The effects of major impurities on the transport of hydrogen through palladium

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Title:
The effects of major impurities on the transport of hydrogen through palladium
Uncontrolled:
Transport of hydrogen through palladium
Physical Description:
xvi, 195 leaves. : ill. ; 28 cm.
Language:
English
Creator:
Chiu, Leon Lee, 1937-
Publication Date:

Subjects

Subjects / Keywords:
Transport theory   ( lcsh )
Platinum-silver alloys   ( lcsh )
Hydrogen   ( lcsh )
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 183-185.
Statement of Responsibility:
By Leon Lee Chiu
General Note:
Manuscript copy.
General Note:
Vita.

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University of Florida
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All applicable rights reserved by the source institution and holding location.
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notis - ACX9455
oclc - 13416168
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Full Text








THE EFFECTS OF MAJOR IMPURITIES
ON THE TRANSPORT OF HYDROGEN
THROUGH PALLADIUM

















By
LEON LEE CHIU









A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF
THE UNIVERSITY OF FLORIDA
IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF DOCTOR OF PHILOSOPHY








UNIVERSITY OF FLORIDA


April, 1966













ACKNOWLEDGMERTS


The author wishes to express his appreciation to-

Professor R. D. Walker, Jr., Chairman of his Supervisory Committee,

for his interest and advice rendered during the course of this work.

He wishes to thank the members of his Supervisory Committee,

Dr. P. M. Downey, Dr. R. G. Blake, Dr. M. Tyner and Dr. F. P. May.

He is also indebted to Professor R. A. Keppel for his suggestions and

to Mr. Myron Jones for assisting in setting up the equipment.

The author wishes to acknowledge the support of the Harry

Diamond Laboratories, Army Material Command.











TABLE OF CONTENTS


Page


ACKNOWLEDGMENTS........... ...................................... ii

LIST OF TABLES .................. .......... .... ... ... .. ........ v

LIST OF FIGURES.................................. ............ viii

ABSTRACT......... ....... ..... ......... ........ .... .. ......... xiv

CHAPTER

I. INTRODUCTION ............................ .. .. ......... 1

A. General ....... ........ ... ..... .... ......... 1

B. Previous Work.............................. 2

C. Statement of the Problem................... 4

II. THEORY .................... .. .. .................... ..... 5

A. Thermodynamics of the Pd-H and Pd-Ag-H Systems... 5

B. Statistical Thermodynamics and Equilibrium
Isotherms ......................... .......... 10

C. Transport of Hydrogen Through Palladium.......... 18

1. The Adsorption and Dissociation of Hydrogen
in the Palladium Surface............... 20

2. The Diffusion of Hydrogen in the Palladium
Lattice................................ 27

3. Macroscopic Diffusion Equation in Palladium. 33

III. EXPERIMENTAL PROCEDURE ............................... 41

A. Experimental Apparatus.......................... 41

B. Experimental Procedure............................ 45

IV. EXPERIMENTAL RESULTS AND CALCULATIONS................. 47

A. Experimental Evaluation of the Transport Rate Per
Unit Area................................... 47

B. Determination of the Diffusivity of Hydrogen in
Palladium-Silver Alloy...................... 77











TABLE OF CONTENTS (Continued)


Page

C. Temperature and Pressure Dependency of Flux of
Pure Hydrogen in Palladium-Silver Alloy.... 78

D. Effect of Impurities on the Transport of
Hydrogen Through Palladium Silver.......... 90

E. Time to Reach Steady State...................... 171

V. DISCUSSION OF RESULTS AND CONCLUSIONS................ 172

A. Transport Rate of Pure Hydrogen Through
Palladium-Silver Membranes................. 172

B. Effect of Impurities on the Transport Rate of
Hydrogen Through Palladium-Silver Membrane. 173'

C. Conclusion ................. ......................... 176

VI. RECOMMENDATIONS FOR FUTURE STUDIES.................. 178

t NOMENCLATURE................. ...................... 179

LITERATURE CITED............................................. 183

APPENDICES..................................................... 186

A. APPARATUS.................. .. ................. ..... 187

B. EXPERIMENTAL PROCEDURE............................... 189

A. Preparation of the Palladium Silver Membrane.... 189.

B. Procedure A................................... 189

C. Procedure B............. ............ ............ 190

C. FLOW PATTERN IN THE DIFFUSION CELL................... 193

BIOGRAPHICAL SKETCH ............................................. 195











LIST OF TABLES


Table Page

1 The Rate of Transport of Hydrogen Through Palladium
Silver Membrane (Procedure A)........................ 48

2 The Rate of Transport of Hydrogen Through Palladium
Silver Membrane (Procedure B)........................ 49

3 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane(30% CH., 10% N2,
60% H2; B = 0.55 x 10" ............................... 51

4 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (30% CH4, 10% N2,
60% H2; B = 1.08 x 10-5).............................. 52

5 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (30% CH4, 10% N2,
60% H2; B = 1.88 x 10- ) .............................. 54

6 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (30% CH 10% N2,
F 60% H2; B = 2.80 x 10-") ........................... 55

7 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (10% CH4, 10% N2,
80% H2; B = 0.38 x 10-5) .............. ..... .......... 57

8 Effect of Impurities on .he Rate of Transport of Hydrogen
Through Palladium Silver Membrane (10% CH 10% N2,
80% H2; B = 0.52 x 10-5).............................. 58

9 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (10% CH4, 10% N2,
80% H2; B = 1.11 x 10" )........... ......... .. ...... 60

10 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (10% CH4, 10% N2,
80% H2; B = 2.95 x 10-5)......... ............... 61

11 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (25.6% N2, 74.4% H2;
B = 0.93 x 10-5)......................... .. ...... .. 63

12 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (25.6% N2, 74.4% H2;
B = 2.46 x 10 )...................................... 64

13 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (19.8% CH4, 80.2% H2;
B = 1.25 x 10" ).................... ...... ..... ..... 66










LIST OF TABLES (Continued)


Table Page

14 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (19.8% CH4, 80.2% H2;
B = 3.24 x 10 )......... ... ..... ....... ............ 67

C 15 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (21.5% C02; 78.5% H2;
B = 0.86 x 10 ) ... .......... ........ ......... ........ 69

16 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (21.5% CO2, 78.5% 2;
B = 2.32 x 10- )...................................... 70

17 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (21% CO, 79% H2;
B = 0.99 x 10-5). ... .... ...... ... ............. 72

18 Effect of Impurities on the Rate of Transport of Hydrogen
Through Pallad um Silver Membrane (21% CO, 79% H2;
B = 2.52 x 10" )....... ...... .. ...... ..... .... .. ..... 73

19 Effect of Impurities on the Rate of Transport of Hydrogen
Through Palladium Silver Membrane (Pure hydrogen, stop
cock grease present near the membrane; B: None)...... 75

20 Diffusivity of Hydrogen in Palladium-Silver: Procedure A. 79

21 Diffusivity of Hydrogen Palladium-Silver: Procedure B.... 80

22 Multiple Regression of the Constants in Equation (108)... 125

23 Effect of Impurities on the Maximum Rate of Transport of
Hydrogen Through Palladium Silver Membrane (30% CH,
10% N2, 60% H2) ....................................... 152

24 Effect of Impurities on the Maximum Rate of Transport of
Hydrogen Through Palladium Silver Membrane ( 10% CH ,
S10% N2, 80% H2)........................................ 153

25 Effect of Impurities on the Maximum Rate of Transport of
Hydrogen Through Palladium Silver Membrane (25.6% N2,
74.4% H2)................................. .......... 154

26 Effect of Impurities on the Maximum Rate of Transport of
Hydrogen Through Palladium Silver Membrane (19.8% CH, -
80.2% H2)............................................. 155











LIST OF TABLES (Continued)


Table Pane

27 Effect of Impurities on the Maximum Rate of Transport of
Hydrogen Through Palladium Silver Membrane (21.5% CO2,
78.5% H2) ............. ............ ................... 156

28 Tabulation of k2 in Equation (115) for Different Gases
and Temperature............ .............. .......... 157

29 Multiple Regression of the Constant in Equation (108) for
.the Maximum Transport Rate .......................... 170


vii












LIST OF FIGURES


Figure Page

1 Equilibrium Isotherm for the Pd-H Systems............. 7

2 Equilibrium Isotherms for Ag-Pd-H System at 250C....... 9

3 Logarithm of the Equilibrium Pressure Versus Silver
Content...... ............ ...... .............. ....... 17

4 A Plot of Critical Temperature Versus Silver Content... 19

5 Interstitial Sites for a Face Center Cubic Lattice..... 29

6 Atomic Plane of Diffusion in the Metal Lattice......... 30

7 Value of SST for different T = D#2t/L2................. 37
2
8 Value of SST for Different T Dt/L ................... 40

9 Apparatus for Measuring Transport Rate of Hydrogen
Through Palladium...... ........................ .... 42

S10 Diffusion Cell Upstream Flange......................... 43

11 Diffusion Cell Downstream Flange....................... 44

12 Diffusivity of Hydrogen in Palladium Silver............ 82

13 The Rate of Transport of Hydrogen Through Palladium
Silver Membrane at Different Temperatures (Procedure
A) ................. ......... ........ ........ ........ 84

14 Determination of the Energy of Activation.............. 85

15 The Rate of Transport of Hydrogen Through Palladium
Silver Membrane at Different Temperatures (Procedure
B) ................ ..... ..... ................. 86

S16 Determination of the Energy of Activation............... 87

17 A Plot of Log C Versus Log P ......................... 88
mm
18 A Plot of Log C Versus 1000/T.......................... 89

19 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane at Different Temperatures
(30% CH4, 10% N2, 607. H2; B 0.55 x 10- ).......... 91

20 Determination of the Energy of Activation.............. 92


viii











LIST OF FIGURES (Continued)


Figure Page

21 Effect of Impurities on the Rate of Transport of
Hydrogen Through Palladium Silver Membrane (30% CH4,
10% N2, 60% H2; B = 1.08 x 10-) ..................... 93
r 22 Determination of the Energy of Activation.............. 94

23 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane at Different Temperatures
(30% CH4, 10% N2, 60% H2; B = 1.88 x 10" )........... 95

24 Determination of the Energy of Activation............... 96

25 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane at Different Temperatures
(30% CH4, 10% N2, 60% H2; B = 2.80 x 10") ........... 97

26 Determination of the Energy of Activation............... 98

27 Effect of Impurities on the Rate of Transport of H
Through Pd-Ag Membrane at Different Temperatures
(10% CH4, 10% N2, 80% H2; B = 0.38 x 10-5)........... 99
28 Determination of the Energy of Activation............... 100

29 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane at Different Temperatures
(10% CH4, 10% N2, 80% H2; B = 0.52 x 10" )........... 101

30 Determination of the Energy of Activation............... 102

31 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane at Different Temperatures
(10% CH4, 10% N2, 80% H2; B = 1.11 x 10 )........... 103

32 Determination of the Energy of Activation............... 104

33 Effect of Impurities on the Rate of Transport of H2
C Through Pd-Ag Membrane at Different Temperatures
S(10% CH4, 10% N2, 80% H2; B = 2.95 x 10 )........... 105
34 Determination of the Energy of Activation............... 106

35 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane at Different Temperatures
(25.6% N2, 74.4% H2; B = 0.93 x 10-5)................ 107

36 Determination of the Energy of Activation................ 108











LIST OF FIGURES (Continued)


Figure Page

37 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane at Different Temperatures
(25.6% N2, 74.4% H2i B.= 2.46 x 105) ................ 109

( 38 Determination of the Energy of Activation................ 110

39 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane at Different Temperatures
(19.8% CH4, 80.27 H2; B 1.25 x 10-5) ................ 111

40 Determination of the Energy of Activation................ 112

41 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane at Different Temperatures
(19.8% CH4, 80.2% H2; B = 3.24 x 10-) ................ 113

42 Determination of the Energy of Activation................ 114

43 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane (21.5% CO2, 78.5% H2;
SB = 0.86 x 10" ) ..................................... 115

44 Determination of the Energy of Activation................ 116

45 Effect of Impurities on the Rate of Transport of 12
Through Pd-Ag Membrane (21.5% CO2, 78.5% H2;
B = 0.86 x 10-5) ....................................,, 117

46 Determination of the Energy of Activation................ 118

47 Effect of Impurities on the Rate of Transport of H.
Through Pd-Ag Membrane (21% C02, 797. H2; B = 0.99 x
10 )................................................ 119

48 Determination of the Energy of Activation................ 120

49 Effect of Impurities on the Rate of Transport of H,
Through Pd-Ag Membrane (21% CO, 79% H2; B = 2.52 x
10-5) ................................................. 121

50 Determination of the Energy of Activation................ 122

51 Effect of Impurities on the Rate of Transport of H2
Through Pd-Ag Membrane at Different Temperatures
(Pure H2 with small amount of grease vapor).......... 123

52 Determination of the Energy of Activation................ 124











LIST OF FIGURES (Continued)


Figure


53 A Plot
t =

54 A Plot
t =

55 A Plot
t =

56 A Plot
t =

57 A Plot
t =

58 A Plot
t o

59 A Plot
t =

60 A Plot
t =

61 A Plot
t =

62 A Plot
t =

63 A Plot

64 A Plot

65 A Plot

66 A Plot

67 A Plot

68 A Plot
t =

69 A Plot
t =

70 A Plot
t =


of B Versus B/NA (30% CH4, 10% N2, 60% H2;
3000C) ................ .............. ..........

of B Versus B/NA (30% CH4, 10% N2, 60% H2;
340 C)................ ........... ...... ......

of B Versus B/NA (307 CH4, 10% N2, 60% H21
380 C) ...........,... ... ................ .......

of B Versus B/NA (30% CH4, 10% N2, 60% H2;
420C) ....... ........... ........... ........

of B Versus B/NA (30% CH4, 10% N2, 60% H2;
4600C)............. ............. .. .......

of B Versus B/NA (10% CH4, 10% N2, 80% H2;
300C) ..........................................

of B Versus B/NA (10% CH4, 10% N2, 80% H2;
340C) ..........................................

of B Versus B/NA (10% CH4, 10% N2, 80% H2;
380 C)............ ... .... ....... ...............

of B Versus B/NA (10% CH4, 10% N2, 80% H2;
4200C)........................................

of B Versus B/NA (10% CH4, 10% N2, 80% H2;
4600C)........... ............... ...............

of B Versus B/NA (25.6% N2, 74.4% H2; t = 300C)

of B Versus B/NA (25.6% N2, 74.4% H2; t = 3400C)

of B Versus B/NA (25.6% N2, 74.4% H2; t 380C)

of B Versus B/NA (25.6% N2, 74.4% H2; t = 420C)

of B Versus B/NA (25.6% N2, 74.4% H2; t = 4600C)

of B Versus B/NA (19.8% CH4, 80.2% H2)
300C) ................. ........ ...............

of B Versus B/NA (19.8% CH4, 80.2% H2)
340o C ....e ......A ..... ...4..... 1.. ........

of B Versus B/NA (19.8% CH4, 80.2% H2)
380C) ........ ... ..... .... .....................


135

136

137

138

139

140


Page











LIST OF FIGURES (Continued)


Figure

71 A Plot
t =

72 A Plot
t =

73 A Plot
t =

74 A Plot
t =

75 A Plot
t =

76 A Plot
t =

77 A Plot
t =

78 A Plot


I


of B Versus B/NA (19.8% CH4, 80.2% H2;
420C)........... ...............................

of B Versus B/NA (19.8% CH4, 80.2% H2;
460C)...........................................

of B Versus B/NA (21.5% C02, 78.57 H2;
300 C)..... ..... .......... ................ ...

of B Versus B/NA (21.5% CO2, 78.5% H2;
340oC)...........................................

of B Versus B/NA (21.5% CO2, 78.5% H2;
380C).........................................

of B Versus B/NA (21.5% CO2, 78.5% H2;
4200 C)...........................................

of B Versus B/NA (21.5% C02, 78.5% H2;
460o C) ........... ................... ............

of NA/(N A)MAX Versus B ........... ......0.........


79 Effect of Impurities on the Maximum Rate of Transport of
H& Through Pd-Ag Membrane at Different Temperatures
(07 CH4, 10% N2, 607. H2) ............................

80 Determination of the Energy of Activation...............

81 Effect of Impurities on the Maximum Rate of Transport of
H, Through Pd-Ag Membrane at Different Temperatures
(10% CH4, 10% N2, 807 H2)...........................

82 Determination of the Energy of Activation...............

83 Effect of Impurities on the Maximum Rate of Transport of
H, Through Pd-Ag Membrane at Different Temperatures
(25.6% N2, 74.4% H2).................................

84 Determination of the Energy of Activation...............

85 Effect of Impurities on the Maximum Rate of Transport of
Hn Through Pd-Ag Membrane at Different Temperatures
(19.8% CH4, 80.2% H2)...............................

86 Determination of the Energy of Activation...............

87 Effect of Impurities on the Maximum Rate of Transport of
H( Through Pd-Ag Membrane at Different Temperatures
(21.5% CO2, 78.5% H2) ................ ......... ....


144


145


146


147


148


149


150

158


160

161



162

163



164

165



166

167



168









LIST OF FIGURES (Continued)
FiLure Pare
88 Determination of the Energy of Activation .. ............ 169
B-1 Pressure Correction for the McLeon Gauge Reading........ 191
S























C


xiii












Abstract of Dissertation Presented to the Graduate Council in
Partial Fulfillment of the Requirements for the
Degree of Doctor of Philosophy


THE EFFECTS OF MAJOR IMPURITIES ON THE TRANSPORT
OF HYDROGEN THROUGH PALLADIUM


By


Leon Lee Chiu


April, 1966


Chairman: Prof. Robert D. Walker, Jr.

Major Department: Chemical Engineering


> The purpose of the investigation was to study the effect of

major impurities on the transport of hydrogen through solid palladium-

silver electrodes.

Experimental data were to be gathered on the effect of

impurities such as C02, CO, N2 and CH4 on the transport rate with

temperature, pressure and bleed rate as parameters. These impurities

might be expected to be present in the effluents from ammonia or

hydrocarbon reformers. The temperature range covered extended from

3000C to 4600C and pressure range from 1069 mm Hg to 2310 mm Hg.

The transport rate of pure hydrogen through 0.004 inches thick

palladium-silver foil can be described by an equation of the form:

1
n 7 -70 60 1.34
NA = klP exp E = 3.8 x 10 .60exp ( R

where NA transport rate in gm.moles/cm2sec.


xiv











P = pressure differential in mm Hg

R gas constant

T absolute temperature in OK

IE a energy of activation

ki = constant
n'

Calculation of diffusivity in the palladium-silver alloy gives

an equation of the form:


D = 5.9 x 10 exp 0RT
RT
Comparison of this diffusivity with that for pure palladium indicates

that introduction of silver lowers the diffusivity.

Introduction of impurities lowers the transport rate of

hydrogen through palladium-silver foil. This can be attributed to

the following effects: (1) hydrogen is diluted by the impurities;

(2) impurities hinder the diffusion of hydrogen in the gas phase;

(3) occupation of adsorption and dissociation sites by impurities. The

overall effect of impurities is, therefore, to lower the concentration

of hydrogen atoms in the upstream surface of the palladium-silver foil,

and since the diffusion rate in the alloy is directly proportional to

concentration, the transport rate decreases.

The transport rate of hydrogen through 0.004 inches thick 25%

palladium-silver foil with impurities can be described by the following

relationship at certain temperature and pressure:

1
B n PE B
A Amax B k / 1 RT B k

where NAmax maximum transport rate obtainable, i.e., when the bleed
rate is infinite












B bleed rate

kl,k2 = constant

= exponential constant
n
AE energy of activation
Comparison of the equation for NAmax with NA for pure hydrogen shows

that the value of is lower and the energy of activation AE is
n
higher when impurities are present. This suggests that surface

effects are present when impurities are introduced. Furthermore, the

term B/(B k2) is probably caused by effect (2). It is also expected

that because of effect (1), the partial pressure of hydrogen should

be used in the equation instead of total pressure.















CHAPTER I


INTRODUCTION


A. General

Since Thomas Graham (1) investigated the transport of hydrogen

through palladium in 1868, numerous investigators (2,3,4) have made

the same study. However, the results vary from one investigator to

another, sometime as much as a thousand times. Recently, some

investigators (5,6,8) have succeeded in narrowing this variability by

simply using a continuous system. Previous investigators almost

exclusively used static systems, which when the feed gas contains

small amounts of impurities, permit the impurities to-accumulate on:-the

upstream side of the palladium membrane, thereby producing erroneous

results. A continuous system bleeds part of its feed gas to the

atmosphere, so that the impurities do not accumulate on the upstream

side of the membrane.

The use of a continuous system does not entirely eliminate the

variability of the results, for there are also other factors involved.

In view of the fact that the transport of pure hydrogen through

palladium is still subject to controversy, the transport of pure

hydrogen has been subjected to detailed analysis. These factors

which will be studied are the thermodynamics of the palladium-hydrogen

system, which is important for knowing the characteristics of the

solubility of hydrogen in palladium; adsorption processes at the surface

of the palladium. which will tell whether a certain impurity would

chemisorb or physically adsorb at the surface; atomistic diffusion









2

mechanisms inside the solid, which deal with atomic diffusion through

different crystallographic plane; and finally the effect of dislocation

in the solid on the diffusion rates. Some of these discussions will

be qualitative in nature, but the author trusts that they will serve

as a catalyst for future research.

B. Previous Work

As mentioned previously, the transport rate of pure hydrogen

in pure palladium produced numerous inconclusive data mainly because

the investigators used static systems instead of continuous systems.

Lombard and Eichner (8) were among the first to use a continuous system

for obtaining data; however, their transport rates were very or

relatively low owing to contamination of the membrane by brazing with

silver solder. Darling (7) using commercial hydrogen showed that, for

a static system, the transport rate decreased rapidly with time; he

attributed these results to the fact that impurities blocked the

entrance of hydrogen at the surface. When a bleed was imposed, the

transport rate did not vary with time, thus lending evidence to his

thesis.

Hurlbert and Konecny (5), using a continuous system, observed

that surface reaction is not the rate-limiting process for membranes

thicker than 20 microns. DeRosset (6) used pure palladium to study

the transport rate of impure feed gas with an upstream pressure of

1-700 psig and a downstream pressure of 0-300 psig.

Commercially, Engelhard Industries (9) and Milton Roy both

use palladium-silver alloy as the separation barrier for their small

scale hydrogen purifier. Union Carbide (10) has constructed a large













scale hydrogen purifier using palladium as membrane, but few operating

data are given. A mixed feedstock of gases can be used in all of

these commercial hydrogen purifiers.

Pure palladium membranes have the disadvantage of cracking and

distorting when used for a long time, especially when the membrane is

cycled through heating and cooling in an atmosphere of hydrogen.

However, Union Carbide uses its palladium membranLe continuously without

shouting down, and the life of the palladium is, therefore, prolonged.

Pure palladium usually results in a higher transport rate at high

pressures and medium temperature than palladium-silver alloy, because

the maximum solubility of hydrogen in pure palladium is greater than

palladium-silver alloy. Engelhard Industries and Milton Roy utilize

a palladium-silver alloy in their diffuser. Since these units are

usually small and are often shut off and turn on, the palladium alloy

has an edge over pure palladium.

The bulk of the measurements of hydrogen transport through

palladium are for pure palladium membranes and for a downstream

pressure of greater than an atmosphere. When divergent results were

obtained by the investigator for the transport of hydrogen through

palladium usually qualitative explanations were given.

McBride and McKinley (10) found that when carbon monoxide,

methane, or hydrogen sulfides were present in the feedstock, they

reacted with palladium at a temperature slightly above 400C to form

palladium carbides and at a lower temperature to form palladium

sulfides. Hurlbert and Konecny (5) observed sulfide formation at

around 350C. Several investigators (5,11) noticed that air will












reactivate a poisoned palladium membrane when heated at high temperature;

this the author believed to be a removal of poison by oxidation. The

palladium oxide formed in this case can be easily removed when the

Membrane is exposed to an atmosphere of hydrogen, and this process

will be examined thermodynamically in a later section. There also

exists a possibility that carbon is deposited as a result of a

dehydrogenation process, in which the surface carbon may also diffuse

inside the metal, thus further poisoning the membrane.

C. Statement of the Problem

The primary object of this investigation was to study the

effect of major impurities on the transport of hydrogen through

C solid palladium-silver electrodes. Hydrogen-oxygen fuel cells

generally use porous material as electrodes and pure hydrogen as fuel.

The use of solid electrodes has the advantage of preventing the pene-

tration of the electrolyte into the electrode. The use of impure

hydrogen as fuel would reduce the operating cost considerably.

Experimental data were to be gathered on the effect of impuri-

ties such as CO2, CO, N2, and CH4 on the transport rate with temperature,

pressure and bleed rate as parameters. These impurities might be

expected to be present in substantial quantities in the effluents from

ammonia or hydrocarbon reformers. The temperature range covered

extended from 3000C to 4600C and pressure range from 1069 mm Hg to

2310 mm Hg.












CHAPTER II


THEORY


A. Thermodynamics of the Pd-H and Pd-Ag-H Systems

The rate of diffusion of hydrogen through palladium is directly

-proportional to the solubility of hydrogen in palladium. Since the

equilibrium isotherms give-information on solubility as well as on

phase transitions,.it is therefore important to know the characteristics

of these equilibrium isotherms. Information on phase transitions is

valuable since the diffusion coefficient changes when a phase change

occurs.

Sieverts and co-workers (12,13,14) found that hydrogen adsorbed
1/2
in palladium according to P law at high temperature and low pressure.

This suggested that hydrogen molecules dissociate into atoms before

entering the crystal lattice, indicating that hydrogen possibly exists

in palladium as atoms. However, Norberg (15) and Isenberg (16) proved

experimentally and theoretically that hydrogen exists in the palladium

lattice as quasi-free protons. The electrons are attached more

closely to palladium atoms than to the proton.

Paramagnetic susceptibility studies (17) show that susceptibility

decreases with the amount of hydrogen absorbed and drops to zero when

there are about 0.55 hydrogen atom per palladium atom. This is

attributed to the hydrogen electron going into the d shell of the

palladium atom, decreasing the number of positive holes and hence the

paramagnetism.

Gillespie and :Qaltaun (18) obtained the:equtlibrium











isotherms for the Pd-H system shown in Figure 1. It may be observed

that at a constant temperature and at low pressure, the solubility of

hydrogen increases as pressure increases, Section A to B in Figure 1.

At point B the curve becomes horizontal, indicating that the solubility
C increases even though the pressure remains constant. This increase in

solubility at constant pressure continues until a point is reached

when an increase in pressure is again necessary to increase the

solubility, as shown in Section CD in Figure 1. The first portion of

the isotherm AB represents an a-phase, the horizontal portion BC

indicates an Ca-3 phase transition, while the last portion of the

curve, CD, represents the 3-phase.

The length of the a-3 phase transition decreases as the

temperature increases and finally disappears altogether. The tempera-

ture and pressure where it just disappears is called the critical

point, and for the palladium-hydrogen system it is around 20 atmospheres

and 295C.

Nace and Aston (19,20) studied the heat capacity of Pd2H at

low temperatures ranging from 16 to 340K and found that tetrahedral

PdH4 is formed at a temperature of less than 50K. The PdH4 structure

is located at the corner of the palladium lattice. At temperatures

B higher than 500K the PdH structure dissociates into simpler hydride,

and at room temperature this model will be indistinguishable from the

quasi-free proton model. It can be concluded, therefore, that above

room temperature, the protons are distributed randomly at the

interstitial sites.

The lattice parameter of the a-phase is 3.9831; this expands to



























































0.2 0.4 0.6 0.8


Figure 1.
for


Equilibrium Isotherm
the Pd-H Systems


2400 r


2000


1600 -


M1200


P4


800





400





0


0.0















0
4.025A for the s-phase.

To improve the mechanical properties of the palladium membrane

in an atmosphere of hydrogen, palladium is alloyed with silver.

SIntroduction of silver into the palladium lattice changes the equili-

brium isotherm. Although the equilibrium isotherm for the Pd-Ag-H

systems is similar in shape to the Pd-H system, the critical point

is lower and the maximum solubility is less than for pure palladium.

It was mentioned earlier that the electron of the hydrogen atom goes

into the d-band of the palladium atom. Since the added silver atoms

fill some of the d-band vacancies in the palladium atoms with their

own electron, it will decrease the maximum solubility of hydrogen in the

alloy. However, in the a-phase region at low temperature, hydrogen is

more soluble in the alloy than in pure palladium. Figure 2 (39) shows

this characteristic for a 250C isotherm. It may be noted that for this

particular isotherm, the equilibrium pressure of hydrogen for the

a-A phase transition diminishes with increase in silver content up to

30 per cent. Very few data are available for the Pd-Ag-H system,

especially at high temperature.









9






4





3





2



Palladium 16.5

1 "
C 00
S10% Ag-Pd 3.8 m



0 20,% Ag-Pd 0.9 mm

267. A-Pd 0.3 m


-1





-2
0 0.1 0.2 0.3 0.4 0.5 0.6

H/Me (Atomic Ratio)

Figure 2. Equilibrium Isotherms
for Ag-Pd-H System at, 25C


mm


0.7 0.8











B. Statistical Thermodynamics and Equilibrium Isotherms

Lacher (21) obtained a theoretical equation for the equili-

brium isotherms by statistical thermodynamics based on an interstitial

hydrogen model. Libowitz (22) arrived at a similar equation using a

Vacancy model. However, the Lacher model is a better model since it

is based on a realistic quasi-free proton model which has been

confirmed by several investigators.

Here an equation will be derived which is a combination of the

models used by Lacher and Fowler (21,37). The assumptions made in

the derivation are:

(1) There is a fixed number of interstitial sites, Na,

where the hydrogen atom can be absorbed.

S(2) The energy of interaction between a pair of nearest

neighbors of hydrogen is equal for all pairs.

Let the number of pairs of neighboring hydrogen atoms in a

particular configuration be NHH, and let 2NHHH be its interaction
z
energy. Then from statistical thermodynamics (37), the expression

for the partition function for this system will be:
2EHH
-N 2cHH

Q Zg(N ,NHH)exp H [ AT (T) a (1)


where Q partition function

g(NH,NH) = total number of distinguishable configurations of NH atoms

z number of nearest neighbors

NH = number of hydrogen atoms in the lattice.











eH *a total interaction energy at saturation per atom

k Boltzmann Constant
T = temperature
* aH(T) the partition function for the internal degree of
freedom of an absorbed hydrogen atom referred to the
ground state at infinite separation
Defining NHM by Equation (2)


exp g(NH,N )
NH


Sg(NHNHN)exp -NHR T (2)
NHH
SSubstituting Equation (2) into (1) the partition function will be

in the form


Q [a (T) ]NA exp /xkT wg(N RNqHf) (3)
NMH

but
g(NHP ) NH (N -. NH) (4)





Q a. (T) NexpN H 2c HkT a (5)
NH' (Ns Nu)

From statistical thermodynamics the Helmholtz free energy,
F, can be written ast

F kTlnQ (6)


Substituting the value of Q from Equation (5) to equation











(6) and using Sterling's approximation

F/kT = -N lnN + NHlnNH + (N -H)n(N NH) NHlnaH(T)


+ m,2 /zkT (7)


The equilibrium or average value of NHH can be expressed

from statistical thermodynamics as:
S"-NHH 2e/zkT
NHHg(NH,NHH) exp
N HH g(N NH)exp"NHH2cH kT (8)

NHH

Each occupied site has z neighbors, and with perfectly random
NH
arrangements each site has a probability of being occupied. N

Therefore the average number of neighbors of any given N is z -. The

total equilibrium number of pairs of neighbors will be:


N = ( i Ns(z > z (9)
HI 1 NH 2 N(

But NHH = NH for random distributions (38); therefore

Equation (9) becomes

F = -N lnN + NHnNH + (N In(N N) NHna(T)
kT a s H H ( NH)1H H H(T

(15 2
+ NkT (10)

The chemical potential can be written as:


= ) kT In N InaH(T). +
T,N
I* T











kT In Ina (T) +


where 0 the fraction of sites occupied but

"E/kT
a%(T) exp qH(T)p (12)

where

(-e ) is: the energy required to remove an absorbed H atom, far
removed from any other absorbed H-atoms, from its lowest state in

the metal to rest at infinite dispersion.

qH(T) is the partition function for vibration of absorbed
H atom relative to the lattice.

p is the spin weight of the proton.

Defining XR as the absolute activity and using Equation (12)

Se + 2*HH
ji/kT- ..8 exp kT
*exp e q(T)p (13)

The absolute activity in the gas phase consisting entirely of
diatomic molecules of hydrogen at a pressure p is:

1(G)/2 1/2 FD/kT (22HkT)3/2 8-2kTp2 1/2
(G) ) exp D x 3 x 2-
-h 2h

(14)
where eD energy required to dissociate a hydrogen molecule from
its lowest state into two free H-atoms each in its
lowest state.
MH atomic mass of hydrogen

h = Planck Constant

M I moment of inertia of the hydrogen molecule.











Equating Equations (13) and (14)

S 2 2(e)H + 2:HK + ID)k/T (22M.kT)3/2
P- (.---6)kTexp x 3

8 2 HkT
8x N2 T 2(15)
2h2 fqH(T) 2

Let P )be defined by Equation (16)

), kT (2MRkT )3/2 82M 2(s + 4HR +
P kT (27r2MkT) 8r kT xpkT
'/ fqH(T)3 2 h 2h

2(eH + "Ha + ?e D /KT '
K(T)exp H + rH (16)

where
C k (252MgkT)3/2 82 kT
K(T) k= 2T-- L 3/ 2h (17)
(T)3 h 2h

Therefore Equation (15) will be simplified to:

P 1 ( )( \2 (2e 1)2 /kT(18)


If EM<0, there will be a critical temperature given by:

SHH/kTc = 2 (19)

T critical temperature
c
It is not possible to determine theoretically all of the
parameters in Equation (15), therefore experimental data must be
obtained to evaluate these constants. To do this it is convenient
to convert Equations (16), (18) and (19) to a molal basis.












P( -K' (T)exp 2( EI + ED)/RT(20)
2 (20)

(1) (2 )2Eexp (21)


-EH/RTc 2 ; (22)

The constants KI(T) and ER + EHI + ED are obtained from the
plot of lnP( ) versus 1. While EH is obtained from the critical
temperature by using Equation (22).
Lacher (21) obtained the following equation similar to equation
(20)

log) 7.4826 1877.82 (23)

He also found that Tc = 568K, so that EHR--2(R)(568). Taking the
log of Equation (21) and substituting the corresponding value of
EHR one obtains

1. P 1)+ 2l 8e 986.7(20 -1) (24)
log Pd lo 2g 1 +- T

On inserting Lacher's value for log P( ) Equation (24) becomes

1877.82 + 986.7(20 1)
logPM 7.4826 T + 21og T
MM T 1-6 T

t8 e 891.2 + 1973.40
7.4826 + 21og -1 T (25)

Equation (25) is plotted in Figure 1 along with typical
experimental data. It can be seen that Equation (25) correlates very
well with the data.
Equation (25) is obtained by using'pure palladium data,











therefore it cannot be used for the palladium-silver alloy. However,

the few experimental data available for the palladium-silver alloy

suggest a similar pattern. Since there is a lack of data for the

whole range of the equilibrium isotherms for the palladium-silver-

hydrogen system, an extrapolation method will be used to predict

these equilibrium isotherms,

The equilibrium isotherms for the Pd-Ag-H system at 25 C

for several silver contents were shown in Figure 2. It can be seen

that the equilibrium pressure for the a-A, phase transition decreases

in proportion to the silver content. This phenomenon can be used

to predict some of the constants in Equation (21) for the Pd-Ag-H

system.

SIn Figure 3 a plot of logP (6) versus the silver content

of the alloy obtained from Figure 2 at 25 C yields the following

relationship

logPn = 1.2165 6.52XAg (26)

where XAg is weight fraction of silver.
Ag
Assuming that this relation applies also to other temperatures,

so that

a A 6.52 when T = 298C (27)

Ca = 1942

and


f 191242
= log P XAg (28)
no l o T Ag
Inserting this value for log ( in Equation (23) we obtain






































C


0
1-




00



0


00





-1 I I -
0 .10 .20 .30

Weight Fraction Silver

Figure 3. Logarithm of the Equilibrium
Pressure Versus Silver Content












log &N .) 7.4826 1877.82 1942
8inal2} T T Ag

1877.82(1 +X )
k 7.4826 1877.8 (29)
T
8 For the prediction of M8 for the Pd-Ag-H system, a plot of

T versus XAg is made. Only two points are known for this plot; one

of the points is obtained from the data on the 30% Agof Makrides (23),

and the other is for pure palladium. Assuming a straight line
relationship Figure 4 was constructed.

One conclusion which can be shown from Figure 4 is that
decreases as the amount of silver increases. This can be explained
by the fact that the total interaction energy at saturation per mole
twill decrease because the solubility of hydrogen is decreased by the

addition of silver. Makrides (23) used the ratio of maximum solubility
of hydrogen in alloy to that in palladium to correct the value of

EHH in the alloy.
The value of Tc for the 25% silver alloy is about 3500K;
therefore the equilibrium isotherm expression for the 25% silver alloy

will be:

7.4826 2og 1635.52 + 1218 (30)
log =- 7.4826 + 21og -- T (30)

C. Transport of Hydrogen Through Palladium
The transport of hydrogen through palladium can be attributed
to the following series of processes:

(1) The hydrogen gas molecule is adsorbed and dissociates
into hydrogen atoms at the upstream surface.























































0.1 0.2


Ag


A Plot of Critical Temperature
Versus Silver Content


700


600





500




E4
400





300





200


Figure 4.











(2) The adsorbed hydrogen atom enters into the crystal
lattice and becomes a proton and a quasi-free electron.

(3) The proton diffuses through the palladium lattice.

(4) At the downstream surface the proton recombines with

an electron to form a hydrogen atom.

(5) Two hydrogen atoms combine to form a hydrogen molecule.

(6) Hydrogen molecules desorb from the downstream surface.

Each of the steps above may be the rate-controlling one; it
is therefore important to discuss them separately.


1. The Adsorption and Dissociation of Hydrogen in the Palladium
Surface

The hydrogen molecule before diffusing through the metal must
First adsorb in the metal surface and subsequently dissociate into

two hydrogen atoms. Adsorption processes can be broadly divided

into two types depending on the amount of heat evolved 'during

adsorption; these are (1) physical adsorption, (2) chemisorption.

The heat of chemisorption is generally higher than the heat
of physical adsorption, since in chemisorption chemical bonds appear

to be formed between the gas and metal atom. In physical adsorption

van de Waals forces are the forces acting between molecules,and

these are generally small; thus the heat evolved is generally small.
C
Electrochemical determination of the heat of adsorption of hydrogen

or finely divided palladium shows a heat of adsorption of 27.5 kcal/mole

(24), which is in the range of chemisorption.

Chemisorption is usually the first step toward the dissocia-
tion of the hydrogen molecule on metal surfaces; it is found to be











true especially in heterogeneous catalytic chemical reactions.

The conditions in which surface effects determine the rate

of diffusion are the following:

(1) low pressure and low temperature,

(2) very thin membrane,

(3) blocking and poisoning of the surface by impurities,

(4) physical condition of the surface.

Hydrogen molecules are adsorbed and dissociated on certain

active sites in the metal surface, the number of molecules adsorbed

and dissociated being proportional to the product of the number of

molecules striking the surface and the probability of adsorption

and dissociation. This condition therefore requires relatively high

pressure and temperature. At low pressure the number of molecules

striking is greatly reduced, resulting in a reduction of the trans-

port rate. The rate of dissociation increases exponentially with

temperature, and proportionally with square root of pressure. This

means that temperature should produce more profound effect than

pressure.

The surface effect will also be the rate-controlling factor

if the thickness of the metal membrane is greatly reduced so that

the resistance to flow offered by the metal membrane is negligible

compared to that of the surface. This means that the metal membrane

will diffuse all the gases that the surface has dissociated. Hurlbert

and Konecny (5) found that at upstream pressures of 1 to 7 atmospheres

and temperature around 350C, surface effects are rate-limiting for

membranes thinner than 20 micron. This limiting thickness, of course,












will vary for different temperaturesand pressures.

The blocking and poisoning of the surface by impurities is

caused by occupation of the active sites by foreign atoms (25,26).

The following kinds of substances can cause poisoning:

(1) impurities in the feed gas,

(2) vaporized metal,

(3) impurities in the metal,

(4) metal oxide formation.

Impurities in the feed gas, such as hydrocarbon vapor and

hydrogen sulfide, decrease the transport rate greatly at temperatures

in the range 4000C to 6000C (25). This was explained by McBride (10)

as caused by the chemical reaction of these two gases with palladium

forming palladium sulfide or carbide. The formation of palladium

sulfide is instantaneous and irreversible. The formation of palladium

carbide may involve a more complicated reaction, and may be a very

slow process; furthermore the carbon atoms at the surface may diffuse

into the palladium lattice, thereby further decreasing the transport

rate.

Oxygen and water react with palladium to form palladium oxide.

If an atmosphere of hydrogen gas is introduced, the following reaction

will occur

PdO + H2 Pd + H20 (31)

From thermodynamics

log K -AFf/2.3RT (32)

where K = the equilibrium constant for a reaction.

AFof the free energy of formation at 2980K in cal/mole.












For the reaction above


AFof = Af (product) AF (reactant)

= -54.64 (-13.45) = -41.19 kcal.

Substituting the value of AFf and a temperature of 623 K

to equation (32)

logK = 14.5

K = 3.2 x 1014

P
20 14
--- = 3.2 x 10 (33)
H"2

Therefore
-5
P = 5 x 10-5 P
PH2 P20

Therefore if the vapor pressure of water is around 23 mm Hg,

the corresponding equilibrium pressure for hydrogen will be

1.2 x 10 13mm Hg; since the pressure of hydrogen is usually above

760 mm Hg, it can be concluded that all of the PdO will be

converted to palladium.

Similarly for the silver, the reaction will be


Ag20 + H2 = 2Ag + H20 (34)

P = 1.2 x 1012 P20
12 820

From this it can be concluded that no Ag20 will exist when a

hydrogen pressure of more than 760 mm is present.

Many investigators have found that an inactive palladium

membrane.can be reactivated by heating in an atmosphere of air;












however, this method does not produce a lasting effect. Recently,

the use of low energy electron diffraction (27) has led to some

understanding of the situation when certain gases are adsorbed on

B the metal surface. It was found that the surface atoms rearrange

when a gas is adsorbed. The adsorption of oxygen on nickel, for

example, causes rearrangement of all three crystallographic planes

of nickel (100, 110, 111 surfaces). Since palladium is similar to

nickel in crystalline structure, i.e., both are face centered cubic

and both are transition metals, it seems reasonable to assume that

adsorption of oxygen causes surface rearrangement. In these

circumstances the transport rate will be relatively high at the

start;, then when the surface rearranges to the equilibrium configura-

C tion, the transport rate will decrease. This was observed by

Makrides (23), but he offered a different explanation, namely that

the decrease in transport rate was caused by impurities.

When the diffusion cell is operated at high temperatures some

of the metal may be vaporized and is deposited on the surface of the

membrane. This would be expected to decrease the transport rate.

Such metals as lead and iron in the form of FeC13 can poison the

palladium membrane. Surface diffusion of foreign atoms from the

Vicinity of the palladium membrane, such as copper gasket, also slows

down the transport rate.

Assuming that there is no effect exerted by neighboring

molecules, the time in which a molecule stays at the surface can be

predicted from the heats of adsorption and the physical properties

of the metal. This residence time of the molecule at the surface can












be used as a measure of the poisoning effect of certain molecules.

According to De Boer (28) the adsorption time of a molecule

in the surface is given by:

r Toexp (35)
RT

-13 MV2/3
where T = 4.75 x 10 -3 (36)
o T(

T = time of adsorption

M = mean molecular weight per constituent atom
3
V = molar volume in cm

Ta = melting temperature OK

T = temperature OK

R = gas constant, cal/moleK

AH = heats of adsorption, cal

The residence time for hydrogen on palladium at room tempera-
.2
ture is about 10 secs. If a gas has a much larger adsorption time

than hydrogen, then the gas can be said to be a poison.

Trapnell (29) indicated that unsaturated hydrocarbons, such as

ethylene, chemisorbed on the transition metalsaccording to the equation:

CH CH
I I
4Pd + C2H4- Pd Pd + 2PdH (37)

The heat of adsorption in this case can be estimated by using

Pauling's (30) equation for single bond energies.


E(X Y) = E(X- X) +E (Y Y) + 2.306( Y)2 (38)


where E(X Y) is the bond energy between X and Y












LX is the electronegativity.

The initial heat of chemisorption qo can now be written as:


qo = 2E(Pd-Pd) + E(H-H) + E(C-C) 2E(C-H)


+ 46.12(pd C + d-H (39)

Substituting the values

E(Pd-Pd) = 15.5

E(H-H) = 104.2

E(C-C) = 83.1

E(C-H) = 98.8
2
MPd-C = 0.09
2
Pd-H 0.01

one obtains a value qo of 22.5 kcal and an adsorption time of

4 x 103 secs. Similarly, this approach yields an adsorption time for
-2
hydrogen of 4 x 10-2 sees. Therefore it can be concluded.that for

an equal mole fraction of hydrogen and ethylene at room temperature, the

ethylene will be adsorbed more than hydrogen. However, the acetylinic

complex formed in Equation (37) is slowly removed by gaseous hydrogen,

presumably as ethylene:

CH = CH
I I
Pd Pd + H2 2Pd + C2H4 (40)

or
H H
I I
Pd- Pd + C2H4 -+ 2Pd + C2H6 (41)












2. The Diffusion of Hydrogen in the Palladium Lattice

There are several theories which attempt to explain the absorption

of hydrogen in palladium and the mechanism of its diffusion through the

palladium lattice. Some of these theories are:

(1) A chemical compound is formed when hydrogen is absorbed

in the palladium lattice.

(2) Hydrogen is rift occluded in the palladium lattice.

(3) Hydrogen forms an interstitial solution either as atoms

or protons in the palladium lattice.

Simons and Ham (31) considered the diffusion of gases through

metal as pure chemical phenomenon, i.e., a chemical compound is formed

between the gas and the metal. This theory would suggest that diffusion

of hydrogen is accomplished by the kinetic dissociation of the compound,

and, since a concentration gradient exists in the metal membrane, the

movement of hydrogen will be toward the low pressure side. This theory

may be valid if-the bond between the metal and gas is sufficiently

strong to consider it a compound. However, since hydrogen diffuses

through palladium quite rapidly at elevated temperatures, it appears

that this mechanism is of minor importance. Nace (19,20) has suggested

that chemical.bonds are formed between the hydrogen and palladium. The

hydrogen diffuses through palladium in this case is assumed to occur as

the movement of hydrogen atoms by the following mechanism: (1) rotation

about a parent palladium atom; (2) bonding to, and subsequent rotation

about a neighboring atom. When the temperature is raised to room

temperature, the bonds are broken, and the hydrogen atoms are randomly

distributed so that an interstitial solution is formed.












Smith (32) believes that hydrogen diffuses through palladium

via rifts, a rift being a deformed or dislocated portion of the metal

crystal possessing a great ionization power because of imbalanced

forces in the stressed metal. This theory was concluded to explain
t the greater solubilities and diffusion rates observed when the metal is

deformed by cold working. It is believed that the formation of rifts,

as shown by line-broadening in the X-ray diffraction spectra, causes

hydrogen to be occluded in the metal. Kydonius (33) found that sonic

vibration increased the rate of mass transfer through palladium by

producing dislocations. It would be hazardous to assume that the

mechanism of diffusion is mainly through rifts in dislocation. Because

if this is true, other metals such as nickel and copper can be made to

C have the same transport rate as that of palladium; this has never been

accomplished experimentally. The probable reason for the increase in

the absorption or diffusion rate in stressed metal is that in stressed

metal the dislocations serve as a reservoir for the hydrogen and at the

surface dislocation increases the surface activity. However, the majority

of hydrogen appears to diffuse interstitially.

The diffusion of hydrogen in the palladium lattice can be

described from an atomistic point of view. It was shown earlier that

* the proton occupies certain interstitial sites in the palladium lattice,

the most probable sites being those shown in Figure 5. These sites

are located at the edges and at the center of the face-centered cubic

lattice.

Diffusion appears to involve hydrogen jumping from one inter-

stitial site to another. From these considerations an equation can be



















A














Figure 5. Interstitial Sites for a Face Center Cubic Lattice.
0 Indicates Metal Atom, X Indicates the Interstitial Position






derived to describe these processes (40,41); Consider the interstitial

position of a face-centered cubic lattice as shown in Figure 6. Three

atomic planes are drawn in. this figure separated by a distance of X.

Assume that there exists a concentration gradient of hydrogen along the

x axis which is perpendicular to the (001) atomic plane. A hydrogen

in an interstitial position may jump in forward, backward, or in a

direction perpendicular to the x-axis. Let P be the probability for

a given interstitial hydrogen to make a jump per second and f P be the

probability for a jump per second in the forward direction. Also

assume the probability for a forward and backward jump to be equal. Let
2
the number of diffusing particles per cm on the plane located at x at















-I


-I -


Figure 6. Atomic Plane of Diffusion
in the Metal Lattice






the instant t be represented by n(k). Using Taylor series expansion

one therefore gets


n(x +X) *n(x) + + ..... (42)






2
where n(x + X) the number of hydrogen per cm at plane x + X

2
n(k X) the number of hydrogen per cm at plane x X
at time t

The increase of the number of particles located at plane x at instant

t + 6t will be:


IL











6n(Wt) = frPr n( + X) + fr rn(" -) 2frrn() r 6t (44)


6n(x) Pf r t n Xn2 (45)

from whence we have

? EPX2 an (46)
t rr x2
Comparing Equation (46) with Fick's second law we see that

D = fP X2 (47)
rr
where D = diffusion coefficient

f = a geometric factor and for a f.C.C. lattice is equal
r to 1/3 when the atomic plane is 001 plane.

The probability Pr is given by (36)

P I 9- (48)
r h Q+

where Qt = partition function of the activated state
Q = partition function of the normal state.

Further simplification of equation (48) yields


P 1 exp h )exp- 1 (49)

where v = frequency of vibration of a linear oscillator

AF =- free energy of activation.

For the case where hv((kT Equation (49) reduces to


PF /RT- v e-wF/RT (50)
P = vrexp (50)
and -F/RT
D = f eVXaxp (51)











For a face-centered cubic lattice with lattice constant a,

and using relationship AF = AE TAS Equation (51) becomes

1 2(a \d AS/R -AX/RT -1 2 tS/R -tE/RT
D = v 2e ) exp exp- aexp exp-

S-1E/RT
= D expE (52)

where AS = entropy of activation

AE energy of activation
1 2 AS/R
Db = 2 La exp (53)

Calculating D with estimated values of AS, v and a
13 -1
v 1.75 x 101 sec
-8
a = 3.9 x 10-8 cm

C AS p(iE/T) = 0.18 (J0 0.46

leads to
1.75 13 8 2 0.46/1.98 1.75x -3 2
D 12- x 10 x (3.9 x 108) exp 0.46 98 1.75 x 10 sec.
o 12
(54)
If the hydrogen is diffusing normally to 001, 010 or 100 plane,

the diffusion constant would be the same; however, if the hydrogen is

diffusing normally to 110 plane, the values of fr and X would change,

indicating that solids are, in general, anisotropic. Initial calcula-

tions for diffusion through the 110 plane indicate a higher diffusion

coefficient. From these equations it can also be predicted that an

expanded lattice, such as a A-phase, would have higher diffusion

coefficient provided that no covalent bond is formed between the hydrogen

and the palladium atom. The diffusion coefficient in Ag-Pd alloys (34)

was found to decrease with increasing silver content. This is











anticipated since silver is a poor hydrogen diffuser. One problem

that may arise in the Pd-Ag alloy is the order-disorder phenomenon

of Pd and Ag atom in the lattice. As discussed by Krivoglaz.aad Smirnov

(35) the order-disorder of the alloy will affect the value of
energy of activation. This is further complicated by the fact that

metal crystals are not perfect; therefore, the diffusion would be in

different crystallographic planes, which were shown above to possess

different diffusion coefficients.

3. Macroscopic Diffusion Equation in Palladium

The macroscopic equation for diffusion of hydrogen in palladium
can be written as:

CA
t + *NA = RA (55)

where CA = concentration of A

NA = molar flux of A
A
RA = chemical reaction rate of A

V" = del operator
This can be written in rectangular coordinate as

aC iN bN aN
--+ x+ +-RA (56)
o ot ax y cA

-D CA *
where NAx -= + CA (57)

v = molar average velocity
2C v /IC
n 1 i n i
In the diffusion of hydrogen through solid, v* will be near zero, and









34

since there is no chemical reaction, RA 0. In this investigation,

the flow is in a single direction only, say the x-direction; therefore

Equation (56) becomes

cA ^Ax
-F +- = 0 (58)

but NA A (59)


therefore ~CA A(60)


Assuming the solid to be isotropic

aC DB2C
A A
3 2 (61)
ax

Let us assume that the upstream surface reaction is very fast

so that equilibrium condition prevails between the surface and hydrogen

gas. The corresponding boundary conditions and differential equation

will be:

B.C.1 C = Ci, x = 0, t>O (62)

B.C.2 C = 0, x = L, t>0 (63)

B.C.3 C = 0, O(L, t = 0 (64)


J, 0o0 (65)

Let v = C/Ci (66)

then

B.C.4 v = 1, x = 0, t>O (67)

B.C.5 v = 0, x = L, t>0 (68)

B.C.6 v = 0, 0<(L, t = 0 (69)












S2 OO(L, t>0 (70)


Taking the Laplace transform of Equation (70) with respect to t


sV(x,s) v(x,0) Dd2V( ) 0 (71)
dx
where
V /vexp-Stdt (72)


since v(x,0) = 0 (73)

Integrating Equation (71)


V Clexp+x + C2expqx (74)

where q = 1/2 (75)

Applying B.C. (4) and (5) to eliminate constants C1 and C2


V [ ex(L-x)q ep-(L-x)q]
V = qL -, ep exp
s(exp exp *qL

Ssinh(L-x)q (76)
s sinhqL
y+iw ..
V 31 s s exp sinh(Lx)q de (77)
27ri a sinhqL ---

The inverse Laplace transform of Equation (77) with poles of a 0,
and s = Dn2r
2and a n 1, 2, 3 is
L 22
2n2 2t

+ exp L sn L Cos r



L- +2 exp sin n (78)
n L












The diffusion flux across plane L at any time t will be:


N DdC,
xinL dxx
S-22
DC, 2DC i 72t
=--+-- (-l)nexp L (79)
L L L
nh1

The diffusion flux at infinite time will be

DC
N = ~i (80)
t -.0ao L

This equation represents the steady-state value of the

diffusion flux. Therefore the fraction of the steady-state value

reached at time t, SST, will be the ratio between Nx=L and Nt o

Thus the value of SST becomes
2 2
0 -Dn t t
N 2
SST w X-L 1 + 2 )(-1)nexp L (81)
t -0+ o2

Letting T the value of SST for different values of T
L
is plotted in Figure 7.

Figure 8 can be used to find the time to reach 907 of the

steady-state value. For example, if L 0.01 cm, D I 10 cm /sec.,

the time t to reach 90% of equilibrium value will be (with T 3 when

SST = 0.90 from Figure 7):

-6 2
3 (10 )(3.14) t(82)
T = 3 2 (82)
(0.01)

and t 30 secs.

In the case where there is a surface effect, the equation

will be of the form














































2
T -=w
2
L


Value of-SST for different T


1.0





0.8





0.6


0.4





0.2





0


0 2 4 6 8


Figure 7.











B.C.7 k -(C -C =k kG(C C), x 0, t)O (83)

B.C.8 C 0, x L, t>O (84)

B.C.9 C 0, .0x
ac D2v
S. ), 0O (86)

Using Equation (66) the Laplace transform will be

V = Clexpq + C2expq(87)
where l/2
wq = ]/2 (88)

Applying the boundary conditions to eliminate C1 and C2 we obtain

k L sinh(L-x)q
Ss(qLCoshqL + k LsinhqL) (89)

The inverse Laplace transform is

k1 y kGLexp sinh(L-x)qdB
v 21 (90)
y i m s(qLCoshqL + kCLsinhqL)

2
The poles are s = 0, and a s 2 where are the roots of the
L
transcendental equation

tan kG (91)
G
Solution of Equation (90) by residue method results in

k G (L-)
V =
1+kGL k2t
L 2 (L-x)gn
+ 2(kGL)2 exp s in L (92)
n S0 on( 2 + (kGL)2 + kGL)











Now N
x~L


-DC dv
dx


2 m -D 2t
kDC 2D(k0L) C exp n2t
1+ kGL L Co 2 + (kCL)2 + k L]


(93)
Usngrelatonshp tann-
Using relationship tan -In (94)
G


coas = (-1)n kGL 1/
n 2+ (kGL)


kGDC
N -- +2Dk+ 2DkC
x-L 1 + k L i
G


(95)

-Dt2 t
1/2 exp


S+ (kGL)2 + kGL


(96)


(97)


k DC DCL k
two 1+kGL L 1+k
L G


DC
i
1Im N (9
t 0 L
Equation (98) is similar to Equation (80).

Equation (96) can be used to ascertain the time required to
Dt
reach steady-state by using the parameter T 2 and kGL, thus by
L2
the previous method -n


NL
SST = 1- + 2(1 + kGL)
Nt -.*1o I


2.


(-l)n 2 + (kGL)2 1/2qexp L

n + (kL)2 + kGL


(99)


The value of SST for different values of T and kGL are shown in

Figure 8.


1)











40






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to
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o -4 N 8
II II II II II





I,







0

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ol \ |





LSS







- 0 0 o 0

IBSS












CHAPTER III

EXPERIMENTAL PROCEDURE

A. Experimental Apparatus

The experimental apparatus consisted of a diffusion cell,

pressure measuring system, vacuum system, gas cylinders and a tempera-

ture control system. These are shown in Figure 9.

The diffusion cells, shown in detail in Figures 10 and 11,

consisted of a stainless steel flange, a Pd-Ag membrane, and

copper gasket held together by four bolts. The silver-palladium

membranes, 1 1/8 inches in diameter, were punched from 25% silver-

palladium foil. A cavity 1/2 inches in diameter and 1/16 inches

deep was machined in the upstream flange to serve as a gas chamber;

a gas inlet and outlet to this chamber were also provided as shown.

The downstream flange was similar except that only a gas outlet was

provided; however, a thermocouple well was machined in the downstream

flange. The downstream cavity was connected to a stainless steel (5641 cn

tank which provided enough capacity to prevent the downstream pressure

from changing too rapidly during measurement.

A thermocouple gauge was used to measure the vacuum on the

downstream side from 1-1000 microns. A Mcleod gauge was used to

measure the pressure change in the downstream side of the apparatus

during the diffusion experiment. A pressure regulator was used to

provide the desired pressure from the feed gas cylinder, an extra

pressure gauge is also included in the line.

The temperature control system consists of a temperature

recorder-controller and a tube furnace. A chromel-alumel thermocouple






















































a
u



5 .











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01 w
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>




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z
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was used to measure the temperature of the membrane.

The flow through the system was controlled by a toggle valve,

and a flowmeter was incorporated in the upstream side to regulate the

bleed rate. A rupture diaphragm with a bursting pressure of 50 psig

was installed on the upstream side.

Two Welch vacuum pumps were used for evacuating the system.

Small gas cylinders were used for storage of feed gas and for the

diffused hydrogen gas. The temperature recorder has an estimated error

of loC and the Mcleod gauge has an estimated error of 0.05 mm in

the range of pressure used.

B. Experimental Procedure

The transport rate of hydrogen through the palladium-silver

membrane was measured by trapping the diffused hydrogen gas in the

downstream side for a short length of time and determining the pressure

change during this time interval.

The experimental procedure is important because a different

procedure will give different results. In all these experiments,

unless otherwise specified, the first set of experiments is always

disregarded, because the palladium-silver membrane gave a' lower

transport rate when used for the first time. The transport rate was

found to increase after one cycle and it also became more reproducible.

Two experimental procedures were used to determine the trans-

port rate: Procedure A altered the pressure while keeping the tempera-

ture constant. In Procedure B the temperature was altered while

keeping the pressure constant. In both procedures, the pressure and

temperature was always increased from a lower value to a higher one.









46


Altering this sequence was found to produce different results. A

more detailed description of these procedures is given in

Appendix B.











CHAPTER IV


EXPERIMEINAL RESULTS AND CALCULATIONS

A. Experimental Evaluation of the Transport Rate
Per Unit Area

The transport rate of hydrogen per unit area through 0.106 mm

25% palladium-silver foil were calculated from the pressure change and

time data. The experimental data from these runs are tabulated in

2
Tables 1-19. The membrane area for all these runs was 1.268 cm .

Hydrogen is admitted to the upstream side and the downstream

pressure increases from Pi to Pf at an interval time 0. The moles

of hydrogen diffusing, assuming ideal gas behavior, will be:

V (P- P )
n2 n1 c (100)
n2 1" nl RT

where n1 = gm. moles at the start of the experiment

n2 gm. moles at time 0

Pi downstream pressure at start of the experiment in mm Hg

Pf downstream pressure at time 0 in mm Hg

V volume of the downstream compartment in Cm3

T absolute temperature OK

R gas constant

The transport rate per unit area will be given by:

n2 n V AP
N A = AT (101)
A A0 ART
2
where NA transport rate per unit area in gm.moles/cm sec.

3
V volume of downstream compartment, 5641 cm
c
3
A = area, 1.268 cm

4 time, sees.










48


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AP Pf Pi, mm Hg

Substituting the corresponding numerical values, Equation (101)

becomes:
5641 AP 12P
N 5641 AP = 7.14 x 10-2 b (102)
A = (1.268)(6.236 x 10') OT 714T

Equation (102) is the working equation for calculating the

transport rate per unit area from the experimental data. The values of

NA are also tabulated in Tables 1-19.

B. Determination of the Diffusivity
of Hydrogen in Palladium-Silver Alloy

The diffusivity of hydrogen in palladium-silver alloy may be

determined from Equation (30) and the diffusion flux from Table 1 and

Table 2.

The assumptions for these calculations are (1) Equation (30)

is accurate enough for the purpose of these calculations, (2) the

adsorption and dissociation process is fast compared to diffusion in

the solid so that equilibrium exists between the gas phase and the

palladium-silver surface.

Using Equation (80) therefore

N= C (103)
A L
but
but rat.H gm.moles H2 m. at.Pd-Ag
at.Pd-Ag 2 at.H 107 gm.Pd-Ag

S11.62 gm.Pd-Ag
cm3Pd-Ag
also L = 0.0102 cm

r 0.36












therefore

D = (0.0102)(2)(107) NA
(11.62)(0.36) x- (04

Equation (104) is the working equation for determining the

diffusivity.

From the tabulated values of NA in Table 1 and Table 2, and

calculated values of 0 from Equation (30), the values of D for different

temperatures are calculated and tabulated in Table 20 and Table 21. An

average value of D is taken for each temperature in the pressure range.

The logarithm of these values are plotted against 1000/T in Figure 12.

Figure 12 indicates a relationship of the form:

AE
D = Doexp(- -T) (105)

where D = constant
0
AED = energy of activation of diffusion

From Figure 12 the value of D at a particular temperature is found to

be given by:

-3 6560(
D = 5.9 x 10 exp(- RT1 (106)

This is compared with an accepted value (23) of


D = 4.3 x 10-3exp(- 5 0) (107)
RT
c for pure palladium at high temperature; although Do is roughly the same

in both cases, the activation for diffusion differs in the-two materials.

C. Temperature and Pressure Dependency of Flux
of Pure Hydrogen in Palladium-Silver Alloy

The fluxes recorded in Tables 1 and 2 are plotted as logNA

versus logP A straight line relationship is found as shown in
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>- W1 W r1 N









82















1.0





0.8





0.6





0.4



O

0. 0.2






1.3 1.4 1.5 1.6 1.7 1.8

1000
T

Figure 12. Diffusivity of Hydrogen
in Palladium Silver











Figure 13 and Figure 15; a plot of logNA versus 1000/T also gives a

straight line relationship as shown in Figure 14 and Figure 16. These *

results suggest that the flux is related to the pressure and temperature

by:

NA k1n exp (- (108)

where k1 M constant

AE = energy of activation

constant
n

The theoretical verification of Equation (108) can be traced

back to Equation (80) in which

N SD (109)
"A L
but A
but D D0exp )D (110)


C exp (111)

where k3 = constant

AHC = heat of solution

The equation for C should come from Equation (30), but this

can be approximated by Equation (111). Figures 17-18 show that
) Equation (111) is a good approximation for the ranges of the tempera-

ture and pressure used in the experiment. Equation (109) therefore

becomes:
1 1
kD Do AE AHC 1
NA D nexp ( D RT knexp(-dE/RT) (112)

A multiple regression analysis technique was used to correlate










84








-5 2
B: 3.79 x 10- gm. moles/cm2see.
Feed Gas Composition: Pure H2
Procedure: A


1.2 r


1.0 F


0.9 r


0.8 -


0.7


3.0


log P
mm

Figure 13. The Rate of Transport of Hydrogen
Through Palladium. Silver Membrane
at Different Temperatures


460C

420C
3800C
340C

- 300C


to

x


0


1.1 1-


-