T —E UNIVERSITYf OF MICHIGAN INDUSTRY PROGRAM OF TEE COLITEGE OF ENGINRING DIF'FFUSION OF TRITIATTED EYDROGEN IN DENSE GAS SYSTEMS OF HYDROGEN, HYDROGEN AND CARBON DIOXIDE, AND,qYDROGEN AND ARGON Ben G. Bray A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in The University of Michigan 1960 September, 1960 -P^458

,G r\- ~W: |sQ ~ v ( D r$ -.

Doctoral Committee: Professor Joseph J. Martin, Co-Chairman Professor Brymer Williams, Co-Chairman Associate Professor Edward E. Hucke Associate Professor Donald R. Mason Associate Professor W. Wayne Meinke Professor Robert R. White ii

ACKNOWLEDGEMENT The author would like to express his a;preciation to several individuals and organizations for assistance received during the work which is reported in this dissertation. First, I am indebted to my wife who typed the initial draft of the dissertation, and offered support and encouragement during the years required to complete this work. Thanks are also due to the members of the doctoral committee for their suggestions which have been incorporated into' this work; to Professor J. J. Martin who originally suggested the problem and became conuittee chairman; to Professor Go B, Williams who served as chairman and advisor during-:the last year of the work; to Frank Drogosz, instrument maker for the L~pa~tment of Chemical and Metallurgical Engineering who substantially assisted in the construction of the fine tube bundle di-ffusion paths; and to John Davis, graduate student, who assisted in some of the preliminary work and prepared Figures 6 and 24 included in the dissertation, Further acknowledgment of gratitude is expressed toward the Department of Chemical and Metallurgical Engineering staff which provided services and funds for the construction of equipment used in the experimental work and which recommended that I receive personal financial aid during the work; toward the E. I. Du Pont de Nemours and Company, the Shell Oil Company, and the Sinclair Refining Company for fellowship grants received during the doctoral work; toward the staff of the Computing Center at The University of Michigan for providing computer time to simplify the data processing operations required by this work; and toward the Indu;stry Program of the College of Engineering and its contributors for preparing and publishing the final manuscript of this dissertation. To all these and many -others, I am indebted for invaluable assistance received. iii

TABLE OF CONTENTS Page ACKNOWLEDGEMENTSOOOOOO o....OO. ooo00ooooo000000.........o iii ABSTRACT o 0 0 0 0 o a 0.... 0 0 0 0 0 0 0. 0 0 00 00 0 0 0 0. LIST OF TABLESooooooooooooo.ooooooooooooooooooooooooooooo. i LIST OF FIGURES......o oooooooooooooooooooo. 00000000.00000 LIST OF APPENDICES..o......600.00000000000000000.000000. xiii I~ INTRODUCTION OQooaooOOOOOOOOOO O O O OOOaOO 000aa0 1 IIo SUMMARY OF WORK IN DIFFUS:ION.. oOo00000 O..00.ooooonQ0oo00o0 4 Theory of DiffusionO O.o.....oOa.o0o...o*o0a0*.O.0. 4 Prior Experimental. Diffusion Investigations..000..... 14 Dense Gas Experimental Work 0........o000000ooooooooo 18 III. DESCRIPTION OF TEE EXPERIMETTAL APPARATUSo.o.0000o0o0.. a 24 The Diffusion Cell..ooQo...O0oooooooooo.ooo0oo0oO 24 The Current Measuring Circuit. o.Oo.000 o.O v...0 32 The Cell Charging Systemo o000o00o0oO.00.0.00W0.0 35 The Constant Temperature Chamber 0 00.............. 39 IVo PROCEDURES USED IN THE DETERMINATION OF DIFFUSION COEFFIC*IENTS.......O 42 ( Oa~j~~CC~EFF32X.Eooo oooo ooboo aoo,0oo.osoo oo oooo o,o 42 Experimental System.sa 000.0o..4000.00000 0000. 42 Experimental Procedure o....oo..000o0....... 0000o....43 Method of Data nalysis 0000o00.000oo.O.OoO.oOoO...ooO 49 V. EXPERIMEN~TAL DIFFUSION RESULTS..9 o00o n 0 00 o 0.00 00 0 55 VI.o COMPARISON OF RESULTS TO REIATED WORK...oooooo. o.00o c.0000. 70 Comparison to Atmospherilc Binary and H2 Sel.fDiffusion Coefficients0....... 0...o.t.o..ooooo.oo 70 Dense Gas Comparisonsn...00000 0.oQo.0n 0.o.C0000 00Q. 79 -V11. -~7

TABLE OF CONTEITS (cont'd) Page VII. DISCUSSION OF ERRORS AND DIFFICULTIES.......e o.....o o o.. 91 VIII. CONCLUSION AND SIMARY..o4............................... o04 IX. APPENDIXo.................................................. 109 X o N0. MECA TE.........o 4 o o o o o o e 184 XIo BIBL I o o o o o o o o o o o o o o o o o o o o o o.o vo o o o o o u o. o o o 188

LIST OF TABLES Table Page I, Diffusion Coefficients at One Atmosphere.....o...... 17 IIo Experimental Data Recorded......................... 47 III. Diffusion Results, HT-H2..................... 57 IV. Diffusion Results, HT-H2-CO2..................... 58 V. Diffusion Resultsy HT-H2-A......................... 60 VI. Diffusivity-Density Product Extrapolated to Zero Density with Temperature Dependence Notedo.0... 71 VII. Comparison of Extrapolated Results to Diffusion Coefficients From the Literature at One Atmosphere~. 77 VIIIo Low Density Comparison Between Diffusivity-Density Product of Converted Values from Equation (34) and Extrapolated Data a-t 355~C....oooo o........o........ 89 IX. Tabulated Data., Excepting Ionization Currents 0...... 11.l XO Ioniza-tion Current Data...o............O 114 XIo Gas Sample Analyses..0.............oooooooooooo..... 1.43 XIIo Radioactive Samples Prepared0...... 149....o... 149 XIIIo Pseudocritical Constants For Experimental Mixtures.. 163 XIV. Pressure Gauge Calibrations.....0 o............ 165 XVo TRhermocouple Cal.ibrations...0.000.00..00.,40..,.0.0. 168 - x

LIST OF TABLES (cont'd) Table Page XVI. Eyepiece Micrometer Calibrations..o.oo.oooooooo..oo;170 XVII. Diffusion Path Hole Size Determination..o 0.. 0 171 XVCIIo Diffusion Cell Chamber Volumes Determined by Weight of Merc~zryo.......................o 173 XIX. Background Current Calibration. Data.....4.... o o.. 177 XX. Fortran Data Processing Program....0............00... 182

LIST OF FIGURES Figure Page 1. The Diffusion Cell....0...0000..........,.0..,,0, 25 2. Microscopic Photograph of Diffusion Path. A 0o0ooooo.0o 31 3o Microscopic Photograph of Diffusion Path B..o........... 31 4I The IonizatiLon Current Measuring Circuit.......... 34 5o Recorder Trace of Ionization Currents Run 84B... 0.... 36 6. The Cell Charging System3........OVOO..0. OOOO.O 38 70 Semi-log Plot of Ionization Current Difference Versus Elapsed. Time for Diffusion Run 84B.0oooooo.o.. o. 52 8. Diffusion. Coeffi cient Density Relationship for HT-H2-C02 at 35 C.... 0 0..0................... o........ 62 90 Diffusion Coefficient-Density Relationship for HT-H2-CO2 at 100C 0 0.................................. 63 10. Diffusion Coefficient-Density Relationship for HT-H2-t at 3550C OOoo. oo000.oooooooooo000000000n.ooo 64 11. Diffusion Coefficient-Density Relationship for HT-H2-A at 1OOC, 0 o.................. o........ u 0 a 65 12. Diffusivity-Density Product as a Funrction of Density for HT-H2-C02 at 35C......oo.....o...o.......o0000000000000 66 13. Diffusivity-Density Product as a Function of Density for HT-H2-C02 at 1O0OC.oo00~0 FO. 0 00 0 a... 67 14. Diffusivity-Density Product as a Funct;ion of' Density for HT-H2-A at; 35OC.o. o o.o oo o o o 68 15. Diffusivity-Density Product as a Fumction of Density for HT-H2-A at 1..00C., o o.O............0..... 69

LIST OP FIG.ZRES (cont'd) Figures Page 16. Reciprocal Diffusivity-Density Product for HT-H2-CO2 as a Function of Mol Fraction of Hydrogen o....o.......... 75 17. Reciprocal Diffusivity-Density Product for HT-H2-A as a Funct:lon of Mol Fraction of Hydrogen................ 76 18 Enskog Theoretical Predictions Compared to Experimental Resulits for HT-H2-CO2 at 35 ~C * OOO ooo o*ooo 81 19. Enskog Theoretical Predictions Compared to Experimental Results for HT-H2~CO2 at 1OO0C......................... 82 20. Enskog Theoretical Predlictions Compared to Experilmental Results for HT-H2-A at 350C..................... 83 21o Enskog Theoretical Predictions Compared to Experime.tal Results for HT-H2-A at 100~C......o000..............00o 84 22. Experimental Results for HTEH2-CO2 Superimposed Upon. the Slattery(41) Corresponding States Correlation..... 87 23. Comparison. of Data to Chou Equation Converted to HT-H2-C02 System by Dilute Gas Diffusion Theory...000.0 90 24. The Tritium Dilution System.........oo. o..oo..o..o..oo 145 25. Concentxrat.ionsCurrent Ratios HT-CH2-C02 at 35 C o.. o 1 52 26. Ionization Current Ratio for Equal Concen.tration Both Chambers. Diffusion Path A..........4........... 153 27o Ion-ization. Current -Pressture Relation for Di ffusion. Cell HTHH2-CO2 at 35~C,, BET Mol. Fraction = 1.o06 x 10 6 154

LIST OF APPENDICES Page A. TABULATION OF DIFFUSION RUN DATA o.Q o....... o o.. 109 B. SAMPLE CALCULATION FOR DIFFUSION RUN 84B..... o 000.... 138 C. PREPARATION AND AN;ALYSIS OF GAS SAMPLES o o o. o O o 1 42 Non-Radioactive Gas Samples.......4......O. 142 Radioactive Sample Preparation.0........... o.o. 144 D. CALIBRATION OF DIFFUTSION CELL FOR HT CONCENTRATION.... 150 Eo COMPRESSIBILITY FUNCTIONS USED FOR DENSITY CALCULATIONS 158 Fo MISCELLANEOUS CALIBRATIONS AND CALCULUATIONS........... 164 1o Pressure Gauge Calibrations...........o 165 2. Thermocouple Calibrations...... o............ 168 3. Diffusion Path Hole Size Determinations.. 0 169 4, Cell Chamber Volume Determinatilons......... 173 5o Cel-l Constant Calculation.......000........ 174 6. Background Calibratiorn. Datao......o. o....oo 175 Go COMP'UER PROGRAM FOR DATA PROCESSING..o o. oo n.o.O 178

I. LNTRODUCTION The molecular interactions whl.ch occur in the gas phase have long been of interest to men irn many branches of science. These usually complex interactions result in a nuumber of phenomena whl.ch are readily noted by even the scientifically untrained i.ndividual~ Some effects of the interactions, such as the macroscopic state effects, are static while others are dynamic with respect to timeo'The phenomenon of diffusion is a physical, dynamic process and is termed a transport property because it occurs as the result of a gradient which causes the space displacement of a certain entity, in this case, of mass. In order to facilitate the quantitati.ve discussion of' diffusion, the coef.fi.cient of diffusion has been defined v'hich provides a means for comparisorn or prediction. of diffusion processes in systems of interesto Attempts have been iade to theoretica@lly predict diffusion in a general. manner, wit h varying degrees of success~ Man.y experimental determinations of specific diffusion coefficients have been madeo At the present ti.me diffusion processes can be qutantitabfi'vely described theoretically to within normal experimnen.tal. accuracy for sille systems at moderate temperatu.res and at pressures less than or near one atmosphereO Theoretical attempts havre not su.ccessfully generalized the description

of diffusion processes at elevated densities where the complexities of molecular interactions are intensified. The investigation described in this dissertation was undertaken in order to attempt to increase the understanding of the diffusion processes occurring in dense gases through the taking of experimental data. The specific objectives realized in the investigation were: l o The modification of the basic quasi steady-state equipment constructed by 0'Hern so that a larger range of operating densities could be investigated. 2, The design and construction of one or more diffusion paths which successfully eliminated any appreciable effects of convection and yet for which the geometry could be satisfactorily deteApined in order that diffusion cell calibrations based on diffusion measurements need not be made. 3. The investigation of diffusion occurring in the two ternary systems, HT-H2-C02 and HT-H2-A and the binary system HT-H2, for which no previous dense gas diffusion data had been taken. Diffusion coefficients have been determined in this investigation at 35~C and 1000C for tritiated hydrogen, BIT, diffusing through hydrogen and three mixtures each of H2 and A and H2 and C02 containing approximately 19, 62, and 93 percent hydrogen. Comparisons of the results have been made with the theory and results of other investigations where

similarities existedo The ensuing text is a presentation of applicable theory and the si.milar experimental investigations from the literature, the equipment and methods used in the present experimental work, and the results and comparisons related to the diffusion processes investigated.

-.4 IIo SUMMARY OF WORK IN DIFFUSION Gaseous diffusion is related to the state variables since diffusion occurs as a result of the same molecular movements which are responsible for the characteristic pressure effect of a confined specific quantity of gas at a given temperature. Diffusion, however, is also time dependent and it is normally defined as the net flow of a given component with respect to time which is caused by diffusion potential gradient, the diffusion occuring in the direction of reduclng that gradient. This definition has been expanded to include self-diffusion in a single component system since it is convenient to think of selecting certain molecules of a system and considering their net migration into parts of the system where fewer selected molecules reside0 This molecular selection in a one-component system can very nearly be carried out in the laboratory with use of radioactive isotopes, stereoisomers or ortho and para hydrogen. Theoretical and empirical attempts to predict diffusion are, then, necessarily associated with the state variables. The theory and experimental work reported in the literature having some direct bearing on this work will be presented in this sectiono THEORY OF DIFFUSION In the attempt to describe unknown phenomena, men search for relations between the unknown and familiar phenomena and make comparisons

between themo Scientists attempt to make quantitative comparisons by finding relations involving certain constants which are hopefully independent of one or more important variables affecting the phenomena. Diffusion is usually described quartitatively by Fick t s Laws which relate the diffusion potential gradient to the rate of diffusion by means of a constant of proportionalityg the diffusion. coefficient, D. If the diffusion potential is taken to be concentration, Fick's first law of diffusion for steady state two component equal molar counter diffusion iso J1 = -D12 V C1 (1) where Jj is the molar flux of compone:nt.1, (d is the concentration of component i, and 1iJ is the diffusion coefficient of i in J' Actually, D1j defined in this manner has been fo,und to be dependent upon the con - centration to some extento According to the theoretical derivations of Enskog (13) and Chapman (8) this dependence could be a maximum of only thirteen percent in a binary system if the ratio of molecular masses of the diffusing components was inmfiniteo This maximumr dependence was derived by first lettling the molar ratio of the t-wo compon.e:.nts approacb zero and then i.nfinityo Experimental deterrmnations of this corncentra-, tion dependence on the diffusion coefficient have been made on. binary systems of the components involved in t!his invest igat;ion. Althlo-ugh the numeri.cal results from the literature are present;ed later in this sectl.on,.

a comparison of the latitude of the actual concentration dependence to the theory is warranted here. For the H2 - D2 system (having the same ratio of molecular masses as the HT - 12 system) the maximum percent dependence was found to be three percent of the average. For H2 - A the maximum dependence was seven percent; for H2 - C02 it was nine percent. For diffuslon determinations inrvolving a sizable concentration difference this concentration dependence causes the resulting diffusion coefficients to be an integral average for the concentrations involvedo For determinations involvin.g only a trace amount of one of the components, the concentration dependence effect is negligible~ In a general t;wo component system involving only diffusion for which diffusion flow is measured wlth respect to a stationary set of axes we must define the molar flux, Ni, of component i for which: N1 = J1 + (N1 + N2) Y1 (2) However when the molar average velocity past the stationary coordinates is zero, as with the use of negl.igible amount of a radioacti.ve t;racer, then N1 = -N2 and N1 = J1o For one dl.mensional diffusion the change of concentration with respect to time of an element o.f volume of unit area cross section to f.ow and Ax thick is the difference between flux in and out divlded by the thickness Ax, or:

-7AJC1) - (JJ)x + l =x D12 () G A x Ax As Ax, Ae, AC1 approa-ch zero: ac a2s cl D12 (4) ae ax This relationship is frequently used as the basis of experimental determinations for the coefficient of diffusion and is often referred to as Fick's second lawo By the method of Enskog and Chapman, theoretical attempts to predict diffusion coefficients are based upon a choice of molecular model which in turn describes the manner by which molecules affect each othero The mathematical models which best predict these interactions are complicated in nature and become very diffSicult to manipulate except in the most ideal conditions. One such mathematical model with which a considerable amount of work has been done is the Lennard-Jones, or 6-1.2, poten.tial model. A rather complete treatment of this model can be found in (17) reference and therefore only a cursory description will be included here. Attractive and repulsive potentials for this model are based on the distance between centers of the interacting molecules~ The attractive forces are inversely proportional to the sixth power of the sdparation; the repulsive forces are inversely proportiornal to the twelfth power

-8of the separation. If two such molecules directly approach each other, they first experience an increasing attraction and then a more violent repulsion as they become very close togethero In space, two molecules could approach in other than a direct collision path and experience only an attractive force. If one considers all random approaches and the resulting angles of deflection and energy transfers as predicted by the potential function, one can calculate a "collision integral", Q (lsl)* which is dependent upon temperature and species of molecules colliding. This collision integral can be used to predict the first approximation diffusion coefficient, D12, of a binary mixture of dilute gases where only two body collisions are likely to occur by the expression: [D12]1= 16 1 1 i)* In this relation, the collision integral a (1,1)* is a function of the reduced temperature, (KT/C12), where E12/K is a measure of the attractive force between the two components and a12 is the collision diameter for (1,2) collisions occurring. The collision integrals for a large range (17) of reduced temperatures are presented in tabular form in reference (7) There is no reason to suspect that Equation (5) represents the best molecular model for theoretical prediction of diffusion coeffici.ents. However, these predictions are probably within the experimental accuracy of most experimental diffusion determinations at low pressures.

-9 Further approximations to diluite gas diffusion coefficients are based on concentration dependence and rarely predict coefficients which. differ, from the first approximation by more than five percent. Different methods of computing second approximations have been. suggested by Chapman and Cowling (8) and by Kihara (22) Both are complicated functions involving the temperature and molecular weights of the components as well as the composition.. Mason (26) has surveyed these two methods of making second approximation calculatiorns and noted that they predict nearly identical results even though the Kihara method i.s reported to be considerably easier to use. These further approximations take the form of corrective factors to the first approximationo [D212 = (2) (6) (c) Based on the principles of Stefan-Maxnell, Wilke (47) derived arn equation which relates the average diffusion coe.fficient of a given component through a multicomnponent mixture to the binary diffusl.vities of the given comaponeam with each of the otherss 1-Y1 = Y2 f _~ + (7 ) D1 D12 D13 In. this equation yi represents the mole fraction of component i, and DT. is the binary, diffusion coefficient~ This relation has been found -to predict the data of Ch.ou (9') wLth excellent accuracy

-10For gaseous systems which are compressed to high densities, a given molecule can be influenced by attractive and repulsive forces of more than one other molecule at a time. The assumption of only two body collisions necessary in the development of Equation (5) is no longer valido In addition, for very dense gases the actual volume occupied by molecules themselves becomes appreciable and the shielding of one molecule by another will cause a differernt number of collisions than would be predicted by the motion of point masses in space. Many attempts have been made to derive applicable relations to represent the actual molecular interactions which govern the rate of diffusion at high densities~ Because of the extreme complexity of the physical situation xand the inabllity to completely describe this situation in a simple manner by mathematical means, a successful rlgorous formula has not been derived which ut.lizes the more realistic molecular force rmodelso The closest approach to a riogorous and applicable relation to predict diffusion coefficients in dense gases was formulated by Enskog and presented in considerable detall by Chapman and Cowling (8)o This theory is based on the rigid sphere molecular model orly, but allows for the appreciable diameter of a molecule in a dense gas with respect to its mean free path. Further compensation for the proximity of molecules has not been includedo The results are again in the form. of a corrective factor, Y, which is applied to the dilute gas prediction, Do, at the

high density' D = Do/Y (8) The factor, Y, accounts for the difference in the probability of collision between low and high density gaseso Enskog made the derivation for selfdiffusion in a system of identical molecules and represented Y by the funlction: Y = y/ 2 Sn -y 3 V Where: Y - -- 1 = -2 3 + 0~6250 ( Tn ) + y= 3 3R 32 4 o 2869 (1 2 na) + 0 115 ( —— n ) + 3 3 (10) In Equatorns (9 ) and (CL),, is the diameter of the rigid spherical molecule, n is the molecular density at the system conditions, and bo is the second virial coefficient for the rigid sphere equation of state. Thorne (42) has modified the theory for use with diffusion. ir:. a. two component system, z12 = 1 +-1n!~1 (8 _ 351_) +_2 2 (8 2.... 12 e n sit (11) Further expansion of Equation (11) has not been atcomplished even though the further terms would make import;n.t contri.butions to Y12 at rather low densities.

-12 Realizing the inadequacy of the rigid sphericpl model to represent actual molecular interactions, Enskog suggested that a better value of y might be obtained from state data by substitution of the "thermal pressure", T(6P/ aT)V, for pressure, P, in the first part of Equation (9). The "thermal pressure" is part of the following differential relation for pressure which is derivable from thermodynamic considerationso EXTERNAL PRESSURE = THERMAL PRESSURE + INTERNAL PRESSURE 5( +0V (5) T (12) v + )( In ordther that D approach Dessure at low density thenbe assumed egligccording to Equation (9) Y RT| (133 In order that D approach Do at low dens'lty then accordi.ng to Equation (9) the product, y, must approach the value of the solid sphere model second virial coefficient, bo, at low density~ In order for this to occur, then, bo = B(T) +' B(T) (14) dT B(T) is the second virial coefficient for a real gas model, the virial equation being: PV -1 + (T + (15) RT V

En the virial equation further terms become negligible as the densilty approaches zeroo According to this treatment, the dense gas correction factor i.s a measure of the inability of the first two terms of the virial equation to represent the actuadl P-V-T relationship0 Slattery (41) has presented an empirical correlation for pre.diction of diffusivities which. is based on the Enskog theory. Since the Enskog development includes the other transport properties as well as diffusion, Slattery has prepared a corresponding states correlation for the prediction of diffusion coefficients by using only state relations and viscosity data. This correlation is in the form of' a chart and relates the ratio of the diffusivity -pressure product at, the desired conditions and the samle product at its dilute gas value, PD/(PD)o, to the reduced pressure; PR, with the reduced temperature, TR9 as parameter0 The resulting chart i.s very similar in. appearanice to the corresponding states compresssbi.ility factor, Z, chart; and not without reason, since: PD Z _RD (~6) (PD)o (0 O p As has been stated, it is felt that density is the state variable which is best suited for correlation of diffusion coefficients~

PRIOR EXPERIMENTAL DIFFUTSION INVESTIGATIONS Many investigators have determined diffusion coefficients for the molecules of one gas into one or more other gaseso Work was first done with gases at nearly ideal gas conditions in reasonably uncomplicated equipment. The experiments were normally based on the two statements of Fick's laws, Equations (1) and (4), the former describing experimental systems in steady-state or quasi steady-state, the latter describing un.steady-state experiments the analysils of which may require complicated mathematics relating the boundary values necessitated by the experimental procedures choseno With an increase of interest concerning the interactions between like and unlike molecules, experimental investigations were carried out with near self-diffusion and diffusion at conditions where ideal gas conditions no-Tonger exist~ Because of the large number of diffusion investflgations which have been made only the ones with some direct bearing on the present work will be included here. Several types of equipment have evolved from the attempts to determine diffusion coefficients but only tewo have thus far been used in dense gas measurements0 The quasi steady-state equipment of interest is described in detail in Section III of this dissertation since it is

the method used for experimental results presented here. The unsteadystate, or Loschmidt (25) type, equipment is usually made up of two similar cylindrical sections initilally containing dissim1lar gases at the same pressure which can be connected elther by turning them into conjuncetion or by removing a partition between them,, Normally the determinations are made by conrnecting the sections for a measured.length of time, then disconnectlng them and determining the mixed average concentrations of the samples remaining in each of the two sectionso Srnce only initial arnd final integrated concentrations are determined, the mathematical analysis becomes a boundary value problem. Certain procedure variations have been utilized which charnge the type of boundary values encountered. See Jost (21) or Crar:k (l ) for specific examples. No low pressure diffusion data for the ternary systems of the present investigation, HT-H2-C02 and BT-H2-A, have been taken, although diffusion coefficients have been determined for the single componrent and binary systems of the compon,ents P.nvclved. Perhaps the best; laboratory determia.rtaM.on of sel fdi affusior. coeffficien.ts invol.'ved the diffusion of para-hydrogeri in normal hydrogen by Harteck and, Schmidt (15). Other approximati.ons to determriation of self-dffusio.n of hydrogen. at'Low pressuxre involved the use of deuterium in the bianary system D2-H2 in the works of Heath, Ibbs, arnd Wild (16) Waldman, (6) ad Groth and Harteca (14) Satisfacto.y agreement w$as found bet,ieen the fou.r

separate determi.natilons after the D21H2 results had been corrected for the molec'ular weight dependence predicted by Equation (5) where: D L 0 1+M21 (17) D12 M12 J ( Thus, for converting isotopic diffusl.on -to selffdiffusion: Dl, = D12 2 1./2 (18) For Equation (18)9 1 denotes natural hydrogen and 2 denotes deuaterium for this application. The deuterium investiga-tions were made in unsteady-state modiffed Loschmidt-type equipment~ The Waldmann experimental work was primarily deslgned for thermal diffusion determinations with the ordi:nary diffusion coefficiernt; bei.ng derived as a secondary result. Several studies of binary diffusion o.- h.ydrxogen and argon at low pressure have been made. Groth an.d Earteck (14) also measured concentration effects on the diffu.sivit,.es of bin,ary mixtures~ For several systems they reported an increase tir. the di.:ffuSiLonL coeffic.,c.ent for increased, mole fraction of the h)eavier com poento Wald Made thermal diffu.slion stu.dies for mutua. difffusLo. in. the E2-Ay system and reported ordinary diffusion. coefficients for thih,s system as welL Boardmanr and Wild (5) modified the Loschm:idt type equipment and made atmosH2-C02 system0 Several other investigators have studied diffusion

-17between hydrogen and carbon dioxide in the -unsteady-state or Loschmidttype cell. Boyd, Stein, Steingrimsson, and Rumpel (6) used interferometric methods of gas composition analysis wit;hin the cell in their determinations. Roth (39) and Lonius (24) also determined mutual diffusion coefficients of H2-C02 at atmospheric conditions, Schafer, Corte, and Moesta (40) used a quasi steady-state type cell in their determinations of the temperature and concentrationl effects on diffusivity in the H2-C02 system at atmospheric pressure. Table I is a composite presentation of self diffusion and binary diffusion coefficients in systems of interest with respect to the present work. These results, when corrected to present experimental conditions, will be compared to extrapolated results from the data taken in conjunctLion wlth this dissertation. TABLE I DIFFUSION COEFFICIENTS AT ONE ATNVSPHERE Investigators Temperature ~C D,cm2/sec H2 - Self Diffusion: Harteck and Schmidt (15) 0 1o285 + 0OQo25 Heath (D2-H2) (16) 15 1024 Groth.and Harteck (14) 99 percent D2(D2-H2) 0 1o135 99 percent H2(D2-H2) 0 10166 Waldmann (D2-H2) (46) 20 1o21

TABLE I (conto) Investigators Temperature ~C D,cm2/sec H2-A Binary Diffusiono Boardman and Wild (5) 20 0.77 Waldmann (46) 20 0~77 Groth and Harteck (14) 99 percent H2(H2-A) 0 0.7418 99 percent A (H2-A) 0 0.6905 99 percent D2(D2-A) 0 0o5345 99 percent A'(D2-A) 0 0.4999 H2 - C02 Binary Diffusion: Boardman and Wild (5) 20 0o639 Boyd (6) 25 0.646 Schafer, Corte, Moesta (40) 100 percent C02(H2-C02) 35 0.720 100 percent H2 (H -C02) 35 0.656 Waldmann (46) 20 0.60 Roth (39) 0 0. 544 Lonius (24) 20 0.622 Chapman and CoVIing (8) 0 0o 550 DENSE GAS EXPERIMENTAL WORK High pressure gaseous diffusion measurements have been. limited in number and scope. Most such determinations have been made using a radio= active tracer material as the measured diffusing component. All have been for the ultimate purpose of determining Fick diffusion coefficienrts, as defined by Equation (1), for the systems and conditions studied. The experimental procedures varied conslderably and both unsteady-state and steady-state techniques are represented in published dense gas diffusion data determlnationso

Several investigations involving carbon dioxide have been made because of the relative ease of the preparation of samples containing known amounts of carbon-14 dioxide~ Timmerhaus and Drickamer (43,44) and Robb and Drickamer (38) have determined self-diffusion coefficients of carbon dioxide in a range of pressures from half an atmosphere to 1000 atmosphereso Although data from these investigations were considerably scattered, a deflnite trend of disagreement from the Enskog dense gas theory was noted at the higher densities~ Enskog calculations for the comparison were made using collision diameters derlved from the LennardJones potential molecular model0 The measurements were made with a series of packed columns; different size columns were used for different pressure ranges, Column calibrations were accomplished at low density by comparison of data with known diffusivities and then overlapping the ranges of succeedingly higher density columnso Radiation from continously increasing concentrations of carbon-14 dioxide at the low concentration end of the column was detected by means of a scintillation crystal arnd counter0 Jefferies and Drickamer (19) used the same equipment for determinations of self-diffusion in methane to 300 atmospheres using tritiated methane as the traced diffusing component. Results agreed well with Enskog calculations to moderate densities. In a later work these (20) authors measured dense gas diffusion coefficients in the C02-(4 system with carbon-14l dioxide as the traced material in an attempt to

-20verfy the agreement and disagreement with Enskog's theory for systems of self-diffusion in CH4 and C02 respectively. To 225 atmospheress a fifty-fi'fty molar percent mixture of these compounds was reported to agree with the dense gas theory. For a seventy-five molar percent C02 mixture, a definite deviation was naoted at the higher densities4 OQHern and Martin (30,31) also studied self-diffusion in C02 14 using a C 1402 diffusing component4 Diffusion. coefficients were determined within a temperature range of 010(00C and wit;hin a pressure range from 2 to 205 atmospheres. The very consistant resul.ts of O'Hern, if plotted as the diffusivity-density product against the density, indicate a small inlitial increase in the product to intermediate densities but a general overall insensitivity of the product to density over the entire range of experimental pressureso These results are not in agreement with Enskog theory predictl.ons based on the solid sphere molecular model which indicate a decreasing p D-product for increasing densityo The diffusion cell used was of the quasi st;eady-state type, the analysis of which was based upon Fick s first law' of diffusion, Equation (1). Since a porous bron.ze plug was used as the diffusion path for the O'Heerm investilgation, a calibrat'ion of the cell was necessary in which high densty diffusivity trends were extrapolated to low density where accurate absolute diffus'ion measurements have been made.

-21 Chou and Martin (910) used the O'Hern diffusion equipment in study.n.g diffuslvities of C 02 in four mixtures of 002 and H2 and three mixtures of C02 and C3H8o Experimental work was carried out between 6 and 250 atmospheres at temperatures of 355~ 38~50 and 1000 centigrade. The same insensitivity of the diff usion coefficilent-density product as a function of density was noted for these two systems~ The form of the Wilke equation, Equation (7), for predicting mult'icomponent diffusion coefficients from binary coefficients predicts the results within eight percent over the entire density range'investigated~ Chou found that D for the Cl402-C02-H2 system varied approximately as the absolute temperature raised to the 1027 pover~ This form of temperature dependence is based on some of the earlier formsE of equations proposed for pred'icting diffusion coefficients which were in turn based on an ideal gas. Becker, Vogell, and Zigan (1) studied nitrogen self-diffusion at 200C between pressures of 20 and 90 atmospheres and found that the denslty-diffusiviLty product was independent of pressure rin this range. Nitrogen-15 was used as the traced component in this system. A similar Investigation by these authors for 002 using C1302 indicated a thirty percent'increase of the producti between pressures of 15 and 52 atmosphereso The suggested explanation for this increase was that carbon dioxide molecules tended to coagulate at the higher densities0

-122 Berry and Koeller ha3ve measured rates of diffusion of binary systems of hydrogen-nitrogen. ard methane-ethar,e at 400C9 600C, and 770C to 670 atmospheres and of binary systems of nitrogen-methane and ni.trogen-ethane at 400C to 170 atmospheres. They found that the calculated diffubsion coefficients based on the Lennard-Jones model with Thorne's binary dense gas correction diverged below their experimental data for increasing densities~ However, the experimental di.ffusivities also gradually diverge below dilute gas predictions, As would be expected the data was predicted with reasonable- accuracy by the Slattery corresponding state correlation. The diffusion cell used for the Berry and Koeller investigation was a high pressure modification of the Loschmidt unsteady-state cell. I.t was similar to the cell used by Drickamer and coworkers exceptirng that it lacked the column packlng which n.ecessitated cell calibrations in the work of the lattero Another differe.nce involved the determination of concentrations, which was accomplished at the end of a given run by mass spectrometry by Berry and Koellero'Teaperature dependence was found to be expornential in form, similar to the dependence predicted by equations for liquid diffusiono -E/RT DL = b2e (19) Timmhaus an Dicamera (44) also found tat their data was predicted by a temperature fun.ctiona. of this form0

(29 3 Mifflin srid Bennett (29) have determined diffusion coefficients by the quasi steady-state method employed b~ O0Hern (30) and Chou (9)Q Self-dffusilon in Argon was studied usnlg the radioisotope Argon-37 at 4904~C in a pressure range between 68 and 291 atmosphereso Although the results were considerably scattered, agreement with the Enskog dense gas theory based on actual P-V-T relatizonships was reported. The data was said to tend below ideal gas predictions d above Eskog predictions based on the soli,d spherlcal molecular model0

III0o DESCRIPTION OF EXPERIMENTAL APPARATUS Much of the equipment used in, this investigation was the same or similar to equipment used by O'Hern (3O) and Chou (9) in experimental work for their doctoral dissertations at The University of Michlgano The major differences from theilr equipment were in. the diffuslon cell, itself, and in the sample preparation apparatuso In Ian attempt toward brevity, the chief purpose of this section will be to thoroughly describe the innovations produced in this work and to treat the equipment introduced by their works in brief descriptions concerned mainly with operating characteristeics It is felt that the sample preparation, equipment can be best described in conjunction with the actual samples prepared, For this reason, description of that equipment is included in Appendix C together with the analyses of samples prepared~ Therefore, equipment described in this section will be l'mited to apparatus utilized d-uring an actual diffusion run0o THE DIFbUSION CELL The diffusion cell used for t;he experimental vwork presented in this dissertatior was similar to the one used by O(Herrn and Chou in their experimental work0 There were two chief differences which will be pointed out in the ensuing description of the cell0 Figure 1. is a sectional drawing of the diffusion cello

-25 - n O U) Ir cr w 0 0 1- W I rI d Q M 0 0 Z I ) f - 01 WU o0 - - 0 r- w * 0 I~~ kO~ I~~~~~~~~~~~0 o0 03 O nL - - 0 -r W ( r~~ ~ ~~~ - IW C) U1: 13U a-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~r 0 U0 o-~~~~~~~~ 0 a. L 0 U% r o=x O O z C" U- Z ~W~~~~~~~~~~~~~~~~~~~~H O cr ~ ~ ~ ~ m O rnU) ~~ I L~~~ VrlllY,I~IIII W IH I- ir O.A w'!-cf)~~~~~~~~~~~~H l~l o U)0 H LLI~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-L w I U)~ ~I - -z C ~I ri o JJ z.... j o 1 1.1 11 W n~. ~lr%ll~P~~~~I O O w> C3 _JT ~ v / 03 (/ -- nn -- O n -J

-26The cell consisted of two chambers, one above the other, connected by a permeable diffusion path which was designed to curtail bulk flow between the chambers once an equilibrium pressure was reached after charging. In the diffusion measurements, gases introduced into these chambers ideally had exactly the same composition except for a trace of radioactive isotope which was introduced in greater concentration into the upper chamber. This radioactive isotope served as the traced diffusing component in the experiment. The concentration of the isotope in either chamber at any time was determined by an ionization chamber technique. The cell body was designed in such a manner that an electrode extended into each chamber which was entirely insulated from the body of the cell. A 200 volt direct current potential was maintained between the electrode in each chamber and the cell body. There was no appreciable potential difference between the two inserted electrodes although they were not connected electrically. Radiation from the radioactive material caused ionization of the gas within the chambers, and the ions were collected by the electrodes and wallso The current resulting from such a collection can be measured and is related to the concentration of the radioactive material in the chamber. If the concentration of the radioactive material is low enough, this relation is a direct proportion. In order to simplify the analysis

of the results, ionization current calibrations of the cell were made to determ'ine the concentration below which this direct proportion relationship was valid~ The results of these calibrations are located in Appendix Do For all experimental runs, concentrations of the tracer were small enough that direct proportionality held between the concentration of radioactive material and current measuredo Continuous current measurements were made for each chamber of the cell, and the result was an accurate time-concentration relationship for the diffusing component. The desired diffusion coefficientswere determined from these time-concentration relationships Because diffusion measurements were desired at pressures of greater than 5000 pounds per square inch, the cell and fittings were designed and pressure tested for greater than one and one-half times this pressureo The cell itself was constructed from a solid stainless steel block 2 1/41 x 2 1/41' x 3 3/4"' The positive electrodes were introduced at opposite ends of the cell body in one inch threaded electrode plugs that screw into similarly threaded sockets in the cell body. Two oneeighth inch pressure tubing fitting threaded sockets were machined into one face of the cell body to provlde an entrance for the gaseous systems into each of the two chambers. The chambers themselves were cylindrical

-28 - shaped, approximately one inch in diameter, and half an inch deep. A partially threaded recepteacle was machined through the one-half inch of steel separating the chambers to accept a flanged permeable diffusion path. This diffusion path, a major difference from previous equipment, was a bundle of fine stainless steel hypodermic needle tubes. Two such tube bundles were constructed, one from tubes having an inside diameter of approximately 0009 inch, the second from tubes with approximately 0o017 inch inside diameter. The bundles were formed in, such a manner that the interstices between individual tubes were completely filled0 Bundle A, with 0o017 inch tubes, consisted of 47 tubes, of which six were accidentally sealed off during construction~ It was constructed by inserting one-inch lengths of the tubing sealed at both ends into a one-half inch long flanged diffusion path shell, dipping the result into hydrochlo ric acid and then into molten solder which flowed into the interstices and was solidified~ The sealed ends of the tubes were then cut off with a cutting wheel and the cut surfaces were ground flat with a fine grinding wheel. At this point it was found that many of the tubes were filled with burrs caused by the grinding or by the grinding material itself. All but six were successfully cleaned out by drilling0 The final length of this bundle was 0.451 inch.

-29Diffusion path B, with 0.009 inch tubes, consisted of 136 tubes of which nine were sealed up during construction. The clogging of holes caused in the construction of bundle A indicated that another method of construction would be necessary for a bundle of tubes of smaller diameter. A two inch length of 0.006 inch wire was inserted into each of 136 one-inch lengths of 0.009 inch inside diameter hypodermic needle tubingo One end of each tube was sealed, sealing the wire in place. The tubes were then placed, one by one, into a one half inch long flanged diffusion path shell, which contained a solidifying epoxy resin mixture, in such a manner that the unsealed ends of tubes tzith tires protrudig were not wetted by the liquid resin. After the resin solidified, the sealed ends of the tubes were cut off and ground to a flat surface with a surface grinding machine. The wires were then removed from the tubes and reinserted from the finished end, The remaining unfinished end was then ground to a flat surface and the wires were again removed leaving the tubes open. Particles of grinding material, grease, and dust were removed in an ultrasonic cleaning instrument bath which contained water and ordinary kitchen detergent. The ends of the holes were inspected and measured by a microscope before installation in the diffusion cell. The measurements of hole diameters and diffusion path length are recorded in Appendix F.

Figures 2 and 3 are photographs taken through a microscope of diffusion paths A and Bo A closer visual examination of the tube bundle ends through a microscope revealsthe openings to be clean and almost perfectly circular in shap.e The measurements of these tube openings are listed in Appendix F. The average deviation of diameters measured from the average of all tubes measured was almost exactly one percent for diffusion path Bo The pressure limitation imposed by the electrode plug design was perhaps the most serlous shortcomiing of the diffusion cell used by 0 Hern and Chouo The teflon insulation used in these plugs offered excellent resistivity characteristics, but, lacked rigidity under the maximum pressures attained in these investi.gations, about 3750 pounds per square inch. In order to increase the pressure range available to this cell, a type of plug was developed which had both the necessary resistivity and strength to withstand high pressureso Since the ionization currents to be measured were of the order -11 -12 of 10 to 10 amperes, it is clear that the electrode plug insulation resistivity must be of the order of 1017 ohms or higher if the background currents produced by the 200 volt potential across the electrode insulation are to be negligible0 Since no commercially available electrodes could match this resistivity and yet withstand pressures of the

-31 -.:< 4 _. -':.:- ~;:.:~,i. ~ j ~.:' -:.-A "Ix.8.':''.:i ""]'':v;'}:'iw8g ~.~~~~~......-,,-,.... X i''''':''.-.....: F?igure 2. Microscopic Photograph of Diffusion Path A. Magnification 96X....... ii ~::~.~.~4... I...?:' ~~:; Fgr}. M c ocpi c P hoogap ofDfuio ahB ~,~Mgifcto 9X.

-32order of 9,000 pounds per square inch with a negligible leakage of hydrogen, the decision was made to attempt to convert an available high pressure electrode making it conform to the resistivity requirements. The attempt was successful. Two modified Conax electrode glands were purchased which would satisfy the pressure requirementso The ceramic insulators and specially designed electrodes were varnished with DowCorning NO, 994 silicone varnish and baked for 25 minutes at 2750C. Using a teflon packing, the carefully assembled plugs satisfied the resistivity requirements. Background currents were not entirely eliminated, however, and were corrected for in diffusion coefficient calculationso The background calibrations Included in Appendix F show that this background was less than one percent of average measurements for 35~C runs. Background currents were somewhat higher for the 100~C runs. THE CURRENT MEASURING CIRCUIT The ionization currents caused by tritium disintegration and collected by maintaining a 200 volt potential between. the electrodes and the cell body were measured by a sensitive current-detecting instrument, a Beckman Ultrohmetero The instrument was actually u.sed as a current amplifier in this investigation. The current from the cell, the order of magnitude of which being micro-micro amperes, was passed thiough a high internal resistance in the Ultrohmeter. The voltage across this

-33resistance was determined electronically and amplified for output to a continuous recorder. The input signal to the Ultrohmeter, being such a small current, was extremely sensitive to fluctuation. For this reason, careful pains were taken to shield the input cables and cable connections. In order that capacitance and resistance effects of shielding do not cause transient measuring difficulties, the Ultrohmeter electronically maintains the potential of the shield to within a few millivolts of the potential of the input lead without sacrificing shielding characteristics. Figure 4 is a schematic drawing of the circuitry employed in measuring ionization currents. For equipment simplification, it was desired to alternately amplify the currents from the two cell chambers with the Ultrohmeter, and record both amplifications on the same recorder chart. This was accomplished by switching the input to the Ultrohmeter from one electrode to the other at convenient time intervals. Since some of the runs lasted approximately two days, this switching was done with a Flexopulse automatic time switch which allows variable equal measuring periods for the two channels of up to one hour. In order to maintain the two electrodes at the same potential and thereby eliminate a potential gradient through the diffusion path, a double-pole double-throw switching arrangement was employed which shorted one electrode to shield potential while the other electrode was connected to the Ultrohmeter input.

-34DIFFUSION CELL 11I I I II I I I I I I I II I I Ir I l......AUTOMATIC lI lI SWITCH IL ~I I!I L I.. _ I. J / —-0 I i' —— i -- ------ I -' —t-IT -— 0?? —-e., II L0 RECORDING | |.X — I I, I-o I; | ~ECK MANl I OTENT METER Figure 4. The onization Current Measuring Circuit. ~~~~~ J...~ +. I I'1 I~~~~I RECORDING 0 -o BECK MAN R A ~ULTRQHMETER POTENTIOMETE Figure 4. The Ionization Current Measuring Circuit.

-35Serious disturbances caused by the switching were effectively eliminated by carefully shielding and desiccating the switched circuit. Two singlepole double-throw microswitches were employed which were mechanically switched by eccentric cams driven by the timing mechanism of the Flexopulse timer. The output signal from the Ultrohmeter is a current which is proportional to the input current. This output current is passed through a wire-wound resistor which is connected between the terminals of a Brown Recording Potentiometer. The resulting recorder chart trace is proportional to the ionization current produced in the diffusion cell chambers. An accurate 500 micro-ampere ammeter was used for balancing the Ultrohmeter output to zero for zero input. Figure 5 is a typical recorder trace taken during diffusion run number 84B. Note the alternate periods of recording the currents from the two diffusion cell chambers. Segments of the broken curves have been connected by lines drawn with ships curves. THE CELL CHARGING SYSTEM The diffusion cell was charged through one-eighth inch ste~l high pressure tubing which was connected directly to the cell body into the two one-eighth inch fitting sockets. The tubing connected to the lower chamber was used chiefly for entrance of non-radioactive gas sample, the upper for entrance of radioactive gas sample. Each tube contained

FIGURE 5 45 RECORDER TRACE OF IONIZATION CURRENTS RUN NUMBER 84B 0 5 10 15 2 25 30 2 35 40 45 50'0 3 -35.... - - UPPER CHAMBER IONIZATION CURRENTS o 5 10 is 20 25 30 35 40 45 50 30 2 0 5 10 15 io 25 30 35 40 45 5I 20 12 15 0 5 10 15 20 25 30 35 40 45 50 10 10 5 S - 0 -tO ---- 2s —- 0 —------- --- -- — 40 —--- 45 50 ULTROHMETER DATA: VOLTAGE RANGE: 2.0 INTERNAL RESISTOR: LOll ORJS

-37No.14. copper wire to reduce diffusion into or( out of the respective chamber through the tubing mouth. Diffusion run pressures were measured by one of two pressure gauges which were connected to the cell through the tubing to the lower chamber. These gauges had ranges of 0-1500 pounds per square inch for the lower pressure runs, and 0-104000 pounds per square inch for the high pressure runs. The gauges were calibrated before and after the diffusion runs, the calibration data being presented in Appendix F. The cell was pressurized to operating pressures by a manually operated hydraulic pressure generator which pumped oil over mercury in one leg of a U-shaped tube, thus compressing gas over mercury in the other leg. This pressurizing system is shown in Figure 6 together with the remainder of the equipment necessary for the cell charging. Non-radioactive gas from bottles (N) was allowed to expand into the pressurizing system through one side of a two-way valve after passing through silica gel for drying. The valve was closed and the manual generator was cranked until the ambient diffusion cell pressure was attained, the diffusion cell side of the two-way valve was opened, and cranking was resumed until either the desired pressure was attained or the crank came to its end. A thirtr cubic-centimeter volume of gas could be elevated in pressure for each complete stroke of the generator, the mass quantity of gas per stroke being;

-38W Izwu I~ ~ ~~~~~Q wml3 au on W ~ ~ W I o z I 0 I~~~~~:,1 I z L w1I I W WI LL W CO I I I~~~~~~~~~t II I 1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ — ~)w ~-Z~~~~~~~~~~~~~~~~~~~~~~~1 cc ) 0 z~ U~~~- a.Z ol >-gf W(I:W ZZ Cz L ))~~~ ZU gr w H~~wt~ Dcf 0: z wS r >M < 0 0 (D 3(3 Q J 5~~~~~~~L O~~~~~~xJ ~~t b ~ ~ ~ hf )

-39dependent upon the available gas pressure~ For the highest pressure runs as many as ten complete strokes of the generator were necessary to bring the diffusion cell to run pressure. Radioactive gas was always added to the diffusion cell when the cell pressure was sufficiently less than the radioactive sample bottle pressure so that no additional pressurizing was necessary to transfer the desired amount of radioactive sample. THE CONSTANT TEMPERATURE CHAMBER This part of the OVHern-Chou experimental equipment was used without modification except for insignificant repairs which were required because the chamber had set idle for several years. It is de(?) (30) scribed more completely in references and. The chamber itself was an air bath constructed of insulating blocks which were cemented together with asbestos. The dimensions of its interior were 18" x 18" x 31". The chamber was heated by four electrical resistance heaters; one was utilized for rapid heating, two large variable output heaters were used for maintaining a constant heating effect during diffusion runs, and the fourth was used as a variable control heater which operated intermittantly during runs and was in turn controlled by a mercury expansion switch and temperature controller. Air was circulated within the chamber by a fan mounted at the rear of the chamber which drew air from the lower part of the chamber past the heaters and forced it out at the topo

-40oSix copper-cons tantan thermocoup'les were placed inside the temperature chamber. Two were embedded in the diffusion cell itself, at opposite ends so that temperature inconsistencies could be detected. The calibrations of these thermocouples are recorded in Appendix F0 The other four thermocouples were located at strategic points of the chamber. All six were connected through a six-position rotating switch to a common cold junction immersed in distilled ice water i9.n a dewar flask and to a portable potentlome ter which was used to determine the thermocouple potentials. The diffusion cell was clamped to a piece of transite insulating board at the center of the chamber and covered by a transite box which was lowered in place at the start of a diffusion run. Although the air temperature in the chamber itself varied as much as hal.f of a degree centigrade during a control heater heating cycle at a chamber temperature of 1000C, the change of temperature of the cell, as indicated by the thermocouples embedded in the cell body, was entirely undetectable during a similar cycle,, The diffusion cell temperature during an entire run was normally constant to withlin 02 of a degree centigrade0 Because the diffusion cell was positioned with one cell chamber above the other during diffusion measurements, it was important that the lower chamber should at no time contaltn gas of higher temperature than that in the upper chamber, since convection would most certainly occur through the tubes of the diffusion path0 For this reason, the upper portion of the cell body was maintained at a slightly higher temperature than the lower portion, a temperature difference averaging

about 0.2 of a degree centigrade. This temperature difference was not difficult to maintain, in fact it would have been far more difficult to prevent, since the freshly heated air from the blower fan circulated from top to bottom in the portion of the constant temperature chamber containing the diffusion cell. Figure 6 illustrating the charging system shows the extent of the equipment located within the constant temperature chamber. Valves on the charging lines to the cell body were mounted within the chamber to insure against tubing heat conductance effects being present in the cell. Although valve stems did necessarily stick through the temperature chamber walls, it was felt that heat conducted along these stems did not appreciably affect the cello The equipment was designed in such a way that, barring difficulties, the constant temperature chamber could be sealed at the start of the first experimental diffusion run and not be opened until the last run had been completed. Actually, the chamber was opened on four occasions to repair leaks in the electrode plugs or the charging system.

IVo PROCEDURES USED IN THE DETERMINATION OF DIFFUSION COEFFICIENTS The basic operation of the equipment used has been included along with the equipment descriptions covered in the previous section. This section will present the experimental work from the standpolnt of actual steps followed, items of data recorded, and methods used in the analysis of the data in order that diffusion coefficients could be determined o EXPERIMENTAL SYSTEMS In the experimental work, diffusion was observed quantitatively in two ternary systems. In both systems tritiated hydrogen, HT, was the radioactive, traced diffusing component. The gaseous diffusion media were composed of, first, mixtures of hydrogen and carbon dioxide, and, second, mixtures of hydrogen and argon. An obvious degeneration of both ternary systems is the diffusion of HT in hydrogen, and this sub-system was also investigated. At first consideration, these systems seem to be two binary component systems with some of the rmolecules of one of the components tagged in such a manner that they can be detected in order to reveal the characteristics of the phenomenon of interest, Indeed, investigators have treated similar systems and phenomona in this manner. The physical dimensions and chemical properties of a HT molecule are very nearly identical. with those of a H2 molecule. Furthermore, an examination of gases used in the diffusion runs would not reveal the presence of a third component except due to radioactl.vity, since the actual

-43ratio of HT molecules to total molecules was approximately one to 2,000,000. However, due to the difference in masses between H2 and HT, they cannot be treated as the same molecule in a diffusion analysis. Diffusion was investigated at two temperatures for each system, 350C and 100 o. EXPERIMENTAL PROCEDURE The experimental work was divided into two basic parts, the preparation of equipment and samples to be utilized in the determination of diffusion coefficients, and the actual measurements pertaining to the phenomena which lead to the evaluation of the diffusion coefficdents. The former part has alread.y been covered in the equipment and sample preparation sections of the previous text and appendix. The function of this section wlll be to describe the latter procedures carried out with the previously prepared equipment and samples. Since it was not necessary that the constant temperature chamber be opened except for repairs, a given temperature was malntained in the chamber during the entire series of runs with a given system at that temperature. Similarly, during runs with a given system composition, the cell did not require complete flushing between runs in order to insure the uncontaminated homogeneous distribution of the two major components. However, since the most general procedure is of interest, these items will be included in the description. The experimental procedure for a data run started by first bringing the constant temperature chamber to the desired run temperature.

-44 This was brought about by operating all four chamber heaters simultaneously until the chamber was at the approximate running temperature desired as measured by the four chamber thermocoupleso The mercury expansion switch was adjusted to make and break contact at this temperature by either adding or removing mercury, a coarse adjustment, or by raising or lowering the contact wire, a fine adjustment. The chamber was then allowed to operate overnight in order that it and the diffusion cell come to equilibrium temperatures. The following day a check was made wi.t+h the thermocouples embedded in the cell body to see if an equilibrium temperature hacteen reached. If no further temperature increase was noted in half an hour, the procedure was continued~ The valve to the mercury leg of the cell pressure gauges was closed, and the cell and pressurizing leads were evacuated to a pressure of 50 microns of mercuryo System gas was expanded into the evacuated portion and then removed by re-evacuation. System gas was again expanded into the evacuated equipment, and the cell was pressurized to approximately 200 psig as indicated by the pressure gauge in the pressurizing equipment~ The valve to the cell. pressure gauges was then opened and these gauges were used in further cell charging operati.ons0 At this point, radioactive gas, from the sample bottle containing the same concentration of major components as the particular system gas, was introduced into the upper chamber of the diffusion cell., The cell. was pressurized to a total pressure of about 400 psig wth radioactive gas, this pressure being dependent upon the desired run operating pressure. It was found that the most stable and accurate measurements of

-45the ionization current could b-e made at the highest range of the Ultrohmeter for which the concentration of HT-ionization current relationship was a direct proportion. The desirability of this direct proportionality has been discussed thoroughly in Appendix D. The Ultrohmeter range satisfying this condition occurred using the 10 ohm internal resistor and the 2.0 voltage range scale. For this range a full scale recorder trace deflection corresponds to an ionization current of approximately 2 x 1011 amperes. All diffusion runs except for a few exploratory runs near the beginning of the experimental work were made using this instrument range. In order to do so, the amount of radioactive sample to be added for a given run had to be calculated so that the right amount of HT was present in the upper chamber at the desired run pressure to give a nearly full scale recorder trace deflection for that chamber. It was desired that the recorder trace for the upper chamber be nearly full scale on the recorder chart in order to take the fullest advantage of the sensitivity of the instruments. Similarly, it was desired that the recorder trace for the lower chamber be close to zero at the start of a run in order that the concentration difference at that time be a maximum. By the method of charging being described, an initial ratio of tritium in the upper chamber to tritium in the lower chamber of ten was usually attained. The radioactive sample was slightly more rich in hydrogen than the corresponding non-radioactive sample due to the method of preparation of the tritiated samples which is discussed in Appendix C. This helped to prevent bulk convection which might have been caused by a slightly higher concentration of hydrogen and therefore lower density gas in the lower chamber,

-46After the radioactive material had been added, the cell was pressurized with non-radioactive sample through the lower chamber to slightly greater than the desired run pressure. A small amount of gas was then released to flush the upper chamber charging tube of tritiumrich gas, thereby reducing the possibillity of HT entering the upper chamber during the run by diffusion. This flush. was also valuable if the amount of tritium charged was greater than necessary to cause full scale chart deflection using the optimum instrument range. The concentration of tritium in the cell chambers began equal.izing by dliffusion as soon as bulk flow through the diffusion path due to the charging operation subsided. As quickly as possible the Ultrohmeter was balanced to zero for shorted input and a satisfactory chart speed and time switch period were chosen and set. The recording potentiometer was then adjusted for zero and standardized and the recorder trace of the alternate chamber concentrations was started, The cell temperature was then determined and recorded from the two thermocouples embedded in the cell body. The cell pressure was read and recorded from the 1500 psi pressure gauge if the pressure was below this value or from the 10,000 psi gauge if above. For runs with pressures above 1500 psi, the 1500 psi gauge was isolated from the system by a valve, Table II lists in abbreviated form the data recorded for a given experimental run.

TABLE II EXPERIMENTAL DATA RECORDED Item Remarks Run number and date Sample percent hydrogen Measured after each run for H2-C02 runs. Other component Carbon dioxide or argon. VoR. Voltage range and Ultrohmeter range, ----- is internal resistor R approximately current (amps) required for full scale deflection. Chart speed Variable from 1 to 6 inches per hour in one inch increments. Charging information Samples used and to what pressure they were charged. Pressure These three measurements were Upper end thermocouple usually made at several reLower end thermocouple corded times during a run. Frequently for overnight runs, only startirg and finishing conditions were recorded. Chart traces of ionization Figure 5 currents and zero current traces Date and time of completion of run Background (each channel) Taken at regular intervals between experimental runs ia less than 1 percent of average ionization currents at 350C.

The end of an experimental run was entirely a matter of judgment or convenience. Upon observing Figure 5 it is seen that the separate chamber ionization current traces approach each other as the conentrations equalize due to diffusion, If both chambers responded identically to equal concentrations of tritium, these traces would come together only after an infinite time. However, since the accuracy and resolution of the equipment and analysis was better when a large ratio of chamber concentrations was present than when the concentration ratio was small, runs were normally stopped, if it was convenient, when the ratio of currents was about a third of the initial current ratio, On a few occasions, the runs were allowed to proceed to "infinite time", or until the ratio ceased to vary. In each case the ionization current calibrations in Appendix D were corroborated; the ratio of lower chamber current to upper chamber current at equalized concentration was always approximately 0.96. As is pointed out in the appendix, this is also the approximate ratio of the respective chamber volumes. After the end of an experimental run, the cell was vented into an operating hood which expelled the slightly radioactive gases above roof level. three stories up. If further runs were to be made using the same concentration of major components, the venting was completed at a cell pressure of approximately 200 psig and charglng for the next run was done with this as the starting pressure. If another concentration or system was to be run next, the cell was completely vented and flushed with the new system gas as previously describede

METHOD OF DATA ANALYSIS The type of diffusion cell used in this investigation was initially chosen because of its simplicity and the relative ease of analyzing the data. It was one of a class of cells termed as quasi steady-state diffusion cells. The mathematical analysis from which a diffusion coefficient is determined from the data is dependent upon two important assumptions. The first is a multi-part assumption which concerns the gradient causing diffusion. It is assumed that concentration is at least proportional to this gradient. This part of the assumption is probably very good for this investigation since the diffusing component, HT, is present in such low molecular fraction, approximately 1 to 2,000,000. The other parts of this assumption are that this concentration gradient is linear through the diffusion path, and that the reference plane which defines the diffusion process is stationary with respect to the equipment. Since the net molar flow through the diffusion path is negligible, this latter part is probably a good assumption. The second assumption is that there is complete mixing in the two chambers of the cell, that the only resistance to transfer by diffusion occurs in the diffusion path. This assumption is also a good one since the cross-sectional area of the chambers is very large in comparison to the cross-sectional area of the diffusion path. Using these assumptions we then can relate the rate of change of concentration in the two chambers to a coefficient of diffusion, D, by Fick's Law.

50 For Chamber 1: V d~~~~C _C Vldl dC = 12 (20) dO dx L. For Chamber 2: V dC _ C 2 V2 dC2 = + DA dC +DA 1 2 dX L (21) dO dx L (21) Where. 0 = time. Vi, V2 - Volumes of Chambers 1 and 20 C19 C2 = Instantaneous concentration in Chambers 1 and 2o A = Open cross sectional area of diffusion path. L = Length of diffusion path. Subtracting (21) from (20) and rearranging: d(Cl C2) -I,;DA (_ _ 1 + (22) (C1 c2) L V1 -V2 This can be integrated to result in: in (C1- C2) - DA ( 1 + 1 ) 0 + constantl (23) L V1 V2 For the concentrations of tritium used, the ionization current, Ij, is proporti.onal to the concentration., Cj, in a given chamber,j. If -the chamber geometry is different for two ionization chambers, a constant of proportionality, f, is necessary in order that a comparison be made between the respective currents produced by a given concentration of

tritium in the two chambers. For the cell used in this investigation this constant was determined experimentally and is very nearly equal to the ratio of the free volumes of the chambers. This calibration is presented in Appendix D. Substituting the respective ionization currents into Equation (23) the result is then: in (fI1 - 2) - DA ) + constant2 (24) L V1 V2 If the natural logarithm of the quantity, (fI1- I2), is plotted versus the elapsed time for a series of values of the currents, I1 and I2, at different times,!e, as recorded on the recording potentiometer trace, the slope of the resulting straight line will be KD, the product of the cell constant, K. A (k1 + 1 ), and the coefficient of diffuL V1 V2 sion at the conditions of the experimental run...Figure 7 is this plot for run 84B. Perhaps a more objective way is to fit the same experimental data to the equation of a straight line by the method of least squares. The equation fitted was: ln(fI1 - I2) A 1 1 (25) L* A _ + - ) = DO + constant3 L V1 V2 The coefficient of time in this equation, D, is the desired diffusion coefficient. The latter procedure is easier if an automatic digital computer is available, and was the method used for this investigation. The computer programming techniques are covered in Appendix G. In the calculations, two more corrections were made in determining the Fick diffusion coefficients. The first is the previously mentioned background current which was subtracted from the respective

-52 - 0 () c) w tO -C IL) l Cl) 9 U 0 w C -P ro Lrx I " M ~t'r.~ - 40 E-,.ri,-1 EQe cd b0.a) 0 0 0 0 0 0 0 SJ.INfl 1HHD ~ H3MOl 3ddfl1dn

-535ionization current from each cell chamber and which was probably caused by the very small conductivity of the electrode plugs. The second correction is made for the HT-H2-CO2 system onlyo Since the sample bottle storage temperature was below the critical temperature of one of the components, carbon dioxide, there was a possibility that two phases could exist in the storage cylinders. For this reason the vent gases after each run were analyzed in the Orsat-type analysis equipment. A small random variation in the hydrogen-carbon dioxide composition was noted between runs from the same storage bottle. The overall variance was at maximum about a percent and showed no definite trends as might be expected if two phases existed continually. Since the variation of composition was small, a correction was made in the calculations to base the runs on a single composition, the simple average. This correction was based on dilute gas diffusion theory, Equation (5), where~ DAB DCD B A/ MA + MC MA MB MA Mc Letting A denote HT, B denote the pseudo property of the H2-C02 mixture which occurred in the diffusion run, and C the pseudo property of the average composition of mixtures of runs made with the same sample bottle, then; (MA + MB) (26) (MA + Mc) The corrections made by Equation (26) were never greater than half a percent of the resulting diffusion coefficient.

-54The Appendix A contains the following information recorded for each diffusion run madeo 1o Run numbero 2. Mole fraction hydrogen. 3~ Chart speed. 4. Average absolute pressure. 5. Average readings of the two thermocouples embedded in the diffusion cell body. 6. Average cell temperatureo 7. Compressibility factor of the diffusion mixture0 8. Ultrohmeter voltage range used for the diffusion run. 9. Values of time at which ionization currents were read from the recorder charts0 10. Ionization currents for each value of time0 Upper chamber ionization current0 Lower chamber ionization current. Zero current chart deflection0

-55V. EXPERIMENTAL DIFFUSION RESULTS The diffusion coefficients calculated from the data taken as described in the previous section are presented in this section. The results are presented in three forms. The first is a complete tabulation, Tables III, IV, and V, of the diffusion coefficients determined for each run subdivided into sections of same composition and tempera'. ture. The second form of presentation is a series of four graphs, Figures 8& 9, 10 and 11, each plotting the relationship of the diffusion coefficient to the density for a system at a constant temperature. Curves have been drawn to associate the data results from each single concentration of sample, The third presentation of results is also a series of four graphs, Figures 12, 13, 14 and 15, each plotting the diffusion coefficient-density product versus the density. It can be seen from Equation (5) based on ideal gases that the diffusion coefficient is inversely proportional to the density at densities where the gas molecules behave ideally. The D p versus p charts indicate at a glance the non-ideality of the particular system with respect to the density since Equation (5) would predict points along a line parallel with the abcissa, The results from both diffusion path bundles are combined in all three presentations. This difference is indicated in each case. A minor portion of the total data was taken using the larger hole size path because it was felt that convection was more nearly eliminated by using the bundle of 0.009 inch tubes,

On each graph of Dp verses p at both temperatures appears a value for the diffusion of HT into hydrogen which represents the experimental atmospheric self-diffusion coefficlent of hydrogen reported by Harteck and Schmidt ( 5) The experimental value has been converted to the HT-H2 system by the molecular weight correction, Equation (17), and to the experimental temperatures of the present investigation by the temperature dependence predicted in Equation (5) for dilute gases: 3/2 D c T (27) t(lel)l Further comparisons of the present results to results from the literature will be made in a following section of this work.

-57TABBLE III DIFFUSION RESULTS, HT -H2 Run Pressure Density Diffusivity, D D lx103 No. Psiae gm. moles/liter cn2/sec x 103 HYDROGEN AT 35 ~C 40B 5394 11.83 4.49 53o16 32B 5244 11.57 4.48 51o 83 37B 5231 11,53 4.55 52.47 38B 5174 11.43 4.70 53573 72B 4388 9.97 5.37 53555 36B 4076 9.o 38 5 59 52.46 34B 3699 8.63 5.98 51.61 31B 2866 6.90 7.71 53o19 35B 2652 6.43 8.20 52~73 29B 2469 6.o 04 8.58 51o82 33B 1994 4-96 10.65 52.83 87B 1671 4 20 12o56 52~ 80 39B 1474 3.75 14.57 54.56 30B 1057 2.732 20.14 55 01 88B 916 2.379 21o74 51Q72 73B 819 2.135 24.93 53 22 HYDROGEN AT 100~C 42B 5117 9.61 6.23 59.85 46B 4667 8.o 90 6o 60 5879 41B 3569 7.05 8o66 61o05 44B 2986 6.oo00 10o 11 6072 45B 2129 4.4o0 13e85 60o 96 47B 2119 4.38 13046 59.03 43B ]1256 2~676 23.04 61.64

TABLE IV DIFFUSION RESULTS, HT-H2 -CO2 Run Pressure Density, p Diffusivity, D Dp x 103 No. Psia gm. moles/liter cm2/sec x 103 XH2 = 0,628 at 35~C 14B 5074 12.84 1.966 25,24 16B 4021 i0o 6o 2.507 26.57 4A 3543 9.46 3.11 29.40 10B 3091 8,34 3 43 28.62 liB 1912 5024 5056 29o11 3A 1361 373 7.46 27.80 12B 1124 3.07 9.54 29.32 15B 686 1 866 16.23 30030 5A 623 1.692 17.71 29.95 XH2 = 0.933 at 35~C 17B 5094 11o33 3.86 43574 18B 4132 9~53 4 67 44. 45 19B 3068 7 36 5 99 44~ 10 20B 1999 5.00 9.07 45,32 23B 1954 4.go 9.27 45.39 22B 884 2. 305 20.01 46 11 XH2 = 0.189 at 35~C 28B 4884 19 61. o646 122.68 27B 3001 15.29 0.974 14go90 24B 2069 10,22 1.778 18.17 25B 1056 3,700 5.30 19.60 26B 513 1, 544 13o 36 20.63 XH2 = 0.628 at 1000C 48B 4979 10o04 2.833 28.44 49B 410o6 8.51 3 52 29,96 51B -2950 6 30 4~ 97 31 30 53B 2109 4,58 7.24 33o16 50B 1498 3.28 10o32 33.85 52B 756 1 670 20,73 34.61

-59TABLE IV (cont.) Run Pressure Density, p Di5fusivity, D Dp x 103 No. Psia gin. moles/liter cm /sec x 103 XH2 = 0.933 at 1000C 54B 5114 9.61 5.17 49~70 59B 4122 7.99 6.51 52.00 56B 4109 7.97 6.12 48.80 55B 2554 5.22 10.15 52,92 57B 1508 3.19 16.38 52.25 60B 1024 2.~ 24.11 53.06 58B 671 1.4b59 36.9 53.83 XH2 = 0.189 at 1000C 61B 5063 14.06 1.246 17.52 62B 4353 12,51 1.460 18.27 63B 2834 8.15 2.637 21,48 64B 1489 3.84 5.92 22,73 65B 718 1.715 13.62 23.37

TABLE V DIFFUSION RESULTS, HT-H2- A Run Pressure Density, p Di~fusivity, ~ Dp x 103 No. Psia gmo moles/liter cm /sec. x 10 XH2 = 0.195 at 35~C 74B 5051 12o51 1.682 21o04 75B 4272 10 93 1.952 21o 33 78B 3300 8.71 2 440 21.25 77B 2401 6o 51 365 23o76 79B 1472 4o01 6o07 24.33 76B 725 1o968 12~47 24~54 XH2 = 0.624 at 35~C 81B 5204 11.92 2 695 32.12 85B 4398 10o36 3o 09 31o 99!A 4074 -9o72 3545 33o50 80B 3544 8.62 3.83 32.98 86B 2775 6.o 93 4.85 3355 82B 2099 5 35 6.47 34.61 83B 1253 3 27 9,99 32 74 2A 936 2.46 14o47 35.67 84B 769 2.033 17553 35562 XH2 = 0.926 at 35 C 66B 5309 1164 4oo00 46,56 67B 4031 9o27 5.o8 47.10 69B 3270 7o74 6.o6 46.96 68B 2417 5.92 8~24 48~75 70B 1489 3 78 12,51 47 10 71B 816 2.127 22.53 47 27 XH 0.195 at 100~C H2 89B 5237 10o.40 2 303 2395 90B 4173 8,59 2,826 24,25 91B 3164 6~70 379 25~40 92B 1998 4.34 6~26 27.18 93B 1209 2. 66 10o 37 27.62 94B 633 1.402 20.11 28o19

-61 - TABLE V (cont.) Run Pressure Density, p Di5fusivity, Dp x 103 No. Psia gmo moles/liter cm /seco x 1096B 5409 10 ~29 3.53 36.27 98B 4459 8.55 4.13 36.o01 95B 3745 7.46 5.13 38.22 97B 2586 5.35 7.14 38.19 99B 1424 3.05 1o 39 40o83 100B 724 1.577 25.29 39~88 XH2 = 0.926 at 100~C 10lB 5144 9.65 5.28 50.95 103B 4318 8.29 6.14 50.91 102B 3086 6,18 8.43 52.08 104B 2460 5.03 10.47 52.72 105B 1381 2.93 18 51 54.21 106B 815 1.762 30.4 53.63

I0 -2 5 4 I 2 2 3 4 5 6 8 10 2 3 4 5 6 8 100 p,GRAM MOLS / LITER Figure 8. Diffusion Coefficient-Density Relationship for HTl-H2-C02 at 35~C.

-638 o~ 8 -3 2 3 4 5 6 7 8 9 10 15 20 p, GRAM MOLS/LITER Figure 9. Diffusion Coefficient-Density Relationship for HT-H2-C02 at 1000C.

4 2 3 0 ~ DIFFUSION PATH A I0 2 3 4 5 6 7 8 9 10 15 20 P,GRAM MOLS / LITER Figure 10. Diffusion Coefficient-Density Relationship for + DIFFUSION P-A at 35C. HT-H2-A at 355C.

-65 - 3 -2 I0 (CJ 98 3 10-3 ~1 2 3 4 5 6 7 8 9 10 15 20 P, GRAM MOLS/ LITER Figure 11. Diffusion Coefficient-Density Relationship for HT-H2-A at 1000C.

-6660 55 o 100 % H - 0 0 0 o 0 50 45 _93.3 ~~~~~~~~40~~0 0 40 o -f35 c~' 30 +~~~~~~~~~~ 0~~~~~~~~~~~~ x 0 25 20 0 /8.9 o~~~~~~~~ 15 10 + DIFFUSION PATH A 0 DIFFUSION PATH B HARTECK AND SCHMIDT (15) 5 0 0 2 4 6 8 10 12 14 16 18 20 P,GRAM MOLS/LITER Figure 12. Diffusivity-Density Product as a Function of Density for HT-H2-C02 at 350C.

-670 )I00 % H 60'( 55 (9 50 45 0 DIFFUSION PATH B A HARTECK AND SCHMIDT (15) I — 40 -0 cn 35 0 30 25 I.9 20 15 0 2 4 6 8 10 12 14 16 18 P,GRAM MOLS/LITER Figure 13. Diffusivity-Density Product as a Function of Density for HT-H2-C02 at 100~C.

-68 - 55 O 0 IOO%H2 0. r |?100 % H2 50 o.- t -I ---- o 92.6 45 + DIFFUSION PATH A I-9w~ ~0 DIFFUSION PATH B 40 A HARTECK AND SCHMIDT(15) O,o 35 30 25 20 0 2 4 6 8 10 12 14 p, GM MOLS / LITER Figure 14. Diffusivity-Density Product as a Function of Density for HT-H2-A at 35~C.

-6960 55 c 45 A HARTECK AND SCHMIDT(15) ~.) 0 40 35 30 25 0 2 4 6 8 I0 12 P,GRAM MOLS/LITER Figure 15. Diffusivity-Density Product as a Function of Density for HT-H2-A at 100~C.

-70VI. COMPARISON OF RESULTS TO RELATED WORK An attempt is made in this section of the dissertation to compare the experimental results presented in the previous section to extperimental and theoretical works found in the literature which are related to the present work. Since little or no data is reported for the same systems as were studied here, extrapolations and conversions to similar reported systems were made using theoretical expressions which are available. In the first part, related low density binary and hydrogen self-diffusion coefficients were derived by extrapolation of the present data and compar-ed to the reported atmospheric density coefficients for the same systems. The second part involves comparison of the present data with the accepted methods-of predicting dense gas diffusion coefficients by theoretical or empirical means. Since the dense gas diffusion data of Chou (9,10) includes the system, C140 -H2-C02, which is very similar to the HT-H2-C02 system reported here, special comparison is made between these results. COMPARISON TO ATMOSPHERIC BINARY AND H2 SELF-DIFFUSION COEFFICIENTS In order to make a low density comparison of the present data with values from the literature, the trends of the dense gas diffusion results as plotted as the diffusivity-density product in Figures 12 through 15, were extrapolated back to zero density. By this means the low density product, (D p )4o was evaluated for each system at each temperature for each composition of the major components. These extrapolated results are presented in the first part of Table VI.

TABLE VI DIFFUSIVITY-DENSITY PRODUCT EXTRAPOLATED TO ZERO DENSITY WITH TEMPERATURE DEPENDENCE NOTED Mole Exponent of Predicted Fraction Arsolute Temperature Hydrogen (Dp)o 35~C (Dp)o 100~C Temperature Dependence 103~ x 103 D 1 T n of Equation xlO~ xlO~ 12 (5) HT-H2 n n 1 o00 53.8 60o7 o.63 o064 HT-H2-A 0o195 25,4 28.8 o.66 0.70 0,624 36.4 41.2 0.65 0,70 o0926 48.2 54.4 o.63 0.70 HT-H2-C02 0.189 21.2 24~o 0o64 0,72 0O628 31.0 35.2 0,66 0.72 00933 46.7 53.4 0.70 0.72 C140H2 -CO02 (Chou data) 1.27 0.72 The remainder of Table VI indicates the temperature dependence of these extrapolated values and shows comparison between these values and the dependence predicted by the Lennard-Jones potential dilute gas theory, Equation (5). The classical form of temperature dependence is that the diffusion coefficient is proportional to the absolute temperature raised to a constant power, D12 a0 Tn. Classical theory also predicts that the exponent,n, is 1 1/2. Since at constant low pressure the density is inversely proportional to temperature, this temperature exponent appears as 1/2 in expressions where the coefficient of diffusion is equated to a function involving temperature and densityo Although the classical theory temperature dependence has been shown to not be valid over a wide temperature range, the form has been retained and experiments

(18) reported in the International Critical Tables indicate values between 0O5 and 100 for the constant exponent of temperature over moderate ranges of the temperature. Over the range of temperature covered in the present investigation, an exponent of 2/3 describes the temperature effect noted for the binary system, HT-H2, and both ternary systems, HT-H2-CO2 and HT-H2-A within seven tenths of a percent. The LennardJones potential predicts an effective constant exponent of the absolute temperature of o0.64 for the HT-H2 system, 072 for the HT-HE2-C02 system and 0~70 for the HT-H2-A system. Chou (9) found that an exponent of 1l27 best described his data in the C 02-H2-C02 system. For the binary system of C14 02C02 O'Hern's (30) experimental diffusion coefficients extrapolated to zero density by means of a diffusivity-density plot at 350C and 1000C are proportional to the absolute temperature raised to the O095 power. The low density product, (D p)o can be predicted accurately for any concentration of either experimental ternary system with respect to the major components, H2-C02 or H2-A, in the vicinity of the experimental temperatures, 350C and 1000C, by Equation (28). This semi-emperical equation is based on the form of the Wilke equatilon, Equation (7), and relates (D p)o to the absolute temperature, T, and the mol fraction of hydrogen, YH2~ 2/3 (D p)o a(T)'/ 15 (28) 1 - (1-0.853a) YH2

-73Where~ (D p)o is in cm o gram mols sec liter T is the absolute temperature in ~K. a = 15j9/(qa2) 12 is the Lennard-Jones,"collision diameter" between the two major components, in Angstroms. Values for the low density diffusivity-density product for HT-H2 can be predicted as a trivial case of either ternary system. The fourteen values of (.D p)o presented in Table VI for various experimental concentrations and temperatures of the investigated systems are predicted by Equation (28) with an average deviation of less than one percent. Chou used a procedure for comparison of diffusion coefficients in a ternary mixture to binary and self-diffusion coefficients from the literature. Since such a comparison is desirable for the present work, a similar procedure will be used here. The systems of study, HT-H2C40Q2 and HT-H2-A, involve three binary mixtures of interest, HT-C02, HT-A, and HT-H2. The diffusion coefficients of the last of these, HI-I2, have been experimentally determined in this work. The Wilke (47) eqUation, Equation (7), is the basis of the extrapolation made to give values of the diffusivities for the remaining two binary systems of interest, HT-C02 and HT-A. As previously stated, this equation relates the diffusion coefficient of one component,in a multicomponent mixture to the individual binary diffusion coefficients of the component with each of the remaining components separately. At constant density, p, for a

-74ternary mixture of components 1, 2, and 3 in which the mole fraction of component 1 is negligible, Equation (7) can be writteno 1 - Y2 ( 1. 1 ) + 1 (29) D1 P D12 P D13P D13 p This form of the equation indicates a linearity between the reciprocal diffusivity-density product of the trace component in a ternary mixture and the mole fraction of one of the other components. The values of this reciprocal at y2 = 0 or y2 = 1 are respectively the reciprocals of the products involving the two binary coefficients of diffusion. Figures 16 and 17 are plots of the zero density reciprocal diffusivity-density products versus mole fraction of hydrogen for the two ternary systems studied. Although the four points for each isotherm do not fall exactly along a straight line, that form of representation is satisfactory within the experimental accuracyo Values for the diffusivity-density products of the related binary mixtures, HT-C02 and HT-A, were evaluated from these figures by extrapolation to the ordinate where the mole fraction of hydrogen is zero, This value of the product at YH2 = 0 represents the diffusion coefficient at the particular temperature for dilute gas diffusion occuring as predicted by the dilute gas diffusion equation, Equation (5). Values for the coefficient of diffusion evaluated at one atmosphere from these extrapolated product values are presented in Table VII together with values obtained from the literature

-75 - 60 -- 50 40 k 10 10 0 0.2 0.4 0.6 0.8 1.0 MOLE FRACTION HYDROGEN Figure 16. Reciprocal Diffusivity-Density Product for HT-H2-C02 as a Function of Mol Fraction of Hydrogen.

-76 - 60 50 40 0 20 I0 0 0.2 0.4 0.6 0.8 1.0 MOLE FRACTION HYDROGEN Figure 17. Reciprocal Diffusivity-Density Product for HT-H2-A as a Function of Mol Fraction of Hydrogen.

TABLE VII COMPARISON OF EXTRAPOLATED RESULTS TO DIFFUSION COEFFICIENTS, cm /sec FROM THE LITERATURE AT ONE ATMOSPHERE DHT_H2 DHT-CO2 DHT-A 35 ~C i00 oc 35 C 100 ~ 35 ~C 100l ~0C This Investigation 1.36 1,86 0.47 0o.64 0.57 0.78 Harteck and Schmidt 1.362 1.862 Heath, Ibbs, and Wild 1.39 1.90 Waldmann 1.32 1.80 o0.48 o.66 o.61 o084 Groth and Harteck 1.389 1,899 0o.615 0.852 Boardman and Wild 0o 05 0o700 0,61 o.84 Boyd, Stein, Steingrimsson, Rumpel o0495 o.688 Schafer, Corte and Moesta 0.52 0.72 Roth 0.485 0.675 Lonius 0.492 0.682 Chou 0,490 0 754 Equation (5) 1.357 0.507 o0607 The literature coefficients have been converted to the experimental temperatures by the dilute gas theoretical temperature dependence of Equation (5) which for constant pressure is: T3/2 D T (27) Q(l1l)* Since some of the diffusivities reported in the literature regarded diffuslon in mixtures containing ordinary hydrogen, a conversion was also necessary to account for the difference in molecular weight between tritiated hydrogen and ordinary diatomic hydrogen. This conversion was made according to the molecular weight dependence predicted

-78by dilute gas diffusion theory which is~ D2 + I M2 11+/ (17) L M1M2 For the transposition of the coefficient of diffusion of a binary mixture to that of another binary mixture which differs from the first only in that one component of the second binary is another isotope of one of the original components, this expression can be expanded to: 1/2 2 Ml + M3 D12 = D 13 (26) _M3 M1 + M2~ + Since the molecular weight difference between isotopes is normally small, inaccuracies which may be caused by this conversion are smal.l The points attributed to Chou were transposed from values reported at 350C and 100~C for the binary system of C1402-H2o These points were derived from the C14 02-H12-CO2 ternary system by the Wilke equation extrapolation used in the present work. The isotope conversion equation, Equation (18), was used to transpose the diffusivity for both members of the Chou binary system since the desired comparison was between data for the HT-C02 system0 The Chou value of the diffusion coefficient at 350C agrees well with the value derived in this investigation. However, at 100~C the values are considerably differento This fact was noted in the previous discussion concerning temperature dependence which indicates that the data from the present

-79investigation agree with the dilute gas theoretical predictions with respect to temperature effect better than do the data of Chouo Comparison of the results, excepting those of Chou, shows the values of the diffusion coefficients derived from the present investigation for the binary systems, HT-H2, HT-C02, and HT-A, to be respectively 0o4, 5.2, and 6.9 percent below the average of the converted values from the literature at 35~0C. At 1000C the respective values are 0O39 6.8, and 7.6 percent below the literature values, It must be pointed out that this extrapolation is at best an approximation and should bnly be regarded as a rough check of results. DENSE GAS COMPARISONS. The theoretical treatment of Enskog and Chapman which was outlined in the theoretical section of this dissertation is the only nonempirical reference of comparison of the dense gas diffusion data presented here. As was stated,this theory was developed for the solid spherical molecular model and allows for the size of individual molecules to be appreciable with respect to the distance between molecules. Calculations for the systems of this study have been made assuming the ternary systems to be binary systems composed of the two major components in each, H2-C02 and H2-A, This approximation is satisfactory since the theory is chiefly based on volumetric or state considerations and the ternary mixtures investigated here were binary mixtures from this viewpoint; the molecular fraction of HT in each case was negligible, about 5 x 10-7 The results of this comparison are presented in Figures 18,

-8019, 20, and 21 for the HT-H2-C02 and the HT4H2-A systems at 550C and 1000C respectively~ At a given density,,P Equation (8) can be rewritten as. (D p) 0 D p = o (30) y where (D p)o is the dilute gas prediction at that density. This dilute gas product is constant with respect to density since according to dilute gas theory the diffusivity is inversely proportional to density. The theoretical. curves on each graph for HT-H2 are calcula'ted using the extrapolation, (D p)o, as the dilute gas prediction and calculating the correction factor, Y, by the Enskog relation, Equation (10), for a single component gas, The theoretical curves for mixtures of H2-C02 and H2-A were calculated by the Thorne relation, Equation (11), for binary gas mixtures using the (D p)o's extrapolated from the data. It will be noted that the theoretical predictions based on the solid spherical model. diverge below the experimental data in each case0 It appears that the theoretical curves calculated by the Thorne expansion approach the data at the higher densities0 This is due to the fact that unavailable further terms of the Thorne expansion are becoming important at the higher densities~ The Enskog expansion for single component systems includes a sufficient number of terms so that further terms are neglibible within the experimental density range0 It is clear that theoretical predictions based on the solid spherical molecular model are inadequate for the prediction of diffusion at high densities for the systems studied0

-81 - 60 55 C/VSKo,3 50 100 %H DA TA 45 93.3 40 35 0 0 3 62.8 25 20 18.9'5 I ISK MLAN LINEE FOR DATA'HRV 10 0 2 4 6 8 I 0 12 14 16 18 P, GRAM MOLS / LITER Figure 18. Enskog Theoretical Predictions Compared to Experimental Results for HT-H2-C02 at 355C.

-8260 t IDA 7A 1 1)5-1100 % H2 55 50 93.3 45 o~~~~~~~~~~~~~~~~~~~~~~~~~~ 0-i N0 4 00 ww 00 _35 — 62.8 30 25 18.9 20 MEAN LINES FOR DATA Sol 15 0 2 4 6 8 I0 12 14 16 18 P, GRAM MOLS / LITER Figure 19. Enskog Theoretical Predictions Compared to Experimental Results for HT-H2-C02 at 100~C.

-83 - 55 MEAN LINES FOR DATA ENSKOG-THORNE SOLID SPHERES 50 45 45, ic~92.6 % H 40 - 35 62.4 30 25 20 0 2 4 6 8 10 12 14 P, GRAM MOLS/LITER Figure 20. Enskog Theoretical Predictions Compared to Experimental Results for HT-H2-A at 35~C

55 50 9 1 I I I ~ — 2.6 I% H2 45 0 2 40 62.4 % 35 30 25 MEAN LINES FOR DATA 20 — ENSKOG-THORNE SOLID SPHERES 0 2 4 6 8 10 12 14 P,GRAM MOLS /LITER Figure 21. Enskog Theoretical Predictions Compared to Experimental Results for HT-H2-A at 100~C.

-85Enskog realized that although the solid spherical model made the mathematical solution to dense gas transport property predictions possible, that that model would not be representative of real gas molecules. He suggested, then, that the "thermal pressure" of the gas species, determined from experimental data at the desired conditions, be substituted into the derived equations in place of the pressure evaluated according to the equation of state for solid spheres. This "thermal pressure" and its substitution into the Enskog theory has been treated in the theoretical portion of this paper. Since experimental state data can be represented by a compressibility factor, Z(T,V), in the equation of state: PV Z (T,V) RT (31) Then the partial derivative of pressure, P, with respect to temperature;, T, at constant specific volume, V, can be evaluated: ( = R [Z(TV) + T (Z(T,)) ] (2) 1 Z V- T (32) Substituting this expression into Equations (13) and (9) and making cancellations where possible, the resulting expression for the Enskog density correction factor, Y, to the diffusion coefficient is: h Z(T,V) + T( Z _v)) (33) bo J- 6T~a

-86 - where bo B (T) + TdB(T) (14) dT If accurate data for the second virial coefficient, B(T), and the compressibility, Z, are known, a more realistic prediction for the diffusion coefficient can be made. Using the excellent synopsis of data for hydrogen prepared by the National Bureau of Standards (48), this method of computation of the dense gas diffusion coefficient was carried out for hydrogen for the experimental range investigated. The results of this calculation are presented in Figures 18 and 19 together with the predictions based on the solid spherical molecular model. It is to be noted that this method better predicts the data of this investigation than does the method based on the rigid sphere model. The theory of corresponding states has been used by Slattery(41) to prepare charts for predicting dense gas coefficients of diffusion. Figure 22 is a reproduction of the corresponding states chart with the results of this investigation: for the HT-H2-C02 system superimposed upon it. A similar chart can be found in reference (37) upon which the bulk of dense gas diffusion data is superimposedo The apparent agreement noted at higher densities is to a large part due to the fact that the chart as presented differs from a compressibility factor chart only by the factor of D/(D)o which is never very far from unity' within the range of the chart.

0 OD t~~~ z 0 2 W P 0 ~~ ~ ~ ~ ~ ~ ~ ~~J., 0 =., lLiOZ Q:Io0 Ch (1) ~_) 02..... 0 M~~ (P — 10 1V) OI Oa c\j~~~~~~~~~~~~c z8 OOO CD w c/)C/ e-'-(0-I-I tf)CD (I)J00 N N - - N~~~~~~~~~~~~~z Z H~~~~~~~~~~~~~~~~ ~N-o ~o ~~~~~~~~~~oo a \ \~\,'el ( I U): / / 0 u I~0 - (3.) O ~O r-..b 1'' to 0 CI d /o 0,iI III /,1. N. -, 0,.. ~?~. C., o) N - o0,- - o o o 6 o 6 o 6 oi c ~(dOa) daO,Il~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~xC M cU O Q, aD ~~~~~~~~~~~~~~~e u, \r~~~~~~0, 0 0 o O~~~~~do)~~~~~~ 1-lo

-88The only quantitative comparison with dense gas diffusion data which will be made here involves a ternary system which very olosely rese.nbles the HT-H2-C02 system of this investigation, the diffusion data reported by Chou (10) with the C1402-H2-CO2system. Chou fitted his data empirically to an equation the form of which was based on the Wilke equation for predicting multicomponent diffusion coefficients. Since the Chou data diffusion coefficient-density product did not vary appreciably with density, the empirical equation contains the inverse proportionality of diffusivity to density predicted by dilute gas theory. D 14 = 3.2 x 102 7 (4) p (1-0.82 y'H) where Y' H = yH2/(1-ycl402 ). Since YC1402 was negligible for each diffusion run, Y'H = YH2' In order to convert the diffusion coefficient of C 02 through mixtures of H2 and C02 predicted by this equation to the coefficient of HT through mixtures of H2 and C02, dilute gas theory relationships were used. This is justified since Equation (34) is basically the form of dilute gas theory with respect to the important variables of temperature, density and composition. The conversion used corrects for the molecular weight, M, the effective collision diamter, a, and the collision integral, a (1a 1)* of the diffusing Oonmponent with respect to the major components, hydrogen and carbon dioxide. 1/2HT C140 av DHT = DC1402 CMHT2 MHTC0 + T

-89In this relation Mavg represents the average molecular weight of the mixture in which diffusion is occurring. The resulting comparison between converted values from the Chou empirical equation and the data points from this investigation taken for the HT-H2-C02 system at 350C is presented in Figure 23~ The converted equation values for the diffusivity-density product agree well with the extrapolated low density products, (D p)o of the data from this investigation. Table VIII presents this comparison numerically. However, except for the high hydrogen content mixtures, where the transposition made is likely to be less accurate, the HT-H2-C02 results diverge below the converted Chou predictions with increasing density. TABLE VIII LOW DENSITY COMPARISON BETWEEN DIFFUSIVITYDENSITY PRODUCT OF CONVERTED VALUES FROM EQUATION (34) AND EXTRAPOLATED DATA FOR HT-H2- CO2 AT 35~C Mole Fraction H2 (D P)EQ.o (34) (D p) Percent. 1.03 x 110 Difference* 0o189 20.9 21.2 1.4 0.628 30o4 31.0 2,0 0~933 44.9 46.7 4.0 1.o000 51.9 53.8 4.o * Percent Difference 100~ (D - (D E ( 4) (D P)EQN (34)

-9055 -.. ~ 3 ~ 10 0 H 5 45 cb 93.3 40 ucn 35 CY I 1 62.8 ~~30~ 0 20o I VALUES FROM EGN. (34) CONVERTED TO HT-H -CO SYSTEM 15 O 10 0 2 4 6 8 10 12 14 16 18 20 p,GRAM MOLS/LITER Figure 23. Ccnparison of Data to Chou Equation Conmrerted to RT-E2-C02 System by Dilute Gas Diffusion Theory.

-91 VII. DISCUSSION OF ERRORS AND DIFFICULTIES Since the experimental works of O'Hern and Chou were carried out with much of the same equipment used in this investigation, many of the sources of errors and difficulties were the same as those described in their dissertations. However, the introduction of new equipment, materials, and techniques into the present work has created a few new ideas to be discussed with the old ones in this section. ACCURACY OF RESULTS The comparison of the results of this investigation to the theoretical and experimental results of other works has been presented in the previous section. This comparison reflects the general accuracy of the results presented here. In order to show the consistency of the results of this investigation, smooth arbitrary lines have been drawn on the respective graphs of results which appear to best fit the data at each single temperature and composition of gas. Since the graphs of the diffusion coefficient-density product, Figures 12, 13, 14, and 15, most clearly indicate the deviations from these smoothed result lines, they have been chosen for use as the basis of the discussion concerning consistency. With the exception of the two runs, runs 13B and 21B, for which no diffusivity could be evaluated, the average percent deviation from the smoothed results is about one percent. Only two, runs 24B and 83B, of the ninety-five successful diffusion data runs with the smaller hole diffusion path, path B, show greater than five percent

-92 deviation from the lines drawn. A total of eight runs have greater than a three percent deviation. The five experimental, runs made with the larger hole diffusion path, path A, in place have a considerably larger average deviation percent from the smoothed results, slightly less than four percent0 A greater deviation might be expected for runs with this path since bulk convection is more likely to occur through the larger holes. However, no trend of deviation between the runs with different diffusion paths was noted. Sixteen diffusion runs were made with the HT-H2 system at 35 C. The average deviation of these runs is less than one and onehalf percent0 Because of the large number of points taken for this single temperature and composition, perhaps this is the best estimate of the overall consistency of results. However, although the data seem to be inclusively consistant, several systematic sources of error to be considered here might well cause the absolute error of the results to be different from the error indicated by the percent deviation from the arbitrarily drawn smooth lines0 Most of the possible causes of error to be considered here would cause deviations which would show up in the mathematical analysis of the resultso According to the analysis of the diffusion cel.l, the Fick coefficient of diffusion is determined from the slope of the linear relationship between the logarithm of the concentration difference between chambers of the cell and the elapsed -time of the diffusion run0 Sizeable error caused by a phenomenon which is not proportional to the

concentration difference would result in curvature of this supposed linear relationship. Only the analyses of the two unsuccessful runs, runs 13B and 21B showed evidence of curvature of this relationship over the entire duration of the run. Some other runs showed curvature during the first ten percent of the run which could be attributed to the period when the system was coming to quasi steady-state or during the last part of the run when the chamber concentration differences were too close to equilibrium to give accurate results. MASS TRANSFER AT THE SURFACE Use of a diffusion path which restricts transfer by bulk convective processes may introduce transfer by a mechanism which is related to the amount of surface area per unit length parallel to diffusional transfer. Unless the driving force associated with the surface transfer is the same as that causing diffusion, an appreciable surface transfer wiuld cause curvature in the semi-log straight line relation. ship just discussed. The two diffusion paths with different sized hole were used in order to detect surface transfer which might be proportional to the diffusion gradient. Diffusion path A, constructed of tubes with an average inside diameter of 0,0428 centimeter has a ratio of cross sectional open area to parallel surface area which is 1l9 times as great as the same ratio for path B with tubes having an average inside diameter of 0.0228 centimeter. Although the proof of the absence of surface transfer is not irrefutable because of the scatter of the data,

-94the virtual agreement between results using the two diffusion paths indicates that surface transfer is not a substantial part of the mass transfer occurring between chambers of the cello More conclusive proof could have been gained if an even greater variance of the open area to surface area had been attained. However, construction of a bundle of smaller tubes than those used in path B would have been a nearly impossible task. Threat of convective transfer would have seriously curtailed the use of a bundle having much larger diameter holes than those in path Ao END EFFECT OR CONCENTRATION GRADIENT IN THE CHAMBERS The mathematical analysis of experimental work was partially based on the assumption of complete mi.xing in the two cell chambers. This assumptlon disregards the presence of end effects at the openings of the tubes of the diffusion path. The close agreement of the results with low density values from the li.terature is an indirect indication of the lack of important end effects since the cell constant was entirely determined from cell geometry. The ratio of diffusion path to chamber cross sectional areas was almost exactly one percent. The resistance to diffusional transfer of the diffusion path was therefore nearly completely controlling, and very little of the total concentration gradient could have been maintained in the chambers. It is felt that no appreciable error was caused by end effects0

-95CAPILLARY EFFECT In order that the results be representative coefficients of diffusion for the gaseous mixtures studied in the investigation, the number of collisions of gaseous molecules with molecules in the walls of the diffusion path must be negligible in comparison with inter-gaseous molecular collisions. A comparison involving the path minimiun tube diameter to the maximrum mean free path of molecules at diffusion run conditions indicates compliance to this condition. The mean free path of a hydrogen molecule at the minimum experimental density of 1.402 gram moles per liter is 3.1 x 10-7 cm. Pollard and Present (34) have derived an expression which predicts the diffusion coefficient, D, of rigid spherical molecules in a capillary from the diffusion coefficient in free space, DFS. D = DFS (1 - ) (36) where X is the mean free path and d is the diameter of the capillary tube. The term 3/4 x/d is, then, the fractional correction which must be made for diffusion occurring in a capillary. The maximum value of this term for the experimental conditions.is 0.000010. Although the expression is valid only for rigid spherical molecules it serves as a satisfactory indication of order of magnitude of the capillary effect. The error introduced by using the bundles of tubes as diffusion paths is probably negliglble.

MEASUREMENT OF CELL GEOMETRY There is a possibility of error resulting in incorrect values for the cell constants of the two cell configurations. Perhaps the largest uncertainty could be attributed to the measurement of tube diameters. Although considerable care was taken to remove burrs covering portions of the ends of tubes which might have been causea'uring the construction of the tube bundles, the measurement of the ends of the individual tubes may have caused the introduction of error. The incomplete sample of tubes actually measured may have introduced error, although the averaged results for the two entirely independent sets of measurements for tube bundle B produced the same average tube diameter well within one tenth of a percent. The measurements on path B3, themselves, had an average deviation from the average of approximately one percent. Additional error could have been introduced by determinations of the volumes of the cell chambers and diffusion path length. Average deviations from the averages of these measurements were considerably less than one tenth of a percent, however, It is estimated that the maximum possible error in determination of the respective cell constants is two percent. DENSITY DETERMENATION The results of this investigation as presented as functions of the density of the diffusing gases are relatively sensitive to errors made in determining the densities, Since excellent data concerning the state behavior of hydrogen at the experimental conditions are available,

-97little error was introduced here. However, PVT data for mixtures of carbon dioxide and hydrogen and argon and hydrogen are not available for the greater part of the experimental conditions. For the lower fraction hydrogen runs generalized compressibility correlations were used to predict the experimental densities from the experimental temperatures and pressures. Pseudo-critical properties were calculated by the methods of Prausnitz (35,6) for use in conjunction with the Pitzer (3233) compressibility tables. State conditions for mixtures of carbon dioxide and hydrogen were predicted with a maximum deviation of 2.2 percent and an average deviation of 13 percent in the temperature range between 2730K and 4750K and in the pressure range between 3000 and 7500 pounds per square inch absolute by these correlations. Further discussion concerning the state relations is presented in Appendix E. It is felt that the compressibilities of mixtures of hydrogen and argon are predicted by the Pitzer-Prausnitz relations with at least as good an accuracy as the less ideal mixtures of hydrogen and carbon dioxide. CONVECTIVE TRANSFER The temperature of the cell body was maintained at a nonfluctuating temperatuire by surrounding it with insulating material within the constant temperature chamber to eliminate'"thermal pumping" which might occur between the cell chambers0 The diffusion path was constructed of small diameter tubing in order to reduce the possibility of convective currents causing transfer of material between the chambers0

-98With the diffusion cell resting with one chamber above the other, two further measures were undertaken to reduce tendencies toward convection in. the cell. The upper chamber was maintained at approximately one tenth of a degree centigrade higher temperature than the lower chamber during 350C runs and three tenths of a degree centigrade higher temperatureduring the 1000C runs. The radioactive gas mixture introduced into the upper chamber contained approximately one percent more hydrogen than the mixture in the lower chamber. This radioactive mixture, on the average about one tenth of the total amount of gas in the upper chamber, caused a result of about a tenth of a percent higher hydrogen content in the upper chamber. Both of these measures made the gas in the upper chamber slightly less dense than that in the lower chamber, thus reducing the possibility of interchamber convection0 Although convective transfer could probably not be totally eliminated, it is believed that convection between chambers was reduced to a negligible amount except for runs 13B and 21B which indicate a definite non-linear relationship between the log of the concentration difference and time. IONIZATION CURRENT MEASUREMNT The chief difficulties encountered encountered during the investtigation involved the reduction of errors and inconsistencies introduced by measurement of the ionization currents. The small order of magnitude of the currents measured was responsibl.e for these difficulties0 A considerable length of time was required for the preparation of a measuring circuit for which the background and leakage currents

-99 - were small with respect to the desired ionization currents. Detailed descriptions of the circuit components are located in Section III of this dissertation. The background currents were never entirely eliminatedo For runs at 350C the background current for each channel was less than one percent of average current measurements. For runs at 1000C the background currents varied, although they remained reasonably constant for a given series of runs at that temperature. After each of the two occasions of electrode plug insulation repair the values for the background current of both channels differed from those from before the repair. The first repair was necessitated after soap solution had been placed on the electrodes to locate a gas leak which had been detected at the start of a series of runs at 1000Co The soap solution destroyed the coating of silicone varnish which had been used to increase the resistivity of the electrode plug ceramic insulators0 The second repair was necessitated after mercury from the compression leg had. entered the d.iffusion cell and similarly destroyed the varnish coating. On both occasions operations were shut down for about a week while satisfactory varnish coatings were replaced. Backgrounds for both channels varied from two to about five percent of average current readings for runs at 100 ~Co The error i.ntroduced by background currents at 35~C is probably rot appreciable. The variation from constancy of the backgrounds at 1000C could conceivably have introduced an error of as much as three percent into the resultso This error is probably smaller, however, since the difference between backgrounds of the two channels of current

-1.00omeasurement is the important quantity~ The close agreement between the temperature dependency of the experimental results and the values predicted by dilute gas theory and from data in the literature indirectly indicates that the error caused by uncertainty in the measurements of the background currents at 1000C is small. The background. measurements are covered in greater detail in Appendix Fo The absolute accuracy of the Beckman Ultrohbmeter is stated to be between three and five percent for the range of measurements of this investigation.0 However since only relative accuracy is required for the measurements resulting in diffusion coefficients, the error introduced by this instrument is believed to be considerably less than one percent0 The recorder speeds of from one to six inches per hour were all checked. and found to be accurate to within one-tenth of a percent0 MATERIAL LEAKAGE Although various amounts of gas leakage were detected during the investigation after a change in operating temperature and once due to valve wear, there was no occasion of serious leakage during a diffusion run. The maximum percent leakage per unit time occurred during run 102B at a pressure of 3086 pounds per square inch and a temperature of 1000C during which a oa8 percent drop in pressure occurred in the 4 1/2 hour duration of the run0 For most runs no appreciable drop in pressure was noted. The maximum fractional error introduced by a materlal leak would. be equal to the fractional drop in pressure divideed by the total fractional change in concentration in a unit of time. This

-101 - maximum possible error amounts to 1.0 percent for the run having the greatest percent leakage. CHEMICAL REACTION It is conceivable that components of the diffusion mixtures could react together and thereby cause erroneous results. Hydrogen and argon do not react together. The possible reaction between hydrogen and carbon dioxide, H2 + C02 = H20 + CO (37) has been discussed by Chou in connection with his diffusion work. He found that the maximum equilibrium concentrations of CO and H20 would be 0.68 percent and 0.22 percent at 100~C and 35~Co There is considerable question as to whether equilibrium would be reached in a reasonable length of time. The effect of even the equilibrium concentrations of these materials would be considerably less than the sum of the percentages of CO and H20 since the diffusion coefficient is not sensitive to the presence of small amounts of impurities. The diffusion coefficient could be affected by the radiation and surface catalyzed reaction, 2HT = H2 + T2 (38) since HT is the traced diffusing component. Since the concentration of H2 is extremely large with respect to the other members of the reaction and since T2 is a comparatively unstable molecule at room

-102 - temperature, one of tritlum's chief desirable characteristics is its affinity for replacing hydrogen in organic compounds and thereby "tagging" molecules, there is little chance of an. appreciable amount of T2 being present in the dlffusion mixture with respect to the amount of HT present. The calculated equilibrium ratio of T2 to HT is 00000055 at 280C for the most concentrated radioactive sample handled in the investigation after the initial tritium dilution~ The values of the equilibrium constants used for the calculation were reported by Mattraw, Pachuchi, and Dorfman (27)o ADDITIONAL SOURCES OF ERROR Some other possible sources of error which have been thoroughly discussed by Chou and O'Hern will be mentioned only briefly here because it is thought unlikely that an appreciable error could result from them. Diffusion through the tubing connections to the cell body could conceivably cause small amounts of tritium to enter or leave the cell chambers and thereby introduce error into the results. The open cross sectional areas have been reduced to a minimum by insertion of 14 gauge copper wire into the tube openings. High concentration HT gas was flushed from the tubing to the upper chamber before the start of a run to reduce the driving force causing diffusion through this tubing entrance The presence of radioactivity in the diffusion cell might possibly cause reduction or enhancement of the diffusion occurringo O'Hern made three diffusion runs at.approximately the same density with

l103widely different concentrations of C1402, the radioactive component. He reported that radioactivity had no apparent effect upon the diffusion coefficients determined by the type of cell used in the present investigationo The pressure and temperature expansion difficulties associated with the cell used by O'Hern and Chou which changed the chamber volumes and were caused by the flexability of the teflon insulators was no problem in the cell used in this investigation, since only rigid materials were exposed to the conditions in the chambers. Although the total absolute error introduced by these possible sources could conceivably exceed five percent, it is felt that the actual error is less than two percent. DIFFICULTY IN DIFFUSION PATH CONSTRUCTION The most time consuming task connected with this investigation involved the construction of the diffusion paths used. The detailed methods of construction of each are described in Section III of the dissertation. Each path was the result of many unsuccessful attempts over a period of months0 These pains were taken because it is felt that the resulting tube bundles were the heart of the investigation.

CONCLUSION AND SUMMARY The primary purpose of the work covered in this dissertation was to investigate diffusion in the dense gas phase for systems for which there has been no such data available. Accordingly, Fick diffusion coefficients have been determined and are reported here for two ternary systems, HT-H2-CO2 and HT-H2-A, and one binary system, HT-H2, at temperatures of 35~C and 1000C and to pressures of 370 atmospheres. Three mixtures each of the two ternary systems were investigated; the mixtures contained approximately 19, 62, and 93 percent of hydrogen and negligible traces of HT, the remainder in each case being respectively carbon dioxide or argon. Except for the larger molecular weight of tritiated hydrogen, diffusion in the HT-H2 system could be thought of as self-diffusion since the physical sizes of the two species of hydrogen molecule are nearly identical~ The diffusion coefficient-density product for each constant composition of the systems studied decreased with respect to increasing density at both experimental temperatures. This decrease with increasing density was less pronounced for the high hydrogen content mixtures than for the high carbon dioxide or argon content mixtures. The maximum percentage decrease noted within the range of densities investigated occurred for the 19 percent hydrogen, 81 percent carbon dioxide sample at 350C which had a 40 percent drop of the produ.ct below the value of the diffusivity-density product extrapolated back to zero density. The results presented for the systems are consistant with

-105 - respect to themselves, the maximum and average percent deviation of the individual data points from arbitrary smooth lines drawn through the points at each given concentration and temperature being six and one percent respectively. The diffusion cell used for the investigation is of the quasi steady-state type. It is felt that this cell is superior to others used in similar investigations in some respects. One advantage stems from the automatic continuous monitoring of concentration in both chambers throughout the entire diffusion run. This type of concentration determination quickly indicates irregularities which may occur and makes possible the utilization of the data from only the best part of the diffusion run. Methods involving only initial and final composition measurements produce results which must include transients which occur at the start of a run. The mathematical simulation of a diffusion determination for the cell of this investigation is also far less complicated than of those which require the solution of boundary value equations based on Fick's second law. The cell used in the present work required no calibration based upon diffusion results0 The construction of tube bundles from fine stainless steel hypodermic needle tubing allowed the determination of the cell constant to be made entirely from measurements of the cell geometry0 Electrode modifications made in this investigation extended the density range of the O'Hern cell substantially, and did away with chamber volume expansion due to internal pressure since only rigid materials of the electrodes were in contact with the Internal conditions.

The results of the investigation were found to compare reasonably well with results from the literature. The results, extrapolated to low density showed good agreement with the Wilke (47) equation for prediction of multicomponent diffusion coefficients from binary coefficients of the components. 1 Y1 Y2 + Y7_ +._ (7) D1 D12 D13 The binary coefficients of diffusion for HT-C02 and HT-A evaluated by the extrapolation of the Wilke equation to zero mole fraction of hydrogen show fair agreement with values of the binary coefficients from the literature which have been converted to allow for the difference in molecular weight between H2 and HTo The experimentally determined values for the diffusivity of HT in hydrogen extrapolated to one atmosphere agree to within 0.4 percent of the average of converted values from the literature. The temperature dependence of the extrapolated low pressure values of the diffusivity agrees well with dilute gas theory predictions based on the realistic Lennard-Jones potential0 Values of the diffusivity-density product extrapolated. to low density are proportional to the absolute temperature raised to the 2/3 power to within 0.7 percent for all compositions of the three systems studied. The Lennard-Jones potential theory predicts an effective constant exponent of O.64 for HT-H2, O070 for HT-H2S-CO2 and. 0.72 for HT-H2-A for the temperatures investigated.

-107The predictions of the Enskog (13) dense gas theory based on the solid spherical molecular model diverge below the experimental results for the diffusion coefficients for increasing density. The apparent fair agreement between the experimental results and the Thorne (42) expansion for the dense gas correction to dilute gas theory occurs because important further terms of the Thorne expansion have not been derived theoretically nor evaluated. The Enskog theory based on evaluation of the "thermal pressure", T (6p) from actual state data of the diffusion mixture shows closer agreement to the results for HT-H2 than do the Enskog calculations based on the solid spherical molecule. It is believed that similar calculations based on actual PVT data of the respective H2-C02 and H2-A systems would predict the experimental diffusion coefficients at the investigated densities with reasonable accuracy. However, the lack of such state data makes this prediction impossible. The results of this investigation have fair agreement with the Slattery corresponding states correlation, but the ultimate value of this chart is questioned since the major contribution of the deviation from the low density values, to which the correlation compares high denslty values, is due to the compressibility of the gases of the diffusion mixture rather than to the diffusion coefficient. Since part of the dense gas diffusivity experimental data reported by Chou (10) involved a system, C1402-H2-C02, which was very similar to the system, HT-H2C02, of this investigation, a special comparison between these results was made, The respective values agree to

within four percent at low densities but the values from the pxlesent work are increasingly loker than the Chou values at higher densities. The values attributed to Chou which were converted to the HT-H2-C02 system by dilute gas theory relationships for this comparison were evaluated from his empirical equation which predicts inverse proportionality between the diffusion coefficient and. the density at all. densities investigated. The larger than theoretically predicted temperature dependence noted by Chou for the C1402-H2-C02 system was not observed for the similar HT-H2-C02 system of this investigation. Recent data reported by Berry and Koeller (3) and Miffl'in and Bennett (29) indicate the systematic decrease of the diffusivitydensity prod.uct with increasing density which was noted. for the results of this investigation. The author would like to recommend further attempts to relate the dense gas diffuslon data with either theoretical or empirical state investigations. Since diffusion in a binary mixture is chiefly a function of (1,2) collisions, or interactions between the two different species of the mixture rather than between members of the same species, perhaps an investigation involving the non-idealities of mixing of gases would clarify the dense gas diffusion picture to some extent.

APPENDIX A TABUIATION OF DIFFUSION RUN DATA 1. Table IX, Run Data Excepting Ionization Current Data. 2o Table X, Ionization Current Data. -lo9

-110The uncorrected ionization currents listed in this appendix are in chart units since the analysis of the slopes in order to determine diffusion coefficients did not require further conversion to current units in amperes nor to concentration in mass units per unit volume. However, the netessary equations to make these conversions will be presented here in case such a conversion is desired. It will be remembered that the absolute accuracy of the Ultrohmeter is stated to be from three to five percent for the ranges utilized in this investigation. Although this accuracy probably did not enter appreciably into the diffusion results of this work, it must be taken into account for any conversion from chart units to absolute current units. The relation for conversion from chart units on a 20 space full scale chart is: I, amps m (I,chart units) (Voltage Range) (39) (Internal Resistor)(17a 36) The voltage range refers to the Ultrohmeter range and is listed for each run in Table IX. The internal resistance for every run of the investigation was 1011 ohms. For runs taken using a 50 space full scale chart, the factor, 1736,9 must be replaced by a factor which is 5/2 times larger, 43540. The currents converted by this formula must first be corrected for the chart deflection for zero current and the background currents listed in Appendix Fo The respective concentrations may be determined from the thus determined currents by determining the concentration-current ratio for the particular run pressure from Figure 26 of Appendix D.

-111 - TABLE IX TABUIATED DATA, EXCEPTING I ONIZATI ON ICURRENTS Run H2 Mole Chart Pressure Average Avg. Compressi- Voltage Number Fraction Speed Psia Millivolts Temp. bility Range Thermocouple ~C Factor Upper Lower LA 0.624 1 4074 1.407 1.403 3550 1.128 2.0 2A 0o624 6 936 1,408 1.403 35.0 1.022 2.0 3A 0.628 6 1361 1.418 1.4L4 35.2 0o910 2.0 4A 0,628 2 3543 1.417 1.414 3552 0.910 0.5 5A 0.628 6 623 1,402 1,398 34.9 0.960 1,0 lOB 0O628 3 3091 1.405 1o401 34.9 0.997 5.0 llB 0.628 3 1912 1.401 1.399 34.9 0.982 5.0 12B 0,628 3 1124 1406 1.403 355.0 0.984 2.0 13B 0,628 1 4176 1o408 1.404 35.0 1.039 0.5 14B 0,628 1 5074 1.407 1.404 3550 1,063 2.0 15B 0,628 6 686 1.401 1.398 34.8 0.989 2,0 16B 0.628 2 4021 1.402 1.399 34o9 1.021 2,0 17B 0.9396 1 5094 1.406 1.404 35.0 1.210 5.0 18B 0 9334 2 4132 1.409 1,406 35.0 1.167 2.0 19B 0o9316 2 3068 1.407 1,405 35.0 1.121 1.0 20B 0.9335 4 1999 1.409 1,407 35.0 1,076 1.0 21B 0.9390 6 909 -- 1404 1.402 34,9 1,037 5.0 22B O o 9330 6 884 1,403 1.401 34.9 1 032 2.0 23B 0,9264 4 1954 1.403 1.400 34.9 1.074 2.0 24B 0.1889 1 2069 1.403 1.401 34.9 00545 1.0 25B 0. o1820 2 1056 1.403 1.401 34.9 0.768 1.0 26B 0o1921 4 513 1,403 1.401 34.9 0.894 2.0 27B 0.1839 1 3001 1.405 1.403 34o9 0.528 1,0 28B 0.1924 1 4884 1.406 1.404 35.0 0.670 2.0 29B 1.000 4 2469 1.407 1.403 3550 1.101 2,0 30B.l o 000 6 1057 1.404 1.402 34.9 1.041 5.0 31B 1,000 4 2866 1.407 1.404 35.0 1.118 2.0 32B 1,000 2 5244 1.406 1.404 35.0 1,220 2.0 33B 1.o000 4 1944 1.401 1.399 34,9 1.082 2,0 34B 1.000 3 3699 1,404 1.402 34.9 1.153 2.0 35B 1o000 3 2652 1.408 1.406 35.0 1.109 2.0 36B 1.000 2 4076 1.406 1.404 35.0 1,169 2.0 37B 1.000 2 5231 1.404 1.402 34.9 1o221 5.0 38B 1.000 2 5174 1.409 1.407 35.0 1.218 2.0 39B 1.000 6 1474 1.402 1.399 34.9 1.059 2.0 40B 1.000 2 5394 1.406 1.403 35.0 1.227 2.0

4112 - TABLE IX (cont.) Run H2 Mole Chart Pressure Average Avg. Compressi- Voltage Number Fraction Speed Psia Millivolts Tempo bili ty Range Thermocouple ~C Factor Upper Lower 41B 1,000 3 3569 4.291 4,271 100,4 1,126 2.0 42B 1,000 2 5117 4,271 4,252 100.1 10183 2.0 43B 1,000 6 1256 4.277 4.262 10001 1o043 2.0 44B 1.000 4 2986 4,277' 4,262 100.1 1.105 1.0 45B 1.000 5 2129 4.282 4.268 100.2 1.075 5.0 46B 1.000 3 4667 4.259 4.245 99.8 1.165 2.0 47B 1.000 6 2119 4,258 4.247 99.8 1.075 2,0 48B 0.6342 1 4979 4.268 4.247 99O9 1.102 2.0 49B 0,6277 1 4106 4.267 4.248 99.9 1.072 2.0 50B o0.6380 3 1498 4.267 4.247 99.9 1.015 2.0 51B 0,6264 2 2950 4.261 4,246 99,8 1,040 2.0 52B 0.6272 6 756 4. 262 4 243 99.7 1 oo6 2,0 53B 0,6264 3 2109 4.268 4.248 99,9 1.024 2.0 54B 0 9329 2 5114 4,268 4.251 99.9 1o183 2.0 55B 0o9268 4 2554 4.267 4o251 99.9 1.088 2,0 56B 0.9279 3 4109 4.268 4.250 99.9 1.145 2.0 57B 0.9352 6 1508 4,262 4,245 99.7 1.050 2.0 58B 0.9323 6 671 4,261 4,246 99.7 1.022 2.0 59B 0.9287 3 4122 4.265 4.253 99.9 1.146 2.0 60B 0,9257 6 1024 4,262 4.246 99.8 1.034 2,0 6l1B 0,1924 1 5063 4.269 4.255 99,9 0o800 2.0 62B 0o1925 1 4353 4,272 4.262 100.0 0.773 2.0 63B 0,1975 1 2834 4,268 4.257 100.0 0.773 2.0 642B 0 1894 2 1489 4,266 4 253 99 9 0 862 2.0 65B 0o1905 4 718 4.266 4.253 99o8 0,930 2,0 66B 0,926 2 5309 1o409 1.405 3550 1o227 2,0 67B 0o926 2 4031 1.41.0 1.407 35.1 1o170 2.0 68B 0o926 4 2417 1,408 1o405 355.0 1,099 2.0 69B 0.926 3 3270 1.409 1,406 35~0 1.136 2.0 70B 0,926 5 1489 1,409 1.406 3550 1.o60 2.0 71B 0,926 6 816 1,409 1.407 35 0 1.032 2.0 72B 1,000 2 4388 1,410 1,407 35.1 1o184 2.0 73B 1.000 6 819 1.409 1,405 35o0 1o032 2.0 74B 0,195 1 5015 1o408 1,405 35o0 1o086 2,0 75B 0.195 1 4272 1241o 1,408 35o1 1.052 2.0 76B 0.195 4 725 1,409 1,407 3550 00991 2,0 77B 0o195 2 2401 1,409 1o405 3550 0.993 2.0 78B 0,195 1 3300 1,410 1.406 35l1 1c019 2.0 79B 0o195 3 1472 1.410 1.407 35o1 0.989 2.0 80B 0.624 3 3544 1.409 1.406 35.0 1o106 2.0

-113TABLE IX (cont.) Run H2 Mole. Chart Pressure Average Avg. Compressi- Voltage Number Fraction Speed Psia Millivolts Temp. bility Range Thermocouple ~C Factor Upper Lower 81B 0,624 1 5204 1.409 1.406 35.0 1.175 2.0 82B 0.624 3 2099 1.409 1.407 35.0 1.055 2.0 83B 0~ 624 5 1253 1.408 1.405 35.0 i.030 2,0 84B 0.624 6 769 1.410 1.408 35.1 1,018 2,0 85B 0.624 2 4398 1.411 1.408 35.1 1.142 2.0 86B 0.624 3 2775 1.409 1.406 35.0 1.078 2,0 87B 1.000 6 1671 1.Qo4 1.402 34.9 1.068 2.0 88B 1.000 6 916 1.407 1.405 35.0 1.035 2.0 89B 0,195 1 5237 4.267 4.246 99,8 1.119 2.0 90B 0.195 1 4173 4.273 4.253 lQO. 1.080 2.0 91B 0O.195 1 3164 4.276 4.255 100.0 1.049 2.0 92B 0.195 2 1998 4.280 4.256 100.1 1,022 2.0 93B 0.195 L ~ t 209..28 4262 100.2 1.009 2.0 94B 0 195 6 633 4270 4.253 100.0 1.003 2.0 95B 0,624 2 3745 4.285 4.265 100,2 1.116 2.0 96B 0o624 1 5409 4.287 4.266 100.3 1.168 2,0 97B 0.624 3 2586 4.286 4,264 100.2 1.074 2.0 98B 0.624 1 4459 4.285 4.263 100.2 1,137 2.0 99B 0.624 5 1424 4.284 4.260 100.2 10038 2.0 100B 0,624 6 724 4.284 4.264 100.2 1.020 2.0 101B 0,926 1 5144 4.283 4.260 100.2 1.185 2.0 102B 0.926 3 3086 4,281 4.258 100oo 1.110 2.0 103B o,926 2 4318 4.282 4.260 100.2 1.158 2.0 104B 0,926 4 2460 4.257 4.247 99.9 1.086 2.0 105B 0.926 6 1381 4.274 4.254 100.0 1.048 2.0 106B 0,926 6 815 4.274 4.254 100.0 1,028 2.0

TABLE X IONIZATION CUaRRENT DATA Run No, Time (Chart Spaces) Ionization C-urrents (Chart Units) Lower Upper Zero 1A 2 7, 43 47,84 3.65 4 9,94 46.15 3o65 6 12,15 44,55 31 65 8 14,113 43,05 3165 10 15482 41.64 3.65 12 17.25 40o39 3065 14 18455 39,27 3o65 2A 3 7.87 49,01 3165 6 10, 53 47.23 3.65 9 12q85 45 50 3.65 12 14,94 43.91 3. 65 15 16.73 42.,50 3,65 20 19,23 40 51 3.65 25 21,23 38,84 3 65 30 22,84 37.40 3o 65 3A 3 3,66 13,92 1 54 12 4,55 13o07 1.53 21 5 30 12 38 1o 53 30 5o 88 11.81 1.53 39 6,,36 11,33 l 52 48 6,77 10o 95 1, 52 57 7,13 10,65 1.52 66 7*39 10.39 1.53 75 7,61 1018 1, 53 84 7,80 10o01 1.52 93 7,96 9,85 1,52 102 8,09g 9,74 lo51 4A 2 4, 58 17 89 1, 52 10 5,44 17,22 1.52 20 6,34 16,43 1.51 30 7,06 15, 76 1 51 45 7*,93 14, 93 1.50 60o 860 14,30 1,54 75 9.04 131574 1,55 90 9,46 13.34 1,53 105 9.74 13100 1.52 120 10.11. 87 1o 53 135 10l536 12,o69 1.53 150 10,50 L2. 53 1T 51

-115TABLE X (cont,) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Iower Upper Zero 5A 2 4.43 17.48 1.59 5 5,39 16.68 1.60 10 6,67 15.53 1.61 15 7,60 14, 61 1.62 20 8.36 13.88 1.61 25 8.92 13.32 1.6o 30 95533 12,88 1.60 35 9,69 12.54 1.59 40 9,95 12,28 1.59 45 1o, 14 12. 07 1. 58 50 10.29 11,92 1.58 55 102o40 11.80 1.57 60 10,52 11L71 1.56 10B 5 3.82 14.80 1.61 15 4,.59 14,31 1.62 25 5,27 13.75 1,63 35 5.84 13.28 1.63 45 6.34 12,88 1.635 55 6.77 12.428 1o63 65 7o15 12.14 1.63 75 7 47 ll 87 11.87 1,63 85 7074 11.63 1.63 95 7,98 11, 40 1 63 11B 2 3*26 13,22 o 59 5 4.11 12o,90 1,58 10 4.58 12,45 1.58 20 5.36 11.68 1,57 30 5-97 11.07 1,57 40 6,44 10,57 1.57 50 6 82 1o. 18 1,58 6o 7,13 9.91 1 59 70 7,40 9,68 1.6o 12B 2 5 23 172 46 1.58 5 5,93 16,88 1o 58 10 6.88 16,o04 1,58 15 7.67 15,29 1,58 20 8.32 14.67 1.57 25 8,87 14,16 1o 57 30 9.28 13572 1056

TABLE X (cont.) Run No, Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 35 9.63 13D38 1.56 40 9.94 135 08 1.60 13B 2 7.27 13.83 1.61 5 8.08 13o 20 1.60 10 8.74 12.62 1.59 15 9.1 12.29 1.58 20 9,32 12.07 1.56 25 9.48 11.9o2 154 14B 5 4.93 16.26 1.54 10 5.80 15o87 1.54 15 6.45 15.51 1.,55 20 7.02 15013 1.55 30 7.92 14.40 1o55 35 8.29 14,0o6 o 55 45 8.88 13550 1o 56 55 9.538 13o08 1.56 65 9.70 12.76 1.55 15B 2 5.52 18.90 1.58 5 6.17 18.35 1.58 10 7.11 17.52 1,58 15 7.89 16o77 1.58 25 9.11 15.63 1.58 35 9.98 14.79 1. o 58 45 10.58 14.20 1.58 55 11.03 13579 1.58 16B 5 4.91 17.91 1.59 10 5.89 17.21 1.62 15 6.82 16.52 1.63 20 7.63 16.02 1.68 25 8.26 15.49 1.68 30 8o 73 15o03 1.68 35 9.17 14.63 1o 68 40 9~55 14.29 1.68 45 9o 88 14.02 1.68 50 10O14 13578 1.68 55 10,35 130.57 1.68

TABLE X (cont.) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 17B 5 3.73 13.68 1.60 10 4.84 12.82 1.61 15 5 70 12.06 1.62 20 6.35 11o37 1.62 25 6.86 10.92 1.61 30 726 10,53 o 60 35 7.57 10.22 1.59 40 7.80 9.98 1.58 18B 5 5-76 17.63 1.62 10 6.57 16.91 1.61 15 7.28 16,30 1.60 20 7.87 15.72 1.59 25 8o38 15.23 1.58 30 8.81 14.79 1.57 35 9.17 14.43 1.56 40 9.47 14.12 1.55 45 9.72 13o83 1054 50 9,93 13.57 1.53 55 10.14 13.36 1.52 19B 2 7.02 19.32 1.56 5 7.68 18 72 1.55 10 8.61 17.89 1.53 15 9.37 17.18 1,51 20 9.96 16.55 1.50 25 10.48 16.04 1.49 30 10,90 15,62 1,48 35 11.23 15.27 1.46 40 11e52 14098 1.45 45 11074 14.77 1.44 50 11.o90 1457 1,42 20B 2 5.63 13.88 1061 5 5.98 13556 1.60 10 6.48 13.11 1.60 20 7.27 12,37 1o59

-18 - TABLE X (conto) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 30 7.83 118o 1.58 40 8.26 11039 1058 50 8.59 11005 1.57 21B 10 5.24 14.59 1.56 15 6.14 13.86 1o57 20 6.9o 13519 1 o 58 25 7.48 12.63 1.59 22B 10 4031 13.47 1.58 15 5.14 12.73 1.57 20 5.83 12,10 o157 25 6.41 11o 56 1.56 30 6.86 11.14 1.56 35 7.21 10.78 1.55 23B 10 4.47 16.92 1.52 15 5.27 16.17 1051 20 6.oo 15.50 1.49 25 6.59 14.92 1.47 30 7.13 14.39 1,45 40 7.94 153056 1o43 50 8.55 12o92 1.43 60 9.02 12o43 1.43 24B 5 4.63 17o16 1.40 10 5,22 16.54 1.30 15 5~77 15097 1.20 20 6.22 15,42 1.05 25 6.61 14.90.90 30 6.95 14.43 o75 35 7.27 14o00.60 40 7.50 13.60.43 45 7.68 13.23.21 50 9.23 14.27 1.54

TABLE X (cont.) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 25B 5 5.98 18.42 o 58 10 6.83 17o48 1o 52 20 8.09 15.92 1 o 37 25 9o 01 1571 1.62 30 9.42 15.21 1.61 35 9-79 14,78 1.59 40 10o.o8 14o43 1.57 45 10e35 14,12 1.55 26B 6 4.07 16.71 1.57 10 5.02 15.87 1.56 15 6.oo00 14.92 1.55 20 6.77 14.12 1.53 25 7.45 13.47 1.51 30 7.94 12.97 1.50 35 8.32 12 54 1o 49 40 8.65 12.17 1.48 27B 30 7.63 16.47 1.60 40 8o13 16o03 1o61 50 8.57 15.65 1.63 60 8.97 15.29 1.63 70 9o29 14.97 1e61 28B 40 5 36 17o 30 1.48 50 5.84 16.93 1.46 60 6,20 16 48 1,42 70 6.78 16 33 1.60 80 7.17 16.00 1.59 90 7.49 15.69 1.58 100 7.81 15.43 1.57 110 8.11 15o17 1.56 120 8.37 14.94 1.55 130 8.57 14.69 1.53 140 8 76 14.44 1 o 50

-120TABLE X (cont.) Run No, Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 29B 3 2.82 18.16 1056 6 3.47 17.63 1.56 10 4.25 17O00 1.56 15 5.11 16.33 1.56 20 5.84 15.75 1.56 25 6.48 15.23 1.56 30 7.03 14.78 1.56 35 7.54 14 38 1o56 40 7~97 14.03 1.56 45 8.32 13.73 1.56 30B 10 7.16 18617 1.57 15 8.16 17.29 1.57 20 9.01 1.652 1.57 25 9.67 15o91 1.57 30 10,21 15038 1.57 35 10.63 14,95 1.57 40 11.00 14.6o 1.57 45 11.29 14.33 1.57 31B 5 5,10 15.49 1o56 10 5 69 1496 1.o 56 15 6.21. 14.50 156 25 7.05 13072 1.56 35 7.74 13.05 1.56 45 8.28 12,59 1.55 32B 10 5 66 18,28 1o54 15 6.51 17.61 1.54 20 7,22 16Q97 1.55 25 7.83 16.38 1.55 30 8~35 15.88 1Q55 35 8.82 15044 1.54 40 9.22 15,03 1.54 45 9~57 14.72 1.53 50 9.89 14o45 1.53

-121 TABLE X (cont.) Run Noo Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 33B 5 6.85 16.73 1o53 10 7.58 16.03 1.53 15 8.20 15047 1053 20 8.73 14.96 1053 25 9.17 14.53 1.53 30 9-54 14.19 1053 35 9.87 13.89 1.53 34B 10 4.62 16o33 1. 51 15 5.37 15.83 1.52 20 6,01 15.23 1.52 25 6.56 14.86 1,51 30 7.03 14,42 1.51 40 7.81 13570 1,51 50 8.44 13513 1.51 60 890 12.69 1.o 51 35B 10 5.18 14.23 1.53 15 5.91 13o63 1.53 20 6.51 13.12 1.53 25 7.01 12.68 1.o 53 30 7.46 12.29 1053 35 7.82 11.97 1.53 40 8,12 11 70 1.53 45 8,37 11.47 1.53 36B 10 5.49 15.82 1.56 15 6o31 15o17 1056 20 6.99 14.56 1o56 25 7.60 14,03 1c56 30 8,11 13o58 1055 35 8.52 13.21 1.55 40 8o84 12089 1.55 37B 10 5.80 14.10 1.53 15 6.33 13.64 1.53 20 6.81 13o21 1.54

-122 - TABLE X (cont.) Run Noo Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 25 7.21 12.83 1.54 30 7.55 12.50 1.54 35 7.86 12.21 1.55 40 8.13 11.97 1.55 38B 5 3.27 18.92 1054 10 4.33 18 04 1.54 15 5.27 17o17 1o54 20 6,10 16.43 1.54 25 6.76 15.79 1.54 30 7~35 15.25 1.54 35 7.86 14o77 1.54 40 8.30 14o34 1.54 45 8.71 13o 97 1.o 54 39B 15 8.16 17005 1.54 20 8.76 16.52 1.56 25 9.28 rI. o4 1.56 30 9-73 15.64 1.57 40 10o45 14.97 1.58 40B 5 3573 19.90 1.57 10 4.77 18.94 1.57 15 5o71 18.10 1o57 20 6.50 17. 36 1.57 25 7.21 16.72 1.57 30 7.80 16.14 1o57 35 8.30 15.66 1o57 40 8.77 15,23 1o57 45 9o13 14.85 1.57 41B 10 6.82 17o58 1.56 15 7.67 16.79 1o55 20 8.38 16.11 1i55 25 8.98 15o55 1o54 30 9.49 15.07 1.53 35 9o 89 1466 1 o 52 40 10. 24 14o33 151 45 1053 14.05 1.50

-123TABLE X (conto) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 42B 10 6.76 18,78 1.57 15 7.78 17.88 1.55 20 8061 17,01 1.53 25 9.27 16.30 1.50 30 9.83 15.70 1.48 35 10.25 15.25 1.46 40 10.63 14.86 1.43 45 10o93 14o53 1.42 50 11.19 14.27 1.41 43B 10 6.87 17.37 1.59 15 7.90 16439 1.56 20 8.73 15.54 1.54 25 9.35 14.86 1.53 44B 2 8.29 17.15 1.59 5 8.61 16.72 1.58 10 9oll 16.16 1.57 15 9.53 15.66 1.56 20 9.92 15.23 1o55 25 10.24 14.87 1.54 45B 10 5.40 15.87 1.62 15 6.25 15.18 1.61 20 6 94 14o54 1.61 25 7.50 13599 1.60 30 7.98 13553 1.60 35 8~36 13.13 1.59 46B 10 5.83 18.54 1.58 15 6.70 17,92 1058 20 7.50 17.34 1.58 25 8.14 16.80 1.58 30 8.67 16o34 1.58 47B 5 4.42 18.78 1.57 10 5.40 17.95 1.57 15 6.28 17.28 1o57 20 7~02 16.71 1.57

-124TABLE X (cont.) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 48B 5 5.76 19067 1.57 10 7.10 18.89 1.57 15 8.12 18.16 1.57 20 8.97 17.44 1.57 25 9.64 16.87 1.57 30 10o22 16.40 1 5 7 35 10o68 15.98 1.56 40 11 o6 15.62 1o56 49B 5 4.83 18.67 1.60 10 6.36 17.54 1.60 15 7.53 16-72 1.60 50B 5 4.75 17.77 1.62 10 6004 16.60 1.62 15 7~07 15.71 1.62 20 7.88 14o97 1o62 25 8.52 14037 1.62 51B 5 4.25 19.17 1.60 10 552 18.32 1.60 15 6.56 17o58 1.60 20 7~ 37 16,97 1.60 25 8.08 16.46 1,60 52B 2 3.63 13592 1o64 5 4.24 13531 1.64 10 5.06 12,47 o.64 15 5076 11i84 1.64 53B 2 3.23 19.60 1.59 5 3.97 18.95 1,59 10 5004 18,02 1.59 15 5094 17.21 l.59 20 6~72 16.52 1.59 25 7040 15095 1o59

-125TABLE X (conto) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 54B 2 6.oo 19.67 1.58 5 6.72 19.22 1.58 10 7.70 18.48 1.58 15 8.53 17.78 1.58 20 9.22 17.20 1.58 25 9.82 16.68 1.58 30 10.28 16.24 1.58 35 10.68 15,87 1.58 40 11.03 15 54 1.58 45 11 35 15.27 1.58 55B 5 4.o09 1884 1.63 10 5031 17.89 1.63 15 6.27 17o15 1.63 20 7.09 16.47 1.62 56B 3 3.30 19.43 1.65 6 3.97 18.95 1.65 10 4.8o 18.4o 1.65 15 5.67 17.76 1.65 20 6.42 17.18 1 66 25 7.11 16.65 1.66 57B 10 5.83 18.31 1.67 15 6.85 17.41 1.67 20 7.69 16.67 1.67 25 8.37 16,04 1.68 30 8,97 15055 1.68 58B 4 6.57 17.88 1.65 6 7~36 17.18 1.65 8 8.03 16.57 1.65 10 8.63 16o03 1.65 59B 2 2087 18.13 1.58 5 3052 17.68 1.58 10 4,53 16.97 1.58 15 5.36 16.33 1.57

-126TABLE X (cont.) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 60B 2 4.2 19.0 1,58 5 5.36 18.03 1o58 10 6.74 16.81 1,59 15 7.85 15.83 1.59 61B 5 4.64 19.94 1.56 10 5.33 19o50 1.55 15 5.92 19.10 1054 20 6.43 18.71 1.53 25 6.91 18.32 1o53 30 7.33 17o94 1.52 40 8.05 17.24 1.51 50 8.69 16.63 1.50 60 9~23 16.13 1.48 70 9.67 15o73 1.45 62B 5 3-73 19.09 1.55 10 4,52 18.54 1o55 15 5.21 18o05 1.55 20 5.78 17.61 1.54 25 6~33 17.19 1.54 30 6.82 16.83 1.55 63B 2 3.81 17.08 1.58 5 4.55 16.63 1o57 10 5.59 15093 1.56 15 6.44 15 34 1n55 64B 2 3.17 19o19 1.54 5 4.07 18.44 1o54 10 5.33 17.40 1.55 15 6.36 16.55 1.55 65B 2 3.82 19.20 1.52 5 4.82 18.38 1.52 10 6.17 17.27 1.52 15 7.26 16,38 1.53

.127TABLE X (cont.) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 66B 5 3.12 19038 1.53 10 4.12 18.64 1.53 15 4.94 17.92 1.52 20 5.68 17.23 1.52 25 6.36 16.62 1051 30 6.93 16.04 1051 35 7.43 15.54 1.50 40 7.87 15.10 1.50 45 8.27 14.67 1.49 67B 3 5.88 41,59 3.70 6 7,53 40o27 3.70 10 9.45 38.58 3.69 15 11.53 3,652 3-69 20 13029 54.93 3.68 25 14.83 33.36 3.68 30 16.05 32.14 3.67 40 18.23 30.20 3.65 68B 3 3.50 16.83 1.53 6 3.98 16o38 1.53 10 4.59 15.84 1.53 15 5028 15.23 1.53 20 5.87 14.70 1.53 25 6.38 14,24 1.53 30 6.87 13.84 1.53 35 7.31 13.48 1.53 40 7.62 13519 1.53 69B 3 2.60 18.32 1.54 6 3.20 17.83 1.54 10 3.91 17.23 1,54 15 4,71 16,52 1.54 20 5.40 15.90 1.54 25 6~02 15.37 1.54 30 6.55 14.87 1.54 35 7004 14.43 1.54 40 7.50 14.02 1.54

-128 - TABLE X (con.t. ) Run No, Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 70B 3 6.20 43.69 3.65 6 7.90 42.43 3.65 10 9.99' 40.81 3.65 15 12.23 38.87 3.65 20 14.o09 37.15 3.65 25 15.66 35060 3.65 30 17.07 34.28 3.65 35 18426 33.18 3.65 40 19.27 32021 -3o65 71B 2 6.77 46.83 3.69 4 8.56 45~33 3569 6 10,25 43587 3.69 8 11o77 42.46 3.69 10 13.14 41.24 30.69 12 14.38 4013 3o 69 14 15052 39,12 3.69 16 16.55 38.14 3.69 18 17.47 37.27 3.69 20 18 31 36048 3o 69 72B 5 3.23 18064 1.53 10 4.~ 37 17060 1,50 15 5.30 16.62 1.48 20 6.07 15.73 1.45 25 6.78 15003 1.40 30 7533 14.40 1.35 35 7.83 13o90 1530 40 8.25 13547 1.25 45 8.62 13.10 1.20 73B 2 6.78 17.67 1.53 4 7.38 17.17 1.53 6 7.87 16o75 1.53 8 8.30 16.37 1.53 10 8.66 16.o00 153 12 9.00 15 69 1 53 14 9.32 15042 1.53 16 9.60 15D15 1.53 18 9.86 14,93 1053

-129TABLE X (cont.) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 74B 10 5.81 19.17 1,60 15 6.50 18.65 1.60 20 7017 18.17 1.59 25 7-79 17077 1.58 30 8.33 17.42 1.58 35 8.80 17.04 1.57 40 9.18 16 68 1.57 45 9.52 16Q32 1.56 50 9.80 15095 1.55 75B 10 6.29 19.06 1.56 15 7.06 18056 1.56 20 7.75 18.07 1 56 25 8.35 17o58 1.56 30 8.88 17.12 1.56 35 9.35 16 68 1.56 40 9.74 16.34 1.56 45 10O13 16.00 1.56 50 10.45 15.72 1.56 76B 3 13.18 49.28 3.67 6 15.23 47.64 3.67 10 17.63 45.75 3.67 15 20.10 43.63 3.67 20 22.12 41.82 3.67 25 23.77 40.24 3.67 30 25.17 38.95 3.67 35 26.26 37.92 3.67 40 27.23 37~03 3.67 77B 3 5.42 18o85 1.57 6 5.89 18.46 1.57 10 6.50 17.99 1.57 15 7.15 17048 1.57 20 7.69 16.98 1o 57 25 8.18 16.56 1.57 30 8.63 16.18 1.57 35 9.02 15.86 1.57 40 9.42 15.56 1.57

-130 - TABLE X (conto) Run No. Time (Chart Spaces) Ionization Currents(Chart Uni.ts) Lower Upper Zero 78B 3 5.26 19.26 1.58 6 5.94 18 90 1.58 10 6.75 18040 1.58 15 7.66 17.79 1.58 20 8.42 17.23 1.58 25 9.02 16.68 1.58 30 9.57 16.22 1o 58 79B 3 5o27 19.49 1o 56 6 5.80 19.04 1.56 10 6.47 18.49 1.56 15 7.18 17.87 1.56 20 7.83 17.31 1.56 25 8.39 16.81 1.56 30 8.87 16.38 1.56 35 9.29 16.02 1.56 40 9.68 15.68 1o56 80B 3 2,08 19.23 1.55 6 2.50 18.90 1.55 10 3.03 18.50 1.55 15 3.67 17.99 1.55 20 4.23 17.52 1.55 25 4.74 17o06 1.55 30 5.18 16.64 1.55 35 5.63 16.25 1.55 40 6.03 15.87 1.55 45 6.42 15055 1055 50 6.75 15.23 1.55 55 7.07 14.93 1.55 81B 3 2.76 19.80 1.57 6 3.63 19.18 1.57 10 4.63 18,38 1.57 15 5.72 17.43 1o57 20 6.62 16.57 1.57 25 7.37 15o90 1.57 30 7.99 15.28 1057

-131TABLE X (cont.) Run Noo Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 82B 3 2.37 15 87 1.56 6 2.91 15o37 1.56 10 3.55 14o77 1.56 15 4.25 14.12 1.56 20 4.85 13554 1.56 25 5~39 13504 1e56 30 5.84 12o63 1o56 35 6,24 12,25 1.56 40 6.63 11.93 1.56 83B 3 2X53 18.68 1.55 6 3519 18.18 1.55 10 3594 17.61 1.55 15 4.81 16.93 1055 20 5.56 16034 1.55 25 6.23 15.83 1.55 30 6.84 15037 1.55 35 7o35 14.98 1055 40 7~77 1463 1o 55 84B 3 6.65 45.15 3.71 6 8,60 43524 3571 10 10.86 41.05 3571 15 13.29 38.67 3.71 20 15.35 36 73 3 71 25 17.03 35511 3.70 30 18.43 33.74 3~70 35 19o54 32~58 3070 40 20,53 31.65 3570 85B 5 2.73 18099 1 56 10 3552 18.46 1.56 15 4.27 17o93 1.56 20 4.92 17,42 1.56 25 5.48 16,92 1o 56 30 6o01 16.43 1o 56 35 6.50 16.00 1.56 40 6.93 15,62 1.56 45 7~33 15.25 1.56 50 7.68 14 91 1o 56

K132TABLE X (cont. ) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 86B 3 2.21 18.87 1,55 6 2.71 18.44 1.55 10 3.33 1.7.91 1.55 15 4,06 17,29 1.55 20 4.70 16.73 1.55 25 5.29 16.23 1.56 30 5.83 15.77 1.56 35 6.31 15 37 1 56 40 6,72 14,97 1.56 45 7.12 14.63 1o56 87B 5 11.00 46,50 3,75 10 13.48 45.26 3.75 15 15.65 43~92 3075 20 17.57 42.59 3,75 25 19.20 41.37 3.75 30 20,65 40533 3575 35 21,93 39037 3.75 40 25303 38.47 3075 45 24.04 37.71 3o 75 88B 3 7~93 47.26 3.78 6 10.67 45,48 3.78 10 13574 43o19 3078 15 16.83 40.56 3.78 20 19.22 38.47 3.78 25 21o17 36.82 3.78 30 22 73 35~ 47 3578 35 23089 34,36 3078 89B 10 17o36 49.90 3.67 15 19.65 48.19 3~ 66 20 21.58 46,82 3.65 25 23.27 45.56 3.64 30 24,77 44.28 3.62 35 26.09o 43025 3.60 40 27.17 42~26 3058 45 28.17 41.45 3,56 50 29.03 40o82 3.54

-133TABLE X (cont ) Run Noo Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 90B 3 14.53 48.44 3.68 6 16.45 47.26 3.68 10 18o75 45.84 3.68 15 21o13 44.25 3.68 20 23.11 42~82 3o 68 25 24,81 41.65 3~68 30 26o17 40059 3~68 33 26.92 400o6 3.68 91B 2 14.13 48.76 3565 4 15.86 47~57 3.65 6 17o37 46.50 3.65 10 20.06 4454 3.o 65 15 22.76 42~50 3.65 20 24.87 40.78 3.65 25 26.52 39-57 3~ 65 350 27.92 38.63 3.65 35 28.95 37.83 3.65 92B 3 14.24 46.93 3.69 6 16.14 45~ 39 369 10 18 39 43.65 3.70 15 20.63 41.80 3 70 20 22.49 40o33 371 25 24.11 39.14 3.71 30 25.42 38.11 3.72 35 26 50 37.20 3o 73 40 27 n40 36.59 3.74 93B 3 13.65 47.46 3.78 6 15.33 46.27 5.78 10 17 34 44.82 3 78 15 19o47 43514 3.78 20 21.26 41o 62 3.78 25 22,76 40o36 3.78 30 24.03 39~33 3.78 35 25o12 38.41 3.78 40 26,02 37.66 3 78

-134TABLE X (conto) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 94B 3 12,13 47 97 3 71 6 14o27 46,09 3.71 9 16.16 44,47 3o 71 12 17.86 43.07 3 71 15 19.28 41 78 3 71 20 21.29 39 92 3 71 25 23.01 38.46 3771 30 24 35 37.20 3 71 35 25.41 36.25 3.71. 95B 3 6.60 46.72 3072 6 8.44 45,02 3 72 10 10o63 43o 08 35 72 15 13o05 41 o02 372 20 15013 39,23 3.72 25 16.88 37.66 3572 30 18 34 36 30 3o 72 35 19.55 35519 3,72 40 20.64 3419 3o 72 96B 3 6.89 46.63 3 75 6 9~53 44.92 3.74 9 11.83 43.24 3.73 12 13.84 41.o 60 3 72 15 15o57 40o15 3.71 20 18.04 38.08 3.70 25 2000 36o 37 3.69 30 21,47 34.97 3 68 35 26~68 33~75 3,6T 97B 3 6.36 48.47 3o64 6 8.27 46,95 3.64 10 1058 45~08 3o 63 15 13.13 43~05 3.62 20 15.23 41,29 3o61 25 17o04 39.83 3.60 30 18.64 38.57 3059 35 20.00 37.46 3.58 40 21.15 36~ 49 357

.135TABLE X (cont.) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 98B 1 5.76 39 17 3o 74 3 7.48 37.92 3-74 6 9-79 36.26 3.74 9 11 75 34 75 3.73 12 13 52 33~ 37 3.73 15 14.96 32.20 3.73 20 16.91 30,53 3.72 25 18.40 29.33 3072 30 19.53 28.28 3.72 99B 2 5036 45000 3.75 5 7.19 43.23 3.74 10 9.84 40o.66 3.73 15 12.13 38043 3572 20 14.03 36.55 3571 25 15.65 34.97 3.70 30 170o4 33060 3.69 35 18.19 32.57 3.68 40 19.20 31075 3.66 100B 3 6.81 45013 3.63 6 9.54 42.74 3.63 9 11.99 40o61 3~ 63 12 14.01 38,68 3.63 15 15.77 37006 3.63 18 17,23 35 ~66 3.63 21 18 47 34,53 3.63 24 19.49 33.49 3.63 27 20,42 32.65 3~ 63 101B 1 7 80 48,22 3574 3 10o32 46.06 3.73 6 13.60 43~33 3.72 9 16,24 40,92 3o71 12 18,46 38.97 3070 15 20.23 37535 3.69 18 21.71 35 95 3 68 21 22,84 34.82 3567 24 23577 33587 3.67

-136TABLE X (cont. ) Run No. Time (Chart Spaces) Ionization Currents (Chart Units) Lower Upper Zero 102B 3 7.38 4691 3o 67 6 9.52 45.16 3.6T 10 12.08 43518 3867 15 14.58 40.97 3.67 20 16.80 39.18 3.67 25 18.61 37.64 3,67 30 20.05 36.35 3.67 35 21.27 35.18 3o.67 40 22,38 34, 25 3.67 103B 3 7.08 44.87 3.73 6 9.28 43513 3.73 10 11087 41,16 3o73 15 14.58 39~02 3573 20 16076 37~17 3573 25 18.57 35063 3.73 30 19.98 34.29 3.73 35 21.14 33.28 3573 40 22.16 32~45 3o 73 104B 3 7.16 47,67 3.67 6 9.16 45.97 3.67 10 11 53 43.88 3.67 15 13598 41,70 3067 20 16.08 39.89 3.67 25 17,82 38533 3.67 30 19.42 36.94 3.67 35 20.63 35083 3567 40 21.64 34.85 3567 105B 3 8.30 46.24 3070 6 10o41 44,41 3.70 10 12.84 42.16 3-70 15 15035 39.84 3070 20 17.47 37~95 3070 25 19.16 36533 3070 30 20 57 35003 3-70 35 21.72 33593 3-70 40 22.57 32~99 3.70

-137TABLE X (cont.) Run Noo Time (Chart Spaces) Ionization Current (Chart Units) Lower Upper Zero 106B 1 8.26 49.34 3.83 3 10071 47.29 3.82 6 13594 44.43 3.81 9 16.65 41.94 3.80 12 18o71 39~97 3.79 15 20.41 38.34 3.78 20 22.74 36.24 3577 25 24.34 34.66 3576 30 25053 33~57 3~75

-138 - APPENDIX B SAMPLE CALCULATION FOR DIFFUSION RUN 84B Data Date: December 8, 1959 Major Components: H2, A Mole Fraction H2: 0o624 Operating Pressure: Four readings at 763 PSIG Operating Temperature: Thermocouple 53 Four readings at 1o410 MoVo Thermocouple 5: Four readings at 1408 MoVa Charging Data: Cell pressurized to 422 PSIG with Sample Go Cell pressurized to 455 PSIG with Sample 1 Cell pressurized to 800 PSIG with Sample G0 Upper tubing entrance flushed to cell pressure of 763 PSIGo Recorder Chart Speed: 6 inches per hour0 Voltage Range: 2.0 volts. Ionization Currents Read From Figure 5, also in Table XO

-139Time Uncorrected Ionization Currents (Chart Units) (Chart Spaces) Upper Lower Zero 3 45o15 6.65 3.71 6 43.24 8.60 3o71 10 41o 05 10o 86 3.71 15 38.67 13.29 3071 20 36.73 15o35 3o71 25 35o11 17~03 3.70 30 33574 18.43 3570 35 32.58 19.54 3.70 40 31o 65 20.53 3 70 Background Currents (Chart Units) Upper Chamber, 0.26 (50 space chart units) Lower Chamber, 0.09 (50 space chart units) CALCUIATIONS: Atmospheric Pressure = 14 PSIA Gauge Correction - -8 PSIA Absolute Run Pressure, P = 763 + 14 - 8 = 769 PSIA Absolute Run Temperature Upper Thermocouple (3) T = 308o30K (35,100C) Lower Thermocouple (5) T = 308.20K (35,00C) Compressibility Factor, Z = P/RT 1. o018 R = 1,2059 (psia) (l )/(gram mole) (K) Density, p (6 9) ZRT (1. 018) (1.2059) (308.2) = 2033 gm. moles liter

THE CONCENTRATION, C, AT CONSTANT DENSITY IS PROPORTIONAL TO THE CORRECTLED IONIZATION CURRENT, I, FOR EACH CHAMBER CUpper c f IUpper CLower ~ ILower FOR THE TIME OF THREE CHART SPACES (ONE-SIXmT OF AN HOUR) IUpper (IChart) Upper (BackgroundUpper Zero = 41o15 - 0.26 - 3o71 = 41o18 ILower = (IChart) Lower - (Background)Lower -Zero = 6~65 - 0,09 - 3o71 = 2~85 f = Ratio of ionization currents with same HT concentration in both chambers f = 0~958 (for diffusion Path B in cell) (f IlUpper - ILower) (0 958)(41018) - 2.85 = 36600 TIME (Chart Spaces) f IUpper - ILower (Chart Units) 3 36 o60 6 32 821 10 28o463 15 23 7.53 20 1,9 83425 16.602 30 13o889 35 1.1.668 40 90787 FIGURE 7 IS THE SEMI-LOG PLOT OF THESE POINTS, THE SLOPE OF THE RESULTING STRAIGHT LINE IS1 SLOPE =-0o01559 - Time Chart Units,

-L41 - THE CELL CONSTANT WITH DIFFUSION PATH B IN PLACE K = 0.01025 cm'2 (3 Chart Spaces )(2 303 log10 UNIT CONVERSION FACTOR = Inch lge 2303 3600 sec./hr. 1200 TEE DIFFUSION COEFFICIENT, D~ D = (2.303) Lope) (Chart Speed) = (2~303) (0.01559)(6) (1200) (K) (1200) (0.01025) D = 0o0175 cm /sec Dp ~ (0o0175)(2.033) = 0.0356 cm gm.moles sec liter COMPUTED BY METHOD OF LEAST SQUARES: D = 0,01753 cm2/sec p. 2.033 gm. moles/liter D p = 0.03562 cm2 o moles sec liter yH2= 0.624 YA - 30.76 T = 350C

APPENDIX C PREPARATION AND ANALYSIS OF GAS SAMPLES For the diffusion investigation, it was necessary to prepare several samples of mixed gases of known concentrations. NON-RADIOACTIVE GAS SAMPLES Three samples of mixtures of hydrogen and carbon dioxide were prepared having approximately 19, 63, and 93 molecular percent of hydrogen respectively. Similarly, three samples of mixtures of hydrogen and argon were prepared having approximately 19, 62, and 93 molecular percent of hydrogen respectively. These samples were prepared from cylinders of nearly pure hydrogen, carbon dioxide, and argon havling manufacturers stated purities of 99.8 percent, 99.9 percent, and 99,6 percent respectively. These gases were purchased from the Matheson Company, Incorporated. The samples were prepared by adding either carbon dioxide or argon to an evacuated Number 3 gas cylinder to a pressure dictated by the desired molecular fraction, and then pressurizing with hydrogen to 1500 psia. The resulting samples were then equilibrated and analyzed to determine the exact molecular fractions, Mixtures of hy.drogen and carbon dioxide were analyzed with an Orsat-ltype apparatus in which the carbon dioxide was absorbed in strong caustic. Mixtures of hydrogen and argon were analyzed by a mass spectrometer,

Table XI is a presentation of the sample analysis data taken before and after the diffusion runs for mixtures of hydrogen and carbon dioxide and after diffusion runs for hydrogen-argon mixtures. TABLE XI GAS SAMPLE ANALYSES Sample Date Orsat VoloData Percent H2 Percent C02 Percent A Analysis Initial Final Method A 7-9-59 82.88 775 31 93.28 6.72 -_ -- Orsat C02 Absorption A 7-12-59 87.48 81.66 93535 6,65 t A 9-19-59 92.05 85,86 93,28 6.72 " A 9-19-59 86.74 80.93 93030 670 A 9-20-59 86.88 81o00 9323 6.77 11 C 7-7-59 81o30 51.08 62083 3717 C 9-13-59 86.82 54.52 62.80 37.20 _ C 9-14-59 87.13 54~65 62.72 37.28 I. D 7-16-59 91.78 17.32 1885 81.15 D 7-16-59 87.97 16.66 18.94 81.06... D 10-10-59 86.52 16,38 18.93 81o07 -. 11 D 10-12-59 89.96 16.98 18.88 8112 E 1- -60 -- -- - 92 55. — - 7~45 Mass Speco No. 5364 F 1- -60 o.. —- 19.47 - -- 80 53 Mass Spec. Noo 5337 G 1- -60 o — -- 63536 - -- 37.64 Mass Spec. No. 5338

RADIOACTIVE SAMPLE PREPARATION Radioactive samples were prepared from the samples of the above mixtures by addition of small measured amounts of tritiated hydrogen to separate portions of each gas mixture in smaller sample bottles. With the knowledge available at the time, it was necessary to prepare the radioactive samples accurately since the response of the equipment to tritium disintegrations was not known~ The range of the equipment may not have extended into a region where the ratio of concentration of tritium to current produced was constant. In this event, the accurate calibrations afforded by accurate samples would be necessary for data analysis. Gaseous tritium, T2, is available for purchase from the United States Atomic Energy Commission in reasonably pure state, the chief impurity being traces of daughter compounds which are produced by its radioactive disintegration. The radioactive strength of pure tritium is about two and one-half curies per cubic centimeter of gas at one atmosphere of pressure and zero degrees centigrade temperature. Due to this relatively high strength for a small quantity of gas, it was found necessary to dilute the tritium to considerably lower concentrations, first with hydrogen and subsequently with the hydrogen-carbon dioxide and hydrogen-argon mixtures to be studied. These dilutions were carried out in the gas dilution equipment schematically shown in Figure 24. Tritium was diluted to known molecular fractions with this equipment. The basic idea involves the

-145z z2 0 a Z QW. RO D 0 Dof zo o a. L&J~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~, W Z — J w (h I - WC/) z>- a-).~.., Dw ~ ~ o CD 0~~~0 40 0 r4 wu,w ~ ~ ~ ~ ~ ~ I- Cl - ) o - gD 4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~4: ~w z E') WC w cr D~~~~~~~~ a. (3 L. I.) 0 ~ ~ ~ ~ ~ ~ ~ ~ 0 Ur. w~~~ W~~~~~~~~~~~~~~~~~~~~~~j ~ ~ ~ ~ ~ ~ ~ ~ ~ r w~~~~~ I-a W I- ZE 0,~.-r gx - ~ i rr ~:i d~lFr QD, r -,.,,D Po ~~~~~~~~~~o o w t fQ~b o3

the measurement of the pressure and temperature of a known volume of gas and thereby determining its mass by a suitable relation of state. The dilution equipment was made up of two sections, the low pressure section for dilutions below one atmosphere absolute pressure, and the high pressure section. The former section was constructed of steel high-pressure tubing and fittings. The two sections were connected by a short length of high vacuum rubber tubing. Pressures were measured in the low pressure section by means of a cathetometer and mercury manometer and by a McLeod vacuum gauge. In the high pressure section pressures were measured by a bourdon tube pressure gauge. Temperatures were measured by means of a thermocouple and portable potentiometer. Both sections were constructed in order that they be relatively leak-tight. The glass section was tested to retain a pressure of one micron of mercury without ntMiceable increase in pressure for one hour after being isolated from the vacuum pump. The high pressure section was tested to retain gaseous hydrogen at a pressure of 1000 pounds per square inch without noticeable decrease in pressure for a day after being isolated from the gas source, The following description refers to Figure 24~ The tritium was shipped in two small glass vials each with an easily broken finely drawn glass tip (L) inside of the exit neck. Upon receipt of the vials, a female ground glass tapered joint was fused to the exit neck of each vial. This joint matched the male joint (J) located below the dilution flask. When a tritium dilution was made, a vial was connected

to the low pressure dilution section by this ground-glass joint (J) with a small piece of iron (K) resting in the exit neck of the vial on the unbroken glass tip. The McLeod macuum gauge was placed. in its first positi.on as located in Figure 24 and with the connecting valve (C) between the high and low pressure sections closed, the glass section was evacuated to less than one micron of mercury absolute pressure, With stopcock (F) closed and stopcock (I) open, the piece of iron (K) was elevated by a magnet and allowed to fall, breaking the glass tip (L) and causing the tritium to expand into the evacuated dilution flask, mercury manometer tube, and McLeod gauge. After a suitable waiting period, stopcoQk (I) was closed and the pressure and temperature in the dilution flask were measured using the McLeod gauge and the thermocouple (T), thus determining the total mass of tritium in the enclosed known volume. After evacuation of the remainder of the low pressure section together with the high pressure section, throttling valve (C) and stopcocks (H) and (E) were closed, and with stopcock (F) open, hydrogen was carefully expanded into the glass system through valve (C) diluting the tritium and bringing the pressure in the dilution flask up to slightly less than one atmosphere. Pressure and temperature measurements were made using the mercury manometer and thermocouple and thereby the extent of dilution was determined quantitatively.

Further dilution was effected by allowing determined, amounts of this hydrogen-diluted tritiumn to expand into evacuated steel sample bottles which were then pressurized with hydrogen or mixtures of hydrogen and carbon dioxide or hydrogen and argono Since the amount of radioactive sample from the dilution flask was very small with respect to the amount of non-radioactive sample in the sample bottle, the resulting radioactive mixture was almost exactly the same concentration as the non-radioactive sample. The radioactive mixture was, however, slightly rich in hydrogen, the light component. Table XII is a list of the radioactive samples prepared by dilution of the two vials of tritium with hydrogen, hydrogen-carbon dioxide mixtures and hydrogen-argon mixtures. Samples 2, 3 and 5 were prepared for use in the hydrogen-carbon dioxide diffusion runs. Samples 6-12 were prepared to be used without further dilution for calibration of the diffusion cell for ionization current-tritium concentration relationships~ Samples 13-16 were prepared for use in the hydrogen and hydrogen-argon diffusion runso

-149TABLE XII RADIOACTIVE SAMPLES PREPARED HYDROGEN-CARBON DIOXIDE, FIRST TRITIUM VIAL Sample Percent H2 Total Moles Moles HT Rado Strength, Curies X 107 GM. Mole 2 62.8 0oo0948 5~27.322 3 18.9 0.0955 4~99 ~ 303 5 93o3 0.1334 5.51.240 6 62.8 1.264 12o.72.0292 6A 62.8 1.242 774 o.0181 7 62,8 1. 311 0o568.00126 8 93 3 1o 196 0o 602 o 00146 9 62.8 1. 324 2o 85 00624 11 18.9 0.o 832 0o 577.00201 12 62.8 0.773 0 o419.00157 HYDROGEN-ARGON, SECOND TRITIUM VIAL 13 100 1o 015 142 8.407 14 19.5 0.937 111.2.344 15 62,4 0.978 67.6.200 16 92~6 1.167 7302.182

-150APPENDIX D CALIBRATION OF DIFFUSION CELL FOR HT CONCENTRATION At the onset of the experimental work presented in this dissertation there was no information available concerning the ability of radiation caused by the radioactive disintegration of tritium to cause ionization in gases at high pressures. It was not known what concentrations were necessary to cause detectable ionization currernts in an ionization chamber at these pressureso For this reason a study of concentratlon-lonization current relationships was made with the diffusion cell before any diffusion determinations -were made. Information was desired concerning a molecular fraction of tritium, if there was one, below which there was a direct proportionality between tritium concentration and the ionization current; produced in the diffusion cell within the desired experimental pressure range Radioactive samples 6-12 were prepared for use in these ionization current calibrationso These samples were of known varying radioactive strengths or known tritium molecular fractiono For a calibration run, the sample was compressed into the diffusion cell by means of the pressurizing equipment to an initial pressure of greater than 5000 pounds per square inch. Ionization currents from each cell chamber were

-151determined and recorded with the current measuring circuit and recording potentiometer. The pressure was decreased to about 500 pounds per square inch in about five equal steps, the ionization currents for each' chamber being measured at each constant pressure step. The calibrations were carried out at 350 centigrade with samples of H2-C02 containing 62.8 percent hydrogen of four different known tritium molecular fractions. Three different results were derived from the ionization current calibration data of which two were actually used in the determination of diffusion coefficients. These three were: 1) the tritium concentration-ionization current relationships presented in Figure 25, 2) the ratio of chamber sensitivities with the chambers containing the same molecular fraction of tritium as presented in Figure 26, 3) the absolute ionization current for each chamber as a function of pressure as presented in Figure 27 for one calibration run. In Figure 25 the ratio of concentration of tritium to ionization current produced in the lower chamber is plotted versus the cell pressure. If the concentration were proportional to the current for all four sample concentrations at all pressures within the range of the abcissa, the points for all four calibration molecular fractions would fall along the same line. This fact is true for the lower pressures, but as the pressure is increased, the lines representing the two higher

-152350 (o 300 200 Q~~~~~~~~~~~~~~~~~~~~~~~~~~Q 4 + 250 0* O ~200 IS 100 MOL RUN SAMPLE FRACTION HT. SYMBOL -6 B 6 1.006 x 10 0, C 7 0.0433 x 10( + E 6 1.006 x 10 6 F 9!0.215 x I() II3 -6 F 9 0.215 x 106 G 6A 0.623 x I6 A 0 0 1000 2000 3000 4000 5000 6000 PRESSURE, PSIA Figure 25. Concentration-Current Ratio HT-H2-C02, 350C.

-153I i I 0 0 U') OO 0 IF>9 4-) O o0 8 0.rH 05 e O F0 0 ~L a. d C x +0 0 *- 0 + 0 pq c r-H tO OUH ~~~ 0x+~~~~~~~~~0O0 ~ ~ c ~~~n ~ ~ ~' )o i ot o 0 * 0 + w~~~~~~~~~~~0a O 0 41cf)~ ~ ~ ~ ~ ~~~( ~l i r~ I. 41 I 18 o + o0 E)~ ~ ~ ~ ~ ~~~~~~~~~\ — b0 x. *>~: 4G+,1 o 0 + 0 CD ~ N-U') qj ~ 0) 0) (3) 0) 0) 0O d d d d d d d l:3ddfl 3mo-11

-15460 - 59 58 57 56 w W55 a. 53 C. 0 Y 52 z 51 w QI 0 50 z 0 49 N Z o 48 47 46 45 ---- 0 1000 2000 3000 4000 5000 6000 PRESSURE, PSIA Filgure 27. Ionization Current-Pressure Relation for Diffusion Cell HT-H2-C02 at 3g~C. HT Mol Fraction = 1.006 x l0-.

-155 fraction samples split off from the line representing the proportionality, first the highest fraction and then the next highest fraction. The two lower molecular fraction tritium samples fall along the same line, the line of proportionality, for the entire pressure range studied. This indicates that as ldng as diffusion measurements were made using molecular fractions of tritium below the molecular fraction of Sample 9, the proportionality would hold between the concentration of tritium and the ionization current produced in the chambers. The currents in question quite fortunately were convenient to measure w4'th the apparatus available. Had the measurements had to be made on more concentrated samples the calculations would have been greatly enhanced0 The ratio of sensitivities of the two cell ionization chambers was the second bit of information necessary from the ionization current calibrations in order to determine the diffusion coefficientso It was certainly conceivable that the two chambers would respond differently to the same concer -r.ation of tritiumo Figure 26 is a plot of the ratio of the current from the lower chamber to th. current from the upper chambetz, when both chambers contained the same concentration of tritium, versus pressure. Although the scatter appears to be considerable, the actual variance is only about plus or minus about one and one-half percent of a mean value. Note that the mean value, about 00953, is very close to

-156the ratio of the chamber volumes when diffusion path A is installed in the diffusion cello Spot check values of the ratio of sensitivities of the two ionlzation chambers when diffusion path B is installed indicate that the ratio is 0958 which is close to the ratio of the chamber volumes with this path in place. Chou (9) suggests that this sensitivityvolume ratio relationship occurs because for larger volume chambers there is less chance for ions to migrate to the chamber wallso The third result derived from the ionization current calibrations is interesting although not essential to the diffusion determinations. It is included mainly for this reason and because the trends shown reflect upon the accuracy of the calibration determinationso Figure 27 is a plot of the absolute currents from the two chambers of the diffusion cell during one calibration run as pressure is reduced by steps with a constant molecular fraction of tritium sample in both chambers. As pressure is decreased, the current in each chamber increases and goes through a maximum at about 1500 pounds per square inch, the maximum for different samples occurring at different pressures that seem related to the molecular fractions of tritium in the samples0 The currents then rapidly decrease toward zero for zero pressure of radioactive sample in the cello This behavior might be explained due to two phenomena which occur simultaneously but to different extents at different gas densitieso

57At low pressures as the quantity of gas in a confined chamber is increased, also therefore the quantity of radioactive material is increased, the conductivity of the gas due to ions formed by radioactive disintegration might be expected to increase proportionately to the amount of radioactivity present. However, as the pressure increases and molecules are forced closer together, it becomes more difficult for ions to migrate to the walls and be collected before they are reunited.. This phenomenon would tend to reduce the currents below the proportionality and pass them through a maximum as the effect becomes more important than the increasing radioactivityo That this maximum occurs at higher pressures for lower tritilum fractions might be attributed to the fact that ion recombination is concentration dependent, the ion concentration being lower in lower tritium fraction samples~

d158APPENDIX E COMPRESSIBILITY FUNCTIONS USED FOR DENSITY CALCULATIONS Since the density of a substance is the macroscopic physical quantity which is proportional to the number of molecules in a given volume, this property is probably the best independernt variable to use in conjunction with describing diffusion phenomenao Density, or compressibility data is very limited for the two systems studied in this investigation} especially in the pressure range between 2000 and 5500 pounds per square inch. For these reasons it was imperative that a generalized correlation be found which satisfactorily described the volumetric behavior. Chou (9) in his work with H2-C02 mixtures found that the generalized compressibility factor chart presented by Dodge (12) predicted with good accuracy the limited data of Verschaffelt (45) and Krichevskii and Markov (23) if the pseudo critical properties of the mixtures were obtained by the following relations: TC = YC2 (TC)C02 + H2 [(TC)H + 16] (40) PC YC02 (PC)C + H2 + 16] (41 ) These relations differ slightly from the generally used equations predicting volumetric behavior of hydrogen from generalized comf pressibility charts in that the constant, 16, is used instead of the

-159constant} 8, for determining the pseudo-critical properties of hydrogen. The maximum pressure of the data used for this comparison is only 1800 pounds per square inch. A recently published generalized compressibility relation by Pitzer and co-workers (32,33) which was adapted for use with mixtures by Prausnitz (35) is the relation chiefly used in this investigation. Prausnitz predicted the compressibilities of two mixtures of C02-H2 in the temperature range of 2730 to 4730K and the pressure range of 3000 to 7500 pounds per square inch with a maximum deviation of 2.2 percent and an average deviation of 1.3 percent. Pseudocritical properties of all of the mixtures of C02-H2 and A-H2 in this investigation were calculated by the Prausnitz method. The Pitzer compressibilities were used for the 19 and 62 percent hydrogen mixtures of both systems at both 350C and 100~Co The measured compressibilities of pure hydrogen were used for 93 percent hydrogen mixtures of both systems and for the pure hydrogen diffusion runso The 93 percent hydrogen mixtures of both systems were treated as if they were pure hydrogen at the pseudo reduced temperatures and pressures of the mixtureso The Pitzer generalized gas compressibility correlations are based on the usual two reduced parameters, Pr and Tr,which in turn are based on the critical properties PC and TC, and a third property, W, the acentric factor. The acentric factor is a measure of deviation

-160from a "simple fluid", for which the acentric factor is zero. Molecular potentials of such'"simple fluids" (A, Kry Xe, and CH4)can be described accurately by the Lennard-Jones or 6-12 potential. Potentials of other molecules deviate somewhat from this form in a manner which can often be described mathematicallyo However, perhaps the best way to predict this devlation in order to facilitate its use is by an empirical method using an easily measured physical property, vapor pressure. The molecular potential has its greatest overall effect when molecules are clustered as in the liquid stateo The vapor-liquid equilibrium, or vapor pressure for a pure component, should be a good manner of determining the molecular potential deviations. The acentric factor, c, for a certain pure component is defined by the equation: X = -log Pr - 1.00 (42) where Pr is the reduced vapor pressure of the pure component at a reduced temperature of Tr 0.7. This acentric factor is indicative of the slope of the vapor pressure curve of the components, which in turn is dependent on the entropy of vaporization of the material. The acentric factor is therefore related to the increase of the entropy of vaporization of the component in question over that of a?simple fluid".

The acentric factor, c,~ is used as the factor of a correction which is added to the compressibility correlation of a "simple fluid"o It is applied in the following manner: z- z(o) + z(l) + _ (43) where: Z is the desired compressibility, z(0) is the compressibility of a "simple fluid" with the same reduced properties~ z(l) is the correction to the "simple fluid" compressibility at the reduced propertieso Prausnitz has presented a method for calculation of pseudocritical properties of mixtures for use wlth the Pitzer compressibility relations by use of second virial coefficient relationships. Only the method of calculation of these properties will be presented hereo The information necessary for the calculatlon of the pseudocritical properties for a binary mixture with mole fractions, Yiy are: the critical properties, TC, VC, ZCs and the acentric factor, w, for each component, the graphical tables of two variables, r and s, which are given by Prausnitz as tabular functions of Tr and cDm and the following relationships which are presented in five steps.

-16621) (TC)l2 = [(TC)1 (T)2 /2 (44) (VC)12 - 1/2 [ (VY)l + (VC)2] (45) 2) YCm = y21 (VC) + 2Yl12(vC)12 + Y22 (VC)2 (46) %m = Ylwi + Y2CD2 (47) 3) = Y1 (Vc)1 (TC)1 + 2yly2(V)12 (TC )12+ (48) Y22 (Vy)2(TC)2 = Y2 (YC) (TC )1 + 2Y1Y2(YC)12(TC)122 + 2 2 4) T = ~+~I~7r 72 ( )50) 54) TCm. =-c (501) 2 s. om RCm 5) p = C Yl(ZC)l + Y2(ZC)2] (51) VC=m YCm, PCms (m are the pseudocritical constants necessary for use with the Pitzer compressibility relations. Before step 4 can be evaluated, a value for the reduced temperature must be determined in order to evaluate the variables, r and s. It can be approximated with sufficient accuracy by Equation (52). Tr= T (52) r (/VCm)

-163Table XIII is a presentation of the values of the pseudocritical properties and acentric factors calculated for the experimental mixtures used. TABLE XIII PSEUDOCRITICAL CONSTANTS FOR EXPERIMENTAL MIXTURES H2-C2 MIXTURES Fraction H2 TCm OK PCm; Psia Vm, cc/gm mole n (Pc)Km~Yi(PC)J 0.188 263 1035 87.1 0.183 928 0.629 144 768 67.0 0o084 590 00933 58.8 406 53.1 0.015 357 H22-A MIXTURES: 0.195 129.8 656 70.4 0 627 0.624 82.0 498 5908 0 456 0 926 49.3 350 51.9 0 336 For the calculations, pure component pseudocritical constants were used for hydrogen. These are the ones used by Prausnitz and are TC = 43.40~K, V = 50 cc/gm. mole, and ac = 0.

APPENDIX F MISCELLANEOUS CALIBRATIONS AND CALCULATIONS 1o Pressure Gauge Calibrations 2. Thermocouple Calibrations 3. Diffusion Path Hole Size Determinations 4, Cell Chamber Volume Determinations 50 Cell Constant Calculation 6. Background Calibration Data

1. PRESSURE GAUGE CALIBRATIONS The two pressure gauges, Noo C2-473 and Noo C-2456, used for determining diffusion data run pressures and the gauge, Noo C2-515, used for tritlum dilutions were calibrated at the beginning and end of the investigationo Two different hydraulic gauge testers were used for the calibrations, American Gauge Tester No. 1315 at the beginning and Chandler Gauge Tester No. D3-13 at the finish. Table XIV is a listing of the calibrations made. All pressures listed are in pounds per square inch gauge0 TABLE XIV PRESSURE GAUGE CALIBRATIONS 1500 PSI PRESSURE GAUGE NO0 C2-473 Date: January 7, 1959 Gauge Tester Up Down Add Remarks 275 288 288 -13 525 534 536 -10 775 782 783 -8 1025 1032 1034 -8 1275 1285 1285 -10 1475 1484 -9 Date: December 30, 1959 Tested in Place 600 613 -13 700 709 -9 800 809 -9 900 909 -9 1000 1oo9 -9

TABLE XIV (cont.) Gauge Tester Up Down Add Remarks 1100 1110 -10 1200 1211 -11 1300 13511 -11 1400 1411 -11 1500 1510 -10 10,000 PSI PRESSURE GAUGE NO. C-2456 Date: March 24, 1959 1750 1750 0 2000 2000 0 2250 2260 -10 2500 2510.10 2750 2760 -10 3000 3005 -5 3250 3255 -5 3500 3505 -5 3750 3755 -5 4000 4000 0 4250 4250 0 4500 4500 0 4750 4740 +10 These points were taken 5000 4980 +20 at upper limit of tester, not used. Date: December 30, 1959 Tested in Place 1500 1540 -40 2000 2000 0 2500 2500 o 3000 -3008 -8 3500 3506 -6 4000 4003 -3 4500 4500 0 5000 5000 0 5500 5500 0

TABLE XIV (conto) Gauge Tester Up Down Add Remarks Date: January 7, 1949 1000 PSI PRESSURE GAUGE NO. C2-515 250 255 255 -5 350 355 357 -6 450 453 455 -4 500 503 505 -4 600 603 603 -3 750 752 753 -3 850 853 853 -3 900 903 904 -4 950 955 955 -5 1000 1005 -5

-168 - 2. THERMOCOUPLE CALIBRATION The two thermocouples imbedded in the diffusion cell body were calibrated at the start of the diffusion data runs by comparison with two National Bureau of Standards calibrated thermometers. For the calibration at approximately 350C, the Princo No. 460641 thermometer was used which has a range from -50C to 600C with 01o0C divisions. For the calibration at approximately 1000C, the Princo No. 253197 thermometer was used with a range from 480~C to 1020C with O.10~C divisions~ Calibrations were made using the same No0 A12-64 Portable Potentiometer that was used during the diffusion runs for measurement of thermocouple E.M.Fo s. TABLE XV THERMOCOUPLE CALIBRATIONS December 99 1958 Thermometer Thermocouples Corrected cc No03 No 4 Temperature, C PRINCO N0o 460641 34 5 1.386 1.385 34.5 34c 7 1o 395 1o 394 34~ 7 34. 9 1.402 1o 402 34.9 3500 1.408 10407 3500 3501 1.410 1.410 3501 3503 1.418 1.418 3503 3505 1,427 1.426 3505 PRINCO NO. 253197 99.5 4.247 4,242 99.6 9907 4.258 4,253 99.8 9909 4.269 4.264 100o 0 100o0 4.271 4.265 1001o 100.1 4.277 4.272 10002 100.3 4.287 4.282 100o4 10o 5 4o 295 4.290 100.6

-1693. DIFFUSION PATH HOLE SIZE DETERMINATIONS The holes in the diffusion paths A and B were determined by examining the ends of the tube bundles with calibrated microscope scales0 Two different microscopes and eyepiece scales were used, the Noo Y-B-595 Bausch and Lomb binocular microscope before installation of the paths into the diffusion cell, and the Noo MeC3-1155 Unitron binocular microscope after completion of the diffusion runso At no time were all of the hole sizes determined, but on both occasions, two diametrical passes were pade at right angles to each other with measurement of all holes passing into viewo The eyepiece micrometer located on the B and L microscope was calibrated against an ordinary machinists micrometer. The eyepiece micrometer used with the Unitron microscope was calibrated with a B and L stage micrometer having 0.01 mm small divisionso The eyepiece micrometer calibrations are located in Table XVIo The hole measurements for diffusion paths A and B are located in Table XVII.

-170TABLE XVI EYEPIECE MICROMETER CALIBRATIONS February 8, 1959 Bausch and Lomb Eyepiece with Machinists Micrometer Eyepiece Scale Micrometer Scale, inches Objective - 3-Ox 7.5x 0o 100 00977 0.0396 0.090 0.0877 0.0356 0.080 0o0778 0.0317 0.070 0o0682 0.0277 o,o6o 0.0582 0.0238 0.050 0,0487 0.0199 0040 00 o389 0.0159 0.030 0,0289 00o 19 0.020 0,0192 0.0079 0010 0 o0095 o. 0040 0 000 0.0000 0,0000 April 4, 1960 UNITRON MICROSCOPE, B AND L STAGE MICROMETER Eyepiece: Ke lOx unitron micrometer Objective: M 40x N.A. 0.65 T.L. 170 The following readings were made at two scale positions: Two Scale Positions: 100 Eyepiece scale units = 0.02427 cmo 100 Eyepiece scale units = 0~02423 cmo Average = 0,02425 cmo Eyepiece: Ke lOx unitron micrometer Objective: M lOx N.A. 0.30 ToLo 170 The following readings were made at two scale positions: 100 Eyepiece scale units = 0,0968 cm. 100 Eyepiece scale units = 0.0968 cm. Average = 0.0968 cmo

-171TABLE XVII DIFFUSION PATH HOLE SIZE DETERMINATION PATH A, FEBRUARY 8, 1959 DIAMETER. B AND L EYEPIECE MICROMETER SCALE UNITS Vertical Pass Horizontal Pass 0.0392 0.0413 0.0402. o0411 0o0442 0O0421. 0429 0.0403 0.0426 0,0412 000420 0.0393 0,0405 0o 0411 Average Diameter =:00413 S.U. = 0.0420 cm. PATH A, APRIL.4 1960'OIN TRON iMICROkpE FI,TS Veriteal Passorizontal Pass 44.6 43.9 43~9 43.7 46,5 45.2 44.3 44.3 43o9 44.3 43,9 43.3 43.1 43.8 43.00 44.3 46.7 45.1 44.3 46,0 42~7 41.7 Average Diameter = 44~20 S.U. = 0.04279 cm,

TABLE XVII (cont ) PATH B, FEBRUARY 8, 1959 DIAMETER9 B AND L EYEPIECE MICROMETER SCALE UNITS Horizontal Pass Vertical Pass 0.0218 0.0226 0.0230 0.0227 0.0228 0.0216 0.0230 0.0231 0.0231 0.0227 0.0229 0.0228 000225 0.0240 0.0218 0o0230 0o 0220 0.0252 0o0231 0o0229 0.0228 0.0225 000238 0.0220 0.0223 0o0220 0,0231 0o 0222 0.0220 0o0226 0o0228 0,0220 0.0226 0.0224 0 o 0231 0 0224 0.0229 000221 0.0227 0.0222 0.0227 0 0229 00214 0.o 0232 Average Diameter = 0.02267 So.U - 0.02280 cmo PATH B, APRIL 4, 1960 DIAMETER UNITRON EYEPIECE MICROMETER SCALE UNITS Horizontal Pass Vertical Pass 91o8 9302 97.0 94.0 91.1 94,7 94,7 9502 93.9 93.8 90.3 9504 94.o 94o0 94.6 95,3 94.0 92,0 92.2 94 3 94.7 94.7 96.1 93.2 94.8 9359 Average Diameter = 93.96 S.U. = 0.02278 cmo

-1735 4o CELL CHAMBER VOLUME DETERMINATION The volumes of the two cell chambers were determined by inserting a solid steel plug into the diffusion cell in place of the diffusion path plugs and weighing the amount of mercury which could be introduced into each of the chambers. The solid plug had nearly the same dimensions of the diffusion paths, however a small volume correctionl was necessary in order to determine the chamber volumes when the different diffusion paths were in place0 Table XVIII is a list of the volumes determined with the solid plug in place0 TABLE XVIII DIFFUSION CELL CHAMBER VOLUMES DETERMINED BY WEIGHT OF MERCURY Upper Chamber, cc Lower Chamber, cc 7~387 70116 70394 7o120 7~392 7o120 7.101 Average Volume 75391 cc 7o119 cc Correction for Path A 0O0635 cc 000025 cc Correction for Path B -0.0224 cc -0o0201 cc

5. CELL CONSTANT CALCULATION Since the geometry of the diffusion. cell is known. the cell constant can be calculated rather than be determL.ned by a calibration. The cell constant as derived by the mathematical analysis of Section III is related to the cross sectional area of the diffusion path, A, the length of the diffusion path, L, and the volumes of the two chambers, VU and VLo K =A _+ ) (53) L VU VL The respectlve lengths of paths A and B are 1.145 cm. and 1.397 cm. The methods for determination and values for the areas and volumes have been presented in previous sections of this appendix. The value for the cell constant with diffusion path A installed is~ A = 0.05899 cm2 (41 tubes of 0.0428 cm diameter) L = 1.145 cm VU = 7.455 cm3 VL = 7.122 cm3 K = 0.01414 cm'2 The value of the cell constant with path B installed is' A = 0.05176 cm2 (127 tubes of 0,,02278 cm diameter) L = 1.397 cm VU = 7.369 cm3 VL = 7. 099 cm3 K = 0.01025 cm

60 BACKGROUND CURRENT CALIBRATION DATA There was a small measurable current detected by the ionization current measurement circuit for each electrode when the gas in the diffusion cell chambers contained no radioactive material~ This background current was measured at intervals between the diffusion runs and-was found to be relatively constanrt at a given temperature over a given series of runsO After each instance of electrode insulation repair the background currents for runs at 1000C differed from those detected at 1000C before the repairo Electrode insulation repair did not seem to effect the background currents noted at 350Co Although the background was small with respect to the overall current measured during a driffusior. run, less than one percent of average measurements at 350C, the fact that i.t was differenrt for the two electrodes would have introduced an error into the resulting diffusion coefficients had it not been corrected for rin the calculationso Table XIX is a listing of backgrourd corrections made to ionizat'ion currents measured during the diffusion runso The backgrounds are listed in chart units since calculations were made in chart units for convenience. The chamber backgrounds were subtracted from the respective ionization currents from the two chambers before further calculations were carried outo Diffusion runs made after December 5, 1959 were made on chart paper with 50 main divisions full scale ra-ther

-176than 20 divisions full scale. As a result, chart units were smaller by a factor of 2/5 after that date. However, for comparison, values for the background are presented in Table XIX in 20 dlvision chart units. These, of course, had to be in the proper units for their use in the calculations. The backgrounds, as given in chart units based on a voltage range of 2.0 and 20 spaces full scale can be converted to current in amperes by Equation (54) which is a specific case of Equation (39). I (Background (54) (10 )(17.37)

-177TABLE XIX BACKGROUND CURRENT CALIBRATION DATA Full Background* Date Temperature Scale Voltage Zero Lower Upper Lower Upper C iChart Range Channel Channel Units BACKGROUNDS FOR RUNS 1A-5A, 10OB-40B, 66B-88B 6/29/59 55 20 0.02 1.3 5.0 100 0. 04 0.09 8/29/59 35 20 0.02 1.5 6,0 13.1 0.05 0.12 11./16/59 35 20 0.02 1.5 5.5 12.8 0.05 011 12/7/59 35 50 0.02 3.4 10.6 25,7 0.03 0.09 BACKGROUND FOR RUNS 41B-65B 8/17/59 100 20 0.10 1.5 11.7 15,3 0.51 0o69 9/25/59 100 20 0.10 1.5 13.7 15.5 0.61 0o70 10/12/59 100 20 0.10 1.5 11.3 13.5 0.49 0,60 BACKGROUND FOR RUNS 89B-1OOB 12/10/59 100 50 0.05 3.7 9,7 28.9 0.06 0~25 12/21/59 100 50 0.05 3.7 9.4 29.6 o.06 0,26 BACKGROUND FOR RUNS lO1B-106B 1/6/60 100 50 0.05 4.3 14.1 22,0,1o0 o.18 * Based on V.R. = 2.0, 20 chart units full scale.

-178APPENDIX G THE COMPUTER PROGRAM FOR DATA PROCESSING The calculations necessary for the processing of raw experimental data were greatly expedited because of the generous availability Of & high speed automatic computing machine, an IBM 704- vhich is located on the campus of the University of Michigan. It is;believed that the techniques made accessible due to the use of this machine are slightly more objective in nature than the methods used previously in similar works, The method of data analysis has been presented in the previous text, in Section IIIo In the analysis, values of the ionization currents'from the two cell chambers were read -at incremental values of the time from the chart traces prepared by the recording potentiometer0 This data was fit to Equation (25) by the method of least squares and the coefficient of time was the desired diffusion coefficient0 in (fI1-I2).....ln... = 3DG + constant3 (25) A l + 12 L V1 v Equation (55) is the equati-on of a straight line wi,th respect to the dependent variable, the left side of the equation, and the independent variable} time (0). Since any set of data can be fit to a stralght li.ne

by the method of least squares, a check of the validity of the straight line representation for each data run was necessary to determine whether or not there was systematic deviation from this straight line representationo In order to give a qualitative indication of a tendency toward curvature, the same experimental data was first fit to a simple equation of a curved line, of the form: y = A + Bx + Cx2 (55) Since the data taken all were of the same relative size with respect to the variables fit, the constant, C, in Equation Form (55) was a fairly good indication of quantitative tendancy toward curvature. This constant,was tested for size by the computer program and if it was less than an arbitrarily set maximumg the data was then fit to Equation (25) for evaluation of the diffusion coefficiento In the event that the arbitrary limit of C was exceeded, a systematic procedure for further consideration of the data and curvature tendency was carried out by the program. In the data processing method previously used in which the left side of Equation (25) was plotted versus the time, if one or more points was bad, this would be immediately evidento If a suitable explanation could be presented as to the cause, the polnt or points in question could either be revised or eliminated0

-18~ Unless this function was also built into the data processing program, the former method would certainly have been superioro It was felt that at least two such suitable explanations existed which shpuld be allowed to cause elimination of one or more of the points which were incrementally read f'om the recorder trac-s. The first explanation involves one or more points which occur t+o culose to the end of a run when the ratio of the HT concentrations rp-sent in the two cell chambers is too small for the resolution accuracy c' the equipment. It was felt that such points could be safely elimina4vcu if an adequate portion of straight line preceded these points. The second justifiable explanation concerns one or two points read from the beginning of a run which might deviate from the straight line representation because of mass transfer by mechanisms other than diffusion, such as convection caused by temperature inconsistencies. It was decided to allow the program to eliminate as many as two initial points for this reason. The point eliminations were made in the following mannero The set of incremental recorder trace points from a given run was first fit by Equation Form (55) and the constant, C, was tested for curvature effect present in the fit0 If the maximum was exceeded, the last point of the set was dropped and C was evaluated for the remaini.ng data. This elimination was continued until C was within the desired limits or until

-181only four points remained. A large curvature effect in the first four points indicated that the excessive curvature was probably caused by bad points at the beginning of the run. A point from the beginning of the set was then dropped and the entire set including those previously eliminated from the end of the set were then fitted to Equation Form (55). If C was still excessive, points were eliminated from the latter part of the run as before. The program allowed a maximum of two points to be removed from the first part of the run and a total minimum of four points to be fit if the curvature limit was never conformed too The program furnished information in the output as to how many points were eliminated and from which extreme of the set before a successful: fit was accomplished. For most runs, eight or ten points made up the entire set of points and normally all or all but one or two points satisfied the arbitrary curvature effect maximum. This maximum was determined by analyzing some of the runs graphically and setting the limiting constant to correspond with point eliminations which would have been made by critical inspection of the graphs. Only two runs, 13B and 21B, out of the 102 runs were found to be not acceptable due to not satisfying the curvature requirements. Both were calculated graphically and a definite curvature was noted for each. Since no slope could be determined graphically for these runs, no diffusion coefficient was evaluated.

TABLE XX FORTRAN DATA PROCESSING PROGRAM 1F?.R.V. T (.F,, %.,,; ____ __:)F,'Vl y, ( I l 17 -,' * 4 F L.'., F - l.. J F l,. 1.,I F.. 1 ). FORPVAT ( - 11, 1' 3 -!. ~. ) 13 FOMRAT( Ni ti,;. 3', F —: X37 i CtLLC ONlTA -L: i:_ / X37H A' LO'~'Ai& t __ 1 i;AT,~ - i 4 *7' X.37H C... - ND F'.2 * / X37H CF!E' -:i FR' P, / / X1O.H ~ \(O., AL./T X108 1 $ i e,N INC). C,L I- y > -- 1,< T' I T Y X.Ir F. X )DEN. __/TA- NT XD T T DI'iNPTIO\' Y( 5 ),T (, E"' ) Y T, 1, ) 5 ELAD I N P JT T" O 7,1,c, F;,',;,-i c T C' 4 X ^,.,R I TF OT P!T' i'a 6, 13,, CC' T, C,'AX, FP 7R 5R'AD IN3'"T rA E 7,2,N,,'b,!,,rr' P -'& 5"'' v* T7: pI,3 C)O 7 = 1,N 7 REA " IPL,T TAPE 7T,3,T( I ), I),R f ) 7 R I ) _ DO 9 I-'l,fV _ B( I)-(I)!- P-[ E 1 )___ ___ ___ __R R(I)-,-F*lR t I )-'-ZE IR(I ) ) Y(t)=LOGF('R(I)-()) __ 9 T( )=T(I)/CS 14 K=N c5,XT2-., SU1,YT = C. 5 LJYT = CY.,_, Y FK= KI-J+1 ) S 1G I=J,K T-,:-U,V'+T (I) UJHT2=SU,.iT2+T(' )*T(T ) _ __ _ __ _ CSJN'T3= $'1 3+T ( I )*T ( I )*T ( I ) JS I -4=!",T4+' T( I )TI )*T I )*T( I ) __ _ _ _ __ T _ 51'iY = Y'Y-TY Y( I ) Ci T iJ': Y Y T= 2'+V T j % + Y ( I ) "- 1VT I ) ( I ) C-i,K.T2 I' *'....;... T-, T' c' T,,- __ TYS- __ XT2-R<;V*Y- -N-^kSI2' ^l — <.' ttTTF; C 1YT>- lS T3 ) / ( F C'-Lj.W*\X9r- t-;i'T4N S jTS'c j TQ VSUt >'TX2+RUNT T 2 +' T -'r' r.T,c.' T - T V -Z-,, T iJ XT3) IF (;". 3 SF ( C) -CiA X 1 1.1 1i1 L'nLPc=Fr?'*U'\IyT- S_.i': -UJ'Y)/ K-':<'' T2-C!'" l-c qLjT'r ) C-=.t. OP -/( 12.'- - )T ) IF(f') 16,] 7,!6 1 5 C' =- X - * 2. 1 +( ( 1 x'.. r) " + 4 *. ) D= J S'CRTF (''.1 1-~;'", "1'-CU/! (4. i-.Fv"'/r. ) ) 17 D>EN= "- N __ L =-J+1'WRITE O.TPUT TA-E T6,4.,LP N,DEN,D,D rFN,,,J,XH ) _ GO TO 6 12 K=K-1;F (K-J.-2) 11,15,8 15 J=J+! TI (I-.q) /4,1, 11

Table XX is the program used for data processing as listed in Fortran compiler languageo The data was read into the computer on three types of IBM cards. The first type preceded the entire deck of data cards to be computed at a given time and furnished the chamber sensitivity factor, f, the upper and lower chamber background currents, BR and BB, the cell constant, K, and the maximum allowable curvature, C. Following this general information card, the remaining data cards were further subdivided into sets with a set of cards for each data run. Each run set was made up of a general information card followed by cards furnishing data for each increment of time from the recorder traceo The run general information card provided the program with the run number, the sample mole fraction of hydrogen, the chart speed, the run pressure, the run compressibility, the average molecular weight of all runs from the sample bottle used, the number of time incremental points to be read by the program, and the run temperature. Each incremental data card furnished the values of time in chart units, the ionization currents in chart units, and the zero value of the trace when the Ultrohmeter input was shorted. The results of the computations for one run were printed out on the equivalent of a single IBM card giving the run number, the run density, the computed Fick diffusion coefficient, the diffusivitydensity product, three numbers indicating the locations and numbers of any eliminated data points, and the mole fraction of hydrogen in the run sample.

NOMENCLATURE Symb ol A Area, cm2o B(T) Second virial coefficient for real gases, cm3 per gram mole. bo Second virial coefficient for solid spherical molecules. Ci Concentration, gram moles per liter, of ith component. Di Diffusion coefficient, cm2 per second, of one component of a multicomponent mixture. Dij Binary diffusion coefficient, cm2 per second, of ith component through jth coiAponent. Do Diffusion coefficient, cm' per second, evaluated by dilute gas theory. DL Liquid diffusion coefficient, cm2 per second. DFS Diffusion coefficient, cm2 per second, in free space. d Diameter of capillary tube, cm. E Energy constant associated with exponential form of liquid diffusivity temperature dependence. f Ratio of ionization currents of lower toupper chambers containing same HT concentration. (2) fC Theoretically derived factor of the diffusivity which accounts for the concentration, resulting in the second approximation of the diffusion coefficient. Ii Ionization current from upper or lower chambers, i = U, L. i Index, represents number or letter denoting specific entity. j Index, represents number or letter denoting specific entity.

-185 - Symbol Ji Diffusion flux, gram moles per second per cm2o K Cell constant, differs for paths A or B installed in diffusion cell. L Length of tube bundle, cm. MAVG Weighted average molecular weight of components. Mi Molecular weight of component i, computed on the basis of the following atomic weightse- A, 39,944; H) 1.008; T, 3*017; C, 12..OL;011. 0 1LS6'001 Ni Total flux past stationary coordinates, gm moles per second per cm2. n Number of molecules per unit volume. P Pressure, psia. PC Critical pressure, psia, of a pure component. PCm, Pseudocritical pressure, psia, of a mixture. Ps. Reduced pressure, P/PC(m)~ R Gas constant, 10.7315 (Psia)(ft5), 1.20591 (psia)(ter) (lb. mols)(OR) (gm mols)(OK) r Derived constant, listed as function of the acentric factor, a, and TRO s Derived co-astant, listed as function of the acentric factor, W, and TRo T Absolute temperature, ~K, t~C + 273.20 t Temperature, "C. TC Critical temperature of pure component, ~K. TCjn Pseudocritical temperature of a mixture, OK. Reduced temperature, T/TC(m)' i-rCm)

-186NOMENCLATURE (cont.) U Internal energy, Calories per mol V Specific volume, cm3 per gram. moleo Critical specific volume, cm3 per gram mole, of pure component. _Vcp Critical specific volume, cm3 per gram mole, of a mixture. Vi Volume of chamber i, cm 3 i = U, L, x Distance parallel to diffusion flux, cmo Yi Dense gas correction to pure component diffusion coefficient. (Enskog 13) )o Yij Dense gas correction 2 binary diffusion coefficient (Thorne42) ) 0 y PV 1 for rigid spheres; the basis of the Enskog RT relations between the state variables and ddiffusion theory for dense gases0 yi Mol fraction of component i in the gaseous s tate0 Z, Z(TjV) Compressibility factor, ZC Critical compressibility factor0 z(O) Compressibility for gas for which the acentric factor, w, is equal to zero0 z(1) Additive compressibility correction for gases having appreciable acentric factor0 Greek Symbols CX Sign indicating proportionalityo Operator denoting macroscopic difference with respect to distance or time0 V Space gradient operator, ) + t in three ax ay az dimensional space

NOMENCLATURE (cont.) 64 Characteristic parameter of a molecule, i, which describes the attractive force between molecules. Eij Eqiuals (e 1 ej)2 for molecules i, j of a binary mixture. S Time, seconds. k Boltzmann's constant. X Mean free path of a molecule, cmo p Density, gram moles per liter0 ali Parameter of Lennard-Jones potential for a single component, i, known as the "collision diamerter", values from reference (17), aH2 = 2a915A CO2 = 3o897A, aA 3.465A. aij "Collision diameter" for collisions between unlike Q. +aC molecules, i and j, cm, 2 2(ll~)* "Collision integral", function of k_, describing diffusional collisions, Tabular values in RefeAenee (17)o Acentric factor parameter of Pitzer (32) correlation for compressibility of component i. Equals - log PR - 1.00 at Tr = 0~7~ Mean acentric factor for a mixture. Singular subscripts. U Denotes upper chamber of the diffusion cello L Denotes lower chamber of the diffusion cell. 0 Denotes value predicted by dilute gas theory.

-188 - BIBLIOGRAPHY 1. Becker, E, W., Vogell, W. and Zigen, F., Z, Naturforscho, 8a: 686 1953. 2. Bennett, C. 0.., "Diffusion in Binary Mixtures," Chemical Engineering Science, 9: 45 1958. 3. Berry, V. J., Koeller, R. C., "Diffusion in Compressed Binary Gaseous Systemsj," A.I.Ch,E. Journal 6: 274 1960. 4. Bird, R, B,, Advances in Chemical Engineering, Vol. 1, ppo 156-239, Academic Press, New York, 1956. 5. Boardman, L, E. and Wild, N. E,, Proceedings of the Royal Society of London, A162: 511 1937. 6. Boyd, C. A., Stein, N., Steingrimsson, V. and Rumpel, W. F,, J. Chem. Phys., 19: 548 1951, 7. Chang, C. S. W., Ph.D. Thesis, University of Michigan, 1944. 8, Chapman, S. and Cowling, T. G., The Mathematical Theory of Non-Uniform Gases, Cambridge Press, 1939. 9. Chou, C., Ph D. Thesis, University of Michigan, 1954. 10. Chou, C, and Martin, Ji J o "Diffusion of C1402 in Mixtures of C1202-H2 and C 202-C3H8," Ind. Eng. Chemo 49: 758 1957o 11. Crank, J., "The Mathematics of Diffusion," Oxford U. Clarendon Press, London, 1956, 12.'Dodge, B., Chemical Engineering Thermodynamics, McGraw-Hill Book Company, Inc, New York, 1944, 135 Enskog, D., Dissertation, Upsala, 1917, 140 Groth, Wo and. Harteck, P. Z. Physik, Chem., 199: 114 1952, 15. Harteck, P. and Schmidt, H. W. Z. Physik Chem., B21~ 447 1933. 16o Heath, H., Ibbs, T, and Wild, N., Proc. Roy. Soc. (London) A178: 380 1941,

.189 BIBLIOGRAPHY (cont.) 17. Hirschfelder, J 0o,, Curtiss, C, F. and Bird, R. Bo, Molecular Theory of Gases and. Liquids, Wiley, New York, 19.418. International Critical Tables, McGraw-Hill, New York, 1929. 19. Jefferies, Q. Ro and Drickamer, H. G.o Jo Chem. Phys., 160 968 1948. 20. Jefferies, Q. R, and Drickamer, H. G., J. Chemo Phys., 220 436 1954. 21. Jost, W., Diffusion in Solids, Liquids and Gases, New York Academic Press, 1952. 22 -Kihara, T., Imperfect Gases, Asakusa Bookstore, Tokyo, 1949. 23. Krichevskii, I. and Markov, V., Acta Physicochim., U,oRoSoSo 120 59 1940o 24. Lonius, Ao, Ann, Physik, 29: 664 1909o 25. Loschmidt, J,, Sitzungsber. Akad. Wien, 61~ 367 1870. 26. Mason, E. A,, JO Chemo Phys., 235 49 1955. 27. Mattraw, H. C.o Pachucki, C. F. and Dorfman, L,, J. Chem, Phys,, 200 926 1952, 28, Mifflin, T. Ro, PhoD. Thesis, Purdue University, 1959. 29, Mifflin, To Ro and Bennett, Co 0., "Self-Diffusion in Argon to 300 Atmospheres,"' J. Chem,, Phys., 29: 975 1.958. 30. O.Hern, Ho A,, Ph.D. Thesis, University of Michigan, 1952. 31. O0Hern, Ho A. and Martin, J. Jo., Ind. Engo Chem., 47: 2081 1955. 32, Pitzer, K. S. J. Am. Chem. Soc., 770 3427 1955. 335 Pitzer, Ko S.o J. Amo Chemo Soc., 79~ 2369 19570 34. Pollard, Wo and Present, Ro. Phys, Rev,, 753 762 1948o

-190BIBLIOGRAPHY (cont.) 355 Prausnitz, Jo M. and Gunn, Ro, AoIoChoEo Journal, 4: 430 19580 36. Prausnitz, Jo M., A.I.ChoEo Journal, 5: 3.1959o 37~ Reid, R. CO and Sherwood, T. KO, The Properties of Gases and Liquids, McGraw Hill, New York, 1958& 38. Robb, WO L. and Drickamer, Ho G., Jo Chem. Physo, 190 1504 1951. 39. Roth, W., Arch. Eisenhuttenwo, 8: 401 19350 40. Schafer, K., Corte, H., and Moesta, Ho, Z. Elektrochem., 19: 662 1951. 41o Slattery, J. C., M.S. Thesis, Univ0 of Wisconsin, Department of Chemical Engineering, 1955O 42. Thorne, Ho H, cof. Chapman and Cowling (8), 2920 43~ Timmerhaus, KQ Do and Drickamer, Ho G., J. Chem. Physo, 19: 1242 19510 44~ Timmerhaus, Ko D. and Drickamer, H. Go, J. Chem. Phys0, 20: 981 19520 45~ Verschaffelt, J. Eo, Arch0 Neerlandc Scio Exact. Nat,, ll 403 19060 46. Waldmann, Lo, Naturwissenschaften, 32: 222 19440 47. Wilke, CO R,, "Diffusional Properties of Multicomponent Gases," Ch. Engo Prog., 46: 95 1950o 48. Woolley, Ho W., Scott, Ro Bo and Brickwedde, F. Go, Jo Res. Nat'l. Bur. Stdso 410 379 1948o 3 9015 02526 1689