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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 PdH and PdAgH 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 PalladiumSilver Alloy...................... 77 TABLE OF CONTENTS (Continued) Page C. Temperature and Pressure Dependency of Flux of Pure Hydrogen in PalladiumSilver 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 PalladiumSilver Membranes................. 172 B. Effect of Impurities on the Transport Rate of Hydrogen Through PalladiumSilver 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 105).............................. 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 105) .............. ..... .......... 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 105).............................. 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 105)......... ............... 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 105)......................... .. ...... .. 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 105). ... .... ...... ... ............. 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 PalladiumSilver: Procedure A. 79 21 Diffusivity of Hydrogen PalladiumSilver: 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 PdH Systems............. 7 2 Equilibrium Isotherms for AgPdH 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 PdAg 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 PdAg 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 PdAg 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 PdAg Membrane at Different Temperatures (10% CH4, 10% N2, 80% H2; B = 0.38 x 105)........... 99 28 Determination of the Energy of Activation............... 100 29 Effect of Impurities on the Rate of Transport of H2 Through PdAg 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 PdAg 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 PdAg 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 PdAg Membrane at Different Temperatures (25.6% N2, 74.4% H2; B = 0.93 x 105)................ 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 PdAg 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 PdAg Membrane at Different Temperatures (19.8% CH4, 80.27 H2; B 1.25 x 105) ................ 111 40 Determination of the Energy of Activation................ 112 41 Effect of Impurities on the Rate of Transport of H2 Through PdAg 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 PdAg 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 PdAg Membrane (21.5% CO2, 78.5% H2; B = 0.86 x 105) ....................................,, 117 46 Determination of the Energy of Activation................ 118 47 Effect of Impurities on the Rate of Transport of H. Through PdAg 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 PdAg Membrane (21% CO, 79% H2; B = 2.52 x 105) ................................................. 121 50 Determination of the Energy of Activation................ 122 51 Effect of Impurities on the Rate of Transport of H2 Through PdAg 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 PdAg 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 PdAg 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 PdAg 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 PdAg 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 PdAg 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 B1 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 palladiumsilver 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 palladiumsilver 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 palladiumsilver 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 palladiumsilver 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% palladiumsilver 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 toaccumulate 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 palladiumhydrogen 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 ratelimiting 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 1700 psig and a downstream pressure of 0300 psig. Commercially, Engelhard Industries (9) and Milton Roy both use palladiumsilver 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 palladiumsilver alloy, because the maximum solubility of hydrogen in pure palladium is greater than palladiumsilver alloy. Engelhard Industries and Milton Roy utilize a palladiumsilver 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 palladiumsilver electrodes. Hydrogenoxygen 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 PdH and PdAgH Systems The rate of diffusion of hydrogen through palladium is directly proportional to the solubility of hydrogen in palladium. Since the equilibrium isotherms giveinformation 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 coworkers (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 quasifree 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 PdH 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 aphase, the horizontal portion BC indicates an Ca3 phase transition, while the last portion of the curve, CD, represents the 3phase. The length of the a3 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 palladiumhydrogen 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 quasifree 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 aphase is 3.9831; this expands to 0.2 0.4 0.6 0.8 Figure 1. for Equilibrium Isotherm the PdH Systems 2400 r 2000 1600  M1200 P4 800 400 0 0.0 0 4.025A for the sphase. 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 PdAgH systems is similar in shape to the PdH 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 dband of the palladium atom. Since the added silver atoms fill some of the dband vacancies in the palladium atoms with their own electron, it will decrease the maximum solubility of hydrogen in the alloy. However, in the aphase 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 aA phase transition diminishes with increase in silver content up to 30 per cent. Very few data are available for the PdAgH system, especially at high temperature. 9 4 3 2 Palladium 16.5 1 " C 00 S10% AgPd 3.8 m 0 20,% AgPd 0.9 mm 267. APd 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 AgPdH 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 quasifree 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 Hatoms, 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 82kTp2 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 Hatoms 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 EHR2(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 16 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 palladiumsilver alloy. However, the few experimental data available for the palladiumsilver alloy suggest a similar pattern. Since there is a lack of data for the whole range of the equilibrium isotherms for the palladiumsilver hydrogen system, an extrapolation method will be used to predict these equilibrium isotherms, The equilibrium isotherms for the PdAgH system at 25 C for several silver contents were shown in Figure 2. It can be seen that the equilibrium pressure for the aA, 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 PdAgH 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 PdAgH 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 quasifree 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 ratecontrolling 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 ratecontrolling 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 ratelimiting 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 105 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(PdPd) + E(HH) + E(CC) 2E(CH) + 46.12(pd C + dH (39) Substituting the values E(PdPd) = 15.5 E(HH) = 104.2 E(CC) = 83.1 E(CH) = 98.8 2 MPdC = 0.09 2 PdH 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 102 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 ifthe 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 linebroadening in the Xray 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 facecentered 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 facecentered 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 xaxis. 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 ewF/RT (50) P = vrexp (50) and F/RT D = f eVXaxp (51) For a facecentered 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 S1E/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 108 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 Aphase, would have higher diffusion coefficient provided that no covalent bond is formed between the hydrogen and the palladium atom. The diffusion coefficient in AgPd 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 PdAg alloy is the orderdisorder phenomenon of Pd and Ag atom in the lattice. As discussed by Krivoglaz.aad Smirnov (35) the orderdisorder 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 xdirection; 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, 0o
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 /vexpStdt (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(Lx)q ep(Lx)q] V = qL , ep exp s(exp exp *qL Ssinh(Lx)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 S22 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 steadystate value of the diffusion flux. Therefore the fraction of the steadystate 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 XL 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 steadystate 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 ofSST 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. ), 0 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(Lx)q Ss(qLCoshqL + k LsinhqL) (89) The inverse Laplace transform is k1 y kGLexp sinh(Lx)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 (Lx)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 xL 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 steadystate 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 04 to ,4 *0O o 4 N 8 II II II II II I, 0 O  Cl 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 PdAg membrane, and copper gasket held together by four bolts. The silverpalladium 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 11000 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 recordercontroller and a tube furnace. A chromelalumel thermocouple a u 5 . Cd 01 w a > 0 0 & 4Cf4 OX O > S I 0 *0 00 0 0 *S S CC5 IO 4J V4 8 4 10 MC Sr 0 41 0 p44 94( O r 43 .. r @1 .0 0 S00 I c 1 4 I 4 ."4 co . os c s c. "4 0 3A Ma a mr .4 4 r4 00 Q 0 0 0 0 00 o CD .U rf 1 '. * 01 z r4 Pio :1 0i ,4" ~r 0 0 S.. re4 C, a' J' 4 0. S N0 r1 B" i4r 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 palladiumsilver 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 palladiumsilver 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% palladiumsilver foil were calculated from the pressure change and time data. The experimental data from these runs are tabulated in 2 Tables 119. 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 rt n tn sr 0 tsar o oo P< C0 9> 0 CO O ; 4 r4 W4 0 00 00 r rooe, So in 00 p. 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IZNrcOQ 0000 C4M CM4 00000 00000 0000000000r 00000 &A in in in In 14 eq cn '4 In V4 r4 r4 14 C% 0 Pi CM Cn co 0 0 00 S000 0 r W o oH i Sm M CM 00000 'A in in in IA * 9 9 1 * 4. 00n % 1 Cr4 4 mCM ***ae ~h en r4 I o0 0m in in Lm * 9 * 00000 un in in in 00000 l* 9 9 i 9 C4 C4 C4 C4 CM o%0000 o000O SM 4M OMO l(M r4"C4 vI v4C4Nr 4 M r 4 4 B 4 U N 8 1% a N 0 40 943 Al I a CMiwi00 S* S 00000 00000 0a 40 '0 00000 vn en eon eq CM4 N N N N G o o 0 PO r 4r4 N C I U M 1 8 8 i `O * 1"  8 4'i 81 J11 %a I\on oo 80000 en in 00000 P4 ^ r4 0C4 M1 I rM . o P: 00u000 cn ro m en 00000 in in in. n in (" 4n 00000 0% 0 0u 0 0u 4 1l r4I M C4 %Cmo(0'4 ,4,n4CICn i1 PH M9 ~4j 1 aM00 08 o S 6 o en a B r4 V4 C4M C4 iteO egMMM(NN o a .4 *. 3H C.1 E A.,.1 PH* 41 0 69000r A C > 1 C 0 44I m a 0m S 0 00 * **1 o * * r n  n N OM 4 U pJ 0, M U " s I N M M0 C4 C C4 N C o co in A 00 C4 MNN (MM r% Inn in  *%O*** "4o 100000 0 C NN0 CM 0 00000 N I 0)1 0.... 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Acr r# r" "4 r4 0t 0 0 0 0 0%0000 S00 0 v.4 %0 C in Go **** int^ * 9 9 '4".O mon Vo o 0'. m cn C mcc * 9 9 S0% 0 SM C4 M C* CM4 C4 44M C4 A v0 0. 0 0 en ee en an D n O !* 4 4 U S 4( l' a II . a m %ON 0 I lI 1s" 0 a c 00000 NNC4 C4 00000 enel Men en m 0 00 m00 2 113M4 M CM o en o n < i 8< M C 0 A 0 co t Ui4 V4 0 r * m * 00000 ooooo * * 00000 00000 * 9 . 0% OCM f m4 * A 9 Ch 0 0 0 OMWOM8 rlrccN< Ga .4 0 IB p js i i4 I i 1O4.o00 "O0 PQ I 4mmmcmene NM n r4 cc 00 0 0 .o Q 1) 0 CM f4 n C4 rl rP v6tdc 100000 mmmiAAI S. *. n* I (I ooooo o ooo s I0 NNNNC NN N ( 00000 00000 1 00 00oCOCO N N NN 00000 N LA a * I S O S %a Go o o a  olmlopM 00000 Nm r% oo w c000 00 O3mWOM crb *r ca66\o ao "CoO** M M " en in M " r4 "n en 4fe 00000 00000 0 0000 N KclrWaioM OMWOMDr~g ( . * Ci ea \DgN 1U <4e 0 8 41 0 .* ;El a ol 4j Q1 i 1 4: '0 CIr U) Ue 41 0r1\o 0 Ln NM4a 0 C; C;Y z .. e n r4 4: 0 to *00000* U 00000 4 MO Om H ca c(w 0) 0% 0OOO4O 00000 oorO  # P 0 c H V4 CM Pf 1 00 000 on 0 0 Ln a Co oo co o C 00 00 0 o Go Gon o Income 00000 00000 m CM M C C c r4 mn kn %o ooooo % Geno 4 t 0 < Q CMn 0m cn OSAN 0 0 Bw w NE Ei ZNg Cl) Is 5s 0 rs oo000 G4 V4 14 CM eoaoe Ocr)\ drlrN 40000o P1 0 %0D . 11% 00000 S00000 * 4 * 00 a000 Go in m >n m en %oD C co 0>00 rp0 >  6c o in Un V4 4 O 0.NVtU,%O .a a a arc *, a4t g c in o r4 9.1 r41,_ o 4 N % n *a* * MOOO 0 S l S 0 C4 < 4 o ^ n CM "* *1 4 r 4I n I I 'i Di U eg al MU 1 4 % MS Il a 00 . tn * 'A 0 84 I .a 04 i ' *pi c. 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U.'l Cr1)rrr( 00,4 CllCrC4U. eco. o0OCwsi% 000 00w(ri4i oo e 0 %0 CM "4 P4 0%0 00 %DCO mT 0 r4 '0 m 0 0M CM 00000 CM U. MU.' en ** m Sm 0ooo 0 SO0NN 0%< 0 0~ 0M M 4 w4 0 0 v.4 vI 0 SB M W E l < v. a i ** 0 d ' 0 o 4 l *0 m a (a a "a oS eg m n in in m CV NM CM C4C 4 ' Ut~ 8"D~%O0 WI * cwc cn gn enmcnr W M0000 ) al C4 0 C4 C4 SM 0 3 10 EI tn00000 oEl M cn mn cn oo *4 % 'o o' to 0000 ca C 04 O I g 0 M N I 75 00 re 0 0 0 1 N CM Cn Cn 00 r4 a% o %a Ln %so C4 C4 C4 <4 1 cr~OWWWW ..... rr N~cecwe 0w10000 C4mo 4A :C 00000 N CM 04 CNC4 00000 00000 00000 00000 SI 4 u 000; 4 u 043 O. 01 4. OW C0 M S 0 'D 54 I 4 0 P4 0 E C A 00000 C4 'C C CM C CmCM 00000 00000 00000 44 OOmO MN M MNN c m c'4I c4 '4 000 0000 CJ44nU Ur co It VI 4 r C'4 O0o 000  r4l 4 C N 000 0  In U' n Un tn %D o 0 CM4 Ln * r00% en 4 or1M CM ".4C4C' e~O 0P 00 ON 00 0 00000 McO c m MnC V ,4 r4 V4 0 0000 4 00 C4 0 r 0 (P 9 0 CM OrrWyOc rlrM((VC 43 54 U U m 8 42 \0 00 i 0  * O . ..n .a\* c 000 1  fo pD m^ SawAN 00 Ove NN M 0 e 41 4 43 v.4 m Ln co o CM4 C4 NM0 LI 0 Sa 8a ~\ 01 C ~a U 'a 0 ' rS? a i I rm N D cO qC C4 CDi 00000 v to'od 0m oj Ln oo o 00000 0 0 000 l r4 C4 C4 (Owai CMCr) OI\*lOcy 4 i * a *U r AP Pf Pi, mm Hg Substituting the corresponding numerical values, Equation (101) becomes: 5641 AP 12P N 5641 AP = 7.14 x 102 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 119. B. Determination of the Diffusivity of Hydrogen in PalladiumSilver Alloy The diffusivity of hydrogen in palladiumsilver 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 palladiumsilver surface. Using Equation (80) therefore N= C (103) A L but but rat.H gm.moles H2 m. at.PdAg at.PdAg 2 at.H 107 gm.PdAg S11.62 gm.PdAg cm3PdAg 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 103exp( 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 thetwo materials. C. Temperature and Pressure Dependency of Flux of Pure Hydrogen in PalladiumSilver Alloy The fluxes recorded in Tables 1 and 2 are plotted as logNA versus logP A straight line relationship is found as shown in mm t* n 0% 4 rc *n 0 r 4o oo C4 CM C4 V CM * P* g 0n m r o000 o 0 *^ s intf i[ s 0 0 '4 Nr~ U* i i oI0 fOC4 F4%0V4Y1N O\I~tltl * 0 * ON ^ ^ o o o o o o n 00 00 in * 0. 9 . 00000 CO I0CO r 0 0q %C o c0 In co 0n o 4 C) 000 o * 4 CM CMM 00000 % q % N V4 r4 %0 Co 0 C4 4 o4 4 C%44 o'molc 0000 \0oooo 04)\o0 OMWOM NC Un Un 0 in 0 CM ** o C r r4 rI4 P4r 00000 0# 0 000 OMdOlC.4 0 In n 000 r4rI( rl rl 00000 S0 0C 0 0  ooC4o 0CA'00 00000 00000 cn m CV cn v) n 00000 00 000000 cn (A M cn eC 00000 CN CMNC C 4 r4 * *4 4 0 N P 1 40 SI r4* o0 co r r l i4 rll ' "a, 0 pool r4 ! NNN4 NI Ch 04 %Do ir C 1 C4 C4C4 9.4 r4 r4 " 0 u" 0 M 00 4 M C 00000 S 0 U SN e x 4 a 4r4r CO N O N 0 % * O\ O\@hr4r uc 0\0000 wo000O 0 0  0ocn Do oc r4r4 lh C C 00 00 n 00000 cOQM@@r hmaooN 40 0 M0000 M' E r00 00 ( N BL)MNN 00000 '.0 '0 '0 '.0 '0 00000 00000 mC'.)C'. tn o tn a oo i 00o o in r4"4NNN 00000 ..o00 r 0 (n 00 0n 0 0000 o 0 o o< QMWO ,1 M 00000 c4i<^(^ n LrhOVc.In U.)1J 0 rq x "Zil(D cmn cm co m I4 i cn * U. ) ; 0% C 4 4P1 C. 0 0 N 1.48 E' %D C4 AT C4 i fi tn C14 It< *4 4 1 c^ cr cui ^ c o 000 in O n 0 \0 Co 0f *CO 00 0s ' * *1 <;  if ****~ 4) S Nl ~lB a A 0 5 9 S E4 X p8l u In Un 0 0 0  v t4 r4 00000 %0 N 0% 00D 0 o0 O O' QMWQM NC o 0 C a0 in 00000 Sr r4 00 r04 r4 14 P4 *hoooo \0 do ChI 8 r 0vmQM C1C4m 00 s4 4  00000 r4 r41 CJl C4 o'0000 0og'oO'S OmwQAlt~ 00000 WW WW 00000 00000 '0 '0 0 '0 ' or'a'o0' rccmnr e ***** ~o <0 r r4 r m 4 r %a o G0o NM rx C4v 1. r4 10 N r44 r4l N > 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 1718 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  