%. Between these values, a two-phase domain is

observed (Fig. 1). According to Jones and Sykes [13], after

a thermal treatment at 250 �C under vacuum, Pd0.5Cu0.5

contains 66% of the bcc phase and 33% of the fcc phase. During

this work, a first attempt was made to obtain the bcc single-

phase by annealing the as-received fcc foil under vacuum at

200 �C. However, XRD analysis revealed that the structure of

the Pd0.47Cu0.53 foil was still fcc after 556 h of treatment at

200 �C. When the treatment temperature is raised to 250 �C,

a two-phase structure (a mixture of fcc and bcc phases) is

obtained after 26 h. The amount of bcc phase increases with

time. However, all attempts made to obtain the homogeneous

bcc phase by thermal treatment under vacuum from as-

received fcc foils failed. In fact, there is no indication in the

literature that the pure bcc phase can be obtained directly by

treatment under vacuum. All experimental data, in particular

those used to determine the phase diagram of the PdCu system

[9–15] have been obtained using PdCu samples annealed in the

presence of hydrogen. In more recent studies, B2-Pd0.47Cu0.53

has also been obtained by annealing under H2 [19–21].

Fig. 4 – Schematic diagram of the experimental set-up used

for sorption and permeation experiments.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 8 8 3 – 4 8 9 24886

2.2.3. Sample annealing under hydrogenWe then tried to obtain the B2 phase by treatment under H2,

using the same foil which was unsuccessfully treated under

vacuum. Treatment conditions were chosen from the previous

works of Roa et al. [21] and Flanagan et coll. [18]. The sample

was heated for 141 h at 250 �C under 1 bar H2. At the end of the

treatment, the sample was totally de-hydrogenated by

pumping down to secondary vacuum (10�7 mbar) at 250 �C for

1 h. XRD analysis (Fig. 2) clearly indicates that this time, the

single-phase B2-Pd0.47Cu0.53 is obtained. The bcc lattice

parameter is the same in the two-phase sample (annealed

under vacuum) and in the single phase sample (annealed

under H2), suggesting that all the hydrogen has been desorbed.

This is the confirmation that hydrogen promotes the phase

transformation process and leads to the formation of the bcc

structure whereas this is not possible under vacuum.

2.2.4. Isotherms of the (B2)Pd0.47Cu0.53-hydrogen systemThe shape of PdCu-H isotherms depends very markedly upon

the Cu content. Quantitative data for Pd0.47Cu0.53 were

obtained using a 500 mm thick (m¼ 1.6086 g) foil (Goodfellow

Co.). This thick foil was used to measure accurately the

absorption isotherm up to 3 bar. The membrane has been

treated at 250 �C under 1 bar H2 for 120 hours to obtain the B2

structure as discussed in the previous section. XRD analysis

confirmed that a homogeneous B2 structure was obtained. The

sorption isotherm has been measured using an experimental

setup described elsewhere [5], by introducing successive

aliquots of hydrogen. Different isotherms characteristic of the

PdCu-hydrogen system are plotted in Fig. 3. Data obtained in

this work were obtained with Pd0.47Cu0.53 at (curve 1) 523 K and

(curve 2) 298 K. Data from Ref. [18] obtained with Pd0.70Cu0.30 at

303 K (curve 3) and Pd0.80Cu0.20 at 303 K (curve 4) are plotted for

comparison. At low copper contents (<20 at.%), a character-

istic pressure plateau is observed, as for non-alloyed palla-

dium. As the copper content increases, the slope of the

isotherm in the two-phase domain increases and the magni-

tude of hysteresis decreases as well as the hydrogen solubility.

At 53 at.% Cu (this work), hydrogen solubility is low: z

4.8.10�1 mol.m�3.Pa�1 corresponding to H/(PdþCu) z 1.5.10�2

at PH2¼ 2 bar. At such copper contents, hydrogen dissolves in

the alloy to form a solid solution but no hydride is formed.

From a practical viewpoint, this is an advantage because the

mechanical effects associated with the precipitation of

a hydride phase can potentially destroy the membrane.

2.2.5. ConclusionAs a conclusion, it was not possible in this study to obtain the

bcc phase from the as-received sample by treatment at low

temperature (T< 250 �C) under vacuum, even after several

weeks. However, annealing at 250 �C with PH2¼ 1 bar was

sufficient to obtain the bcc phase within several hours. This

observation is in agreement with results reported as early as

in 1966 by Piper [17] who made his experiments at 350 �C and

PH2¼ 5–6.7 bar: hydrogen promotes the phase transformation

of palladium-copper samples from fcc to bcc structure.

2.3. Experimental setup for kinetic measurements

The laboratory-made experimental setup of Fig. 4 has been

used to collect raw thermodynamic and kineticdata. Thissetup

is an adaptation of a classical Sievert’s volumetric setup [22]

which is commonly used for measuring the properties of metal

hydride systems. Briefly, there are four volume chambers (316 L

stainless steel capacities from Swagelok Co.) interconnected

with 1⁄4 ’’ stainless steel tubing: (i) a reservoir chamber

Ch0 (VCh0¼ 1012� 5 cm3), (ii) a reference volume chamber Ch1

(VCh1¼ 56.1� 0.1 cm3), (iii) a gas admission chamber

Ch2 (VCh2¼ 26.4� 0.1 cm3), and (iv) a gas collection chamber

Ch3 (VCh3¼ 45.7� 0.1 cm3). For accurate mass balance calcu-

lations, the temperature is measured at different points along

the gas distribution line. The reaction chamber Ch2 is placed in

a furnace for high temperature (up to 600 �C) measurements.

Different manual valves (MVs, Swagelok Co.) are used for gas

management purposes and for setting initial gas transfer

conditions. A bellows-sealed valve (Swagelok Co.) equipped

with a metering stem tip is placed in the circuit. This needle

valve (NV) acts as a gas flow regulator allowing non-convective

and isothermal gas transfer from Ch1 to Ch2. Pressure trans-

ducers are used to sample transient pressure signals during gas

transfer experiments. The test-bench can be air-purged down

to secondary vacuum levels (1x10�6 mbar) using a turbo-

molecular pumping station (BOC Edwards Co.). The sample foil

is clamped between the admission (Ch2) and the gas collecting

(Ch3) chambers. In a typical permeation experiment under

transient conditions of flow, the permeation membrane is

located in Ch2 and MV3 is open. Ch1 is first pressurized at P1�

(using gas stored in Ch0). Ch2 and Ch3 are equilibrated at

P2� ¼ P3

0. Then MV1 is open. P1(t) in the reference volume

chamber decreases and P2(t) on the upstream side of the

membrane increases. Then the permeation process starts. P3(t)

in the collect chamber begins to rise and permeation proceeds

until the pressure becomes identical in the three chambers.

The driving force to gas transfer is the initial pressure differ-

ence set between the reference and reaction chambers. Thus,

absorption and desorption kinetics are studied in separate

experiments to avoid the problem of treating non-linearities

associated with hysteresis, as discussed elsewhere [5]. In

a typical permeation experiment under stationary conditions

of flow, a source of hydrogen of constant pressure connected to

Ch1 is used as input and P3(t) in the collect chamber is set at

Fig. 5 – Hydrogen flow across a 20 mm thick Pd0.47Cu0.53

membrane as a function of operating temperature, for

different pressure differences.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 8 8 3 – 4 8 9 2 4887

a constant pressure. Experimental results presented in this

communication were obtained using commercial Pd0.47Cu0.53

foils (Goodfellow Co.). Alphagaz grade 2 hydrogen was used

throughout. More details about basic principles of PIS analysis

and the automated experimental setup used to perform PIS

measurements can be found in Refs. [5,6].

Fig. 6 – Hydrogen flow across a 20 mm thick Pd0.47Cu0.53

membrane as a function of the difference of the square root

of pressure, at different temperatures.

3. Data treatment

3.1. Time-domain analysis of permeation kinetics

As can be seen from Fig. 3, hydrogen solubility in PdCu

samples with such high copper contents (Pd0.47Cu0.53) is low

and decreases with temperature. Although equilibrium pres-

sure does not vary linearly with composition over the whole

composition range, experimental isotherms can be approxi-

mated over reduced composition intervals by the model Sie-

verts isotherm (Eq. 1) relating the concentration of atomic

hydrogen CH (in mol.cm�3) to the pressure of molecular

hydrogen in the gas phase (in Pa):

CH ¼ KSðTÞffiffiffiffiffiffiffiffiPH2

p(1)

KS(T) is the Sieverts constant (in mol.cm�3.Pa-1/2), function

of sample composition and temperature. Assuming that

chemisorption of molecular hydrogen into atomic hydrogen is

a fast surface step, then the equilibrium condition (1) can be

combined with Fick’s first low of diffusion, leading to equation

(2) [23] where d is the membrane thickness in cm, DH is the

hydrogen diffusion coefficient in cm2.s�1, P2 and P3 are the

pressure (in Pa) on the upstream and downstream sides of

the membrane respectively:

JH ¼DHKSðTÞ

d

�P1=2

2 � P1=23

�in mols�1 (2)

The linear relationship between JH2 and (Pup1/2–Pdown

1/2 ) in

stationary conditions of hydrogen flow is often used in the

literature as a criterion to assess that surface effects are

negligible and to determine the diffusion coefficient but this is

an assumption which does not always apply.

3.2. Frequency-domain analysis of permeation kinetics

3.2.1. Experimental permeation impedancesFrequency-domain analysis of the kinetics does not require any

simplifying assumption. Hydrogen permeation across palla-

dium membranes is a multi-step process involving at least

surface (chemisorption) and bulk (diffusion of atomic hydrogen)

reaction steps. From a mathematical viewpoint, transient

pressure signals measured during permeation experiments are

a convolution of the responses of individual steps. Convolutions

can be conveniently analyzed and model in the frequency

(Fourier) domain because they are transformed into simpler

algebraic products (following Parseval’s theorem). It is even

more useful to determine the transfer function (TF) of the

metal-hydrogen system which provides a unique description of

its dynamic features as a function of frequency. In favorable

cases, the kinetic features of individual steps of a multi-step

process appear at different frequencies. Hydrogen permeation

across palladium membranes involves solid-state chemical

transformations induced from the gas phase. The transfer

function of such systems is similar to an impedance because it

relates a driving force (the pressure) to a flow of hydrogen. It has

been named a ‘‘pneumato-chemical impedance’’, to refer to the

solid-gas reaction [5]. Using raw kinetic data collected from the

time-domain experiments, experimental pneumato-chemical

impedance diagrams can be calculated as described elsewhere

[5]. Briefly, frequency-dependant impedance diagrams are

obtained using Eq. (3), taking the ratio of two Fourier-trans-

forms: (i) the Fourier transform DP(u) of the transient pressure

difference DP(t)¼ P2(t)�P3(t) across the membrane measured

during the permeation experiment and (ii) the Fourier

transform dn3/dt(u) of the transient hydrogen flow [dn3/dt](t)

entering the collect chamber Ch3 :

ZPðuÞ ¼ ½DPðuÞ�½dn3=dtðuÞ� (3)

[dn3/dt](t) can be directly measured using a mass flow meter or

calculated from P3(t) using Eq. (4), under the assumption that

the law of perfect gases applies (this is justified for experi-

ments made with hydrogen at pressures lower than 3 bars,

such as those considered in this work). In Eq. (4), V3 is the

Fig. 7 – Hydrogen diffusion coefficients measured on

a 20 mm thick Pd0.47Cu0.53 membrane as a function of

temperature. (a) data from measurements in stationary

conditions of flow; (b) data from measurements in

transient conditions of flow.

Fig. 8 – Comparison of transient P3(t) pressure signals (a,b)

and associated transient mass flow signal (c,d) measured

during permeation experiments using a 20 mm thick

single-phase B2 (a,c, 330 8C) and single-phase fcc (b,d,

500 8C) Pd0.47Cu0.53 membrane.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 8 8 3 – 4 8 9 24888

volume of the collect chamber (in m3), R is the constant of

perfect gases and T the temperature ( K):

�dn3

dt

�¼ V3

RTdP3

dt(4)

3.2.2. Model permeation impedancesConsidering the above-mentioned permeation mechanism,

the membrane impedance ZM is the sum of three different rate

contributions, i.e the series connection of Rs1 (the surface

resistance on the upstream side of the membrane due to the

chemisorption of molecular hydrogen into atomic hydrogen),

ZD (the impedance due to the transport of atomic hydrogen

from the upstream side down to the downstream side of the

membrane) and Rs2 (the surface resistance on the downstream

side of the membrane due to the recombination of atomic

hydrogen into molecular hydrogen and desorption from the

surface). Rs1 and Rs2 are taken as pure (frequency independent)

resistances because it is assumed that the corresponding

reactions are first order reactions. The expression of ZD is

obtained by solving second Fick’s law of diffusion using

appropriate boundary conditions. The result is the so-called

Randles impedance, commonly used by electrochemists [24],

but which also applies to this case. In planar coordinates, after

adaptation to the solid – gas reaction [5], the solution is :

ZDðuÞ ¼d

DH

vPH2

vCH

1u cothðuÞ ¼ RD

thðuÞu

(5)

where

RD ¼d

DH

vPH2

vCHin pa=

�mole:cm�2:s�1

�(6)

u ¼

ffiffiffiffiffiffiffiffiffijud2

DH

s(7)

vPH2

vCHis the slope of the isotherm at the hydrogen composition

where the impedance is measured; d is the thickness of the

membrane (in cm); DH is the hydrogen diffusion coefficient (in

cm2.s�1); u is the pulsation (in rad.s�1). From Eq. (5), it can be

shown that the limit of ZD at high frequencies is {0;0} and that

the limit at low frequencies is {RD;0}. The expression of ZM is

finally given by :

ZMðuÞ ¼ Rs1 þ ZDðuÞ þ Rs2 (8)

At high frequencies, the value of ZM(u) is located on the real

axis :

ZMðu/NÞ ¼ Rs1 þ Rs2 (9)

The value of ZM at low frequencies is also located on the real

axis :

ZMðu/0Þ ¼ Rs1 þ RD þ Rs2 (10)

4. Results and discussion

4.1. Time domain analysis of permeation kinetics

4.1.1. Permeation experiments in stationary conditions ofhydrogen flowThe kinetics of hydrogen permeation across a 20 mm thick

Pd0.47Cu0.53 membrane has been investigated in the 40–400 �C

temperature range, in stationary conditions of hydrogen flow.

For each operating temperature, flow measurements (JH is

expressed in mol.s�1.m�2) have been performed at increasing

pressures on the upstream side of the membrane (from

1013 mbar up to 3000 mbar). Hydrogen pressure on the down-

stream side of the membrane was kept constant at atmo-

spheric pressure. Main results are plotted in Fig. 5. Whereas

a mostly linear relationship is observed between JH and

temperature up to ca. 300 �C, a saturation effect is observed at

higher temperatures. This kind of behavior is in agreement

with results previously reported in the literature for PdCu

membranes [25] and could be related to the bcc / fcc phase

transformation which is known to take place in this temper-

ature range. Although according to the data of Fig. 1 [9], the B2

�> fcc phase transformation for this Cu composition

Fig. 9 – (�) experimental impedance diagram measured at

80 8C on a Pd0.47Cu0.53 membrane. (o) the same impedance

after numerical filtration and elimination of the capacitive

effect due to the volume VCh2 of the admission chamber.

(d) model impedance from Eqs. (5) and (8). Fig. 10 – Transient P3(t) obtained during experiments made

at (1) 250 8C; (2) 190 8C; (3) 150 8C; (4) 80 8C; (5) 40 8C.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 8 8 3 – 4 8 9 2 4889

(Pd0.47Cu0.53) starts at ca. 420 �C, a possible explanation for

these results could be that the phase transformation,

promoted by hydrogen, starts at lower temperature, as soon as

280 �C. Indeed, the shape of the phase diagram for this copper

composition is such (Fig. 1) that the temperature at which the

transformation begins is not accurately known. However, this

interpretation is not in direct agreement with other reports. For

example, according to Ref. [25], Pd0.47Cu0.53 is still B2 single

phase at 315 �C and according to [17], the two-phase structure

(B2þfcc) is not obtained at temperatures lower than 350 �C.

Another explanation for this new rate limitation could be the

grain size of metallic crystals. Mean grain size of crystals

increases with operating temperature and this is another

factor detrimental to the diffusion process. These results

outline, at least qualitatively, the significant role played by the

crystalline structure and the microstructure of the samples. In

Fig. 6, the hydrogen flow is plotted as a function of P21/2 – P3

1/2 for

different temperatures. Equation (4) is satisfied over the entire

range of pressure and temperature investigated. As mentioned

above, a linear dependency of JH on P21/2 – P3

1/2 is often quoted in

the literature as a useful criterion to assess that hydrogen

transport by diffusion across the membrane is the rate-deter-

mining step (rds) of the permeation process and that surface

kinetics is fast. DH(T) can be obtained from Eq. (4) using Ks(T)

obtained after linearization of the isotherms of Fig. 3. Results

are plotted in Fig. 7 (curve a). The permeability coefficient

PH2¼DH Ks (in mol.m�1.s�1.Pa-1/2) is often used in the litera-

ture to compare the performances of different membranes.

According to our measurements, a permeability coefficient

PH2 z 1.4.10�8 mol.m�1.s�1.Pa1/2 is obtained at 370 �C on

Pd0.47Cu0.53. This is in accordance with the results of Mc Kinley

[26] who reported a value PH2¼ 1.6.10�8 mol.m�1.s�1.Pa1/2 for

Pd0.473Cu0.527 Cu at 350 �C using a 25.4 mm thick membrane.

Table 1 – Kinetic parameters obtained by fitting the experimen

T (�C) RVA (Pa.mol�1.s) Rs1 (Pa.mol�1.s) Rs2 (Pa.mol�1.s) RD

80 16�109 1�109 1�109 11

4.1.2. Permeation experiments in transient conditions ofhydrogen flow; comparison of permeation kinetics in bcc and fccPdCu phasesTo clarify the role of phase composition on the rate of

hydrogen permeation, the following experiment was realized.

The same 20 mm thick Pd0.47Cu0.53 membrane (Goodfellow Co.)

was used throughout the experiments. The ‘‘as-received’’ foil

(fcc single-phase obtained after a high temperature homoge-

neisation treatment followed by quenching and cold working),

was first transformed into B2 single-phase, using the above

described procedure (250 �C for 141 h under 1 bar H2; the new

B2 structure was confirmed by XRD analysis). This treatment

was sufficient to obtain the B2 structure but probably not to

reduce the concentration of defects produced during cold

working, although no quantitative data has been measured.

The membrane was subsequently mounted in the experi-

mental set-up of Fig. 4, as described in the experimental

section, and a permeation experiment was performed at

330 �C. Then, it was checked by XRD analysis that the

structure was still B2. Then, the membrane was heated over-

night at 500 �C under H2 and a second permeation experiment

has been performed, using the same initial boundary condi-

tions (P1� ¼ 1650 mbar; P2

� ¼ 1400 mbar; DP� ¼ 250 mbar;

P3� ¼ 1400 bar). Finally, the membrane was purged from H2 by

pumping under vacuum and dismantled. XRD analysis

revealed that the fcc phase was predominant. The transient

pressure signals P3(t) measured in the collect chamber Ch3

during the two experiments (330 �C and 500 �C) are plotted in

Fig. 8 together with the corresponding hydrogen permeation

flows. From Fig. 8, it is clear that permeation proceeds faster

through the B2 structure. A noticeable reduction of the

permeation rate is observed once the fcc phase precipitate,

although permeation takes place at a higher temperature. The

tal impedance of Fig. 9 with model equations (5) and (8).

(Pa.mol�1.s) dP/dCH (Pa.mol�1.cm3) d(mm) DH (cm2.s�1)

5�1010 3,3�108 20 5�10�5

Fig. 11 – Impedance diagrams at (1) 250 8C; (2) 190 8C; (3)

150 8C; (4) 80 8C; (5) 40 8C, from the data of fig. 10.

Fig. 12 – Pneumato-chemical impedance diagrams

obtained from the time-domain experiments of Figs.

10 and 11 on Pd0.47Cu0.53: (o) B2 phase at 330 8C and (C)

B2Dfcc phases at 500 8C.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 8 8 3 – 4 8 9 24890

maximum hydrogen mass flow through the bcc membrane is

about two times larger than that measured on the two-phased

sample, using the same initial difference of pressure

(250 mbar). However, these experiments provide no detailed

information on surface (chemisorption of molecular

hydrogen) and bulk (H transport by diffusion) individual

contributions to the overall permeation rate. It is neither

possible to tell whether surface effects are present or not

during the experiments, nor possible to tell whether the

roughness factor on both up and downstream sides of the

membrane has changed in the course of the experiments. If

such effects do exist, there individual contributions to the

overall permeation rate are convoluted and difficult to put into

evidence. To clarify these points, the kinetics of hydrogen

permeation has to be analyzed in the frequency domain as

described in the next section. It is expected that surface and

bulk rate contributions, if both exist, will appear at different

frequencies.

4.2. Frequency domain analysis of permeation kinetics

4.2.1. Separation of surface and bulk rate contributions:principlesThe interest of analyzing the kinetics of hydrogen permeation

in the frequency domain is that surface and bulk rate contri-

butions are expected to be clearly separated. For example, the

experimental impedance diagram measured on the

Pd0.47Cu0.53 membrane at 80 �C is plotted in Fig. 9 in Nyquist

coordinates. This is a semi-circle located along the real axis.

This shape of curve is familiar to the electrochemists. This is

the signature of a circuit in which a capacitance is connected

in parallel to a resistance. In the solid-gas reaction considered

here, the capacitance is associated to the volume of the

admission chamber Ch2, as discussed in [5], and the resistance

is related to the surface and bulk rate effects. The volume of

the admission chamber in the experimental setup of Fig. 4 is

such (VCh2¼ 26.4 cm3) that the membrane impedance ZM is

partly masked. Once the contribution of C2 is removed (by

numerical filtering), ZM is obtained (Fig. 9). According to Eq. (9),

the sum of surface resistances (Rs1þ Rs2) is directly obtained

from the intercept of the experimental impedance ZM with the

real axis at high frequencies and the diffusion resistance RD is

obtained from the intercept of the experimental impedance

ZM with the real axis at low frequencies. The experimental

impedance ZM of Fig. 9 has been fitted using model equations

(5) and (8). Parameter values obtained from the fit are

compiled in Table 1, it can be seen that the kinetics of

permeation is controlled by the diffusion step. Extrapolating

to stationary conditions of flow, the pressure drop due to the

surface resistance would amount to 15% of the total pressure

drop and the pressure drop due to the hydrogen transports

would represent about 85%.

4.2.2. Role of operating temperature on permeationimpedancesTransient P3(t) pressure responses obtained at increasing

operating temperatures are plotted in Fig. 10. The corre-

sponding pneumato-chemical impedance diagrams obtained

from Eq. (3) are plotted in Fig. 11. Noisy diagrams are obtained,

especially in the high frequency (HF) domain, because pres-

sure transducers used for the experiment have a bandwidth

limited to ca. 1 Hz. The shape of the impedance diagrams is

mostly that of a semi-circle along the real axis. As discussed in

the previous section, this is due to the capacitance associated

with the volume of the admission chamber placed in parallel

with the membrane. Membrane impedances have been

obtained by numerical filtering. As the temperature increases,

surface contributions become less significant, as already

reported elsewhere for palladium-silver membranes [6]. After

filtration of the capacitance component, surface and bulk rate

contributions have been separated using Eqs. (9) and (10). The

low frequency value of the diffusion impedance on the real

axis gives the diffusion resistance RD. Using Eq. (6), hydrogen

diffusion coefficients were obtained as a function of operating

temperature. Results are plotted in Fig. 7 (curve b). The

temperature dependence of DH is similar to the one measured

in stationary conditions of flow (Fig. 7, curve a). However, DH

values obtained from PIS analysis at a given temperature are

larger than those obtained from experiments made in

stationary conditions of flow. In the former case, the true DH is

Table 2 – Rate parameters for Pd0.47Cu0.53 obtained from PIS impedance diagrams.

Phase Temperature/�C RD in Pa.mol�1.s dPH2/dCH in Pa.mol�1.cm�3 DH in cm2.s�1

B2 330 3.3x1010 3.2x109 1.9x10�4

fcc 500 5.5x1010 5.8x109 2.1x10�4

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n e n e r g y 3 5 ( 2 0 1 0 ) 4 8 8 3 – 4 8 9 2 4891

measured whereas in the later case, DH values are under-

estimated because surface effects are neglected, especially in

the lower temperature range.

4.2.3. Role of phase composition on permeation impedancesTo further analyze the role of the crystalline structure of the

Pd0.47Cu0.53 sample on the kinetics of hydrogen permeation (see

section 4.1.2.), the kinetics has been analyzed in the frequency

domain. Using the data of Fig. 8 (transient pressures and tran-

sient hydrogen flows), experimental impedance diagrams

associated to the permeation of hydrogen in B2 (330 �C) and fcc

(500 �C) phases have been calculated using Eq. (3). Results are

plotted in Fig. 12, in Nyquist coordinates, in the 1 mHz–1 Hz

frequency range. As previously discussed, the diameter of the

semi-circle along the real axis provides a direct measure of the

diffusion resistance RD (surface effects were found negligible at

these temperatures). The hydrogen diffusion coefficient in both

experiments has been calculated using Eq. (6). Data obtained for

the two phases are compiled in Table 2. The low frequency

impedance of the membrane is higher at higher temperature.

However, the slope of the isotherm increases with temperature.

As a result, the value of the hydrogen diffusion coefficient

obtained from Eq. (6) is almost the same in the two experiments

although the temperature of measurement is different.

Compared to the values of Fig. 7, the same ‘saturation effect’ is

observed: DH is almost constant between 330 �C and 500 �C.

Minor differences can be attributed to different sample micro-

structures and different concentration of defects. The role of

sample microstructure on the kinetics of hydrogen permeation

must therefore be emphasized. Ideally, it should be controlled

and adjusted to optimize the permeation rate.

5. Conclusions and perspectives

Hydrogen purification by permeation through metallic

membranes is a process of great practical interest. In this

communication, we report on the kinetics of hydrogen

permeation across Pd0.47Cu0.53 metallic membranes. Experi-

ments have been made in both stationary and transient

conditions of hydrogen flow and the role of different operating

parameters (operating temperature, surface state, lattice

structure and sample microstructure) on the kinetics of

hydrogen permeation has been evaluated and is discussed.

The permeation mechanism has been analyzed in both time

and frequency domains using an appropriate experimental

setup and pneumato-chemical impedance spectroscopy (PIS),

a useful tool used to separately probe surface and bulk rate

contributions to permeation processes. It has been shown that

surface rate contributions exist but decrease when the

temperature increases. Whereas the kinetics of permeation

rises with temperature from room temperature, new rate-

limitations appear at temperatures as low as 300 �C. Experi-

mental pneumato-chemical impedance diagrams show that

there is no rate-limitation at surfaces. Diffusion-controlled

transport of atomic hydrogen across the membrane is rate-

determining. New rate limitations can be attributed to recrys-

tallization and/or phase transformation processes induced by

the rising temperature and the presence of hydrogen. This is an

indication that the microstructure of these membranes must

be adjusted in order to improve the kinetics of hydrogen

permeation. In terms of perspectives, since surface effects are

not playing a significant role at T > 100�C, it is still possible to

further reduce the thickness of these membranes down to sub-

micron values, without having to pay too much attention to the

kinetics of surface steps.

Acknowledgement

Financial support from the French Agence Nationale de la

Recherche, Plan d’Action National sur l’Hydrogene (AP’H

project ANR-05-PANHd011-04 and EolHy project ANR-06-

PANHd008-06), is acknowledged.

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