ARTICLE pubs.acs.org/JPCA
Temperature Dependence of H Permeation through Pd and Pd Alloy Membranes Ted B. Flanagan* and D. Wang Material Science Program and Department of Chemistry, University of Vermont, Burlington, Vermont 05405, United States ABSTRACT: H permeabilities (normalized fluxes), have been measured through Pd and some Pd alloy membranes at a series of constant upstream H2 pressures with the downstream pressure being ∼0 in the temperature range from 393 to 573 K. From these data, activation energies for H permeation, EP, have been determined. Conditions of constant upstream pH2 are of most interest since most determinations of EP in the literature have employed this boundary condition. Permeabilities have also been measured at a series of constant upstream H concentrations with the downstream concentration being ∼0 and, under these conditions, the slopes of the Arrhenius plots give activation energies equivalent to those for H diffusion. It is shown here that under constant upstream pH2 conditions, nonideality of the H leads to nonlinear Arrhenius plots of P for Pd and especially for some Pd alloy membranes where the H2 solubilities are significant even at moderate pH2. For example, the permeabilities of a Pd0.77Ag0.23 alloy membrane and a Pd0.94Y0.06 alloy membrane are found to be nearly independent of temperature (423 to 523 K) in the range of constant upstream pressures from 16.1 to 81 kPa.
’ INTRODUCTION The goal of this research is to determine H permeabilities (normalized fluxes), P, and activation energies for permeability, EP, through Pd and several Pd alloy membranes under conditions of constant upstream pH2, pup, and also under conditions of constant upstream H content where, in both cases the downstream hydrogen pressure, pdown, is ∼0 where the subscripts on the p refers to the pH2 on the up and down stream sides of the membrane. There have been no detailed investigations of how the Arrhenius plots for the permeability depend on the values of the constant pup employed. While there are H permeation data available for Pd0.77Ag0.23 membranes, there are little data for other Pd-rich alloy membranes. In addition to an investigation of Pd, H permeation data for a Pd0.77Ag0.23 alloy, a Pd0.94Y0.06 alloy, and several PdFe alloy membranes are reported. It is of special interest to examine the Arrhenius plots for the Pd0.77Ag0.23 alloy membranes because unusual plots have been found by Nguyen et al. for this alloy.1 It should be noted that the important property for H2 purification is the flux or permeability which depend on the product of the solubility and diffusion constant. There has been a recent interest in the permeability of H through Pd and its alloy membranes, e.g., refs 15. The following expression gives the steady state flux, J, through a flat membrane J ¼ DH ΔcH =d
where cup and cdown are the upstream and downstream H concentrations in the membrane and the usual negative sign has been omitted by defining ΔcH as positive. For the common experimental boundary condition of cdown = 0, eq 1 reduces to J ¼ DH cup =d When the H behaves ideally, Sieverts’ law is obeyed cH ¼ K s pH2 1=2
ð3Þ
where Ks is a temperature-dependent constant, referred to as Sieverts’ constant.6 If this ideal expression is employed for cup in eq 2, eq 4 is obtained J ¼ DH pup 1=2 K s =d
ð4Þ
where D/H is the concentration-independent diffusion constant. Morreale et al,7 following Buxbaum and Marker,8 define the permeability, P0 , when pdown = 0, as P0 ¼ Jd=pup 1=2
ð5Þ
where P0 has units such as (mol H/s) cm/cm2 Pa1/2. Their definition of permeability is the most common one employed. The prime superscript is employed to differentiate this definition of permeability from that to be employed in this work, P. Under ideal conditions eq 5 reduces to P0 = DHKs. Ward and Dao9 refer
ð1Þ
Received: July 7, 2011 Revised: November 12, 2011 Published: November 28, 2011
where d is the membrane thickness, DH is the concentrationdependent Fick’s diffusion constant and ΔcH = cup cdown, r 2011 American Chemical Society
ð2Þ
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to DHKs as the Sieverts’ law permeability. Crank10 has pointed out that the “permeability constant is a much less fundamental constant than the diffusion constant which is expressed in units such as cm2/s, particularly as different investigators use different units and even different definitions of permeability”. It might be added to this that various investigators in this area have often employed different names for the same quantity. When the H solution is nonideal, the definition of permeability given by eq 5 is unsuitable. Morreale et al.7 employ the following equation for the flux: J ¼ P0 pup n =d
709 K in a low pH2 range, 0.04 to 6.7 Pa, where ideal behavior should obtain. From their data they obtained E/P = 15.7 kJ/mol H over the entire temperature range and, using ΔHH° = 8.37 kJ/ mol H from the work of Salmon et al.,23 they derived E/D = 24.0 kJ/mol H from eq 9. From Holleck’s values of E/D and ΔHH°24 and eq 9, a value of / EP = 13.6 kJ/mol H is obtained over the temperature range from 533 to 913 K which is a somewhat higher temperature range than employed by Koffler et al. The E/P derived from Holleck’s data is somewhat smaller than that given by Koffler et al. but very close to those of Monrreale et al. The experimental values of Monrreale7 and the value derived from Holleck’s E/D and ΔHH°24 are probably the most reliable for E/P. If cup is in the ideal range at all temperatures, eq 9 holds, but if it is not, it can be asked whether or not the analogous equation is valid
ð6Þ
when pdown = 0 where n is determined from experiment and from this, the permeability is given by 0
0
P0 ¼ DH Ks where Ks ¼ cup =pup n
ð7Þ
EP ¼ ED þ ΔH H
Paglieri also defines permeability as DHK0s where K0s is a modified Sieverts’ constant, K0s = cH2/pH2n, i.e., P0 6¼ DHcup/ pup1/2 as in eq 5 but is equal to DHcup/pupn where n becomes 1/2
ð10Þ
11
where these parameters correspond to nonideal values. PdFe alloy membranes are representative of alloys with relatively low H solubilities26 compared, e.g., to PdAg and PdY alloys. It is of interest to compare their Arrhenius’ permeability plots with those of, e.g., PdAg. The most important Pd-based membrane is the Pd0.77Ag0.23 alloy because it is employed commercially for H purification due to its large permeability and absence of a hydride phase change at T g 298 K. It seems that the temperature dependence of the H permeability of Pd0.77Ag0.23 alloy membranes differs significantly from that of Pd membranes.1 It was been recently noted by Catalano et al. 25 that Nguyen et al.1 observed anomalous behavior in the ln P 1/T relationship; that is, there was a maximum in the Arrhenius curves for the permeability which was not explained by Nguyen et al. Catalano et al.25 stated that “such a phenomenon has not been observed by other authors and cannot be predicted by the simple model proposed here”. It will be shown below that this apparently anomalous behavior is a natural consequence of the PdAgH system. For a Pd0.75Ag0.25 alloy membrane, Shu et al.27 found EP = 8.3 kJ/mol H, Nguyen et al.1 report a value of 5 kJ/mol H for above the temperature range where they observed EP ≈ 0, i.e., >523 K, Serra et al.28 report a value of 6.3 kJ/mol H, and Yoshida et al.29 a value of 5.7 kJ/mol H. These values presumably refer to the ideal range of H contents and they are all significantly smaller than the E/P values reported for PdH. From the values of E/D and ΔHH° in the literature,14,30 eq 9 gives E/P = 6.1 kJ/mol H for the Pd0.77Ag0.23 alloy which is close to the experimental value reported by Serra et al.28 (It is assumed that there is no significant difference in the Pd0.77Ag0.23 and Pd0.75Ag0.25 alloy behavior.) PdY alloy membranes are important because they have desirable H permeabilities and have been considered as possible replacements for the Pd0.77Ag0.23 alloy membranes.31 A Pd0.94Y0.06 membrane has been chosen for investigation here because it is close to the composition of maximum permeability.31 Temperature Dependence of Permeability. First the temperature dependence of permeability, or normalized flux, will be determined at constant rup, and second it will be determined at constant pup and for both conditions pdown (rdown) ≈ 0. For conditions of constant rup, it follows from eq 8 that d ln P d ln DH ¼ ð11Þ dð1=TÞ rup dð1=TÞ rup
under ideal conditions. We have previously14 employed the term specific permeability when cdown = 0 as simply P ¼ J d ¼ DH cup
ð8Þ
where P is obtained directly from the measured flux times the membrane thickness. This quantity has also been referred to by others as the permeability,15 the specific permeability rate,16,17 the permeation flux18 and as the normalized flux, i.e., the flux when d and membrane area are unity;19,20 the latter seems to be an accurate description. The permeability, P, or normalized flux, will be defined here by eq 8. Under conditions where Sieverts’ law is obeyed, it reduces to P = P0 pup1/2 when pdown ≈ 0. The advantage of employing eq 8 as the definition of permeability is that the definition does not change when passing from ideal to nonideal conditions. In addition, the cH2 = K0spH2n relationship employed in eq 7 may not be a good approximation for the H2 solubility when the solubility is large even at the moderate pH2 employed for H purification in Pd0.77Ag0.23 alloy membranes.12 Due to the recognition that nonideality can play a role in permeation through Pd and its alloy membranes even at relatively high temperatures,13 it seems that the definitions of permeability employed in eqs 5 and 7 is awkward because a new term, n, has to be introduced for nonideal conditions. This has also been noted by Hara et al.,3 who point out that “Although the n-th power has often been employed to determine permeability for these membranes, it has no theoretical base. These approaches do not consider concentration dependency of the hydrogen diffusivity in the membrane”. At infinite dilution of hydrogen where Sieverts’ law of ideal solubility is obeyed, it follows from either eq 5 or 8 that Ep ¼ ED þ ΔH H °
ð9Þ
where the asterisk indicates ideality and ΔHH° is the enthalpy of /2H2(g) absorption at infinite dilution of H. Monrreale et al.7 give a rather complete table of EP values from the literature for H permeation under constant pup conditions through Pd which range from 11.921 to 20.5 kJ/mol H.22 Their experimentally determined values are 13.8 and 13.4 kJ/mol H (6231173 K) using n = 0.5 and 0.62, respectively (eq 7).7 Koffler et al.16 determined permeabilities for PdH from 300 to 1
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Figure 1. Isotherms plotted as pH2
1/2
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Figure 2. Plots of the ln pH21/2(1 r)/r against r for PdH where pH2 is in bar.
against r for PdH.
Thus Arrhenius plots of P at constant rup have the same slopes, i.e., the same activation energies, as Arrhenius’ plots of DH where r is the H-to-metal, atom ratio. The regular interstitial solution,32 or mean field model, is given by RT ln p
1=2
r þ g1r ¼ ΔμH ° þ RT ln ð1 rÞ
ð12Þ
where g1 is the first order term in a polynomial expansion in r of μEH, the excess or nonideal chemical potential of H and μH° = μH° 1/2μH2° = ΔHH° TΔSH° and the superscript refer to infinite dilution of H. Using eq 12 for conditions of constant rup with rdown = 0, an approximate expression for the permeability (eq 8) activation energy can be derived as ∂ ln P h1 ¼ ED ≈ ED rup R ð13Þ ∂ð1=TÞ rup 2 where h1 is defined by the relation g1 = h1 Ts1. Equation 13 is a rather simple result giving ED as a linear function of rup.13 As noted above, Arrhenius plots of P are generally made under experimental conditions of constant pup rather than constant rup. For the case of constant pup, the following is a general equation for the temperature dependence of P ∂ ln P EP ∂ ln P ∂ ln P ∂ ln r ¼ ¼ þ ∂ð1=TÞ p ∂ð1=TÞ r ∂ ln r T ∂1=T p R
where r is rup. This equation will be employed below for the evaluation of the temperature dependence of the experimental permeabilities determined in this work under conditions of constant pup.
’ EXPERIMENTAL SECTION The alloy membranes were prepared by arc-melting the pure elements under argon, and the resulting buttons were then annealed at 1133 K. They were then rolled into foil of the desired membrane thickness, i.e., from 70 to 150 μm where the thicker membranes were employed for the alloys with large permeabilities, e.g., Pd0.77Ag0.23 . The steady state fluxes were measured from the pressure fall in a known, large upstream volume while the downstream pH2 was ∼0. Steady state fluxes were established very rapidly for Pd and the Pd alloys investigated here. The area of the membranes active for H permeation was 1.77 cm2 and the specific thicknesses have been generally indicated in the tables or figures captions. Isotherms were measured with the same foils in an all-metal Sieverts’ apparatus. ’ RESULTS AND DISCUSSION Equilibrium pH21/2r Data for PdH. Some equilibrium
pH2r isotherms were determined in this study for PdH over the same temperatures employed for the permeability measurements because they are needed to interpret the permeability data. The isotherms are shown in Figure 1 where it can be seen that there are no pressure invariant, plateau regions at the temperature and pH2 ranges of interest here. Figure 2 shows these data plotted as ln pH21/2(1 r)/r against r. The slopes and intercepts of these plots are equal to g1/RT and ΔμH°/RT (=ΔHH°/RT ΔSH°/R), respectively, as defined in eq 12. Plots of ΔμH°/T against 1/T give ΔHH° from the slope and ΔSH° from the intercept (Figure 3). The following values are obtained from the slopes and intercepts for the temperature range 423 to 523 K, ΔHH° = 9.7 kJ/mol H and ΔSH° = 53.1 J/K mol H. These are average values over the temperature interval; the values are smaller in magnitude in the upper temperature interval as compared to the lower interval which is in agreement with the trends found elsewhere.33,34 These average values can be compared to those found by Kuji et al.,33 8.6 kJ/ mol H and 52.0 J/K mol H for ΔHH° and ΔSH°, respectively, at 450 K. L€asser and Powell34 reported values of 8.7 kJ/mol H
ð14Þ where it is assumed that p = pup and pdown ≈ 0. As shown above, the first term on the right-hand-side of the last equality in eq 14 equals ED/R where ED depends on the H-content of the membrane. If eq 12 is employed in eq 14, we obtain under conditions of rdown = 0 0 1 g1r B 1 þ 2RT C r C EP ¼ ED h1 þ ðΔH H ° þ h1 rÞB @ 1 g rA 2 þ 1 ð1 rÞ RT ð15Þ 187
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Table 1. ΔμH° and g1 values for H in Pd (423523 K) T (K)
g1 (kJ/mol H)
ΔμH° (kJ/mol H)
523
32.3
18.04
503
32.7
17.02
473
33.6
15.63
453
34.8
14.35
423
35.8
12.77
Figure 3. Plot of ΔμH°/T against 1/T for PdH.
Figure 5. ln P as a function of ln pup at different temperatures for a Pd membrane (76 μm).
Table 2. Permeabilities (Normalized Fluxes) of H in Pd (102 μm)a
Figure 4. Plot of g1/T against 1/T for PdH.
and 51.8 J/K mol H for these quantities also at the average temperature of 450 K. Plots of g1/T against 1/T are shown in Figure 4 where the slope is h1 = 51.1 kJ/mol H and the intercept, s1 = 36.1 J/K mol H. The latter value agrees with that given by Kuji et al.33 but the former is not as negative as that given by Kuji et al.; however, it is clear that g1 > h1 as found by Kuji et al. H Permeation through Pd Membranes Pressure exponent of P against pH2. Before presenting results for the temperature dependence of P, it is of interest to first determine the pressure exponent for H permeation, normalized flux, through the Pd membranes employed in this investigation because the value of the exponent is a reflection of the nonideality and because this is commonly done for H permeation through membranes. For example, Morreale et al.7 plot J against pupn pdownn with n selected to obtain the best linearity. Results are shown in Figure 5 for the permeabilities (normalized fluxes) plotted as ln P as a function of ln pup with pdown = 0. The slopes of the plots in Figure 5 are the n exponents in eq 16 which is derived using cup = K0spupn (eq 7), 0
P ¼ DH cup ¼ DH Ks pup n
T (K)
P (101.3)
P (50.7)
P (25.3)
P (10.1)
P (5.3)
423
2.47
1.64
1.12
0.67
0.47
473
3.34
2.36
1.61
0.98
0.70
523 573
4.74 6.31
3.27 4.30
2.23 2.96
1.36 1.80
0.97 1.29
a P has units of 108 (mol H/s) cm/cm2 and pup values in kPa are given in parentheses.
seen that the experimental slopes exceed 0.5 at all temperatures, i.e., are in the nonideal range, and the average value is n = 0.54 ( 0.01 with no obvious change with temperature over the range shown. The permeabilities are given in Table 2. Arrhenius Plots for Permeation at Constant Upstream H Concentrations and Diffusion Constants. Diffusion constants, DH, were also derived from the Pd permeability data (423573 K) using DH = Jd/cup where the H concentration at the upstream side of the membrane, cup, is determined from the appropriate isotherms (Figure 1). The DH values depend on r and they decrease in value with increase of rup as observed earlier for PdH.6,35 Arrhenius plots of P at a series of constant rup values are shown in Figure 6. According to eq 13, the slopes equal ED/ R, and in the nonideal range these depend on rup. Results are shown in Table 3 where, instead of EP (const rup), they are indicated as ED since they are equal under conditions of constant rup. These ED values increase with rup as found before for PdH.13 Extrapolation of ED to rup = 0 gives E/D = 23.6 kJ/ mol H for the temperature range 423523 K which agrees with our earlier result of 23.9 ( 0.4 kJ/mol H.35
ð16Þ
where K0s is defined in eq 7. If Sieverts’ law of ideal solubility holds, n = 0.50, as shown by the dashed line in Figure 5. It can be 188
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Table 4. Experimental and Calculated EP Values as a Function of pup where the Experimental Value of E/P Is Employed, i.e., 13.7 kJ/mol H pup (kPa)
101.3
50.7
25.3
10.3
5.3
4.0
EP (kJ/mol) EP (calc. eq 17) (kJ/mol)
12.74 11.65
13.01 12.44
13.08 12.81
13.23 13.19
13.36 13.27
13.39 13.39
Figure 6. Arrhenius plots of permeabilities at constant rup values for a Pd membrane (76 μm).
Table 3. EP (const rup) = ED for the Permeation of H in Pd (102 μm) at Constant rup Values rup
0.010
0.015
0.020
0.025
0.030
ED (kJ/mol)
24.1
24.0
24.2
24.6
25.0
Figure 8. Plot of EP against pup1/2 for a Pd membrane (102 μm).
very close to the value given by Morreale et al.7 and Holleck24 which are probably the best values. It is also close to the value of 13.46 kJ/mol H given by Toda.36 Using the experimental values of ΔHH° and E/D, found here, / EP can be calculated as EP ð13:7Þ13:9
¼ ED þ ΔH H ° ¼ 23:6 9:7
where the value in parentheses is our extrapolated value, E/P, and it can be seen that the sum of our experimental values of E/D and ΔHH°, the value without parentheses, is very close to this E/P. At relatively small r values where eq 12 is a good approximation, the dependence of ED and ΔHH on rup are given as E/D h1rup/213 and ΔHH° + h1rup and therefore from eq 15 g r r EP ≈ EP þ h1 1 ðΔH oH þ h1 rÞ ð17Þ 2 2RT
Figure 7. Arrhenius plots of permeabilities at a series of constant pup values for a Pd membrane (102 μm).
since 0
1 g1 r 1 þ B 2RT C ≈ 1 g 1 r @ 1 g1 r A 2RT þ 1r RT
Arrhenius’ Plots of P at Constant pup. Arrhenius’ plots of P,
or normalized flux, at constant pup are the main focus of this paper because this is the usual experimental condition employed for the characterization of the temperature dependence of the permeability, e.g., ref 7. Figure 7 shows results for a 102 μm Pd membrane where it can be seen that P increases steadily with increase of pup (rup). In addition, there is seen to be an increasing curvature, albeit small, in this range of temperatures as pup increases, e.g., the curvature can be seen to be greater for pup = 101.3 kPa than for 5.3 kPa. EP values (Table 4) have been determined from the best straight lines drawn through these data (Figure 7), and they are seen to decrease with an increase of pup; that is, nonideality enhances the permeation by reducing EP. A plot of the resulting EP against pup1/2 is shown in Figure 8 where extrapolation to pup1/2 = 0, gives E/P = 13.7 kJ/mol H which is
ð18Þ
From eqs 15 or 17, when r f 0, EP f E/P (=E/D + ΔHH°). At small r values the sum ED + ΔHH can be approximated as E/D h1rup/2 + ΔHH° + h1rup/2 using eq 12, i.e., the experimental EP should remain relatively constant and equal to E/P at small r, however, it is found experimentally that it does not remain constant at large r and eq 10 is not generally valid. The values of EP calculated from eq 17 are shown in Table 4 using an average temperature of 473 K and average rup for each pup from the isotherms and the values agree quite well with experiment at low pup but deviate appreciably at higher pup as expected from the nature of the approximation. Values calculated 189
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Table 5. H Permeability through PdFe Alloy Membranes (393523 K) as a Function of pup XFe
pup (kPa)
EP (kJ/mol H)
50.7
13.0
Pd Pd0.981Fe0.019
101.3 50.7
12.7 12.9
Pd
Figure 9. Arrhenius plots of P for a series of PdFe alloy membranes (60 μm) employing the same pup = 101.3 kPa.
Pd0.981Fe0.019
101.3
12.8
Pd0.963Fe0.037
50.7
13.1
Pd0.963Fe0.037
101.3
13.3
Pd0.926Fe0.074
50.7
15.2
Pd0.926Fe0.074
101.3
15.0
Pd0.903Fe0.097
50.7
18.2
Pd0.903Fe0.097 Pd0.875Fe0.125
101.3 50.7
18.5 19.7
Pd0.875Fe0.125
101.3
19.7
Pd0.85Fe0.15
50.7
21.5
Pd0.85Fe0.15
101.3
22.2
Pd0.85Fe0.15
152.0
22.3
from eq 15 are not in much better agreement with experiment at the higher values of pup. The (∂ ln r/∂(1/T))p term which appears in eq 14 is of some fundamental interest for metalH systems. Using the above approximations, an expression for (∂ ln r/∂(1/T))p can be derived as ∂ ln r 1 ðΔH H ° þ h1 rÞ ≈ g1r 1 ð19Þ ∂1=T p R þ 1r RT When r f 0, it follows from this equation that (∂ ln r/∂(1/T))p = (1/R)ΔHH° which also follows directly from Sieverts’ law. The experimental slopes, (∂ ln r/∂(1/T))p at, e.g., 0.10 MPa, can be evaluated from the isotherms (423523 K) and compared to those calculated from eq 19. The experimental slopes are 1218 K and 1836 K from 523 to 503 K and from 423 to 453 K, respectively. The calculated slopes from eq 19 at the average of the two pairs of temperatures are 1460 K (523 to 503 K) and 1914 K (423 to 453 K). The agreement is quite good at the lower temperature interval but not so good at the higher one. H Permeation through PdFe Membranes. The permeation of H through PdFe membranes (60 μm) has been investigated in the range of Fe compositions from Pd0.981Fe0.019 to Pd0.85Fe0.15. Figure 9 shows Arrhenius’ plots of ln P at pup = 101.3 kPa for these PdFe alloys and, in contrast to the Pd0.77Ag0.23 and Pd0.94Y0.06 alloy membranes shown below, the plots for the PdFe alloy membranes exhibit a nearly linear increase of ln P with decreasing 1/T at this relatively high pup, i.e., 101.3 KPa, mainly because the solubilities are relatively low at least for the high Fe content membranes. Table 5 shows some values of EP for these alloys determined at two different pup where EP values are seen to be about the same at the two pressures indicating the absence of nonideality. A transition in behavior can be seen at a membrane composition of about Pd0.903Fe0.097 because, instead of decreasing with pup, EP increases slightly with pup and for the Pd0.875Fe0.125 alloy and Pd0.85Fe0.15 alloy membranes EP either increases or is unchanged with pup. These results are of interest because they demonstrate that the low content Fe alloys, which absorb significant H, exhibit a decrease of EP with pup whereas those with higher Fe contents,
Figure 10. Arrhenius plots of P for a Pd0.77Ag0.23 membrane for a series of different pup values.
which do not absorb much H at moderate pH2, show either an increase or are unchanged with pup. For the Pd0.85Fe0.15 alloy membrane a plot of P (normalized flux) against pup1/2 is quite linear (503 K), but a similar plot for the Pd0.903Fe0.097 alloy membrane (473 K) shows small deviations from linearity. When plots of P against pup1/2 are linear, the permeability is ideal and therefore the Arrhenius’ plots of P in a comparable temperature range should also be linear with slopes equal to E/P/R. For the Pd0.85Fe0.15 alloy membrane, E/D = 29.8 kJ/mol H,26 and ΔHH° = 7.2 kJ/mol H which gives from eq 10 E/P = 22.6 kJ/mol H and the experimental value is 22.2 kJ/ mol H which is within experimental error in view of the uncertainties in E/D and ΔHH°. H Permeation through Pd0.77Ag0.23 Membranes. Some plots of ln P against 1/T are shown in Figure 10 for a Pd0.77Ag0.23 alloy membrane where, in contrast to the steady increase of P with temperature found for Pd membranes (Figure 7), the permeabilities of the Pd0.77Ag0.23 alloy membrane are rather insensitive to temperature. This behavior is similar to that found 190
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Figure 11. Plot of ln DH and ln cH where cH = cup against 1/T for a Pd0.77Ag0.23 alloy membrane (128 μm) where DH is in cm2/s and cH in mol H/cm3. Δ, ln cH; O, ln DH.
the Pd0.77Ag0.23 membrane because the solubilities are too great at the pup employed for the mean field model to be a good approximation. Using the results for the Pd0.77Ag0.23 alloy of Wang et al.14 for / ED and Flanagan et al.30 for ΔHH° in eq 9, E/P = 7.0 or 6.0 kJ/mol H depending on the value of E/D chosen.14 These calculated values of E/P are close to the average vallue given in the literature, i.e., 6.3 kJ/mol H.1,2729 H Permeation through Pd0.94Y0.06 Membranes. Similarly to the Pd0.77Ag0.23 alloy, the Pd0.94Y0.06 alloy absorbs considerable amounts of H, and PdY alloy membranes have been suggested as substitutes for the former.31 Figure 12 shows an Arrhenius’ plot of ln P at a series of constant pup for a 230 μm thick membrane. The behavior is seen to be similar to the Pd0.77Ag0.23 membrane (Figure 10) showing the large role of nonideality and a near cancelation of the temperature dependences of DH and cup leading to a nearly temperature-independent permeability.
Figure 12. Arrhenius plots of P at a series of pup values for a Pd0.94Y0.06 membrane (230 μm).
’ CONCLUSIONS For the first time, permeabilities, or normalized fluxes, as defined by eq 8 have been measured as a function of temperature for PdH at a series of constant pup and also at constant rup. Under the latter conditions, EP = ED. For conditions of constant pup with pdown ≈ 0 in the temperature range from 423 to 573 K, the Arrhenius’ plots of P exhibit a small curvature at moderate pup for Pd membranes; however, the curvature is not as pronounced as for some Pd alloy membranes which are employed for H purification such as the Pd0.77Ag0.23 and the Pd0.94Y0.06 alloy membranes. At very low pup in the ideal solubility range, the Arrhenius’ plots for permeability for the Pd0.77Ag0.23 and the Pd0.94Y0.06 alloys will be linear but such pup are not of practical interest for H purification. It is shown that under conditions relevant for H purification, the permeabilities of the Pd0.77Ag0.23 and Pd0.94Y0.06 alloy membranes are nearly independent of temperature in the range from 423 to 523 K suggesting that lower temperatures may be employed for H purification.
by Nguyen et al.1 except that their data exhibited a falloff at low temperatures not seen here and which may have been due to a surface contribution. In addition, they found a small maximum at about 310 K before the falloff. The present results were not extended to such low temperatures although there may be the start of a maximum at the lowest temperatures for the permeation determinations at pup = 16.1 kPa (Figure 10). At most of the pup employed, it can be seen in Figure 10 that EP ≈ 0 and, consequently, there is little advantage to be gained in employing higher temperatures for H2 purification at least within the temperature range of Figure 10. Less energy would be expended at the lower temperatures and also some catalytic poisons may have a lesser role at lower temperatures, e.g., H2S. Figure 11 illustrates the reason that the permeability of the Pd0.77Ag0.23 alloy does not change much with temperature as a function of 1/T for a Pd0.77Ag0.23 alloy membrane (128 μm) at a constant pup = 20.3 kPa. The two y axes have been chosen to have the same scale and the dependence of the two on 1/T can be seen to cancel, leading to a nearly constant sum, EP. That is, when ln DH increases with decrease of 1/T, ln cup decreases. A similar plot for PdH shows that the increase of ln DH with decrease of 1/T is not canceled by a decrease of ln cup because the changes of solubility with temperature are much smaller than for the Pd0.77Ag0.23 alloy. There will be no attempt to employ eq 17 for
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