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D degree in Mechanical Engineering Emu of we M a jor professor 1/25/83 Date MSU is an Affirmative Action/Equal Opportunity Institution 0-12771 RR RRRRR 1’ RETURNING MATERIALS: )ViESIgi Place in book drop to remove this checkout from w your record. FINES will be charged if book is returned after the date stamped below. 1“" '0 lg; 1:“. 16. I; t I L RRN 1" 002.2005 h...“ . ‘ -... .- u. A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF THE CHEMICAL KINETICS OF AN OXYGEN MICROWAVE DISCHARGE BY Mary Lynn Brake A DISSERTATION Submitted to Michigan State Unviersity in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Mechanical Engineering 1983 6130579 Copyright by MARY LYNN BRAKE 1983 ABSTRACT A THEORETICAL AND EXPERIMENTAL INVESTIGATION OF THE CHEMICAL KINETICS OF AN OXYGEN MICROWAVE DISCHARGE BY Mary Lynn Brake In this dissertation, the degree of dissociation and recombination of oxygen atoms produced in a microwave discharge in oxygen is examined by comparing theoretical models of the kinetic mechanisms to chemical titration_ data. A literature search is used to gain understanding of the chemical and relaxation kinetic mechanisms necessary for the formulation of the theoretical models. A comparison of the theoretical models to experimental results shows that a one dimensional, temperature dependent model of the neutral species of the system can predict the oxygen atom concentration profile as measured by nitrogen dioxide titration. The model also indicates that the temperature of the gas is approximately 1000K and that an overall gas temperature and velocity increase is due to heating by the microwave discharge and not due to the enthalpy change of the species in the system. ACKNOWLEDGMENTS I would like to express my gratitude to Professor Ronald Kerber, my thesis advisor, for his encouragement and interest over the past three years. I would like to thank Professor Jes Asmussen and the students in the Laser_and Plasma Labs for their suggestions and advice. I am ‘0) *4 so grateful to Professors T. Harvey Edwards, John McGrath and Jerry Nolen who served on my guidance committee. I would especially like to thank the following friends: Mr. Jeffrey Hinkle for not only designing the oxygen microwave experiment, but making work, Dr. Thomas Pierce III for graciously providing me with copies of EPISODE and LSODI as well as advice in their usage, Dr. Robert Ball for many hours of badly needed computer consultation and Dr. Mary Beth Kazanski for her constant support and encouragement. Last, he certainly not least, I would like to thank my parents, Richard and Jane Brake for their support these many years and I would like to thank my husband Bob, for enduring many long hours on the road, so that I might be able to finish this project. iii TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES LIST OF SYMBOLS CHAPTER I. INTRODUCTION . . . . . . . . . . . . . . l 1.1 Plasma Chemistry. . . . . . . . . . l 1.2 Previous Models and Experiments 6 1.3 Objectives of Present Research. 7 CHAPTER II. SIMPLE MODELING. . . . . . . . . . . . . 10 2. 1 Simple Model Formulation. . . . . . 10 2. 2 Simple Model Results. . . . . . . . 20 2.2.1 Effect of Molecular Oxygen . 21 2.2.2 Effect of Excited Atomic Oxygen . . . . . . . . . . . 24 2.2.3 Effect of Excited Molecular ‘ Oxygen . . . . . . . . . . . 25 2.2.4 Effect of Ozone. . . . . . . 29 2.2.5 Effect of Pressure . . . . . 31 2.3 Summary and Conclusions . . . . . . 33 CHAPTER III. OXYGEN KINETICS. . . . . . . . . . . . . 34 3.1 Introduction . . . . . . . 34 3.2 Two Body Reaction of Ozone and Oxygen35 3.3 Singlet Delta and Ozone . . . . 41 3.4 Collisional Deactivation of Singlet Delta . . . . . . . . . . . . . . 42 3.5 Oxygen Atom Recombination . . . . . 43 3.6 Ozone Formation . . . . . . . . . . 46 3.7 Wall Recombination. . . . . . . . . 49 CHAPTER IV. MODEL FORMULATION. . . . . . . . . . . . 52 4.1 Model Assumptions . . . . . . . . . 52 4.2 Conservation Equations. . . . . . . 53 4.2.1 Conservation of Mass . . . . 55 4.2.2 Conservation of Momentum . . 55 4.2.3 Conservation of Energy . . . 56 4.3 Differential Equations . . . . . . 58 CHAPTER V. EXPERIMENTAL APPARATUS . . . . . . . . . 61 5.1 Reactor Flow System . . . . . . . . 61 5.2 Plasma Cavity and Microwave System. 63 5.3 Nitrogen Dioxide Titration System . 64 5 4 Titration Technique . . . . . . . . 66 iv CHAPTER VI. RESULTS OF MODEL. . . . . . . . . . . 72 6.1 Comparison of Model to Experimental Results. . . . . . . . . . . . . 72 6.2 Comparison with Other Experiments. . 94 6.3 Temperature and Velocity Predictions 105 6.4 Singlet Delta Formation. . . . . . . 107 CHAPTER VII. CONCLUSIONS . . . . . . . . . . . . . . . 114 7.1 Conclusions. . . . . . . . . 114 7 2 Recommendations for Future Work. 117 APPENDICES A. Suggested Rate Coefficients for the Neutral Kinetics of an Oxygen Discharge. . . . . . . . . . . . . . . 120 B. Equilibrium Constant Determination. . . . . 122 C. Accuracy of Nitrogen Dioxide Technique. . . . . 126 D. Spectroscopic Measurements. . . . . . . . . . . . . 134 D.l Introduction . . . . . . . . . . . . . . . . . 134 D.2 Species Identification . . . . . . . . . . . 135 D.3 Stark Broadening . . . . . . . . . . . . . . . 137 D.3.1 Introduction. . . . . . . . . . . . . . 137 D.3.2 Experimental Apparatus. . . . . . . . . 141 D.3.2.1 Reactor Flow System. . . . . 141 D.3.2.2 Microwave System . . . . 143 D.3.2.3 Optical System . . . . . 144 D.3.3 Results D.3.4 Error Discussion. . . 152 D.3.5 Recommendations for Electron Density Measurements. . . . . . . . 155 D.4 Electron Temperature D. 4. 1 Introduction. . . . . . . . . . . . . 156 D. 4. 2 Experiment. . . . . . . . . . . . . . . 159 D. 4. 3 Results . . . . . . . . . . . . . . . . 160 D. 4. 4 Recommendations for Electronic Temperatures. . . . . . . . . . . . . . 167 D.5 Rotational Temperature of Oxygen . . . . . . . 168 D.5.1 Introduction. . . . . . . . . . . . . 168 D.5.2 Experiment. . . . . . . . . . . . . . . 169 D.5 3 Results . . . . . . . . . . . . . . . 170 D.5 4 Recommendations for Rotational Temperatures. . . . . . . . . . . . 177 D.6 Conclusions. . . . . . . . . . . . 177 E. Rate Coefficients for Charged Collisional Partners in Oxygen Dissociation . . . . . . . . . . 178 LIST OF REFERENCES . . . . . . . . . . . . . . . 182 Table Table Table Table Table Table Table Table Table Table LIST OF TABLES Rate Coefficients for Neutral Collision Partners in 02 Dissociation. . . . . . . . ll Excited States of O2 and O . . . . . . . . 16 Temperature Dependent Rate Coefficients for Neutral Reactions of Oxygen. . . . . . . . 36 Summary of Oxygen Discharge Experiments. . 96 List of Observed Neutral Lines in 02 and Ar Plasmas . . . . . . . . . . . . . . . . 136 Values for C(N ,T ) for H . . . . . . . . 140 e e B The Half Width of Voigt Profilelel. . . . 149 Emission Lines Used to Check Experimental Method . . . . . . . . . . . . . . . . . . 162 Lines used in Temperature Determination. . 164 Bagdlgiads of the First Negative System of 02 . . . . . . . . . . . . . . 172 vi Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure LIST OF FIGURES A schematic showing the energy processes in a microwave discharge. . . . . . . . . . . . . 5 Time history of species concentrations. Initial conditions were 100 % dissociation at an initial pressure of 10 torr where 10 % of the initial 0 atom concentration was in the O( D) state. . 22 The effect of 0/02 ratio on the halflife of atomic oxygen. . . . . . . . . . . . . . . . 23 The oxygen atom halflife as a function of the input ratio of 02( A) to total molecular oxygen . . . . . . . . . . . . . . . . . . . 26 A comparison of two time histories at a pressure of l torr and 100% dissociation. 1) This model included both excited and ground state kinetics. 2) This model included only ground state kinetics . . . . . . . . . . . . . . . 28 The effect of O /O on oxygen atom halflife. (All other initial 0 ncentrations were zero.) . . 30 Effect of pressure on oxygen atom halflife. l) The input ratio of 0:0 was 1:10 with all other input concentrations eq al to zero. 2) The input ratio of 0:0 :0 ( A) was 30:24:16. 3) 100% dissociation.2. ? . . . . . . . . . 32 Recombination rate constant as a function of temperature as suggested by various studies. 47 The formation rate of ozone as a function of temperature for M = O and M = O as suggested by the indicated invegtigators. . . . . . . 50 Experimental Apparatus . . . . . . . . . . . 62 Nitrogen dioxide titration technique . . . . 65 The effect of distance on oxygen atom concentration for several pressures. . . . . 69 The amount of O converted to atoms vs distance from the exit of the reactor cavity for several pressures. . . . . . . . . . . . . . 70 vii Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure 5.5 The amount of O converted to atoms vs distance for seaeral flowrates . . . . . . . 71 6.1 The model based net rates as a function of distance from the exit of the discharge. . . 74 6.2 The solid line is the best fit to the titration data points. The dashed lines are the theoretical lines for different wall recombination coefficients. A recombination coefficient of 0.0005 was found to best approximate the data of the two cases of 8 and 12 torr. . . . . . . . . . . . . . . . 76 6.3 A comparison of predicted O atom mass flow— rates with titration data using independently measured three body recombination rate coefficients . . . . . . . . . . . . . . . . 77 6.4 A comparison of predicted O atom mass flow— rates with titration data using independently measured three body recombination rate coefficients . . . . . . . . . . . . . . . . 78 6.5 A comparison of predicted O atom mass flow- rates with titration data using independently measured three body recombination rate coefficients . . . . . . . . . . . . . . . . 79 6.6 The dashed line indicates the model predic- tions using a 3:1 ratio of relative efficiencies of O :O for three body recombination. The solid line shows the model predicggons using a 1:3 ratio as suggested by Wray. . . . . . 81 6.7 The solid line indicates the model predic— tions using a 3:1 ratio of relative efficiencies of O :O for three body recombination. The dashéd lines show the model predggtions using a 1:3 ratio as suggested by Wray . . . . . 82 6.8-6.11 The solid line indicates the model predictions for O atom decay as a function of distance for several pressures and flow- rates. The actual data points are indicated by the solid circles . . . . . . . . . . . . 84 6.12-6.15 The solid line indicates the model predictions for O atom decay as a function of distance for several pressures and flow- rates. The actual data points are indicated by the solid circles . . . . . . . . . . . . 85 viii Figure Figure Figure Figure Figure Figure Figure Figure Figure 6.16-6.17 The solid line indicates the model 6.21 6.24 predictions for O atom decay as a function of distance. The actual data points are indicated by the solid circles. . . . . . . 86 A comparison of the model predictions (dashed line) of the mass flowrate of NO as a function of flowrate of initial 5 for fixed temperatures at the exit of the d1scharge, and the actual mass flowrate measurements as a function of flowrate of initial 02. . . . 89 The semi-empirical temperatures as a function of inverse flowrate of initial 0 as determined from Figure 6.19 . . g . . . . . 91 Velocity (solid line) and temperature (dashed line) predictions as a function of distance from the exit of the discharge. . . . . . . 105 Model predictions of the final gas temperature (solid line) and velocity (dashed line) as a function of pressure. . . . . . . . . . . 108 Model predictions of final velocity as a function of exit temperature. . . . . . . . 109 The concentrations of important species of an electrical discharge as a function of distance from the discharge . . . . . . . . 110 The solid lines indicate the O and 0 (1A) concentrations as a function of distance when all of the molecular oxygen formed by wall recombination is in the ground state. The dashed line indicates the concentrations whep 30% of the wall recombination produces 02( A). . . . . . . . . . . . . . . . . . . 111 The solid lines indicate the O and 02(1A) concentrations as a function of distance when all of the molecular oxygen formed by wall recombination is in the ground state. The dashed line indicates the concentrations whep 30% of the wall recombination produces 02( A). . . . . . . . . . . . . . . . . . . 112 ix Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure Figure C1 C2 D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11 The net reaction rates as a function of initial 0 /0 ratio. The dashed line indicates the time go deplete the O atom concentration to 1% of its initial concentration as a function of initial 02/0 ratio. . . . . . 130 The net reaction rates as a function of initial 0 /0 ratio. The dashed line indicates the time go deplete the O atom concentration to 1% of its initial concentration as a function of initial 02/0 ratio. . . 131 Experimental Apparatus. . . . . . . 142 The top photo shows an argon plasma at 38 torr with 5% hydrogen added and the second photo shows a pure argon plasma at 38 torr. 145 o The line shape of HB (4861A). . . . . . 147 The electron density as a function of pressure. . . . . . . . . . . . . . . . 148 An example of the photographs used to determine the volume of the plasma. . . . 150 The power density as a function of pressure 153 An example of an argon emission line. . . . 161 Temperature determination from ratios of line intensities. . . . . . . . . . 165 Structure of the rotational levelilgor the first negative band of oxygen . . 171 An example of 02+ first negative band spectra . . . . . . . . . . . . . . . . 173 The inverse of the slope of the natural logarithm of the intensity versus the energy of the upper state is the rotational temp— erature . . . . . . . . . . . . . . . . 175 J! J" LIST OF SYMBOLS cross segtional area of the plasma containment tube (2.54 cm ) Einstein coefficient, probability of spontaneous emission from state i to j rotational constant for upper rotational state (cm-l) speed of light (3.0x10lo cm/sec) specific heat (cal/mole-K) electric field strength energy of state 1 mass flowrate (moles/sec) External force statistical weight enthalpy (cal/gm) = l/o I niHi enthalpy of species 1 (cal/moles) the sgcond line in the Balmer series of hydrogen (4861A) Planck's constant (6.626x10'34 Joule-sec) upper rotational quantum number lower rotational quantum number -23 Joules/K) Boltzmann's constant (1.38x10 path length of emitted light molecular weight (gm/mole) species concentration (moles/cc) xi AA electron density (cm-3) integrated radiance of an atomic line pressure = EniR'T = pRT (torr) 1 pressure increase (torr/sec) of NO2 into a known volume V NO2 R'/M (cmz/secz—K) universal gas constant (8.3x107 ergs/mole—K) entropy of a species (cal/mole—K) temperature (Kelvin) electron temperature linear velocity of gas (cm/sec) partition function shear force density (gm/cc) wavelength of light full width at half height of a Stark broadened line xii 95.5.2238 -.I. INTRODUCTION 1.1 Plasma Chemistry All matter exists in one of four states; solids, liquids, gases, or plasmas. The first three states are the most familiar but plasmas are believed to be the most abundant, with as much as 99% of the universe existing in 1'2 A plasma is defined as any gaseous the plasma state. system containing a sufficient number of electrons and ions such that long range electromagnetic (Coulomb) forces dominate the behavior of the gas. Note that a normal gas acts as an insulator whereas a plasma acts as a conductor.1 A transfer from one state to another can be accomplished through a transfer of energy. Energy added to a solid causes it to melt and become a liquid. Heat added to a liquid results in vaporization and the formation of gases. As even more energy is pumped into a gas, molecules dissociate and neutral species ionize, creating ions and electrons. These free electrons continue to transfer energy to the rest of the gas through elastic and inelastic collisions. In recent years, the uses of plasmas in chemistry have 3-6 gained much attention. There are many advantages associated with using plasmas for producing chemical species. One of the biggest advantages is that the high temperatures of plasmas are associated with producing high 3 which may be yields of pure and ultra-pure substances impossible to produce at low temperatures. This ability to produce non-equilibrium species concentrations at low overall gas temperatures reduces the requirements for heat loss control and durable reactor materials.4 Through optimization, plasma chemistry can not only improve product quality but can reduce labor and handling and reduce utilization of hazardous or costly chemicals.5 Perhaps one of the most important contributions of plasmas in chemistry is the ability to "generate the precursors to the desired products, rather than to produce these products directly".4 There are many applications of plasma chemistry in industry, science and medicine. In particular, due to the reactive nature of oxygen, oxygen plasmas have a wealth of applications. Oxygen plasmas are used to improve the bond strength of industrial materials. Oxygen plasmas can isolate trace constituents in complex organic structures, so that chemical analysis can be used to identify the trace substances. Oxygen plasmas prepare specimens for microscopy in the process of surface etching, thin film deposition and "ashing". Oxygen plasmas are also used in the fabrication of semiconductor devices by removing photoresist, depositing organic. and inorganic dieletric films, and by etching surfaces. (See Reference 5 for details.) Oxygen plasmas can be initiated in many ways; glow discharges, plasma jets, shock tubes, and radio frequency discharges to name a few. Microwave discharges are particularly suitable for plasma chemistry applications because they do not use electrodes which can become contaminated and because microwave power supplies have become both plentiful and inexpensive.7 Microwave discharges are characterized as gases which are partially ionized by absorption of radiation in the microwave region of the electro-magnetic spectrum. Generally, as a gas flows through a "resonant cavity" which contains the microwave radiation, it absorbs electrical energy. The electrons in the gas gain kinetic energy from interactions with the electric field and then transfer some of this energy through elastic and inelastic collisions to the neutral and ionic species of the gas. This energy transfer manifests itself in dissociation and ionization and in populating electronic, vibrational and rotational states as well as causing a thermal energy increase of the gas as a whole. When the gas leaves the reactor cavity, the electrons recombine with the ions and the gas relaxes to an equilibrium state different from the Pre-discharge state. This new state may be characterized by a different temperature, a different velocity or by a different mixture of atoms and molecules. (See Figure 1.1 for a schematic of plasma processes in a microwave discharge.) A potentially useful application of microwave 8 The free. discharges is "free radical propulsion". radical propulsion concept uses the fact that the gas exiting a microwave discharge is at a different state than the initial gas. Originally it was thought that spacecraft propulsion could be obtained from the thermal energy released when dissociated diatomics recombine exothermically.8 It is the purpose of this dissertation to examine the effects of microwave fields on oxygen and to investigate the chemical kinetic mechanisms involved in the transfer of electrical to thermal energy. Such understanding will permit assessment of the use of oxygen plasmas or plasmas of similar gases for various applications including spacecraft propulsion. It will be shown that the thermal energy increase anticipated for spacecraft propulsion is due solely to neutral gas heating and not due to the chemical energy released in recombination. Microwave Energy Electrons Absorb Electrical Energy. Electrons Transfer Energy to Neutral Gas Via Inelastic and Elastic Collisions. Electron Energy Transfer Results in Ionization, Dissociation, Excitation and Heating. Reactor Cavity Energy is Lost Due To Heat Conduction, Convection and Radiation. \V A 1 i . >> . . . . . . = Tex1t T1n1t1a1 T1n1t1al 300 K : Pressure=PO Pressure=PO i IFigure 1.1. A schematic showing the energy procesSes in a microwave discharge. 1.2 Previous Models and Experiments Oxygen plasmas have been examined in a variety of experiments and models. Bell and Kwong9 examined two and three body recombination in a radio frequency discharge 10 and Francis11 have also (13.56 MHz). Mearns and Morris examined three body reCombination of oxygen -atoms with oxygen molecules in a microwave discharge (2.54 GHz). These three studies did not however examine the role of electronically excited states of oxygen atoms and 12 molecules. Bonnet examined oxygen kinetic mechanisms for an electron beam controlled discharge in oxygen that did include excited species of oxygen molecules. Kocian13 studied some of the same mechanisms as Bonnet but for a positive column discharge. Waynel4 compiled an extensive literature review of oxygen kinetic mechanisms in discharges, however he has not examined these mechanisms in a model nor has he compared predictions of a model to experimental results. 5,9 12 Both Bell have used their model in and Bonnet computer simulations to make theoretical predictions about species concentrations as a function of time, atomic conversion (into molecules), Power, pressure and electric field strength. Both include the effect of the electric field, where the electrical energy is absorbed wholly by the electrons. Neither group however makes the distinction between the plasma inside the reactor cavity and the gas system outside the reactor cavity. Bell compares his model with the results of Mearns and Morrislo, but the data taken by Mearns and Morris was measured outside the reactor cavity (where presumably the electric field is not the same as in the reactor cavity and is possibly nearly zero). The amount of molecular conversion was linearly extrapolated back to the exit of the discharge but not into the discharge. To correctly make comparisons with experimental data taken outside the discharge and to make conclusions about the kinetic mechanisms, only that part of the discharge should be modeled. 1.3 Objectives 9f Present Research The objective of this dissertation is to examine the change in oxygen as it travels through a reactor cavity containing a microwave field. This can only be accomplished by understanding the chemical kinetics of oxygen and how they affect the temperature and velocity of the gas. ,The specific objectives listed below are presented in the chronological order in which they were performed. 1. Identify the important chemical kinetic mechanisms of an oxygen discharge from the long list of possible reactions. 2. Determine the importance of electronically excited states to the chemical kinetics. 3. Determine the effect of temperature on the kinetic mechanisms. 4. Compare model predictions of the oxygen atom concentration f the gas after it has interacted with the microwave field with titration data. Examine the effects of temperature and velocity on the model. 5. Examine the overall changes in the oxygen gas due to interactions with the the microwave field. The first objective is accomplished in Chapter II. A simple computer model is formulated that examines the importance of the many chemical reactions by determining which reactions dominate the chemical species derivatives as a function of time. The importance of electronically excited states is assessed at this time. In Chapter III, a literature search of the temperature dependence of the rate coefficients of the important reactions found in Chapter II is discussed. Also, the forward rate coefficient for each important reaction is suggested. A summary of the important reactions and their recommended rate coefficients is given in Appendix A. The ‘formulation of a model which includes the conservation of energy and momentum as well as the continuity equation for each species is formulated in Chapter IV. In Chapter VI the model is compared to experimental results of Chapter V, as well as other models. Velocity, temperature and 02(1A ) formation predictions are made based upon the results of the model. Conclusions based upon. the observations of this work are given in Chapter VII. Electron and ion species collision processes are also very important in electrical discharges. (See Appendix E for a listing of some of the important charged species reactions in oxygen.) However, many experimental parameters such as the electron density, the electron temperature and the electron distribution function are needed to properly model these kinetic processes. These parameters are very difficult to measure in microwave discharges. Appendix C discusses emission spectroscopy techniques for determining electron density, electron temperature and gas temperature in argon and oxygen microwave discharges. In other works such as that of 15 and Bonnetlz, electron and ion collision induced Dettmer processes are discussed for oxygen in DC positive column and e-beam discharges. CHAPTER 1; S IMPLE MODELING 2.1 Simple Model Formulation The first step in modeling the chemical kinetics of any system is to compile a list of the relevent mechanisms, (see Table 2.1). Generally, the neutral kinetic mechanisms important to this dissertation have been studied in ultra-violet flash. photolysis of ozone and molecular oxygen, shock tube studies and electrical discharges. The vast majority of kinetic reactions were studied at one temperature only. The simple model discussed in this chapter examines the relative importance of the probable kinetic mechanisms of an oxygen gas system in chemical nonequilibrium, at the thermal equilibrium temperature of 300 K. Chapter III gives a comprehensive literature review of the temperature dependence of the most important mechanisms found in this chapter. This model is based upon the mechanisms given by Wayne14 and upon a similar model for an oxygen laser.l6 Atmospheric studies”-23 have also provided possible kinetic mechanisms of systems comprised of oxygen. 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I mon H H H mHH Hasmm e AMNNNVE m N N N . o Hflms HNHV 0 MN N N . o HNR3 Hm£ mucowowwmooo much HH< HaemMI x umHoz COHUmHSEHm Houpmsoo CH pom: mmpHm> R >; + HNHvNo .oN >t + HaavNo .mN >n + Agave .qN Axmevm coauomom popcwucoo H.N memH 15 coefficients experimentally measured for each reaction agree well with one another (see Table 2.1). All of the reactions listed in Table 2.1 were included in the computer model and the asterisks denote the forward rate constant chosen for this model. The first few electronically excited states of oxygen atoms and molecules are indicated in Table 2.2. As suggested by Wayne, the products of an electrical discharge of oxygen may contain an appreciable number of electronically excited states of oxygen. This model includes reactions that involve the first excited state of atomic oxygen 0(1D) which is 1.96 eV above the ground state, and the first two excited states of molecular oxygen 1 O A ) and 02(12 ) which are 0.98 eV and 1.64 eV above the 2( ground state, respectively. States higher than 2.0 eV are very short lived and are assumed to have very small concentrations compared with the first excited states. In modeling any system, a few initial assumptions must be made. In this model, the velocity of the flowing system remained constant and the pressure was allowed to vary. Also it is assumed that the electric field outside of the discharge was zero and that the electron and ion densities outside of the discharge were negligible. Also the temperature of the gas was set equal to 300 K, and the initial gas was assumed to be a homogeneous mixture of O, 16 Table 2.2. Excited states of O2 and 0 02 STATE ENERGY(eV) Mean Radiative Lifetime (sec) 3 _ v 0.0 1‘19 0. 8 3 Ag 9 l + 29 1.64 12.0 3 + Eu 4.3 0.03 32- 6.1 4.2x10‘8 U o 3P 0.0 lo 1.96 148.0 150 2.22 0.80 552 9.13 6.0x10'4 35 9.51 1.8x10‘9 17 O2 , O3 , 0(1D), 02(1A ) and 02(12 ). Also, for reactions that involve a third body M, it was assumed that this third body could be in the ground or excited states. The rate of change of the concentrations with time is equal to the sum of all the populating effects minus the sum of all of the depopulating effects. The populating and depopulating effects included were chemical kinetics (two and three body), wall effects and spontaneous emission. The reaction paths of the model are given in Table 2.1 along with the forward rate found in the literature. The chemical reactions may be written k fr ZOL N ‘—"' Z N i ri i ‘ iBri i (2.1) k br where Ni is the molar concentration of species 1, dri and Bri are stoichiometric coefficients and kfr and kbr are the forward and backward rate coefficients respectively. To preserve detailed balancing, the backward rate coefficients are computed from the forward rate coefficients and the equilibrium constants by using the expression K = k /k (2.2) The equilibrium constants were calculated from values found in the JANAF (Joint Army Navy Air Force)68 thermodynamic tables. If the perfect gas law is assumed, then the equilibrium constant is a function of temperature alone. 1nK =1/RTZV H i ri ' + l/R 2v 8 (2.3) eq 1 i ri ' l where Hi and Si are the heats of formation and entropies of species 1 as found in the JANAF tables and Vri = Bri a ri' Thus once the equilibrium constant is determined for a range of temperatures, the backward rate coefficient may be found. (See Appendix B) The rate constants for wall recombination effects were calculated from the reported probability coefficients denoted by Y , where Y is the ratio of the frequency of collisions of atoms with the surface leading to recombination to the total frequency of collisions (see Table 2.1). The rate of wall recombination in a cylinder of radius r is equal to k = V 8kT/nm Y/Zr (2.4) wall 19 the particle flux at the surface, multiplied by the surface to volume ratio multiplied by the recombination probability Y . The mass of the particle hitting the wall is m, k is Boltzmann's constant and T is the translational temperature, which is 300 K for this model. A radius of 8.9 mm was used for these calculations. The chemical rate equations form a nonlinear set of coupled differential equations of the form d[n] = Z A - E B (2.5) dt 1 i i i where_Ai is the populating reaction rate for species n and Bi is the depopulating reaction rate for species n. These differential equations have been numerically solved using an integrating routine called EPISODE written by A. C. Hindemarsh and~ G. D. Byrne (obtained from the Argonne 80 The relative concentrations of National Code Center). different species and the pressure were varied and time histories of the concentrations and their derivatives have been studied. Each reaction has a varying degree of importance depending upon the intial relative concentrations, the pressure and the amount of time evolved since reaction initiation. As will be shown, all of these factors can 20 affect species lifetime. 2.2 Simple Model Results The ultimate purpose of this study is to determine the degree of recombination and dissociation of oxygen in a flowtnabe. The oxygen atom halflife is an important factor in (determining where recombination occurs. Therefore, the input. conditions were varied to determine the importance of indixridual species and reactions on oxygen atom halflife. (The "halflife" is the amount of time taken to decrease the oxygeri atom population by one half its original value.) In addit ion to the concentrations as a function of time, the total reaction rate (the forward rate coefficient multiplied by the reactants minus the backward rate coefficient times the products) for each reaction was studied as a function of time also. These total reaction rates provided insight into the specific mechanisms which affected the time evolution. (Senerally the most important reactions were found to be reactions 1, 2, 11, 14, 15, 16, 17, 19, and 22 for the input cases of mostly dissociated oxygen atoms with trace amOUnts of ozone and excited states. (These conditions beSt approximate experimental conditions.) The reactions that Play the major role will be different for different 21 input conditions. Figure 2.1 shows a typical time history for 100% dissociation at 10 torr. 2.2.1 Effect of Molecular Oxygen The effect of oxygen molecules on the oxygen atom halflife was studied by varying the 0/02 ratio and keeping the initial pressure constant (10 torr) and all other conceentrations equal to zero (Figure 2.2). The larger O/O2 ratio shortens the halflife of oxygen atoms. This is due in part to the fact that at lower ratios (keeping the presssure constant) there are fewer oxygen atoms, so the probaloility of two atoms coming together and recombining is small.. This can be observed in the fact that the total reactzion rate of reaction 15 (O + O + O = 02 + O) is much larger" for large O/O2 ratios than for for smaller ratios. Total reaction rates for reactions 16 and 17 (also three body reactions) are roughly the same for all ratios of 0/02 - The same is true for the wall recombination reaction rate. Also, near the beginning of the run (time less than 10’4 ) reaction 7 (02(12 ) + 03 = 202+ O) and e8PeCially reaction 11 (02(14 ) + 03 = 202 + 0) run backward populating 02(lA ), 02(lz ) and O3 . In partiCular, 02(14 ) is produced to about the same degree re93rdless of input ratio, so it is at a much higher 22 02 A O o -4 03 A 1 O('D) D Ogl'A) I 02 ('2) o '6‘ () <7 -|O-I \\ LOG CONCENTRATION (moles/cc) -'6 l l l fl '6 '4 '2 O 2 LOG TIME (secs) F19UIe 2.1 Time history of species concentrations. Initial conditions were 100% dissociation at an initial pressure of 10 torr where 10% of the initial 0 atom concentration was in the O( D) state. 23 ‘O.8 -I.3 - “a? O l o l "’ I E -|.8 - .1 LI. .J < I (D _ -I El 2.3 P = IO Iorr -2.8 I I I I -|.O —o.2 _ 0.6 L4 2.2 LOG 0/02 Figure 2.2 The effect of 0/02 ratio on the halflife of atomic oxygen. 24 concentration compared with oxygen atoms, at lower O/O2 ratios than at higher ratios, (as high as 10% of initial 0 atom concentration for 0/02 = 0.1). The presence of 02(1A ) was found to slightly increase the halflife of atoms. As time progresses (time greater than 0.01 seconds) reaction 11 runs in the forward direction to a significant degree and helps to populate the O atoms state. Thus at low O/O2 ratios the larger relative fraction of 02(1A ) would have a greater effect on O atom lifetime. 2.2.2 Effect of Excited Atomic Oxygen The effect of 0(1D) on the production and retention of O atoms was found to be negligible after the first few microseconds. The collisional halflife of 0(1D) is found to‘ be microseconds where typically, depending upon the pressure, the 0(3P) ground state halflife is in the millisecond range. Two pressure cases (1 and 10 torr) were examined where the initial condition was 100% dissociation (i.e. all other species started out at zero concentration, so as not to mask the effect of 0(1D)). The initial amount of 0(lD) (varied from 10%-50% of the initial oxygen atom concentration) was found to perturb the time history in the first few microseconds only. After these few microseconds, the time history was insensitive to initial 0(1D) 25 concentration. The 0(1D) depletion mechanism is dominated by reactions 4 and 6 (two body collisional deactivation) and reactions 15 and 16 (three body recombination). These reactions all have large forward rate coefficients. These collisional reactions are all much faster than radiative decay. For the remaining studies the O(lD) concentration was initialized to zero. 2.2.3 Effect of Excited Molecular Oxygen The effect of excited states of molecular oxygen was examined by varying their concentrations separately. A study at a pressure of 10 torr was examined where 60% of the gas has been dissociated into atoms. The 02(12 ) concentration was varied from 0-20% (of the remaining 40% Inolecular gas), leaving the initial 02(1A ), O3 and C(10) set equal to zero. (The remainder of the gas was 02 ground state.) It was discovered that the halflife of the oxygen atoms did not vary at all with increased 02(12 ) input. Like 0(1D), 02(12 ) is quenched in microseconds. The ratio of 02(1A ) to total 02 was varied from 0-100% at l, 5 and 10 torr and 60% dissociation, (see Figure 2.3). The 02(1A.) was found to have a weak effect (n1 oxygen atom lifetime. Generally 02(1A ) is longer lived ‘than oxygen atoms. The 02(12I) helps to create oxygen LIFETIME (II—secs) Figure 2.3 26 [271 |25 ‘ P = l tort l23 ‘ I2I - |I9 - ”7 I I I I l I 0.0 0.2 0.4 0.6 0.8 l.0 ( II '9 I P = 5Iorr ‘ I7 '5 ' l I 7 T l 0.0 0.2 0.4 0.6 0.8 LO 7 P = l0 Iorr 5 3 I I | I I l 0.0 0.2 0.4 0.6 0.8 1.0 02m) / 02620 + 02 The oxygen atom halflife as a function of the input ratio of 02( A ) to total molecular oxygen. 27 atoms by reaction 11 (02(1A ) + 03 = 202 + 0). Ozone is produced as long as there is three body recombination by O + 02 + M (reaction 17). However 02(1A ) is gradually quenched by collisions with oxygen atoms and molecules (reaction 12-14) and with the wall, so it does not have a large effect on O atom lifetime. . The overall effect of excited states was studied by comparing this model to one that contained only reactions 1, 15, 16, 17, 18 and 19 (i.e. all reactions involving excited states in either products or reactants were removed.) When 100% dissociation is assumed (and zero initial excited state population) as much as a few percent of the initial oxygen atom concentration is turned into 1 z) are also 02(1A ). (Negligible amounts of 0(lD) and 02( formed.) Generally, reactions 2 and 14 (recycling of O and 02(1A )) are not important compared with three body recombination at the beginning of the run. In conclusion, the excited states (specifically 02(1A )) do not affect the halflife of the oxygen atoms (when they are present in such small amounts) but they do affect the O atom concentration time history for times greater than the halflife, (see Figure 2.4). This is when reactions 2 and 14 become as important as three body and wall recombination. Since 0 atoms are abundant at the beginning of the run, small amounts of 02(1A ) are produced by reaction 2. Also, (moles loo) 0 LOG CONCENTRATION Figure 2.4 28 -41 I m 1 “'0' ”'2 -I -I4- -6 -4 -2 0 2 LOG TIME (secs) A comparison of two time histories at a pressure of l torr and 100% dissociation. 1) This model included both excited and ground state kinetics. 2) This model includes only ground state kinetics. 29 02(1 A) is more slowly quenched than 0 atoms recombine, therefore, reaction 11 will repopulate the O atom concentration near the end of the computer run (a few seconds) when the O atoms are otherwise consumed. 2 - 2.4 Effect of Ozone The effect‘ of ozone on oxygen atom lifetime was st udied by adding ozone to a system consisting of only 0 _at:oms and varying the ratio of 03/0 (from 0-1) while keeping the pressure constant at 10 torr. As can be seen by Figure 2.5, the atomic lifetime is reduced by addition 0 f ozone. This effect is dominated mainly by reactions 1 and 2 (0 + 03 = products). It is interesting to note that r eaction 2 produces 02(1 A) (as much as 10% of the original 9 as ) . Even though 02(:L A) can enhance oxygen atom lifetime th is effect cannot overcome reactions 1 and 2. Reaction 2 has such a large equilibrium constant and hence such a Small backrate that it never runs in reverse. 30 0.0" -0.8- -l.6 ‘* P=Itorr an P= 5torr LOG HALFLIFE (secs) '3.2' P= I0 torr -4.0- -4’8 7 J t 0.0 0.2 0.4 0.6 0.8 LG 03 / O F igure 2.5 The effect of O /O on oxygen atom halflife. (All other initial concentrations were zero.) 31 2.2.5 Effect of Pressure As expected, higher pressures cause oxygen atoms to recombine into molecules more rapidly. However the effect tends to level off near pressures of l torr and below (see Figure 2.6). The pressure study was used to examine the effects of radiative de-excitation and wall effects relative to collisional recombination and de-excitation. Since O(1D) is quenched fairly rapidly and since 02(12 ) is not produced to any great degree, there was very little radiative de-excitation in spite of their short radiative halflives. It was found that the radiative de-excitation of 02(1A ) (to ground) was at least three orders of magnitude smaller than 2 body quenching (reaction 14) or wall quenching (reaction 22) for all pressures. Wall recombination was found to be very important for low pressures (below 1.0 torr), about equal to three body recombination for intermediate pressures (10 torr), and not very important for high pressures (above 100 torr). Quenching of 02(1A ) was about as important as 2 body «quenching for low pressures and decreased in itaortance at higher pressures. 32 0.01 -0.8‘ " -|.6 ‘ a o e U u u. | :3-24- h 4 3 I g 2 _J-32‘ ~40' -4'8 I I I 1 1 -l.0 -0.5 0.0 0.5 l.0 l.5 LOG PRESSURE (tort) Figure 2.6 Effect of pressure on oxygen atom halflife. 1) The input ratio of 0:0 was 1:10 with all other input concentrationslequal to zero. 2) The input ratio of O:OZ:OZ( A.) was 30:24:16. 3) 100% dissociation. 33 2.3 Summary and Conclusions A kinetic model of an oxygen gas downstream of an electrical discharge and relevant rate-coefficient information found in the literature were presented. Rate coefficients recommended for this model are listed in Table 2.1. A computer simulation was used to examine the relative importance of various kinetic mechanisms involved in oxygen atom recombination. Calculations indicate that three body and wall recombination are important to O atom lifetime, but recombination is sensitive to other parameters as well. _Low pressures, small O/O2 ratios and 02(1A ) were found to prolong the lifetime of O atoms. Ozone and high pressures were found to decrease O atom lifetime. Other higher excited states (02(12 ) and 0(1D)) were found to have a negligible effect on O atom recombination. CHAPTER III OXYGEN KINETICS 3.1 Introduction 39 Literature Search It was determined in Chapter II that two and three body reactions, as well as wall (recombination, are important in determining the overall rate of oxygen atom recombination. Also it was determined that the only important electronic excited species is 02(1A ). The first electronic state of atomic oxygen, 0(1D), and 02(12 ), the second electronic state of molecular oxygen, were found to deactivate very quickly without significantly affecting the predictions of the kinetic simulation. Thus, the species included in the model of Chapter 5 are 0, 02, O3 and' 02(1A ). In simple models of electrical discharges of oxygen (e.g Bell and Kwong9 and Mearns and Morrislo) the kinetic rates are assumed to be constant and are evaluated at a temperature of 300 K. In general, these discharges are at lunch higher temperatures than 300 K and the temperature increases as the gas absorbs electromagnetic energy through inelastic and elastic collisions with electrons. Thus, it its important to know the temperature dependence of the 34 35 dominating mechanisms. The following review gives a summary of investigations that have determined kinetic rate constants either experimentally or theoretically for the important reactions involving oxygen under conditions of a typical experiment. 3.2 Two Body Reaction 9f Ozone and Oxygen Many experimental studies have examined the temperature dependent rate constant of 03 + 02 = 202 using flash photolysis or thermal decomposition of ozone. All experiments were performed near room temperature 19 (200-400 K); however, in reviews by both Hampson and Baulchzz, they recommend rate constants for use over a range of 200 K to 1000 K. As can be seen from Table 3.1, all of the rates are very close to being within experimental error of one another. The rate of Arnold and Comes61 has been chosen as the recommended rate. The product states of oxygen have not been well established. From an experimental study of thermal 62 note that decomposition of ozone, Benson and Axworthy reaction 1 (of Table 3.1) is exothermic by 93.2 kcal and the activation energy is 6.0 kcal. Therefore, there are 99.2 kcal of excess energy available to the products. If spin selection rules are obeyed in the collision of 0(1P) 36 mo QN «N 0H om no me wH wN mN oH NN wH me He No wocmummdm NNMImwN mmN moN NNmImwN omelmmH HNmImwN oomlooN o0¢Io0N mNmI00m mmmIONN oooHIONN oomIOON oomIOON oHanwm ©MMIHON qwmloqm owned oppumumaEdH NooN\NV oNNNNo.owN.NV aoNxNN.NHN.NV NoNxN.N x . N oNooN\eVeoN N N NN.oHNN.o oNxNN.NHo.eV oNxN. N oNxo. N NN\NNNN VoNN Ne\oNN+NNNT Vo oNN NN\NNNNI Vo NN uxou mom Ne\NNNoN V oNNoNxNN. N Ne\ooN+eoNNI V oNNoNxN. N NN\NoN+NNNNI V oNNoNxNNN. o+NN. NV Ne\ooNNIVoNNoNxeN.N Ne\oNNNIVoNNoNxN.N Ne\oNeNI V oNNoNxN. N NN\oNN+NNNNI V oNNoNNNN. o+e. NV NN\NN+NNNNI V MNNoNNNNN. owNN. NV NN\oNoNIVo NNo oNxNNN.o+oa.NV ommaoHoE.oo mama NONE Nznz on: No": N z + o + z + ANNVNo .NI.e o + NoN + No + ANNN mNN A Nov N I ANN Nz” oNxAmN.oHN.NV oNmem. o+o. NV NNm.oNNN.oNNN.oNo.NV w AH\mmoN~IV mmH m x . ofiv mac“ n N x N. v mNNoN m. m x . Aoom\HvNNoN o N x . N\HNNNoN m N oNNNN. o+N. NV oNxNN.oHN.NN oNNNN.oHN.NV ofixm. m ofixm. m odGm.N Ae\oomvm NN Uh NN\omNNNI V INNoN N. N x NN\ONNN INNoN Nm. N I w NN\omN+omNNNIV mNN Ne\omN+mmNNm NN oNxNo.QHN.mV oNxNo. N+N. NV H Noumov N m www.mHoE.uo wuwm N S + o + E + O + O OH HV coauommm HOW mafiafinmnoum N N . o NNmz N<>>0¢9 2 o<0u o m:0—< I ”mo: 325d :35 we: as u lllll .1 N 32...le .2228 .. 96:20.2 .0 IN 526.. It mo=... 33 s. I . $39. 55.6 3528 22:9; 0» 526.. Experimental Apparatus Figure 5.1 63 5.2 Plasma Cavity and Microwave System A 2.44 GHz magnetron oscillator capable of delivering 1000 watts of continuous power was used as a microwave power source. The power was delivered through a water attenuator which allowed the power to be continuously varied from 200 to 800 watts. The magnetron was protected from reflected power by a circulator and a matched load. The microwaves entered the reactor cavity through a directional coupler so that incident and reflected power could be monitored simultaneously. The power absorbed by the plasma was taken to be the incident power minus the reflected power. (Typically the reflected power was less than 5% of the incident power.) It was assumed that there was no drop in power between the power meters and the coaxial probe. Power was coupled to the cylindrical water cooled cavity by an adjustable coaxial probe. The cavity had an I.D. of 17.8 cm and the length could be varied from 6-16 cm with a sliding short. A more detailed description has been given previously7'81. The cavity operates on a number of different modes depending upon cavity length, gas pressure and probe position. The cavity length and probe position were varied until maximum incident power and minimum reflected power were obtained. The optimal 64 conditions were found to be a cavity length of 9.3 cm and a probe depth of 7.6 cm from the cavity wall. 5.3 Nitrogen Dioxide Titration System The nitrogen dioxide flow system consisted of a NO2 supply cylinder, a liquid vapor separator maintained at constant temperature and pressure, a mercury manometer, a fine metering valve and a 6 mm outer diameter glass tube. This glass tube was positioned down the center of the discharge flow tube and had 43 centimeters travel towards or away from the plasma. The tip of the glass titration tube was rounded off, sealed, and eight pinholes were drilled 3 mm from the tube end (see Figure 5.2). These holes formed a ring in a single cross sectional plane so that the N02 met the oxygen in a cross flow pattern. This "maximized reagent mixing" and "provided titration analysis at any cross sectional plane downstream of the oxygen plasma discharge".76 It was possible to determine the atom concentration at any point downstream of the discharge, including the exit plane of the reactor cavity. 9 or Mearnslo) the number of In other systems (e.g. Bell oxygen atoms produced at the exit plane was determined by extrapolating data taken at one or two fixed spots downstream of the exit plane. Thus, this variable probe method of introducing NO2 into the system was a big 65 QUARTZ 0.66 cm TUBE V 1.71”” ’/ //.//'.T:7/////i/ I /: / ///.////§l790m 4:0).029 <——" '7-8 cm Z i (TO/Oéooqoafléb‘I __________ [PYREX PLASMA GREEN GLOW LRESONANT CAVITY Figure 5.2 Nitrogen dioxide titration technique. 66 improvement over previous methods. E14 Titration Technique The oxygen atom titration process is based upon the following reactions: 0 + NO NO + O (5.1) 2 2 82 with a forward rate coefficient at 300 K of 3.3x1012 cc/mole-sec and O + N0 = NO + hv (5.2) 83 at 300 K of with a forward rate coefficient 1.5x107 cc/mole-sec. In reaction 5.1, free oxygen atoms exiting the plasma are scavenged by NO2 (see Figure 5.2) to produce nitric oxide and oxygen molecules. This reaction is very fast compared to reaction 5.2. If the initial free oxygen atom production exceeds the rate at which N02 is being introduced, then reaction 5.2 follows, producing green light which fills the whole flow system outside of the discharge. When the N02 is introduced at a rate equal to or exceeding the free oxygen atom production rate, the green glow downstream of the port is extinguished and the upstream green glow is highly localized. ”When titrating in a darkened room, increasing the N02 flowrate 67 causes the glow to progress upstream, approaching the point of NO2 introduction. This glow becomes sharper and more distinct until it appears to be a truncated cylinder" (see Figure 5.2).76 At this point, the N02 flowrate exactly equals the oxygen atom flowrate and reaction 5.2 does not occur. Thus, by knowing the N02 flowrate, the oxygen atom flowrate can be inferred. The movable titration probe provides 40 atom determination at any cross section downstream of the discharge. (The accuracy of titration is discussed in Appendix C.) The N02 was fed through a fine metering valve with the N02 source maintained in a constant temperature bath (300 K) in a liquid-vapor equilibrium. The back pressure of NO2 was therefore 800 torr. Only vapor entered the titration line because the downstream pressure was never more than 16 torr which is well below the vapor-liquid point at 300 K and the liquid-vapor equilibrium vessel was 10 meters away from the titration experiment. No liquid was ever observed at the titration tip or at any point in the titration line. Due to the corrosive nature of N02, the titration endpoint flowrate was determined by directing the same gas flowrate into a known volume and monitoring the change in pressure as a function of time. This provided a molar flowrate which was one to one with the oxygen atom production rate. 68 The mass flowrate of N02, measured as a pressure increase (P N02) in a known volume (VNOZ) can be related to the oxygen atom flowrate through the following relation: i> v NO NO 2 2 ---------- = flowrate N0 = flowrate O (5.3) kT 2 NO 2 0 where TN02 IS the temperature of N02 (300 K) and PN02 = dP/dt. The oxygen atom concentration can also be determined from PN02 by [0] = n 13 (5.4) NO 2 where Q = VNOZ/ kTNOZVA if v (the linear velocity) is known. (A is the cross sectional area of the flowtube.) The percent of O2 molecules converted to O atoms at any particular cross section can be calculated as one half the flowrate of O atoms divided by the initial 02 flowrate. (This ratio is denoted as percent conversion throughout the text. Figures 5.3-5.5 show typical data.) 69 IO - I . PNOZ _ 0 Stan MAX oIOtorr - oi2 torr Al4torr 7 BIG torr FLOWRATE = (.39 mI/sec m0- 4 PNo2 ‘ (iorr/sec) - m4- .1 IO-2 1 l r I i IT? I ‘ 4 6 BIO 20 40 LOGINSTANCE(Cm) N-i Figure 5.3 The effect of distance on oxygen atom concentration for several pressures. 70 Volumetric Flowrote - (.39 mI/sec Power 3 500mm: o . 6 torr IOO- A = tOtorr I t l2torr o ' l4 torr D = l6 torr a 0 I0- 4— C a) 0 3— (D O. z: 9 a) m: (u > 5 ' 1 t) O I T 1 T I 1 o 2 4 6 e (O m DISTANCE (cm) Figure 5.4 The amount of O converted to atoms vs distance from the exit of the reactor cavity for several pressures. 71 Pressure = I2 torr IOO Volumetric Flowrate l symb°l (ml/sec) A 395 o I .39 I 0.39 I ‘8 c» IO - 2 c o o L— o a Z A 9 (D 0: L1.) > Z N O O O l I I I I I O 2 4 6 8 IO I2 WSTANCE (cm) Figure 5.5 The amount of O converted to atoms vs distance for several flowrates. CHAPTER y; RESULTS OF MODEL 6.1 Comparison of Model 39 Experimental Results The effects of pressure, flowrate and power on oxygen atom production were investigated for the experimental ‘parameters 8 to 16 torr, 0.4-4.0 ml/sec and 200-600 watts of absorbed power. Mearns and Morris10 have suggested that it would be interesting to determine the oxygen atom concentration at the exit of .the discharge. This was tried, but the addition of titrant at distances less than 2 cm caused a change in the plasma emission spectrum. As the atom concentration increases the N02 injection rate must also increase which implies that the Closer to the cavity titration is performed, the larger the upstream penetration of N02. Therefore, the oxygen atom flowrate could not be determined in the exit plane without adversly affecting the plasma. It could however be determined a short distance away from the exit plane. Titration data were measured from the exit of the discharge and not from the end of the plasma. The plasma tended to "blow out" of the cavity for pressures below 14 torr. (For example if the gas is composed of 100% O atoms, 72 73 FNOZ has a maximum value of 6.0 torr/sec for a flowrate of 1.39 ml/sec. As can be seen by Figure 5.3, extrapolation of the data curves back to 1 cm indicates that FNOZ is greater than this maximum for pressures less than 14 torr.) Consequently, the raw data required adjustment when compared to a theoretical model. The distance of titration from the plasma was determined by subtracting the distance the plasma extended from the resonant cavity. Thus, it appears that there was 100% dissociation for the pressures where extrapolation reaches this maximum value. The highest conversion actually measured was 70% at 12 torr and a flowrate of 0.4 ml/sec and 500 watts power absorbed. Since the gas temperature of the experiment is not known, and the temperature as a function of distance in the model is known, the model results are converted into a FNOZ (pressure increase of O atoms to a known fixed volume), so that a direct comparison of the model results can be made to the unaltered experimental data. Figure 6.1 illustrates the fact that 3 body recombination of O atoms (reactions 6 and 7 of Table 3.1) and wall recombination of O atoms (reaction 10) are the important mechanisms. _This case is typical of all of the experimental cases. As mentioned in the previous section, the reaction rate constant as a function of temperature is not always well known, especially for reactions 6, 7, and 74 IO-s: : )I = 5 xi0'5 : PRESSURE =sIon FLOWRATE = L39 mI/sec _ RATE 3 <-2x104| 6 RATE 4 <-.2> I— IOO - I—SOO INH1AL-————N_3oo 52 --°-——-INITIAL TEMPERATURE VELOCITY O I I I T I I O O 2 4 6 8 IO (2 DISTANCE (cm Figure 6.21 Velocity (solid line) and temperature (dashed 11ne) predictions as a function of distance from the exit of the discharge. 103 lower flowrates (longer residence times) alllow for an increase in surface recombination between the exit of the discharge and the titration point. In this study 100% dissociation was implied by the titration data for all flowrates. Experimental data and modeling predictions indicate that there was a smaller fraction of O atoms remaining by the time the gas reached a specific titration point for the slower flowrates. This effect manifests itself due to the relative increase in surface recombination as well as three body recombination effects taking place during the extended travel time. 11 87 Francis comes to the same conclusion as Battey. He produced 0 atoms in a 2.54 GHz discharge and used e.p.r. techniques to observe the decay of the oxygen atoms. He states that when the inverse of the discharge residence time is much smaller than the rate of recombination, then the surface recombination rate constant determines the steady-state atom concentration and the atom concentration will be independent of flow velocity. In Figure 6.19 the surface recombination rate was much larger than the inverse of the residence time for low flowrates, and was somewhat larger than the inverse of the residence time for higher flows. This is why the curve is linear at lower flowrates. So in fact, it is the ratio of surface recombination to residence time that determines if the amount of O atoms 104 produced is dependent or independent of the flow velocity. The assumption that radial and axial diffusion could be neglected was made in several experiments. Based upon a previous analysis, Bell and Kwong assume that the diffusion rate is slow enough in the direction of flow that it can be neglected.' Mearns and Morris also neglect radial and axial diffusion, but they state that this is not necessarily a valid assumption, but that the available data on diffusion is not sufficiently accurate to include it. Francis states that the diffusion coefficient is inversely proportional to the density of the gas, so that the error in neglecting radial diffusion will increase with decreasing pressure and flow velocity. He calculates the diffusion coefficient for conditions similar to that in this experiment and finds that it is very small (to the point where it can be neglected) for pressures of 6 torr and above. Francis also calculates the viscous pressure drop by assuming Poiseuille flow. He finds that this can be neglected in the region of his experiment, which again was in the same region as that of this experiment. In general, there is the concensus between the above experiments and the experiment modeled in this study, that increased flowrate, and increased absorbed power and a decrease in pressure will increase the observed 0 atom concentration at a fixed point downstream of the discharge. 105 There is some question as to the effect of the plasma parameters on temperature and more accurate measurements of temperature will have to be made before any conclusions can be drawn. it; Tempegesqre e24 Veloeity Pregictieee In the previous sections it was shown that a theoretical model could accurately predict oxygen atom concentrations as a function of distance from a microwave discharge, as well as match the pressure and flowrate trends of other experiments. The model was not quite as capable of predicting temperature trends of other experiments but it is very difficult to accurately measure temperature. Neither this experiment, nor the experiments discussed in previous sections quantitatively measured other species known to be present in the discharge, nor did they measure velocity either at the exit of the discharge or after total recombination had occurred. This section discusses the model predictions for some of these parameters which have not been measured. Velocity and temperature are important parameters in assessing the feasability of using a microwave discharge as a source for many potential applications such as momentum transfer which could be used for a rocket thruster. Figure 106 6.21 shows the typical temperature and velocity profiles. The difference between the final equilibrium temperathre and the exit temperature is not large, but the overall temperature increase of the gas from 300 K before it enters the discharge to the final equilibrium (post discharge) temperature is_large. This overall temperature increase appears to be due primarily to the absorption of energy in the microwave discharge and not due to the energy released in recombination downstream of the discharge. The flow velocity on the other hand reaches a maximum at the exit of the discharge where the temperature is large and the average mass per particle is half that of the undissociated gas. As the dissociated gas recombines, the gas velocity decreases and reaches a value larger than that of the initial _velocity but smaller than the velocity of the dissociated gas. It might have been anticipated that the velocity should continue to increase as the gas recombines because of the extra thermal energy released in the three body recombination, but this extra energy indicated by a slight temperature increase is not large enough to overcome the deceleration of the gas due to the decrease in the number of particles per unit volume and the increased mass per particle. (This assumes of course that the pressure remains constant throughout the flowtube. The model results show that the pressure actually increases 107 slightly (by 0.01 torr).) The degree to which the temperature increases and the velocity decreases as a function of pressure outside of the discharge is illustrated in Figure 6.22. An increase in pressure causes an increase in the final temperature and a decrease in the final velocity. However, Figure 6.23 shows that at a constant pressure, an increase in exit temperature causes an increase in final velocity. So, for example, to maximize the final velocity requires a trade—off between minimizing the pressure and maximizing the exit temperature. 6.4 Singlet Delta Formation The model predicts that 02 and O are the only species of importance, by several orders of magnitude (see Figure 6.24). However, if 02(1A ) is produced by recombination of O atoms with the wall, as suggested by Black and Slanger75, 02(1A ) concentration could also be significant. The solid lines of Figures 6.25 and 6.26 represent the concentration of O2 and 02(1A ) when all the O atoms that recombine at the wall do so into the electronic ground state of 02 for a temperature of 2000 K. The dashed lines show the concentration of O2 and 02(1A ) when 30% of the 0 atoms recombined at the wall populate the 02(14 ) state. For a temperature of 1000 K, a maximum of 4% (at 8 torr) and 2% HNAL TEMPERATURE PK) 108 I400 - \ ' I20 - - Temperature at \ discharge exit 'ZSOK \ Initial 02 flowrate (.39rnl/sec (380 ~ ~ IIO 8&3- H00 ‘8 O) U) \ E U )— I340 N P 90 t O O _J UJ > .4 <[ 22 IL I320 - - 80 I300 — - 70 I I T I 6 8 I0 (2 I4 PRESSURE(RNT) Figure 6.22 Model predictions of the final gas temperature (solid line) and velocity (dashed line) as a function of pressure. 109 IOO - Pressure 8 torr Vol. Flowrote 0.42 ml/sec 90 ~ Initial Velocity (5.8 cm/sec 80 " ’8 a) m \ E 70 - N9 ). t o 60 - O _l IJJ > NJ .. <1: 50 .2. LI. 4O - 30 J TI I I I 1 i 500 (000 (500 2000 2500 3000 3500 TEMPERATURE at DISCHARGE EXIT (°K) Figure 6.23 Model predictions of final velocity as a function of exit temperature. llO fl [02] PRESSURE = 8 torr F LOWRATE = l.39 mI/sec 8 Tfl500K [03] < 4 x 10"4 ’8 § % [o] E Z 9 E m 'IO — F. 2! UJ O E 0 -II - . CD [02 ( A)] C) .J -IZ l 1 I I I o 5 4 s 8 I0 12 DISTANCE (cm) Figure 6.24 The concentrations of important species of an electrical discharge as a function of distance from the discharge. LOG CONCENTRATION (moles/CC) Figure 6.25 lll PRESSURE = Btorr FLOWRA‘I‘E = I39 ml/ sec T=2000K DISTANCE (cm) The solid lines indicate the 0 and 0 (1A.) concentrations as a function of distance when all of the molecular oxygen formed by wall recombination is in the ground state. The dashed line indicates the concentrations when 30% of the wall recombination produces l 02( A.). Figure 6.26 LOG CONCENTRATION (moles /CC) 112 '6 7 PRESSURE . I2 torr FLOWRATE = L39 ml lsec T =2ooo K ‘7 " —-— —- ——. —————— [02] -8 ... // / -—" ——————— [02 ('A)] I // / / -9_/ . I -IO— — [02m] I — — .1 I I l I I o 2 4 e 8 I0 I2 DISTANCE (cm) The solid lines indicate the 0 and 0 (1A ) concentrations as a function 3f distance when all of the molecular oxygen formed by wall recombination is in the ground state. The dashed line indicates the concentrations when 30% of the wall recombination produces l 02( A ). 113 (at 12 torr) of the total 02 population was in the 02(1A ) state. For a temperature of 2000 K, a maximum of 15% (at 8 torr) and 10% (at 12 torr) occurred very near the exit of the discharge (less than 2 cm). Thus, the concentration of 02(1A ) could be large at low pressures and large temperatures, if 0 atoms recombine into electronically excited states at the wall. CHAPTER VII CONCLUSIONS 7.1 Conclusions A one dimensional comprehensive model which predicts species concentrations, temperature and velocity profiles by solving the conservation of mass, momentum and energy equations can accurately predict the results of N02 titration of oxygen atoms produced in a microwave discharge as a function of distance. The assumptions used in the model based upon experimental evidence in this and other experiments includes negligible viscous pressure drop and negligible radial and axial diffusion, such that the gas remains in an homogeneous mixture throughout each cross sectional area. The important neutral chemical kinetic mechanisms for oxygen which has interacted with a microwave discharge, as well as the probable rate coefficients of these reactions have been determined from computer modeling and comprehensive literature reviews. The most important mechanisms were found to be three body recombination and wall recombination. The oxygen atom lifetime was found to depend upon pressure and degree of dissociation as well as 114 115 the presence of 02(1A ) and ozone. The presence of 02(1A ) and 0(1D) was found to have a negligible effect on the oxygen atom lifetime. By matching the predictions of the computer model for oxygen atom concentrations as a function of distance to chemical titration results, it was found that the exit temperature was between 1000K and 2000K. It was also found that an increase in flowrate, temperature and power and a decrease in pressure would increase the amount of 0 atoms observed at a fixed point downstream of the discharge. The model also predicts that the final equilibrium state of the gas has a higher temperature and velocity than the initial equilibrium state. There is a very slight post discharge temperature increase due to the stored chemical energy released when the oxygen atoms recombine into molecules, but the majority of the temperature increase occurs in the discharage due to neutral gas heating. The velocity is largest at the exit plane of the discharge where the mass per particle is small and the temperature is large. The velocity decreases as the atoms recombine, resulting in a velocity smaller than at the exit plane but larger than the initial velocity. A microwave plasma could be used for space-craft propulsion, but not for the reasons given in the intial "Free Radical Propulsion" concept. Neutral gas heating is 116 the main mechanism which increases the energy of the gas, not energy stored in the chemical bonds as originally proposed. "Electro-thermal Propulsion" has been suggested as a more appropriate label. Ongoing studies at National Aeronautics and Space Administration - Lewis Research Center in Cleveland and Michigan State University are examining the efficiency of this device and the amount of thrust a microwave discharge is likely to produce. The comprehensive model developed in this thesis can be used in any application of an oxygen microwave discharge. The model is general enough that the many input parameters such as pressure, temperature and species concentrations can be varied until a desired output is obtained which maximizes the performance for a particular application. For example, a maximization of the overall momentum increase will determine the feasability of using an oxygen microwave discharge for spacecraft propulsion or maximization of the 02(1A ) concentration will determine if threshold can be achieved in an 02(1A ) - Iodine laser. The overall layout of the model is general enough that the chemical kinetics of the model can be modified so that the results of any gas exiting a discharge can be examined. For example, inclusion of nitrogen kinetics can be made to examine the processes of atmospheric plasmas. Computer modeling can examine specific parameters and 117 processes which are difficult if not impossible to measure experimentally. Input conditions can be varied and a variety of experiments can be simulated efficiently and inexpensively, and then only a few specific experiments need to be made to check the performance of the model. In conclusion, theoretical modeling of plasmas can lead to a better understanding of the often elusive internal mechanisms of the plasma. 7.2 Recommendations for Future Work The next step in the computer modeling of the chemical kinetics of an oxygen plasma is to include ion-electron reactions to the neutral kinetics model. (See Appendix E for a list of possible reactions.) The important kinetic mechanisms in the plasma itself can then be examined. However, information regarding the electron temperature and electron density becomes necessary. If argon and hydrogen are added to the oxygen plasma in trace amounts, it may be possible to measure the electron density and electron temperature using spectroscopic techniques (see Appendix D). Another interesting modeling study is to examine other simple molecules such as nitrogen and hydrogen in similar neutral kinetic models and experiments. The similarities 118 between oxygen plasmas and other diatomic plasmas can then be assessed. An ambitious project in the computer modeling of the neutral chemical kinetics of an oxygen plasma is to include two dimensional (r,z) variation in density and temperature, as well as radial and axial diffusion terms. Heat conduction and convection terms can then be included in the conservation of energy and momentum. More accurate assessments of the energy loss mechanisms can then be made. The major drawback to this recommendation is that the computer runs will become very expensive. The integrating routines EPISODE and LSODI involve matrix inversions and each added differential equation makes each step of the integrator more complex. Therefore, some simplifications may have to be made to a two dimensional model. There are several experimental studies which can be made to check some of the predictions of the computer model. The placement of a thermocouple downstream of the discharge, past the point of total recombination, will yield the thermal equilibrium temperature of the gas. The magnitude of this temperature will indicate the degree of heat transfer outside of the discharge. Addition of argon to the oxygen plasma and measurement of the argon electronic temperature may lead to information regarding the neutral gas and electron temperatures, particularly if 119 an independent measurement of the electron temperature can be made, for example with electrical probes. Another interesting experiment would be to use a well filtered microwave source and examine the oxygen atom concentration of plasmas generated in a specific electromagnetic mode. The predicted electromagnetic modes were not observed in this experiment due to the fact that the microwave oven is not a filtered source. With a filtered source, it may also be possible to sustain the discharge at much higher pressures. Titration measurements at pressures higher than 20 torr and lower than 1 torr can be compared to predictions of the computer model. The range of validity of the model can then be determined. APPENDIX A 120 m X . Ae\eoNxm.sv mm.oemuos o N w x . Ae\eosxo.ev em.oem-os m N @ um . As\eosxo.ev em.oemioN m N Ae\eozxes.svmm N m . AH\ququ.fiv m H Ae\mosxe.z-vmme.o-seosxz.s w vn . Ae\eonN.ev RSIANOH s z unaumcoo Esfiunwafisqm o Ae\mo~xmw.mlv MH 0 Ae\mosxem.Niv NH N um . Ae\NoNqu.ev m_oN o m x . m.oueNNoN mN e x . m.oustoH mN N w.oemofixfi.w w.Oquonm.~ ofix©.m 0.0 ofixm.fi Aommuuotmaofiv mumm wumzuom NO + m0 + NO + NO + 0 .w NO + NO + NO + O +.O .5 O + NO I O + O + O .o N0 + o + o + Aasto .m No + No + No + A (02 /0) INITIAL Figure C2 The net reaction rates as a function of intial O /0 ratio. The dashed line indicates the time to deplete the O atom concentration to 1% of its initial concentration as a function of initial 02/0 ratio. 132 the system will become equal. Clyne also comments that N02 titration will not be accurate when the concentration is low because, as seen in Figures Cl and C2, other mechanisms become important. 89 on the other hand, conclude that Mearns and Morris fast flowrates of initial 02 give more accurate titration measurements than slow flowrates. If the N02 flowrate is known to within a fixed uncertainty, larger flowrates will have a small fractional error. However, for the experiment described in this paper, the flowrate of N02 was not measured with a flowmeter but by observing the increase in pressure, with respect to time, of the N02. The pressure increase was monitored with a Heise gauge and a stop watch. For very high titrant flowrates, such as those needed near the exit of the discharge where the O atom concentration was highest, the pressure increase was so rapid, it was difficult to measure the instantaneous pressure. Thus, the accuracy of measuring 0 atoms based upon flowrate considerations appears to improve downstream where slower flowrates of N02 are used, but not so far downstream that the O atom concentration is too small. In conclusion, the accuracy of N02 titration is dictated by 1) the 0 atom concentration, 2) the pressure and, 3) both NO2 and initial 02 flowrates. If the oxygen atom concentration is low, or the pressure high, kinetic 133 mechanisms other than reaction (C1) can be important and there will no longer be a one-to-one correspondence between the N02 concentration needed to extinguish the glow and the oxygen atom concentration. This effect can also be present for small initial molecular oxygen flowrates. If the initial molecular flowrate is high however, the time scale of the flowing system approaches the time scale of the kinetics at the titration endpoint. Thus, it is best to titrate at pressures lower than 16 torr for "medium" initial 02 flowrates. Also, it is best not to titrate too closely to the exit of the discharge where very fast NO2 flowrates are needed, nor too far from the discharge where the oxygen atom concentrations are small. The experiment described here was performed with these considerations in mind. APPENDIX D APPENDIX B SPECTROSCOP IC MEASUREMENTS D.l Introduction To correctly model the kinetic processes of a microwave initiated plasma, several parameters such as electron density, electron temperature, gas temperature and species concentrations must be known. There are many diagnostic techniques commonly used to determine these important parameters but in general they are difficult to perform and the technique can perturb the plasma. Emission spectroscopy is a valuable and effective diagnostic tool because it does not distort the electric or magnetic fields of the plasma and many useful plasma parameters can be determined from the same experimental configuration. Emission spectroscopy has been used for many years and there are many excellent references describing both the applications and limitations of the method, as well as suggesting experimental configurationsfl'go‘"96 In this appendix, three experiments are described Which use emission spectroscopy to identify species and to determine three important plasma parameters; the average 134 135 electron density, the electron temperature, and the average wall temperature. D.2 Species Identification Emission spectra of oxygen and argon plasmas were observed for the experiments described in the next three sections. In oxygen, the only lines observed at pressures of 2 torr and above were atomic neutral lines as well as two hydrogen lines H (48618) and Ho (65638). The most 8 prominent lines are listed in Table D1. At pressures below 2 torr, a molecular spectrum was observed. This molecular spectrum was identified as the electronic transition 42 - 4n of 02+. Many rotational branches of several vibrational bands were observed. Due to the complexity of electronic molecular spectra, only a few rotational lines were identified. (See Section D.5) Emission spectra of several argon plasmas were also collected. As in the case of oxygen, the only lines observed were neutral atomic transitions, (see Table D1) as well as Ha’ H and an oxygen atom triplet. B At no time were any atomic ions observed in either the argon or oxygen plasmas. As will be explained in the next section, the electron density was between 1013 and 1014 016 electrons/cc, compared to neutral densities of 1 to 136 Table D.l List of Observed Neutral Lines in 02 and Ar Plasmas Oxygen Atom Lines: 4368 A 6046 R 5022 3 6157 X 5329 R 6455 8 5437 R 7157 X 5577 8 7254 8 Argon Atom Lines: 4164 R 7948 A 4200 R 8006 8 6965 R 8015 8 7067 8 8104 R 7272 8 8115 R 7383 8 8264 8 7504 R 8408 R 7515 R 8425 8 7636 8 8521 R 7724 R 137 . Therefore, the ion density is between 10 and -4 times smaller than the neutral density, and it would 10 be expected that the ion emission would be very low for this case. D.3 Stark Broadening D.3.1 Introduction By definition, a plasma contains both free electrons and ions even though the majority of a weakly ionized gas is composed of neutral species. The ions and electrons create localized electric fields around the neutral species. There is a coupling between the energy of these localized electric fields and the energy of the atoms and molecules, depending upon the orbital angular momentum of the atom or molecule, which causes a splitting of each line emitted by the radiating atom or molecule. This splitting of each line by an electric field is called the Stark 97 98.) The spacing of effect. (See Schiff or Merzbacher each component of each emitted line depends upon the magnitude of the applied electric field. In a plasma however, the ions are at different distances from each atom or molecule, so the applied electric field seen by each atom and molecule will vary. An observed emitted line from a plasma will appear broader than normal due to the fact 138 that the line is composed of many lines, each of which is split by different amounts due to the Stark ~effect. Therefore Stark broadening is a statistical effect which depends upon the number of ions and electrons. The dependence of the width of a Stark broadened line on electron density can be thought of in this simple way. .If rO is the radius of a sphere containing one ion and ni is the number of ions per unit volume, E is the electric fiedd strength and A18 is the full width at half height of the Stark broadened line, then 1 (ion) n = --------- e 3 (D1) (4/3nr I 0 Therefore 1/3 3 r = ------- (D2) (411,, ) e .y 531”“ Coulombs law, where E is the electric field strength 139 + . E a ----- (D3) 2 r 0 So 4Fn 1 e 2/3 E (I ( _._..... ) (D.4) 3 From quantum mechanics (see Schiff97 or _) MertzbachergSIAx « E, therefore 2/3 A1 a n (D5) e The theory of Stark broadening is very complicated. In depth discussions of the theory of Stark broadening can be found in References 90, 91, 93 and 94. A comprehensive literature review of Stark broadening experiments in several elements can be found in reference 99. Due to the simple nature of hydrogen, Stark broadening theory is most accurate for the hydrogen emissions lines. The second line of the Balmer series, denoted HB , is particularly useful as an indicator of electron density because it is very sensitive to Stark broadening, which is helpful for low 140 electron densities, and because it occurs in the visible region of the spectrum at 48618. 91 Griem suggests that the electron density can be written as 3/2 N = C(N ,T ) AA (D6) e e e S where AAS is the full width at half height (fwhh) of the Stark broadened component of the emitted line and C is a coefficient which is weakly dependent upon the eleCtron density (Ne) and the electron temperature (Te). The values for C to be used for the H8 line are tabulated by Griem91 and summarized in Table D.2. TABLE D.2 Values for C(Ne,Te) for H8 Telectron C C ' - 14 _ 15 Ke1VIn Ne-lo Ne—lo 5000 3.84x10ij 3.68x10i2 10000 3.80x10l4 3.58x10l4 20000 3.72x10l4 3.55x10l4 40000 3.76x10 3.53x10 141 D.3.2 Experimental Apparatus D.3.2.1 Reactor Flow System The microwave plasma flow system is shown in Figure D1 and is very similar to the flow system in Chapter 5. The plasma was contained in a 6 mm O.D. (4 mm I.D.) quartz tube situated coaxially with a cylindrical microwave cavity. The gas control system consisted of high purity argon and hydrogen sources, flowmeters, a back pressure monitor and several needle and bellows valves. A constant back pressure of 1400 torr was maintaIned up to a metering valve. Downstream from the metering valve, the gases entered the containment tube via 6 mm copper and plastic tubing and were exhausted to a 58 CFM vacuum pump via 6 mm plastic tubing and 50 mm pyrex tubing. The plasma pressure was controlled by a bellows valve located after the containment tube and the pressure was monitored with a Heise gauge. Discharges with volumetric flowrates of 0 and 5 ml/sec with pressures ranging from 50 to 1000 torr were investigated. MICROWAVE POWER SUPPLY ISOLATOR Figure D1 POWER METERS 6:) C2) JI DIRECTIONAL COUPLERS 4 mm ID QUARTZ TUBE TO VACUUM E 142 BACK " PRESSURE CAVHY PRESSURE C-AVI TY CHART RECORDER VACUUM GUAGE PMT II ‘=::33 LENSES Experimental Apparatus 1 METER, F9 GRATING SPECTROMETER 143 D.3.2.2 Microwave System A 2.45 GHz filtered, variable power supply capable of delivering 130 watts of continuous power was used as a microwave power source. The magnetron was protected from reflected power by an isolator. The microwaves entered a 100,101 through a directional surface wave launcher coupler, so that incident and reflected power could be monitored simultaneously. The power absorbed by the plasma was assumed to be incident power minus reflected power times 70% to account for losses in the coaxial cable connecting the output of the directional coupler to the 102 The isolator and the small coaxial microwave cavity. cable connecting the probe (a loop) to the large coaxial cable were air cooled. The inside of the cavity was also air cooled through a screen viewing port. The plasma was contained in a quartz tube coaxial with the 2.54 cm O.D. cylindrical copper surface wave launcher. The cavity and quartz tube were situated vertically so that the length of the plasma was centered along the length of the entrance slit to the spectrometer. The position of the probe, the length of the cavity and the position of the center conductor were varied until minimum reflected power occurred and until the plasma looked similar to those used in references 100 and 102. 144 D.3.2.3 Optical System The light emitted from the plasma was gathered with two 3.7 cm diameter lenses with focal lengths of 25 cm. The first lens was placed 25 cm from the discharge and the ‘second lens was placed 25 cm from the entrance slit to the spectrometer leaving 50 cm between the lenses. At the exit slit of a grating spectrometer (f9, 1 meter, Czerny Turner) was a high quantum efficiency photomultiplier tube (PMT). The output of the PMT was illustrated on a digital pico-ammeter and a strip chart recorder. The spectrometer, lenses and microwave cavity were aligned using a He-Ne laser situated at the exit slit of the spectrometer. D.3.3 Results Small amounts of hydrogen were added to the argon in an attempt to improve the signal to noise ratio of the H8 line. Due to limitations in the size of the flowtubes, the hydrogen could not be made any smaller than 2% of the incoming argon. At 38 torr and 5% hydrogen, the plasma length was shortened to 20% of the original length, without any hydrogen. Also, the plasma was not sustained at as high a pressure with the hydrogen as without the hydrogen (100 torr vs well over an atmosphere). (See Figure D2.) 145 (‘44 - Figure D2. The top photo shows an argon plasma at 38 torr with 5% hydrogen added and the second photo shows a pure argon plasma at 38 torr. 146 Since this small amount of hydrogen affected the plasma, the density measurements were made without additional hydrogen. There was enough residual hydrogen in the argon bottle and the flow system, such that the Hfgcould be observed. The full width at half height (fwhh) of HB was measured for several pressures at a flowrate of 5 ml/sec and at zero flowrate. The gas temperature was assumed to be 1000 K and the Doppler profile was calculated. The Doppler contribution was assumed to be the only Gaussian contribution to the line and was "deconvoluted" from the 103 (see measured line width using tables of Voigt profiles Table D.3) The Doppler profile only accounted for a few percent of the fwhh. The remaining Lorentzian half width was assumed to be due to Stark broadening and instrument broadening. The instrument broadening was calculated by measuring the width of Ar4200 X which has negligible Doppler and Stark broadening. The insturment broadening was found to be 0.22% i 0.023. The instrument broadening contribution was "subtracted" from the Lorentzian profile to get the Stark broadened fwhh. The electron density was then calculated using equation D6 and Table DZ assuming Te = 10000; see Figure D3 for a sample line and Figure D4 for electron density results. The uncertainty in Te accounts for an error of less than 1%. 147 4860 4859 Figure D3 The line shape of H;3 (4861A). 148 Power 8 (4 watts '5 o Flowrate = 5 mI/sec '0 ' A Flowraie = OrnI/sec D J. Rogers Data 00 0 I4_ 00 IO U 6‘ 0.8A . A E A 8 D O .3 U D o > D I: o P o o OCDO 0 an 2 8 ._ I0'5~ O UJ _I UJ I0'2 _ 1 1 I0| I02 I03 PRESSURE (torr) Figure D4 The electron density as a function of pressure. Table D.3 The Half Width of Voigt Profiles 149 101 Lorentzian Observed 0.993 0.972 0.941 0.904 0.886 0.863 0.794 0.742 0.672 0.655 0.637 0.618 0.597 0.575 0.552 0.527 0.500 0.472 0.442 0.410 0.375 0.338 0.299 ‘ 0.257 I 0.212 0.164 0.113 A black and white photograph of the plasma for each density was placed next to picture would be was measured using Observed 0.083 0.162 0.235 0.301 0.327 0.359 0.441 0.494 0.559 0.574 0.589 0.605 0.622 0.639 0.656 0.675 0.694 0.715 0.736 0.758 0.789 0.804 0.829 0.855 0.882 0.910 0.939 was taken measurement. (See Figure D5.) the plasma so that the scale A ruler of each known. The projected area of the plasma an electronic "digitizer". The average 150 t0 photographs used the the volume of the plasma. example of determine An Figure D5 151 radius of the plasma was found by assuming that the projected area of the plasma could be represented by a rectangle of area 2rL where r is the average radius and L is the length of the plasma, which was also measured. The volume of the plasma was assumed to be cylindrical and approximately equal to nrzL. The power density was estimated by assuming that the plasma extended into the cavity by the same amount it extended outside the cavity.102 The input power was measured with power meters. It was assumed that there was a 30% drop in power between the power meters and the cavity, based upon measurements made by J. Rogersloz. Typical results are shown in Figure D6. The density measurements match previous data quite well (see Figure D4). Rogers'100 data were taken from measurements of the wavelength of a standing wave produced by two surface wave launchers in series. His measurements were made with zero flowrate and his containment tube was horizontal. The measurements reported here were made with one surface wave launcher and the containment tube was in a vertical position. In spite of these differences, the data agree extremely well. Note that there is an increase in electron density with pressure and that flowrate did not affect the electron density. A comparison of measured power density versus pressure 152 for this work and Reference 100, shows similar trends, (see Figure D6). However, Rogers power densities were consistently between one and one and one half orders of magnitude larger than the power density of this experiment. There could be two causes for this. The first is that there is an uncertainty in determination of the extension of the plasma into the reactor cavity. Therefore, the assumption that the plasma extended into the cavity an equal amount that it extended outside the cavity, may underestimate the power density. The other reason is that the heat transfer losses of this and Rogers' experiment were different due to the fact that this experiment was vertical where natural convection is important and Rogers' experiment was horizontal. Reference 100 (p. 57) shows that vertical plasmas have lower power densities than horizontal plasmas. D.3.4 Error Discussion There were several sources of errors in this experiment. 1. The signal to noise was very low with the worst ratio being 5:1. 2. At higher pressures, the signal was weak, so the most sensitive scale of the PMT had to be used. The 153 o Flowrate '6 5mI/aec (03- A Flowrate = 0mI/sec D J. Rogers Data [:1 CI :1 D D [02" U D A m . E D 3 :2 D A E .5 o o oO 2 ‘3 g 0 DJ 3 8 O I 0. IO "‘ A v A o o O O o o o O I I I0l 102 IO3 PRESSURE (Ion) Figure D6 The power density as a function of pressure. 154 signal tended to be very jagged and it was difficult to determine the fwhh. The resolution of the spectrometer was low, due to the fact that the slits had to be opened to increase the signal. In the worst case, the instrument function accounted for 60% of the Lorentzian line function. The electron temperature was only approximately known. This uncertainty will affect the Stark broadening formula by at most one percent. The gas temperature was only approximately known, so the Doppler contribution was also only approximately known. At these electron densities it could account for a few percent error. The plasma was not necessarily stable from one measurement to the next. The power supply occasionally varied, causing the plasma to lengthen or contract. The plasma would occasionally flicker resulting in a slightly different plasma position. There are also errors in the power density due to the way both the power and plasma volume were measured. 1. The boundary of the plasma was not always sharp and clearly defined. Therefore it was difficult to measure the projected area. The assumption that the projected area of the plasma 155 is rectangular and the volume of the plasma is cylindrical may not be accurate. 3. The plasma volume contained in the cavity was not known. 4. The assumption that the input power is 70% of the power measured by the power meters may not be as accurate for this experiment as it was for Rogers' experiment. With these errors in mind, there are several recommendations for improving this experiment. D.3.5 Recommendations for Electron Density Measurements The most obvious recommendation is to enhance the HB signal, although as mentioned this has proven to be very difficult. It may be possible to enhance the HB signal without adversely affecting the plasma by adding small amounts of hydrogen to a nitrogen plasma. However, it takes more power to sustain a plasma in a diatomic gas, so a more powerful power supply will have to be used. If the signal of the H could be enhanced, a B Fabry-Perot etalon could be used, and the resolution could 105 al 106 be improved. and Kreye107 have shown Speer er that a Fabry-Perot etalon system improves the resolution of 156 emitted plasma lines. In particular, Speer showed that grating spectrometers tend to overestimate the linewidth leading to overestimated electron densities. Thus it is important to improve the resolution to make sure that the electron density is not overestimated. Ideally the plasma should be initiated using two .surface wave launchers, as in Rogers' experiment. Then the electromagnetic and the spectroscopic methods of electron density determination could be compared. Also, experiments performed with vertical and horizontal plasmas could help answer the questions of heat transfer and its effect on power density. If an accurate method for determining electron and gas temperature could be found, the electron density could be known with even greater precision and fundamental questions about plasmas might be answered. 924 EleCEEQn Temperature D.4.l. Introduction A plasma is in thermodynamic equilibrium if there exists detailed balancing for every (collisional) interaction process92 and if the collisions take place with "sufficient rapidity that the distribution (of populataion densities) responds instantaneously to any . .. 93 . . change in plasma conditions.” When any gas 18 In 157 equilibrium, "the populations of different energy states corresponding to internal degrees of freedom are given by Maxwell-Boltzmann distributions".95 9 -E /kT i i n = n -- e (D7) 1 0 Z where ni is the density of state i (atoms/cc), 91 is the statistical weight of the state i, T is the temperature, k is Boltzmann's constant, Z is the partition function -E /kT Z = g.e 4 (D8) and E1 is the energy of the state i E = hc/A (D9) 1 i where h is Planck's constant, c is the speed of light and li is the wavelength of the transition i — j. When self - absorption is negligible, the integrated radiance of an atomic line is given by95 158 c h erg N = --— L n A ---- ------------------ (010) ij 40 i ij 1 2 ij sec-cm -steradians where Aij is the Einstein coefficient for spontaneous emission and L is the path length. Plugging (D7) into (010)96 yields 9 A -E /kT -20 i ij 1 Watts N = 1.582x10 ----- n L e -------------- (D11) ij Z A o 2 ij cm -steradians The temperature corresponding to the equilibrium distribution of the electronically excited states of an atom can be determined by measuring the relative populations of two or more electronic states from a neutral . atom. Taking the natural logarithm of (D11) gives 1n ------ = 1n ----- - -- (012) If ln(Nl/gA) is plotted against E/k, then the negative inverse of the slope will be the temperature and the constant 1n(LhcnO/402) will be the y intercept. There are two disadvantages to measuring the 159 95 The first is that this temperature with this method. method is critically dependent upon the accuracy of the line intensity measurements, particularly if the energy spacing between the lines is small (E(1) — E(2) < 0.4 eV) as it usually is for lines used in this method. The second is that this method is very sensitive to errors in the transition probabilities. These unfortunately are large because, for example in argon, they are only known to within at most 25%.104 D.4.2 Experiment The experimental apparatus used to measure the temperature representing the distribution of the atomic electronic states was like that of Chapter V with a few exceptions. The gas employed for the temperature measurements was argon and not oxygen and the power supply was the filtered 100 Watt source described in Secion D.2. The optical apparatus was identical to Section D.2.2.3. The photomultiplier tube (PMT) was calibrated with a 45 Watt quartz halogen tungsten filament lamp which had been calibrated aginst a National Bureau of Standard's source. 160 D.4.3. Results The accuracy of the temperature determination from line intensities was checked by measuring the ratio of intensities of two lines which originated from the same upper state. The ratio of two line intensities is given by 11(1) 9(1)A(1)1<2) (E(1) - 13(2)) - I -n N(2) 9(2)A(2)l(l) kT When E(1) = E(2), then the ratio of the two lines will be a constant _--_ = ____________ (014) Two pairs of lines (see Table D4) were measured to determine if the ratio of areas was equal to a constant. See Figure D7 for an example of an emission line. The values 4 re corrected for the non—linearity of the spectral response of the PMT. For the 7272 A - 6965 A pair, the measured area ratio was 0.26 and the calculated value was 0.29 representing a 10% difference and for the 7383 A -7067 A pair, the measured area ratio was 2.14 and the calculated value was 2.11, representing a 1.4% difference. Under 161 6965 2 6965.0 6964.8 6964.4 6964 2 696 " - Figure D7 An example of an argon emission line. 162 Table D.4 Emission Lines Used to Check Experimental Method o -l -1 8 (A) Ei(cm ) gi Aij(cm )xlO 7272.93 107496 3 0.02 6965.43 ' 107496 3 0.067 7383.98 107290 5 0.087 7067.22 107290 5 0.0395 certain lcircumstances, it is necessary to approximate the intensity ratio by the ratio of the line heights (see Section D.5.3). This approximation was also checked and the first pair had a height ratio of 0.27 representing a 5% difference from the calculated value and the second pair had a height ratio of 2.04, representing a 4% difference from the calculated value. The area and height measurements could be reproduced to within 10% of previous measurements. Thus, within the limits of the experiment, the line intensity technique was valid. It is very difficult to find emission lines which have large energy spacings, which occur in the same region of the spectrum and have similar intensities such that they can be viewed on the same PMT amplification scale. Five lines were found to be suitable for an argon plasma at 6 163 torr. The wavelengths are given in Table D5.104 Figure D8 shows 5 sets of data taken at 6 torr. Each straight line represents data taken at specific spectrometer slit height and width settings as well as specific PMT settings. The average temperature of 7380 K i 840 K was found by averaging the temperatures of the five sets of measurements. If the electronic states are in equilibrium with the free electron gas, then the electronic temperature is the same as the electron temperature. If on the other hand, the electronic states are in equilibrium with the ground state, then the electronic temperature is the gas temperature. The equilibrium of the electronic state depends upon the collisional processes. The electronic states are in equilibrium with the electron gas if the collisional excitation, represented by Ar + e --- Ar* + e (D15) where Ar* is the electronically excited state, is the dominating mechanism. The electronic states are in equilibrium with the gas (ground state) if the deactivation process Ar + Ar* --— Ar + Ar (D16) 164 Table D.5 Lines used in Temperature Determination o Wavelength (A) 7724.21 7723.76 7635.11 7514.65 7503.87 107496 106087 106238 107054 108723 gi Aij(sec— 3 0.127 : 4 0.057 : 5 0.274 i 1 0.430 : 1 0.472 : l)x108 0.032 0.014 0.069 0.108 0.118 Figure D8 In (NA/9A) I65 '5 Tove 3 7380 t 840 K 1 Power Absorbed = 68 w Pressure - 6 ton Flowrate = 0.2 mI/sec '3' 6948 K 6885 K I2- 6606 K H l l I I ] l.5I0 1520 1530 1540 1550 l.560 ENERGY (x 105) (Kelvin) Temperature determination from ratios of line 1ntens1ties. 166 is the dominating process. Further kinetic studies of argon need to be made to determine under what conditions the electronic temperature represents the electron temperature. In a similar experiment where the quartz tube was s'100 (p. 99) found that the situated vertically, Roger electron temperature was between 5000 and 7000 K for tubes of 1.2cm and 2.5 cm regardless of pressure. Note that the temperature measured here for a tube of 1.9 cm diameter is close to this measured range. Rogers' also found that for smaller tubes (1.5 mm and 4.0 mm) the electron temperature may increase with pressure, although his data is inconclusive. Moison et al.108 on the other hand, measured an excitation temperature of 3500 K for plasmas contained in 1 to 2 mm quartz tubes at atmospheric pressure and 70 Watts gbsorbed power. He used six lines between 4251 A and 4345 A to determine the electronic temperature. (These lines were too weak to detect with enough accuracy to be used in this experiment.) Moison claims that his plasma was not in thermodynamic equilibrium because his temperatures were much lower than the 7000 K required for equilibrium at an 3 electron density of 3x1014cm_ (which he measures using Stark broadening) according to the Saha equation. 109 Bloyet et a1. measures the electronic excitation 167 temperature in a 1 mm quartz tube at an input power of 50 Watts while varying pressure (1—2 torr) and flowrate (0 and 0.5 ml/sec). They find that there does not appear to be any correlation between pressure or flowrate and electron temperature and electron density. They report electron temperatures between 5500 K and 6500 K and electron densities between 5.3 and 8.5 x 1014cm-3. D.4.4. Recommendations for Electronic Temperatures An analysis of the rates of the important collisional processes must be made to determine which reaction mechanisms dominate, and whether the assumption that the electronic temperature is the temperature of the electron gas is valid. Examination of the collisional rates as a function of pressure should lead to predictions of the electronic temperatures dependence on pressure. For example, the question, "do the electron collisional processes dominate at all pressures, or is there a mixture of de-excitation as well as excitation processes occurring at high pressures?" needs to be answered. The transition rates and energies of all of the observed spectral lines of the argon plasma of this experiment need to be examined to determine which lines are most suitable for determining the electronic temperatures. 168 The lines need to be far apart in energy spacing and their area ratio must be sensitive to electron temperature especially at high temperatures so that small errors in the area measurements do not lead to large electron temperature errors. If suitable lines are found, Experiments need to be performed at various pressures. Measurements of plasmas in different size tubes need to be performed to compare with l100 Rogers data. The effect of absorbed power and gas flowrate should also be examined. D.5 Rotational Temperature of Ox en D.5.1. Introduction In a plasma, there are many types of equilibrium distributions. Translational equilibrium is attained after only a few molecular collisions, and rotational equilibrium is attained soon afterwards, but vibrational and electronic relaxation may take much longer.1 The rotational temperature may be a close approximation to the thermal temperature whereas the vibrational temperature and especially electronic temperature (see Section D.4) may be "indicative" of excitation mechanisms. The intensity of an emitted rotational line of level J' of the lowest vibrational state is proportional t095’ 96, 110 169 -BJ'(J‘+l)hc/kT N « (J'+J") e (017) J where J" is the lower rotational state, B is the rotational constant (cm‘l),h is Planck's constant, c is the speed of light, k is Boltzmann's constant and T is the rotational temperature. Taking the natural logarithm of (D17) gives J BJ' (J'+1)hC 1n ——————— or - ----------- (D18) J'+J"+1 kT If a plot is made of 1n(N/J"+J"+1) versus -BJ‘(J'+l)hc/k, the slope will be the inverse of the rotational temperature. D.5.2. Experiment Emission spectra of oxygen were observed in the experiment described in Chapter v. The image of the plasma was produced at the slits of the spectrometer using one 16 cm focal length lens76 placed 32 cm from the plasma and 32 cm from the entrance slit of the spectrometer. At pressures above 2 torr, emissison lines due to neutral atomic oxygen and neutral atomic hydrogen were observed. At pressures below 2 torr, the plasma turned from a dull 170 violet color to a very bright white. When a spectral scan of the visible region was made at pressures below 2 torr, it was discovered that the white light was due to molecular emission spectra. The molecular spectrum was identified by 111-121 comparison of spectra measured by others and was found to be the first negative band of oxygen denoted + 4 4 O2 ( Z - H ). D.5.3. Results Since the first negative band of oxygen is an electronic transition, there is coupling which occurs between the electronic and rotational angular momentum, which results in many branches (Figure D9) associated with each vibrational transition of the electronic transition. Each vibrational branch contains many rotational lines. Unfortunately, the vibrational bands tend to be very close to one another, (see Table D6), so that in a range of 150 A, there is the possibility of observing several vibrational transitions associated with this one electronic transition, any of which contains 27 to 48 P, Q or R branches, with several rotational lines contained in each branch.111 Needless to say, the spectrum of the first negative band of oxygen is very complicated. (See Figure D10) ,4 171 FII'1- F935 ' 0 F8t E91" FIO*F8 ' ' +9 F‘7‘l’ , . y : . IIIIIIIII IIIIIIUI EIIIIIII IIIIIIIII _8 '- Q'_-.I— ’- 7: ‘I'IIIII! IIIIIIIII IIIIIIH! IIIIIIIII 7 Fl'gifhxl; Y W ‘ ‘ | . ' . I ‘1 I H I + E53 IIRI I’OII’I‘HR I 4| OII‘RII’R- iIR‘IQI IR. 14. IR. :‘Q' ‘R'IR (041‘s I'Q.‘ FRI. 84 e O. I?» .9. ‘3. 19,. ‘R. Q. 'P.. IqI'R. 4' 'P..i °R.I‘. R OJ 4' "R. ’R E. ‘OI P.‘ “RI. P. ‘9'. e R ‘8' ’9 91}i4 111 I 0 ~LL T , I «A. sis... .- 8': ”azzzzzép \; u . 1'3 K. F" .;F=:—4_::=-_—_.9\ | “4- 9+: .. : g l ‘1 v w :8 c “ Eh' _. ‘j li-xL 7 r1 r__ll AU 1". Figure D9 Structure of the rotationallllevels for the first negative band of oxygen. 172 Table D.6 Band Heads of the First Negative System of 02+ 121 o Wavelength (A) Intensity v'—v" 7150 2 — 5 6856.3 0 — 2 6770 l — 3 6684 . 2 - 4 6419.2 10 0 - 1 6351.1 10 1 - 2 6291.9 6 2 — 3 6232.7 3 3 - 4 6117.2 3 4 - 5 6026.4 10 0 - 0 5973.5 10 1 - 1 5925.7 9 2 - 2 5883.5 8 3 - 3 5847.4 2 4 — 4 5814.4 1 5 - 5 5631.9 10 l - 0 5597.6 10 2 — 1 5566.7 6 3 - 2 5540.8 2 4 - 3 5520.9 2 5 - 4 5295.7 9 2 - 0 5274.7 10 3 - 1 5259.2 6 4 - 2 5251.2 10 5 - 3 5241.0 8 6 - 4 173 III [I III I 5630 5620 56IO 5500 5590 5580 5570 5560 5550 5540 I I I I I I I l I Figure D10 An example of 02+ first negative band spectra. 174 Three of the strongest vibrational bands ((0,0), (0,1) and (1,0)) were analyzed with an approximated resolution of 0.5 3. Since the Q4 branch occurred at the beginning of each vibrational band and was reasonably strong in intensity, it was the easiest to identify. In each of the three vibrational cases, only the first seven lines of the Q4 branch were identified, because the lines of the other branches were superimposed on the higher rotational lines of Q4. Due to the complexity of the spectrum, it was impossible to distinguish the area of any one line from the next. Therefore, only the height of each rotational line was measured. The relative heights approximate the relative areas for this apparatus, as discussed in Section D.4.3. The first seven lines of the Q4 branch in three vibrational bands have been plotted in Figure Dll. The data points do form a straight line as predicted and result in an average temperature of 320 K. The rotational temperature may or may not represent 123 discusses the the average gas temperature. Oldenberg criteria for the rotational temperature to represent the gas temperature. He indicates that when the rotational temperature does not match the gas temperature, a straight line is not obtained when the logarithm of the intensities is plotted against the energy, and the rotational 6.0 ‘ 175 02’ (4}: - 4m E Q4(O,l) S 30‘ I T=343K H s 20- 04(l,0) T=3|2K L0‘ 00 . I ‘ 1 . O ICC 200 300 400 500 B'J (J+l)§_c_ K Figure Dll The inverse of the slope of the natural logarithm of the intensity versus the energy of the upper state is the rotational temperature. 176 temperature tends to result in an overestimation of the gas temperature. Since a fairly straight line is obtained, this rotational temperature is probably the gas temperature of 02+, although not necessarily that of the O atoms or the gas as a whole. In Chapter II, it was found from computer modeling of the neutral kinetics that wall recombination is the dominant mechanism at 2 torr and below, whereas two and three body recombination are the dominant mechanisms at higher pressures. Thus the 02+ is probably due to recombination of O and 0+ at the wall. The computer model predicted temperatures of 1000 K to 2000 K for the overall gas temperature. But since the plasma containment tube was cooled with a fairly strong air flow around the outside of the tube, the tube wall is considerably cooler than the contents of the interior of the plasma. If 02+ is formed at the wall, the rotational temperature would be expected to represent the wall temperature which would be much lower than 1000 K. For this experiment, a rotational temperature of 320 K is consistent with an expected wall temperature. Bozoky and Schmid112 observed rotational spectra in a similar experiment of a high frequency radio discharge. The authors concluded that the rotational temperature was low because they were not able to discern the rotational development of the vibrational band heads, i.e. their 177 resolution was not good enough to separate the rotational lines. 0.5.4. Recommendations for Rotational Temperatures An important recommendation for this experiment is the vary and record the flowrate of the air that cools the quartz plasma containment tube. The wall of the tube heats up dramatically for low and no flowrates because glowing hot spots and melting have been observed. If the rotational temperature of the 02+ represents the wall temperature, then it would be expected that the rotational temperature would rise as the cooling flowrate is reduced. D.6 Conclusions Emission spectroscopy measurements of argon and oxygen plasmas give results consistent with electromagnetic measurements and with chemical modeling results. The electron temperature of an argon plasma at 6 torr was found to be 7380 K. The electron density of an argon plasma was measured from Stark broadening and was found to be in the range of 10-13 to 10'14 electrons/cc which match surface wave measurements for a pressure range of 50 to 1000 torr. Rotational temperature measurements of 02+ indicate the 178 temperature of a cooled containment tube wall to be slightly above room temperature at 320 K. ‘APPENDIX E APPENDIX E RATE COEFFICIENTS FOR CHARGED COLLISIONAL PARTNERS IN OXYGEN DISSOCIATION Reaction . Rate Coefficient Ref. (cc,sec,mole) 1. 0(10) + e + 0 + e 9x1014 17 2. 02 + e + 02+ + 2e 0(E)* 124 3. 02 + e + 0' + 0 6x107 17 4. 0 + e + 0* + 2e 0(3) 127 5. 02 + e + 0+ + 0 + 2e 0(3) 126 6. 02 + e + 0+ + 0' +2e 0(E) 125 7. O + e + O- + hv 7.8x108 l7 8. 02 + e + 02' + hv 1.2x105 . 17 9. 03 + e + 03— + hv 6.0x106 17 10. 02 + e + 02(11) + e 2.9x1ol4 12 11. 02 + e + 20 + e . 1.4x10l4 12 12. 02 + e + 02(12) + e 6.6x1013 . 12 13. 02’ + 02(11) + 202 + e 1.2x10l4 135,17 14. 0’ + 02(11) + 02' + 0 6.0x1013 17 15. 0' + 02(11) + 03 + e 1.8x10l4 135,17 16. 0+ + 02 + 0 + 02+ 2.4xlOi3 128 1.2x10 17 17. 02 + 0 + 02 + 0 3::3i3 129,131 6x10 17 0(E) indicates cross sectional data as a function of energy 179 180 Reaction 18. 0 + 03 + 03 + 0 19. 02 + 03 + 02 + 03 20. 0+ + 0 + 02+ + hv 21. 0 + 02+ 03 + hv 22. 0 + 02 + 02 + 03 + 02 23. 0 ’ + 0 + 0 ’ + 0 24. of + 0 + M + 02+ + M 25. 26. 02 + e + 0' + 0 27. O + 02+ 0 + e + 02 28. 0 + 0 ' + 0 + e 2 3 29. 02- + 02 + 202 + e 30. 02 + 02 + e + 02- + 02 31. 02 + e + O + 02- + O 32. 0' + 02 + 03 + e 33. 03 + e + 0' + 02 34. 0’ + 03 + 202 + e 35. 03— + O + 202 + e 36. 02+ + e + 20 37. 0+ + e + M + 0 + M + 38. Oz+e+M+02+M Rate Coefficient (CC,sec,mole) 3.2x1014 2.4x10l4 6.0x106 6.0x106 0(E) 4.0x10l7 6x1012 3.6x1ol7 15 13 14 1.8x10 8.4xlO 1.2xlO 6.0x107 1.4x1015 2.0x10l4 1.6x10l4 5.1x1o18 3.6x1016 0(E) 3.0x10 5.4X1012 3.2xlOl4 6.0x1012 1.3x10l7 3.6xl021 3.6x1021 9 Ref. 134,17 134,17 137 133 129,131 17 17 133 134 17 17 17 134,135,17 17 17 17 130 17 17 17 17 15 137 137 181 Reaction Rate Coefficient Ref. (cc,sec,mole) + 12 39. 0 + e + 0 + hv 2.1x10 17 40. 02+ + e + 02 + hv 2.4x1012 17 41. 02+ + 02' + 02 + 20 6.0x1016 137 + - l 15 42. 02 + 02 + 02 + 02( A) 6.0x10 137 43. 0+ + 0" + 20 0(E) 16 132 - 1.6x10 '17 44. 02+ + 0' + 02 + o 5.8x10l6 17 45. 02" + 0+ + 02 + 0 2.5x10l7 17 46. 0' + 0+ + M + 02 + M 7.3x1022 137 47. 0‘ + 02+ + M + 03 + M 7.3x1022 137 _ + 22 48. 02 + 0 + M + 03 + M 7.3xlO 137 49. 02' + 02+ + M + 202 + M 7.3x1022 137 4 + 17 50. 02 + 02 + 202 1.2x10 137 51. 03‘ + 0+ + 03 + o 1.2x10l7 137 - + 17 ' 52. 03 + 02 + 03 + 02 1.2x10 137 53. 03' + 02+ + 03 + 20 1.2x1017 137 54. 02+ + o + 0+ + 02 0(E) 136 55. 02(11) + e + 02 + e 6.0x1012 17 LIST OF REFERENCES 10. ll. 12. 182 LIST OF REFERENCES G. Marr, Plasma Spectroscopy (Amsterdam: Elsevier Publishing Co., 1968). N. Krallr and A. Trivelpiece, Principles of Plasma Physics (New York: MCGraw Kill, 1973). 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