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Measurement of thermal electron dissociative attachment rates for halogen gases using a flowing afterglow technique

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Measurement of thermal electron dissociative attachment rates for halogen gases using a flowing afterglow technique
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Sides, Gary Donald, 1947-
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English
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x, 164 leaves : ill. ; 28cm.

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Subjects / Keywords:
Bromine ( jstor )
Chlorine ( jstor )
Electron attachment ( jstor )
Electrons ( jstor )
Fluorine ( jstor )
Gas flow ( jstor )
Ionization afterglow ( jstor )
Ions ( jstor )
Reactants ( jstor )
Signals ( jstor )
Afterglow (Physics) ( lcsh )
Chemistry thesis Ph. D
Dissertations, Academic -- Chemistry -- UF
Halogens ( lcsh )
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bibliography ( marcgt )
non-fiction ( marcgt )

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Thesis:
Thesis--University of Florida.
Bibliography:
Bibliography: leaves 160-163.
General Note:
Typescript.
General Note:
Vita.
Statement of Responsibility:
by Gary Donald Sides.

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MEASUREMENT OF THERMAL ELECTRON DISSOCIATIVE ATTACHMENT RATES FOR HALOGEN GASES USING A FLOWING AFTERGLOW TECHNIQUE













By

GARY DONALD SIDES


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










UNIVERSITY OF FLORIDA


1975















Copyright, 1975, by Gary Donald Sides
















ACKNOWLEDGMENTS


The author wishes to express his appreciation to the many people who have contributed to the completion of this research. Special thanks are due Professor Robert J. Hanrahan, Chairman of his Supervisory Committee, whose tireless efforts on his behalf made this research possible. The author also thanks Dr. Thomas 0. Tiernan, Co-Chairman of his Supervisory Committee, whose co-operation indeed made this dissertation possible. Special thanks are due Professor E.E. Muschlitz, Jr., who was instrumental in getting an assignment for the author at the Aerospace Research Laboratories. Thanks are also due Dean Miller for his technical assistance, Dr. B. Mason Hughes for his advice and computer programming assistance, Julius Becsey for the loan of his direct grid search subroutine, Dr. E. Grant Jones for reading this dissertation and suggesting improvements, and Alexis VanDenAbell for her administrative assistance. The author also appreciates the excellent support of the skilled machinists, draftsmen and glassblowers at the Aerospace Research Laboratories. In addition, the author wishes to express his gratitude to the Aerospace Research Laboratories and the United States Air Force for allowing this research to be completed.

The author wishes to thank his wife, Sarah, both for typing the dissertation and for tolerating the many inconveniences caused by years of graduate study.
iii
















TABLE OF CONTENTS


Page

ACKNOWLEDGMENTS ............................ ....... iii

LIST OF TABLES ............................... vi

LIST OF FIGURES ............................ ... ......... vii
ABSTRACT ................... o................................ ix

CHAPTER I. INTRODUCTORY DISCUSSION ......................... 1

A. Electron Attachment ............................ 1
B. Discussion of Literature Data ............... 5
1. Fluorine .............. ................ 5
2. Chlorine ... . . . . . .. . . . . .............ooo o o oo o oo # oo o o 8
3. Bromine ... ... ................................... 17
4. Summary of Published Data .... o ............... 21
C. Experimental Approach ............................... 23

CHAPTER II. DESCRIPTION OF THE FLOWING AFTERGLOW SYSTEM ..... 26

A. Experimental Apparatus .. - ... ..................... 26
Bo Data Acquisition ................... 41

CHAPTER III. MATHEMATICAL MODEL . .... .............. 54

A. Basic Model ........................ ......... 54
B. Axial Flow Velocity ............................... 56
C. Radial Diffusion of Charged Species ................ 69
D. Inlet Effects ... ............ ............. 75
E. Reactant/Electron Number Density Ratio ... 76 F. Ambipolar Diffusion ... ......... ...... o.... . .*. 77

CHAPTER IV. DATA REDUCTION .................... ......79

A. Jacobian Matrix Technique ........ ...... 81
B. Grid Search Technique .............................. 91










Page


CHAPTER V. EXPERIMENTAL RESULTS ............. ... ....... . .... 105

A. Microwave Discharge Source ......................... 105
1. Electron Energy .................... ........... 105
2. Electron Attachment in Sulfur Hexafluoride ...... 106 3. Electron Attachment in Fluorine ................. 110
4. Sulfur Hexafluoride - Oxygen Negative Ion
Charge Transfer ........... ................. . 111
B. Filament Source .... 0........0.............0.......- . 115
1. Electron Energy ....... ..... sees...... .. 115
2. Electron Attachment in Sulfur Hexafluoride ...... 116 3. Electron Attachment in Fluorine ................. 117
4. Electron Attachment in Chlorine ................ 117
5. Electron Attachment in Oxygen ............ .... 118
6. Electron Attachment in Bromine .................. 121

CHAPTER VI. DISCUSSION OF RESULTS .......................... 128

A. Comparison with Published Data ...................... 128
B. Significance of the Results ........................ 132
C. Assumptions Made in the Derivation of the
Mathematical Model ......... .00............... .e. 133
D. Suggestions for Modification of the Flowing
Afterglow Apparatus and Further Research ....s....... 134

APPENDIX I. ANALYSIS OF THE FLUORINE/ARGON MIXTURE .......... 137

APPENDIX II. ELECTROSTATIC LENS SYSTEM ...................... 139

APPENDIX III. THERMALIZATION OF ELECTRONS BY ELASTIC
COLLISIONS IN AN ARGON AFTERGLOW .............. 145

APPENDIX IV. EXPERIMENTAL DATA .............................. 150

LIST OF REFERENCES o ......... . .......... . .... ... ......... ... 160

BIOGRAPHICAL SKETCH ...... ......... o .... ........... 164















LIST OF TABLES


Table Page

1. Measured First Appearance Potentials (eV) for
Dissociative Electron Attachment in Chlorine ........... 14

2. Measured First Appearance Potentials (eV) for
Dissociative Electron Attachment in Bromine ............ 20

3. Measured First Appearance Potentials (eV) for
Dissociative Electron Attachment in the Halogens ....... 22

4. Thermal Electron Dissociative Attachment Rates ......... 23 5. Rate Constants Determined in the Present Experiments ... 126 6. Comparison of the Present Results with Published Data .. 129

7. Electron Energy Versus Time Calculations for an
Afterglow .............................................. 149
8. Data Listings Key ..... *..................... ..*......... 150
















LIST OF FIGURES


Figure Page

1. Potential Energy Diagram for Dissociative Electron
Attachment to Diatomic Molecules ....................... 2

2. Potential Energy Diagram for Electron Attachment
to Sulfur Hexafluoride .................................. 6

3. Electron Attachment Probability in Chlorine Versus
the Pressure-Reduced Electric Field .................... 9

4. Calculated Electron Attachment Thresholds Versus
Experimental Thresholds Measured by Bradbury ........... 11

5. Electron Attachment Probability in Chlorine Versus
Electron Energy ..................... .................... 12

6. Electron Attachment Cross-Section Versus Electron
Energy for Chlorine and Bromine ...................... 18

7. Electron Attachment Coefficient Versus the PressureReduced Electric Field for Chlorine and Bromine ........ 19

8. Flowing Afterglow Apparatus in the Microwave
Discharge Source Configuration ......................... 27
9. Flowing Afterglow Apparatus in the Filament
Source Configuration ............................... 29

10. Filament Emission Regulator Circuit .................... 30

11. Buffer Gas Rotameter Calibration Curves ................ 33

12. Buffer Gas Volume Flow Rate Versus Flow Tube Pressure ............................................... 34

13. Reactant Gas Linear Mass Flowmeter Calibration ......... 37 14. Comparison of Two Techniques Used to Measure the Reactant Gas Number Density ............................ 40

15. Computer-Interfaced Data Acquisition System ............ 42

vii










Figure Page 16. Magnetic Disc Data File Organization ................... 45

17. Experimental Configuration for the Measurement of Transit Times for Ions in the Flow Tube ................ 58

18. Sample Trace Obtained in the Measurement of Ion Transit Times in the Flow Tube ......................... 60

19. Measured Ion Transit Times in the Flow Tube Versus Pressure for the Microwave Discharge Source
Configuration ........................ ...... . 63

20. Filament Source Configuration for the Measurement of Ion Transit Times in the Flow Tube ..................... 66

21. Measured Ion Transit Times in the Flow Tube Versus Pressure for the Filament Source Configuration ......... 68 22. Dissociative Electron Attachment in Fluorine ........... 85

23. Dissociative Electron Attachment and Br-Formation
3
in Bromine ............ .0........... . ................ 104

24. SF5/SF6 Ratio in the Microwave Discharge Source Configuration ............. . ..... ...... .. .... ... .... 107

25. F- Ion Signal Versus the Partial Pressure of an Argon Metastable Atom Quenchant, Nitrogen, Injected into
the Afterglow .... . ............. .. . ........ . ...o... 112

26. Charge Transfer Between SF and 0 ..................... 114
6 2
27. Dissociative Electron Attachment in Chlorine ........... 119

28. Electron Attachment in Oxygen.......................... 120

29. Formation of Br3 in Bromine .................. 123
3
30. Dissociative Electron Attachment in Bromine ............ 124

31. ElectrostaticLens System ......................... 140

32. Electrostatic Lens Control Circuit ................ 142

31. Electrostatic Lens Performance .............. 143


viii















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

MEASUREMENT OF THERMAL ELECTRON DISSOCIATIVE ATTACHMENT

RATES FOR HALOGEN GASES USING A FLOWING AFTERGLOW TECHNIQUE By

Gary Donald Sides

June, 1975

Chairman: Robert J. Hanrahan
Major Department: Chemistry
Co-Chairman: Thomas 0. Tiernan Aerospace Research Laboratories

A flowing afterglow apparatus was designed, constructed and used to measure thermal electron dissociative attachment rates in the halogen gases fluorine, chlorine and bromine. Electrons were produced in a high velocity buffer gas flow using either a microwave discharge source or a filament source. The electrons and positive ions produced in the source were carried past a reactant gas injection port by the high velocity viscous flow of the buffer gas. The halogen gas injected at that port then reacted with the electrons to form halide ions. These ions were sampled at the end of the reaction tube by a quadrupole mass spectrometer. By monitoring the negative ion signal as a function of the halogen gas flow injected into the reaction tube, electron attachment rates could be deduced. The operation of the flowing afterglow system was checked by










measuring the thermal attachment rate for electrons in sulfur heaxafluoride. The average value obtained for this rate constant was 3.9 � 1.4 x 10-8 cm 3/molecule-sec. The average rate constants obtained for the rates of dissociative electron attachment in fluorine, chlorine and bromine were 3.8 � 1.2 x 10-9,

3.7 � 1.7 x 10-9 and 1.1 � 0.9 x 10-11 cm 3/molecule-sec, respectively. Electrons produced in the source of the flowing afterglow system are rapidly thermalized in the high pressures present in the flow tube. Electron temperatures were estimated to be 300-600eK in the present experiments. The rate of the three-body attachment reaction Br + Br2 + Ar to form Br3 was 1-28 62
also measured and found to be 1.9 � 1.0 x 10 cm6 /molecule 2_sec. A charge transfer reaction, SF6 + 02, and the three-body attachment of electrons to oxygen were also observed using the flowing afterglow apparatus.
















CHAPTER I

INTRODUCTORY DISCUSSION


A. Electron Attachment


Dissociative electron attachment to diatomic molecules is generally thought to proceed by a resonance mechanism in which the electron is first attached to the molecule to form a molecular ion complex.1 The negative ion formed may then undergo auto-ionization (that is, ejection of the electron) and revert to the neutral molecular state or it may dissociate into an atom and an atomic ion. The sequence of steps in equation form are

e- + AA (AA-)* A- +A(i)


This reaction sequence may be discussed in terms of a potential energy diagram as shown in Figure 1. The Franck-Condon region is defined by the line ab. Electrons with an energy between E1 and E2 will be attached by the molecule to form the negative ion complex (AA-)*. The nuclei then begin to separate, their energy following the upper potential curve. During the separation the negative molecular ion is subject to auto-ionization, a process by which it may revert to the neutral state with the ejection of an electron, possibly leaving the neutral molecule vibrationally excited. If the complex ion nuclei separate to

1












(AA')*


w
z w E2
z
0 E
A+A C,
a: AA
LU I
z
ob




R
S


NUCLEAR SEPARATION


Figure 1. Potential Energy Diagram for Dissociative Electron Attachment
to Diatomic Molecules









the radius R without undergoing auto-ionization, then the
s

negative ion becomes stable against auto-ionization and the ion dissociates. The fragments of dissociation, A- and A, have a total kinetic energy between E3 and E4.

The rate of dissociative electron attachment will then depend not only upon the rate of electron capture to form the molecular negative ion but also upon the lifetime of this resonance state against auto-ionization and the time required for the nuclei to move a distance Rs apart. The average lifetime of the resonance state against auto-ionization is written as ti/r where r is the width (in energy units) for auto-ionization and - is Planck's constant divided by 27r. If T is the time required by the nuclei to separate to R=Rs then the dissociative attachment cross-section may be written as


GDA = a exp[-FT/iT] (2)


where aC is the electron capture cross-section and F is the width for auto-ionization averaged over the nuclear separation RC (R=RC at electron capture) to R. since r=r(R) and r(Rs )=O (that is, auto-ionization is no longer possible for R>Rs).1

For the halogen gases fluorine, chlorine and bromine, the electron affinities of the halide atoms are greater than the corresponding neutral molecule dissociation energies. This means that the molecular negative ion, formed by a two-body electron-halogen molecule collision, will be produced at an energy much greater than the dissociation energy of the ion. Thus, the ion formed will dissociate within one vibrational period.









This will be the case whether the molecular ion is formed in a repulsive or an attractive state. In order for thermal electron dissociative attachment in the halogen gases to be possible, the molecular negative ion potential curve (repulsive or attractive) must intersect the neutral molecule potential curve in the Franck-Condon region.

The discussion above indicates the mechanism by which electrons undergo dissociative attachment to the halogen molecules chlorine, fluorine and bromine, whose dissociative electron attachment rates were measured in the current research. In this research the rate of electron attachment to sulfur hexafluoride was also measured. Electron attachment to form a molecular negative ion, such as SF-, may be explained by a
6
two-step mechanism in which the electron is first attached to the molecule to form a molecular negative ion.2 However, the negative ion is vibrationally excited and may eject an electron through auto-ionization unless a process takes place to remove the excess energy. Since relaxation through vibrational transitions is a slow process, it is thought that collisional stabilization is the dominant relaxation mechanism if the pressure is not too low.1 In equation form the electron attachment to SF6 may be written

S6 + e- (SF-)* SF- (3)




where M is the species removing the vibrational energy of (SF-)* through inelastic collisions. If one considers the
6









molecule SF6 as a diatomic molecule SF -F, then the electron attachment mechanism may be explained in terms of the simple potential energy diagram in Figure 2. The Franck-Condon region is again defined by the line ab. Since the cross-section for the attachment of electrons to sulfur hexafluoride is a maximum for thermal energy electrons,3 the potential curve for SF6 must cross the minimum of the SF6 curve. Thus, electrons with an energy between 0 and E2 will be attached to SF6 to form vibrationally excited SF-. If the vibrational energy is removed
6
by collisional stabilization, then a stable negative ion, SF-, results. If the excited negative ion is not collisionally
6
stabilized, then ejection of the electron may occur. If the initial energy of the electron is between E2 and E , then the
2 3

negative ion formed may dissociate.4 It has been shown that the ratio of SF-/SF- in a flowing afterglow is independent of
5 6
pressure.2 This would indicate that the (SF-)* complex probably dissociates within a vibrational period (%10-13 sec).2 It has also been shown experimentally that the ratio of SF-/SF5 6
obtained by the attachment of electrons to sulfur hexafluoride can be used as a measure of the electron temperature or average electron energy.2'5


B. Discussion of Literature Data


1. Fluorine


A thorough search of chemistry and physics literature failed to yield any experimental measurements or theoretical































SF"
6


S-F NUCLEAR SEPARATION


Potential Energy Diagram for Electron Attachment to Sulfur Hexafluoride


Figure 2.









estimates for electron attachment cross-sections, rates, coefficients or probabilities in fluorine. Due to the extreme reactivity and corrosive nature of this gas, most researchers seem reluctant to investigate its properties in kinetics instruments.

The minimum appearance potential of F- ions from the dissociative attachment reaction

e- + F* () F + F (4)



can be calculated from the known electron affinity of the fluorine atom, EA(F) = 3.62 eV,6 and the molecular fluorine dissociation energy, D(F2) = 1.60 eV,7 using the equation


A(F-) = D(F2) - EA(F) + K + E (5)


where A(F) denotes the appearance potential of F- ions and K and E represent the kinetic and excitation energies, respectively, of the products of the reaction. If K and E are zero for the dissociative attachment process, then


A(F-) = 1.60 - 3.62 - -2.02 eV (6) Therefore, the reaction is exothermic and would be expected to have a zero energy threshold. This has been confirmed by Burns8 who demonstrated that F- ions are formed by electrons with zero energy and is consistent with the work of Thorburn,9 who found that the appearance potential of F- ions, produced by dissociative electron attachment to fluorine, was less









than 2 eV, the lower energy limit of his electron source. In addition, DeCorpo and Franklin10 have obtained an appearance potential of 0 � 0.1 eV for F- ions produced by dissociative electron attachment in fluorine.


2. Chlorine


Though several investigations of the electron attachment

mechanism in chlorine have been made, there is still considerable disagreement concerning the threshold value and the attachment cross-section versus energy behavior for this reaction.9'11-17 In addition, no thermal electron attachment reaction rates have been published.

The electron affinity of chlorine, EA(Cl) = 3.82 eV,6 and the molecular dissociation energy, D(C12) = 2.48 eV,7 can be used to calculate the minimum appearance potential for C1- ions in the dissociative attachment reaction, assuming K and E to be zero.


A(C1-) = 2.48 - 3.82 = -1.34 eV (7) The reaction is exothermic and would be expected to have a zero energy threshold.

Bradbury11 used a drift tube method to measure electron

attachment probabilities in chlorine/argon mixtures as a function of the pressure-reduced electric field, E/P which is directly proportional to the average electron energy in the gas. His data are shown in Figure 3. He obtained a threshold of less than 1 volt/cm-Torr for dissociative electron attachment











CI2+ e-CI+CI


3.01-


BRADBURY


)




-


BAILEY & HEALEY


5 10 it 20 25 E/P ( volts/cm- Torr)


Figure 3. Electron Attachment Probability in Chlorine Versus the
Pressure-Reduced Electric Field (After References 11 and 12)


2.0 -


.01-









in chlorine. In order to determine the approximate energy of electrons corresponding to E/P = 1 volt/cm-Torr, the calculated dissociative electron attachment threshold energies versus the measured E/P thresholds for the dissociative attachment reactions studied by Bradbury are shown in Figure 4. This plot indicates that the threshold for dissociative electron attachment in chlorine is in the range less than 0.1-1.1 eV, the energy range corresponding to less than 1 volt/cm-Torr. The dashed lines indicate the range of energy values possible for a given measured threshold (measured in E/P units). Although it is recognized that the average electron energy for a given E/P value is a function of the composition of the gaseous medium, the threshold estimate above should be reasonable since a variety of gaseous environments were used in this "calibration" plot.

Bailey and Healey12 used a drift tube apparatus to determine the attachment probability as a function of the pressurereduced electric field, E/P, for electrons in chlorine and carbon dioxide or helium mixtures. In addition, they were able to convert these data to attachment probability as a function of electron energy data. The resulting data, shown in Figure 5, indicate a threshold for the reaction of about 0.3 eV.

Thorburn9 used a mass spectrometer to determine the

appearance potential of C1- ions formed by the dissociative electron attachment reaction in chlorine. He found the appearance potential to be less than 2 eV, the minimum electron energy obtainable in his source. He also observed an appearance potential, A(CI-), at 4.4 � 0.2 eV which he postulated could







I I I I I I I I I I


4.0H


NH3/Ar 2----- -- --- 0
/ NH3/He NH3 100 N
/NH3/N2


N20/Ar


//
//


/HCI/Ar


. H2S


-Ii I
I 2 3 4 5 6 7 8 9 I0

MEASURED ATTACHMENT THRESHOLD (volts/cm- Torr)


Figure 4. Calculated Electron Attachment Thresholds Versus Experimental
Thresholds Measured by Bradbury


-ok


1.01-


3.0 -






















































1.0 2.0 3


ELECTRON ENERGY (eV)


Electron Attachment Probability in Chlorine Versus Electron Energy (After Reference 12)


Figure 5.









be explained by dissociative electron attachment in chlorine in which one of the products, CI- or Cl, was in an excited state.

Frost and McDowell13 used a mass spectrometer with a monoenergetic electron source and measured an appearance potential of 1.60 � 0.05 eV for CI- ions in chlorine with a maximum at 2.4 eV. This value falls outside the energy range for the appearance potential, A(Cl), deduced from the Bradbury11 data. Neither does it agree with the expected appearance potential of zero deduced by comparing the dissociation energy of molecular chlorine with the electron affinity of the chlorine atom. The resonance observed by Frost and McDowell is probably one in which the molecular ion is formed in an excited electronic state which then dissociates. This would explain the apparently high appearance potential obtained in their work. Frost and McDowell did not see the process producing C1- ions at 4.4 eV that Thorburn9 observed.

Moe14 used an RPD electron gun in a trapped electron apparatus and observed four resonance peaks attributed to dissociative attachment in chlorine. These peaks were located at 0, 1.75, 3.07 and 5.9 � 0.17 eV. The first resonance peak is due to dissociative electron attachment in which the molecular ion potential energy curve intersects the neutral molecule potential energy curve in the Franck-Condon region. The other three resonances are probably ones in which the molecular ion is formed in an excited electronic state which then dissociates. Note that the second resonance at 1.75 � 0.17 eV is probably










the same resonance observed by Frost and McDowell13 with a threshold at 1.60 � 0.05 eV and a maximum at 2,4 eV.

Dunkin et al.15 have reported the qualitative observation of large dissociative electron attachment rates for chlorine in a flowing afterglow apparatus. This finding supports a zero energy threshold, since electrons in the high pressure helium afterglow are known to be near thermal energies.2

Thus, there appears to be some disagreement concerning

the energetics of the dissociative attachment of electrons to chlorine. Table 1 summarizes the observations to date of the first appearance potential for Cf- ions produced by dissociative electron attachment in chlorine.


Table I

Measured First Appearance Potentials (eV) for Dissociative Electron Attachment in Chlorine


A(Cl-)

<0.1-1.1

0.3

<2

1.6 � 0.05

0 � 0.17 ',0


Author(s)

Deduced from BradburyII data Deduced from Bailey and Healey12 data Thorburn9 Frost and McDowell13 Moe14

Dunkin et al.15


These data show the disagreement concerning whether thermal electrons ("10.03 eV) will undergo dissociative attachment in chlorine.









As was previously mentioned, Bradbury used a drift tube method to determine the attachment probability for electrons in chlorine/argon mixtures as a function of the pressurereduced electric field as shown in Figure 3. Extrapolating the measured attachment probabilities, h, to E/P=0 yields h=5 x 10-4 at thermal electron energies. This agrees with a value for h=5 x 10-4 measured by Wahlin.16 Electron attachment cross-sections can be calculated from the observed attachment probabilities using the equation


a - h/X1N1 (8)


where X is the electron mean free path at one Torr and N1 is the number of molecules per cubic centimeter per Torr.18 Since Bradbury did not state the composition of the Cl /Ar
2
mixture used in his experiments, the cross-section was first calculated assuming the thermal electrons to be in 100% chlorine and then calculated assuming 100% argon (that is, much more argon than chlorine), these concentrations representing the two possible extremes. X for thermal electrons in argon is

0.13 cm.19 The calculated cross-section for thermal electron dissociative attachment to chlorine is then 1.2 x 10-19 cm2. The mean free path for thermal electrons in chlorine at one Torr is approximately 0.0005 cm.12 This results in an attachment cross-section of 3.0 x 10-17 cm2. Thus, analysis of the Bradbury data yields a thermal dissociative electron attachment cross-section of 1.2 - 300 x 10-19 cm2. This corresponds to









a rate constant of 1.2-300 x 10-12 cm3/molecule-sec for thermal energy electrons.

As was previously mentioned, Bailey and Healey12 used a

drift tube apparatus to determine the attachment probability as a function of E/P for electrons in chlorine and carbon dioxide or helium mixtures. They also measured the electron mean free path, drift velocity and free path velocity as a function of E/P. These data enabled them to calculate attachment coefficients, cross-sections and rate constants as a function of E/P or electron energy. The attachment probability as a function of E/P is shown in Figure 3. The maximum in the BradburyII data is at 6 volts/cm-Torr while that in the Bailey and Healey data is at 11 volts/cm-Torr. The average electron energy in chlorine and carbon dioxide or helium mixtures for a given E/P is expected to be lower than that in a mixture of chlorine and argon, since electrons transfer energy more efficiently to carbon dioxide or helium than argon.20 Thus, the maximum in the Bailey and Healey data occurs at a higher E/P than the Bradbury data, since the average electron energy is directly proportional to E/P.20 Bailey and Healey also obtained the attachment probability as a function of electron energy; these data are shown in Figure 5. As previously stated, these data yield a threshold for dissociative attachment near 0.3 eV and a maximum at 1.5 eV. The Bailey and Healey data may also be converted to the attachment cross-section as a function of electron energy and to the attachment coefficient as a function









of E/P. These data are shown in Figures 6 and 7, respectively, and as stated above illustrate a significant attachment crosssection for electrons at energies as low as 0.3 eV.
17
Bozin and Goodyear measured attachment coefficients

in pure chlorine as a function of the pressure-reduced electric field. They obtained these data by observing the variation of pre-breakdown ionization currents with distance between parallel electrodes for E/P between 70 and 150 volts/cm-Torr. Their results are shown in Figure 7. In the E/P regions in which the Bozin and Goodyear and the Bailey and Healey data overlap, the attachment coefficients measured by the latter are much less than those measured by Bozin and Goodyear. Bozin and Goodyear interpret this disagreement as being partially due to the neglect of the effects of ionization ignored by Bailey and Healey.


3. Bromine


There is general agreement among researchers that the dissociative attachment of electrons to bromine is a zero energy threshold process. This is expected in view of the fact that the electron 21
affinity of the bromine atom, EA(Br) = 3.49 eV, is larger than the molecular dissociation energy, D(Br2) = -1.97 eV. The minimum appearance potential for Br- ions from the reaction can then be calculated from


A(Br-) = 1.97 - 3.49 - -1.52 eV (9) assuming K and E to be zero. Thus, the reaction is exothermic

















































1.0 2.0 3.0


ELECTRON


ENERGY (eV)


Electron Attachment Cross-Section Versus Electron Energy for Chlorine and Bromine (After References 12, 23 and 24)


1.5








1.0 0.5


Figure 6.































E/P ( volts/ cm -Torr)
Electron Attachment Coefficient Versus the Pressure-Reduced Electric Field for Chlorine and Bromine (After References 12, 17, 23 and 25)


0.8 0.6



0.4



0.2


Figure 7.









and a zero energy threshold is not surprising. Table 2 summarizes the first appearance potentials measured for the bromineelectron reaction. All of the data listed in this table are consistent with a zero energy threshold for dissociative electron attachment in bromine.


Table 2

Measured First Appearance Potentials (eV) far
Dissociative Electron Attachment in Bromine

A(Br-) Author (s)

<0.7 Deduced from Bailey et al.23

0.03 � 0.03 Frost and McDowell13

0.05 � 0.17 Moe14 ft'0.03 Deduced from Truby24




Bailey et al.23 used their drift tube apparatus to investigate electron attachment in bromine and helium or carbon dioxide mixtures. The resulting attachment coefficients versus pressurereduced electric field data are shown in Figure 7. Since they also measured the electron free velocity and drift velocity in these mixtures, the attachment coefficients may be converted to attachment cross-sections. These data are shown as a function of energy in Figure 6.

Frost and McDowell13 observed a maximum Br- ion current due to the dissociative attachment of electrons in bromine at 0.03 eV with the ion signal dropping to zero at 0.72 eV.









Moe14 used the trapped electron technique mentioned above and noted dissociative electron attachment resonance peaks at 0.05, 0.98 and 3.30 � 0.17 eV. The first peak is due to attachment in which the potential energy curve for the molecular ion intersects the neutral molecule potential energy curve in the Franck-Condon region while the other peaks are due to attachment yielding molecular ions, which dissociate, in higher energy states.

Razzak and Goodyear25 measured attachment coefficients

in pure bromine as a function of the pressure-reduced electric field using the same method employed for Bozin and Goodyear's17 chlorine studies. The data obtained by them are shown in Figure 7. The coefficients obtained are again higher than the corresponding measurements by Bailey et al.23

Truby24 used a microwave cavity technique to determine the rate constant for dissociative attachment of electrons in bromine at 296*K. He obtained a value of k = 0.82 x 10-12 cm3/molecule-sec. This corresponds to a value for the attachment cross-section of 0.80 x 10-19 cm2.


4. Summary of Published Data I Table 3 summarizes dissociative electron attachment appearance potential measurements, either published or deduced from published data (for references refer to the preceding discussion), for the halogens.









Table 3

Measured First Appearance Potentials (eV) for
Dissociative Electron Attachment in the Halogens


Gas Appearance Potentials Fluorine 0, <2, 0 � 0.1 Chlorine <0.1-1.1, 0.3, <2, 1.6 � 0.05, 0 � 0.17, --0 Bromine <0.7, 0.03 � 0.03, 0.05 � 0.17, "0.03



Appearance potential measurements indicate that both fluorine and bromine have a zero energy dissociative electron attachment threshold as expected; however, there is some disagreement in the case of chlorine. The measurement of the rate of thermal energy electron attachment in chlorine would help settle the controversy.

Table 4 summarizes thermal electron dissociative attachment rate constants, either published or calculated from published data, for fluorine, chlorine and bromine. These data illustrate the need for further halogen thermal electron dissociative attachment studies. Not only are there no data for fluorine but there are also no definitive measurements for chlorine since the rates shown were extrapolated from data for which the electron energy is greater than thermal. In addition, there is a factor of eighteen disagreement between the rate measurement for bromine and a value extrapolated from the data of Bailey et al.









Table 4

Thermal Electron Dissociative Attachment Rates


Molecule k(cm3/molecule-sec) Author(s) Fluorine none

Chlorine 1.2-300 x 10-12 Extrapolated from Bradbury11

<6 x 10-12 Extrapolated from Bailey and Healey12

large Dunkin et al.15

Bromine 1.5 x 10-11 Extrapolated from Bailey et al.23

0.82 x 10-12 Truby24



C. Experimental Approach


In view of the absence of rate data for the attachment of thermal electrons to the halogen molecules, an apparatus was designed and constructed to obtain this information. A flowing afterglow technique was selected for these experiments after a review of the methods which have been used to measure thermal electron attachment rates. The flowing afterglow method was selected primarily because of the ease with which thermal electrons are produced in the afterglow.2 In addition, this technique has been used previously to measure a thermal electron attachment rate.2

The present experiments were performed in three stages

1. the design and construction of the flowing afterglow apparatus,

2. the use of this apparatus to measure known reaction rates in order to determine whether the apparatus was functioning









properly and 3. the use of the apparatus to measure thermal electron attachment rates for the halogens. The reactions used to check out the flowing afterglow apparatus were


e- + SF6 (SF-)* -M+ SF- (3)
6 6 6


and


SF6 + 0 SF- + 0 (10)
6 2 6 2


Both of these reactions were selected because their rates had been measured using a flowing afterglow technique.2,26 In addition, the thermal electron attachment rate for sulfur hexafluoride has been measured using a variety of experimental techniques.2,27-30 During the course of experimental measurements in the flowing afterglow apparatus, another known reaction rate, that of the


02 + e- - (0)* :2.0 (11)


reaction was also determined as a further check of experimental procedure.31,32 Once the initial tests of the experimental technique were completed, the thermal electron attachment rates for the reactions


e + F2 - (F)* F- + F (4)


e- + Cl2 (Cl2) - Cl- + Cl
2 2


(12)






25


e + Br2 - (Br-)* Br- + Br (13)
2 - 2


were determined. In addition, the reaction rate for


Br- + Br + Ar ) Br- + Ar (14)
2 3


was determined in the course of the experiments.
















CHAPTER II

DESCRIPTION OF THE FLOWING AFTERGLOW SYSTEM A. Experimental Apparatus


The flowing afterglow apparatus in the microwave discharge source configuration is shown in Figure 8. Electrons are produced by a 2450 MHz microwave discharge (approximately

2 watts) in argon buffer gas in a quartz tube with an inside diameter of 1.1 cm. The microwave power supply33 is coupled 34
to the buffer gas by an Evenson cavity and the microwave power is monitored by a microwave power meter35 (not shown). The buffer gas flow is measured by a rotameter36 (not shown) and a linear mass flowmeter.37 The buffer gas pressure is measured at the center of the reaction tube by a capacitance manometer.38 Electrons produced in the active discharge are rapidly thermalized in the high pressure environment (1 to 4 Torr) and flow past the reactant gas injection port, where a gas such as fluorine may be introduced into the afterglow. The reactant gas flow is monitored by a linear mass flowmeter capable of measuring argon flows over the range 1 to 225 atm-microliters/sec.39 Negative ions formed in the reaction tube (19.6 cm in length) are sampled through a 0.23 mm orifice,

0.076 mm in length, located on the tip of a stainless steel 26










REACTANT GAS SOURCE


QUADRUPOLE


REACTANT GAS FLOW TRANSDUCER

VARIABLE LEAK VALVE


L


ELECTROSTATIC
LENS
TO
GATE VALVE COLD TRAP DIFFUSION PUMP


Figure 8.


INJECTION
PORT


DISCHARGE
CAVITY


VARIABLE LEAK VALVE
r'- -- SUFFER
LMF GAS FLOW
TRANSDUCER

COLD
TRAP





BUFFER GAS
SOURCE


CHARCOAL MOLECULAR TRAP SIEVE TRAP-VALVE


Flowing Afterglow Apparatus in the Microwave Discharge Source Configuration


ELECTRON
MULTIPLIER


IONIZER









cone. The cone is maintained at +4 to +13 volts with respect to ground in order to extract negative ions from the flowing afterglow at the end of the reaction tube. The ions extracted are focused by a cylindrical electrostatic lens system into the lens elements of an ionizer. These elements then focus the ions into a voltage-scanned quadrupole mass spectrometer.40 The ions are then mass resolved by the quadrupole filter and detected by an electron multiplier. A preamp-electrometer (not shown) amplifies the resulting signal and provides analog outputs for computer and oscilloscope inputs. The flow tube is pumped by a 1000 liter/minute rotary pump.41 A charcoal trap in the pump line converts fluorine to carbon tetrafluoride in order to prevent mechanical pump degradation. A molecular sieve trap in the pump line prevents back diffusion of hydrocarbons from the mechanical pump.

The flowing afterglow apparatus in the filament source configuration is shown in Figure 9. The basic difference between this configuration and that shown in Figure 8 is the removal of the microwave source and the substitution of a filament electron source. In addition, a sintered glass disc was installed upstream of the source in order to smooth the buffer gas flow through the flow tube. Also, at- this point an automatic flow control system42 was installed so that the reactant gas flow rate could be controlled by a computer during an experiment. The filament source is shown in detail in Figure 10. The filament is a thoriated-iridium ribbon43 which is spot-welded to hermetic feedthroughs mounted in the











REACTANT GAS SOURCE


IONIZER


QUADRUPOLE


ION SAMPLING


REACTANT I GAS FLOW TRANSDUCER

SERVO-DRIVEN LEAK VALVE


VARIABLE
LEAK VALVE


I~~II


INJECTION
PORT


ELECTROSTATIC
LENS
TO
GATE VALVE COLD TRAP DIFFUSION PUMP


SINTERED GLASS DISC


BUFFER
LMF GAS FLOW TRANSDUCER

COLD
TRAP





BUFFER GAS SOURCE


CHARCOAL MOLECULAR TRAP SIEVE TRAP-VALVE


Flowing Afterglow Apparatus in the Filament Source Configuration


ELECTRON
MULTIPLIER


Figure 9.












































Figure 10.


Filament Emission Regulator Circuit


+15V









flow tube walls. The anode is at ground potential and mounted approximately 1.3 mm from the filament. Filament current is supplied by a remotely programmable power supply.44 Electrons emitted by thermionic emission from the filament are accelerated to the anode by the -45-volt negative bias applied to the filament. These electrons produce secondary electrons by ionization of the buffer gas in the flow tube. The secondary electrons are then swept down the flow tube by the axial velocity of the buffer gas and thermalized by elastic collisions in the high pressure environment. Filament emission is monitored by a microammeter.

The filament emission control circuit contains operational amplifiers #1 and #2 which provide the necessary voltage to the input of the programmable power supply. The emission current causes a voltage drop across a 10 kS resistor. This voltage drop is applied through a 50 kS2 resistor to the inverting input of operational amplifier #1. This technique provides feedback stabilization of the emission current. Operational amplifier #3 acts as a comparator to prevent the voltage input to the programmable power supply from exceeding the limit set by the 10 kQ potentiometer. This prevents the passage of excess current through the filament (that is, prevents filament destruction).

The buffer gas generally used in these experiments was argon, the flow rate typically being 10-25 atm-cm3/sec. Two methods were employed to monitor the buffer gas flow in these









studies. Initially, the buffer flow was measured with a rotameter, using both sapphire and stainless steel floats. Calibration curves at 20 psig (regulator gauge pressure) for the rotameter are shown in Figure 11. These curves were obtained using a bubble meter calibration method. Use of the rotameter for measuring flow rates has several disadvantages which severely limit its accuracy and utility. These include the dependence of the calibration on temperature and gas pressure, the poor dynamic range, the difficulty in accurately reading the meter, and the lack of an electrical signal output, which is needed for automated readout devices. Therefore, a linear mass flowmeter was used to measure flow rates for all experiments presented in this report. The flowmeter used to measure buffer flow permits monitoring of flow rates up to 155 atm-cm3/sec with an accuracy of approximately �0.1% of full scale. The calibration of this meter remains constant over a pressure range 1 psia (absolute pressure) to 150 psig. In addition, the meter provides a 5-volt output signal at full scale for use with a readout device. The buffer gas linear mass flowmeter was not calibrated in this laboratory but was calibrated by the manufacturer.37

Figure 12 is a plot of buffer gas flow versus pressure

in the flow tube. The buffer gas flow was calculated from the relation


F = f(T/273.15)(760/P)


(15)












25.0


0
o20.0


-E
0
- 15.0




0

< STAIN


5.00 A SAPP





3.00 6.00 9.00

FLOWMETER READING


Figure 11. Buffer Gas Rotameter Calibration Curves


12.0



































* ARGON - LINEAR MASS FLOWMETER
* ARGON - ROTAMETER, SAPPHIRE FLOAT o HELiUM-LINEAR MASS FLOWMETER o ARGON- ROTAMETER, SS FLOAT


X.00


FLOW TUBE PRESSURE


5.00


(Torr)


Figure 12.


Buffer Gas Volume Flow Rate Versus Flow Tube Pressure


8.00-


4.00[-









where f is the buffer gas flow rate in atm-cm 3/sec, T is the gas temperature (*K), and P is the gas pressure (Torr) at the center of the reaction tube. The agreement between the data obtained using the rotameter with sapphire float and that obtained with the linear mass flowmeter is obvious. The buffer gas flow measured by the rotameter with stainless steel float and the linear mass flowmeter exhibit poorer agreement.

The buffer gas flow rate is maintained constant by regulating the backing pressure behind a fixed leak. The stability of the buffer gas flow has been checked by monitoring the linear mass flowmeter output as a function of time. The observed drift in the voltage output at a given flow rate was approximately

0.007 volt/hour. This corresponds to approximately 0.1% of full scale per hour and is negligible during a typical experiment.

The derivation of the expression relating the linear

mass flowmeter signal output to the buffer gas axial velocity (bulk flow velocity) is given below. The buffer gas flow in atm-cm 3/sec is given by


f = Vb (i0000/5)(273.15/294.26)(Mb/60) (16)



where V b is the voltage output of the linear mass flowmeter (5-volt output, full scale, corresponds to 10000 standard cm 3/sec (SCCM) of air) and Mb is a factor specific for the buffer gas in use. Therefore, the expression relating the buffer gas flow in cm 3/sec to the bulk flow axial velocity may be written










vo = F/wa2 = 2.583 x 104 MbVb/Pna2 (17)



where P is the pressure in Tort at the center of the reaction tube and a is the flow tube radius in centimeters. If argon or helium is the buffer gas, then


v - 7.15 x 103 Vb/P (18)



since a = 1.283 cm for the flow tube used in the current experiments and Mb = 1.43 for argon or helium.

The reactant gas flow rate was monitored with a linear

mass flowmeter for which full scale deflection corresponds to

5 SCCM of air. A monel transducer was used with this flowmeter in order to permit monitoring of corrosive gases. In the experiments reported here, the flowmeter was calibrated for argon since most reactant gas mixtures used consisted of at least 99.8% argon, and thus, the thermal conductivity of the mixture is essentially that of argon. Conversion factors supplied by the manufacturer allow the calculationof gas flow for other gases or mixtures of gases. A typical calibration plot is shown in Figure 13 (data points and solid line). Calibration curves measured over a six-month period were found to differ by less than 2% (slope difference). The full scale flow measured for argon agrees to better than 2% with that calculated by use of a conversion factor given in the flowmeter manual. The dashed line shown in Figure 13 is the manufacturer's calibration. It is concluded, therefore, that the reactant gas flow rates














180 -2





S 1356/
E/

2/





3: 900
.L
z
0








45






t I I
2.00 4.00 6.00 8.00

MASS FLOWMETER OUTPUT (volts) figure 13. Reactant Gas Linear Mass Flowmeter Calibration









are accurate to within 2%. The mass flowmeter has been found to be linear over the flow regime from 1 to 225 atm-microliters/ sec, which corresponds to a 10-volt output from the flowmeter. Since the flowmeter operation depends on the mass flow of the gas to change the temperature along a heated conduit (which in turn is dependent upon the heat capacity of the gas), the flowmeter calibration is independent of pressure over a wide range. The calibration curve shown in Figure 13 was obtained over the range 2 to 20 psig, and no variations with pressure were observed.

From the measured reactant gas flow, the number density

of the reacting species in the reaction tube can be calculated. If argon is the diluent and buffer gas, then the number density of the reactant in the flow tube, calculated from measured reactant and buffer gas flows, is given by


nrLMF 1.61 x 1013 VrCfP/Vb (19)


where Cf is the fractional concentration of the reactant gas and Vr is the voltage output of the linear mass flowmeter used to monitor the reactant gas. As a check against this method of determining the reactant gas number density, the change in pressure in the reaction tube may be monitored as the reactant gas flow is varied, and the number density can then be calculated independently of the linear mass flowmeter signal. Thus, from the ideal gas law









nAP = AP(NA/RT) (20)



or


nAP 3.22 x 1013 AP (21)



if argon is used for these comparisons where NA is Avogadro's number, R is the international gas constant and T is the gas temperature (assumed to be 300*K). The pressure change, AP, is measured in units of millitorr. Figure 14 gives a comparison of the number density of the reactant gas in the flow tube at 3 Torr buffer gas pressure (corresponding to 0.87 volts output from the buffer gas linear mass flowmeter) as calculated by the two methods noted above. The agreement is within at least 9% over the full range of reactant gas flow, thus indicating that the use of the linear mass flowmeter technique to determine reactant number density is satisfactory. The measurement of the partial pressure of the reactant gas mixture during an actual experiment is not feasible, since this corresponds to only about 14 millitorr for full scale flow and thus a small drift in reaction tube pressure during the experiment would introduce considerable error. Such drift probably accounts for the difference observed in the two number density measurement techniques compared above, especially since the deviations observed correspond to a pressure of about one millitorr on a buffer gas total pressure background of 3000 millitorr.














III i
0


0/
0/


o/
0/
0/









o//

S I I I


1.0

A P NUMBER


2.0


3.0


DENSITY


4.0


(1lo4 Cr-3)


Figure 14.


Comparison of Two Techniques Used to Measure the Reactant Gas Number Density


E
0
0

F
U'5
z
w
a

w


z
-.


4.0


3.0


2.0


1.0 -









B. Data Acquisition


The data acquisition system ultimately developed during

the course of this research is shown in Figure 15. The system was designed around a 24K, 16-bit minicomputer and its peripheral devices.45 Analog signals proportional to experimental parameters such as reactant and buffer gas flows, reaction tube pressure, ion signal and ion mass were converted to digital signals by a 14-bit analog-to-digital converter. A relay register was used to advance the mass programmer-peak switching hardware. A 12-bit digital-to-analog converter provided the remote programmed input signal necessary to control the automatic flow system hardware. A cathode ray terminal was used to give the operator input/output capabilities. A storage oscilloscope allowed the operator to display ion signal versus reactant gas flow data at the end of an experiment. The raw data for each experiment were stored on a magnetic disc system to be reduced at a later time.

Once the flowing afterglow system is in the operational mode (traps filled, buffer gas flow set, the desired filament emission current obtained and so forth), a single experiment consists of little more than running the program AFGLO whose outline and listing are at the end of this chapter. Program AFGLO is loaded into the core of the minicomputer from the magnetic disc, where all data acquisition, reduction and storage files are located, by entering a directive at the teletype keyboard. At this point the operator moves to the cathode ray terminal







FILAMENT SOURCE


QUADRUPOLE & FOCUSING LENSES


SINTERED


BUFFER
GAS


REACTANT GAS


Figure 15. Computer-Interfaced Data Acquisition System









and inputs experimental parameters (sampling orifice potential, reactant gas concentration, reactant gas linear mass flowmeter multiplier, the capacitance manometer full scale pressure, the electrometer input resistor value, the number of mass programmer channels used and the A/D converter rate), operating limits (the reactant gas flow stability time, the reactant gas upper flow limit, the number of data points desired and the number of runs desired) and the data file name. Program AFGLO then reads sector zero of the data file to determine three pieces of information: the next sector available in the file for the storage of experimental data and two calibration constants (slope and intercept) necessary for the operation of the automatic flow control system. The D/A converter voltage necessary to obtain the reactant gas upper flow limit is then applied to the programmable input of the automatic flow controller. The reactant gas flow is then monitored until it has been within �0.1 volts of the desired flow for a period of time greater than the reactant gas flow stability time (generally 15 or 20 seconds). At this point the ion intensity of peak #1 is obtained and then the quadrupole is switched through the remaining peaks measuring the ion signal intensity of each. The reactant gas flow, buffer gas flow and buffer gas pressure are also measured at this point. The reactant gas flow is then decremented by an amount determined by the number of data points desired and the upper reactant gas flow limit (the lower limit is always 0.05 volts for









decrement purposes). If the desired reactant gas flow is greater than 0.02 volts at this point, then the D/A converter output is decremented and the data point acquisition cycle repeated. If the desired reactant gas flow is less than 0.02 volts, then the data acquisition process is complete. The average values for the buffer gas flow and the buffer gas pressure during the experiment are then determined and the experimental data and input parameters are stored on a magnetic disc in the data file specified above. A plot of the ion signal of primary interest versus reactant gas flow for the experiment is also displayed on a storage oscilloscope.

The configuration of a magnetic disc data file is shown in Figure 16. The number preceding each stored parameter is the word number within a specific sector. Each data file consists of 501 fixed point sectors; each sector consists of 128 fixed point words. Sector 0 of the data file is used to store parameters needed f9r each experiment such as the next sector available for data storage, the number of experiments stored in the data file and the slope and intercept calibration constants relating the 12-bit D/A converter output voltage to the reactant gas flow obtained. Sectors 1 through 500 allow the storage of 100 sets of experimental data, 5 sectors per experiment. The first 80 words of each block of 5 sectors (one experiment) are reserved for the storage of experimental parameters such as the reactant gas concentration, orifice potential and so forth. Words 81 through 640 of each












SECTOR 0


1. next sector available


2. number of experiments


3. AFC slope calibration


4. AFC intercept calibration


SECTOR 1


1. measured transit time 5. manometer full scale

9. stability time for AFC 13. .. .


17. experiment


21. mass of peak 4


2. react gas conc, mant

6. electrometer resistor

10. # data points

14. buffer gas pressure

18. mass of peak 1

22. mass of peak 5


3. react gas conc, char 7. # mass channels 11. buffer gas flow 15. .. .


19. mass of peak 2 23. mass of peak 6


4. react gas multiplier

8. A/D rate 12. ...


16. ...


20. mass of peak 3 24. orifice potential








81. react flow data pt 1

85. intensity peak 4 pt 1

89. intensity peak 1 pt 2


82. intensity peak 1 pt 1

86. intensity peak 5 pt 1

90. intensity peak 2 pt 2


83. intensity peak 2 pt 1

87. intensity peak 6 pt 1

91. intensity peak 3 pt 2


84. intensity peak 3 pt 1

88. react flow data pt 2


SECTOR 2 SECTOR 5


122. react flow data pt 80


125. intensity peak 3 pt 80


126.
peak


intensity
4 pt 80


123.
peak

127.
peak


intensity
1 pt 80

intensity
5 pt 80


124. peak

128.
peak


intensity
2 pt 80

intensity
6 pt 80


SECTOR 6


SECTOR 500


Figure 16. Magnetic Disc Data File Organization






47


experimental 5-sector block are used to store reactant gas flow versus ion signal data points (up to 80 per experiment). Since this data file is fixed point, some floating point parameters (for example, reactant gas per cent concentration) must be converted to digital form in such a way as to preserve all significant figures.









OUTLINE OF PROGRAM AFGLO


input experimental parameters, operating limits
and data storage file I


read from sector 0 of the specified data file:
the next available sector and automatic flow
control calibration constants

I
output voltage from D/A converter to remote input
---of automatic flow control to obtain the desired reactant gas flow


monitor reactant gas flow until within �0.1 volts of the flow desired for the period of time specif:


using the relay register, switch the quadrupole


led


through the desired masses while measuring the ion signal intensity for each mass


measure the reactant gas flow, buffer gas pressure and buffer gas flow I


maintain a sum of the buffer gas gas flow measurements I


decrement the reactant gas flow. desired <0.02 volts?

IYES
determine the average buffer gas gas pressure measured during the


pressure and buffer reactant gas flow flow and buffer experiment


store the experimental data on magnetic disc in the file specified above 4


plot the ion signal versus reactant gas flow data of primary interest on the storage oscilloscope










C001 FT N,L
C002 PROGRAM AFGLC

C004 C* � C005 C* SOURCE PRCGRAM IS GSFAC. WHEN LCACING, ATTACH THE * C006 C* FILES BACRV, CCNCe ANC CAQR FCR THE CALLS ACCN, * C007 C* RELAY AND CAC, RESPECTIVELY. WHEN LOADING, ATTACH C008 C* THE FILES CDPTR ANC CCPLR FOR THE CALL PLCTR. * CCO9 C* � 0010 C* PARAMETER CHANNEL MULTIPLIER * 0011 C* REACTANT FLCW 0 1 * 0012 C* ION SIGNAL 1 1 * 0013 C* UON SICNAL 2 O * 0014 C* PRESSURE 3 10O * 0015 C* BUFFER FLCW 4 10 * 0016 C* MASS 5 10 * 0017 C* PEAK SWITCI-ING 10 (RELAY) * 0018 C* * 0019 ******************************************************** C020 DIMENSICN NX(80),NY(80) 0021 CCMMCN IRRAY{64C),IFILE(3),JRRAY(10),ION(6) 0022 ICNWC=IC28
0023 CALL RELAY(10,0)
C024 CC 25 I=1,64C
0025 25 IRRAY(I)=O
0026 ******************************************************** 0027 C* * 0028 C* LINES 32 THROUGH 110 REQUIRE THE CPERATOR TO INPUT * 0029 C* EXPERIMENTAL CCNDITIONS AND LIMITS. * 0030 C* , 0031 ******************************************************
0032 WRITE(7,60)
0033 60 FCRMAT(IX, INPUT ORIFICE POTENTIAL (VOLTS) 0034 READ(7,*)POTEN
0035 IRRAY(24)=IFIX(PGTEN*10.) 0036 WRITE(7,70)
0037 70 FCRMAT(1X, INPUT REACTANT GAS CCNCENTRATICN { ) ) 0038 READ(7,*)RCCNC
0039 75 IF(RCCNC-100.)8CIO C040 80 RCCNC=RCCNC*10.
0041 IRRAY(3)=IRRAY(3)+l
0042 GCTO 75
0043 100 IRRAY(2)=IFIX(RCCNC) 0044 IARITE(7,125)
0045 125 FCRMAT(IX, INPUT REACTANT GAS LMF MULTIPLIER ) 0046 READ(7,*)RGMUL
0047 IRRAY(4)=IFIX(RGUL*100.) 0048 WRITE(7,150)
0049 ******************************************************** 0050 C* , 0051 C* EXPERIMENTAL DATA IS STORED ON DISC IN THE FILE * 0052 C* GIVEN FERE. �










0053 C* * 0054 ************************** ************************* 0055 15C FCRMAT(lX, INPUT EATA FILE NAME 0056 REAO(7,175)(IFILE(I),I=l,3) 0057 175 FORMAT(3A2)
0058 WRITE(7,200)
0059 2C0 FCRMAT(1X, INPUT BARATRON FULL SCALE (MICRONS)) 0060 READ(7,*)IRRAY(5)
0061 WRITE(7,225)
0062 225 FORMAT(IX, INPUT ELECTROMETER RESISTOR (5,7 OR 9) 1 0063 READ(7,*)IRRAY(6)
C064 hRITE(7,235)
0065 235 FORMAT(X, INPUT NUMBER OF MASS PROGRAMMER CHANNELS 0066 1 USEC )
0067 WRITE(7,240)
0068 240 FORMAT(1X, INPUT ACC RATE (CPS) I 0069 READ(7,*)IRRAY(8)
0070 kRITE(7,245)
0071 245 FCRMAT(lX, INPUT REFLO APC STABILITY TIME (SEC) 0072 ******************************************************* 0073 C* * 0074 C* APC STABILITY TIME IS TI-E TIME WITHIN WHICH THE * 0075 C* REACTANT GAS FLCW MUST BE BETWEEN THE PRESCRIBED * 0076 C* LIMITS BEFORE A DATA POINT IS TAKEN. * 0077 C*
0078 ******************************************************* 0079 READ(7,*)IRRAY(g)
0080 NCSEC=IRRAY(8)*IRRAY(9) 0081 265 WRITE(7,275)
0082 275 FORMAT(IX, INPUT REACTANT GAS UPPER FLOW LIMIT 0083 1 (VOLTS)
0084 IRCD=14
0085 CALL EXEC(IRCDICNWCJRRAY10,IFILE,0) 0086 C******************************************************** 0087 C* * 0088 C* SLOPE ANC YINTC ARE CALIBRATION CONSTANTS FOR * 0089 C* THE AUTOMATIC REACTANT GAS FLOW CONTROL SYSTEM. * 0090 C* * 0091 ******************************************************l' 0092 SLOPE=FLCAT(JRRAY(3) /ICOO0. C093 YINTC=FLCAT(JRRAY(4))/1C0. 0094 V=UFLIM*SLOPE+YINTC 0095 CALL CAC(V)
0096 *****************************'************************ 0097 C* * 0098 C* AT THIS PCINT TFE C/A CONVERTER SETS THE REACTANT * 0099 C* GAS FLOW AT THE DESIREC UPPER LIMIT BY APPLYING V * 0100 C* VOLTS TO TFE REMOTE PROGRAMMING INPUT OF THE * 0101 C* AUTCMATIC FLOW SYSTEM. * 0102 C* * 0103 ******************************************************** 0104 WRITE(7,300)










0105 3C0, FCRMAT(IX, INPLT NUMBER DATA POINTS DESIRED (80 MAX 0106 1) ) 0107 READ(7,*)IRRAY(1C) 0108 WRITE(7,325) 0109 325 FCRMAT(IX, INPUT NUMBER OF RUNS DESIRED ) 0110 READ(7,*)NRUNS 0111 ***************************************************** 0112 C* 0113 C* AT THIS PCINT THE AUTCPATIC DATA ACCUISITICN 0114 C* SYSTEM TAKES OVER. 0115 C* , 0116 C****** **** 0117 CC 900 N=I,NRUNS 0118 eFSU'=C.C 0119 PRSUM=0.0 0120 CC 350 KK=1,6 0121 35C ICN(KK)=C 0122 CD 375 KK=81,64C 0123 375 IRRAY(KK)=O 0124 V=UFLIM*SLOPE+YINTC 0125 CALL EACV) 0126 CESFL=UFLIM 0127 CALL STAPC(NCSECCESFL) 0128 K=81 0129 4CO CALL EATA(BUFLO,IRFLCPRESSK) 0130 IRRAY(K)=IRFLC 0131 IRRAY(K+1)=ICN(I) 0132 IRRAY(K42)=ION(2) 0133 IRRAY(K+3)=ION(3) 0134 IRRAY(K+4)=ICN(4) 0135 IRRAY(K45)=ION(5) 0136 IRRAY(K+6)=ION(6) 0137 BFSUN=eFSUV BUFLC 0138 PRSUP,=PRSUM+PRESS 0139 K=K+7 0140 CESFL=CESFL-(UFLIM-C.05)/FLCAT(IRRAY(10)-I) 0141 IF(DESFL-C.02)5CC,45C 0142 450 V=DESFL*SLOPE+YINTC 0143 CALL CAC(V) 0144 CALL STAPC(NCSEC,CESFL) 0145 GCTO 40C 0146 5CC IRRAY(11)=IFIX(EFSUt/FLOAT(IRRAYU0f))) 0147 IRRAY{I)=IFIX(PRSU/FLOAT(IRRAY(1O))) 0148 N=JRRAY(1) 0149 JRRAY(2)=JRRAY(2)+I 0150 JRRAY(1)=JRRAY(1)+5 0151 IRRAY(17)=JRRAY(2) 0152 IRCD=15 0153 C *** ******** **,*,******** ,************* 0154 C* , 0155 C* AT THIS PCINT TFE DATA FOR CNE EXPERIMENT IS 0156 C* TRANSFERRED TC THE MAGNETIC DISC SYSTEM AND STORED *










0157 C* IN THE CATA FILE SPECIFIED ABCVE. 0158 C* * 0159 ***************************************************** 0160 CALL EXEC(IRCOICNWCIRRAY,640,IFILEN) 0161 CALL EXEC(IRCCICNWCJRRAYIOtIFILE,O) 0162 ******************************************************** 0163 C* * 0164 C* LINES 169 THRCUGH 180 NORMALIZE THE ION SIGNAL OF * 0165 C* INTEREST VERSUS REACTANT GAS FLOW AND PLOT THE CATA * 0166 C* CN A STCRAGE CSCILLOSCCPE. , 0167 C* * 0168 **** *** ********************* ************** 0169 MAX=O
0170 N=814(IRRAY(lG)-1)*7 0171 CC 600 I=81,N,7
0172 IF(IRRAY(I+2)-MAX)6CC,550 0173 550 MAX=IRRAY(I+2)
0174 600 CONTINUE
0175 CC 700 I=81,N,7
0176 J:-(I-74)/7
0177 NX(J)=IFIX(4C95.*FLCAT(IRRAY(1))/32764.) 0178 700 NY(J)=IFIX(4C95.*0.9*FLOAT(IRRAY{I+2))/FLCAT(MAX)) 0179 N=IRRAY(10)
0180 9CC CALL PLCTR(NX,NY,N)
0181 GETO 265
0182 END
0183 ******************************************************* 0184 C* * 0185 C* SUBROUTINE STAPCO THIS SUBROUTINE CETERMINES WHEN * 0186 C* THE REACTANT GAS FLOW HAS BEEN WITHIN THE DESIRED * 0187 C* LIMITS FOR THE PERIOD CF TIME PRESCRIBED ABOVE BY 0188 C* THE INPUT REFLO STABILITY TIME * CONTROL IS THEN * 0189 C* RETURNED TC TFE MAIN PROGRAM. * 0190 C* * 0191 ******************************************************* 0192 SUBRCUTINE STAPC(NCSECCESFL) 0193 ICCO N=O
0194 1050 CALL ACCCN(IFLCW,O)
0195 REFLC=FLOAT(IFLCW)/3276.4 0196 IF(REFLC-CESFL+C.10)ICOG,1lCO 0197 11CO IF(REFLC-CESFL-C.10)1200,lCCO 0198 1200 N=N+1
0199 IF(N-NCSEC)IC50,130C 0200 13C0 RETURN
0201 END
0202 ******************************************************** 0203 C* 0204 C* SUEROUTINE DATAO THIS SUBROUTINE MEASURES THE * 0205 C* BASELINE ANC ICN SIGNALS FOR UP TO FIVE MASSES, THE * 0206 C* BUFFER GAS FLOW AND THE REACTICN CHANNEL PRESSURE * 0207 C* FOR A GIVEN REACTANT FLOW, WHICH IS ALSO MEASURED. * 0208 C*










0209 C******,, 0210 SUBRCUTINE CATA(BUFLC,IRFLOPRESS) 0211 CCVMCN IRRAY(64G),IFILE(3),JRRAY(10),ION(6) 0212 COMMCN ITIME(5) 0213 SEFLC=C.C 0214 SPRES=0.0 0215 SFL06=0.0 0216 NCHAN=IRRAY(7) 0217 00 2CCO J=1,NCHAN 0218 IF(K-82)135C,14CC 0219 1350 CALL ACCCN(IRRAY(J+17),5) 0220 1400 SIONS=C.C 0221 CALL ACCCN(ICNS,1) 0222 IF(ICNS-3113)18CO,15CO 0223 1500 CC 1600 1=1,1CO 0224 CALL ACCCN(ICNSI) 0225 16C0 SIONS=SICNS+FLOAT(ICNS) 0226 SIONS=SICNS/ICO. 0227 GCTO 1950 0228 1800 CC 19C0 O1=,1CO 0229 CALL ACCCN(ICNS,2) 0230 19CO SIONS=SICNS+FLCAT(ICNS) 0231 SIONS=SICNS/lCOC. 0232 1950 ICN(J)=IFIX(SIONS) 0233 CALL RELAY(10,1) 0234 CALL RELAY(IC,O) 0235 IRCDE=ll 0236 CALL EXEC(IRCOEITIVE) 0237 II=ITIME(1) C238 1960 CALL EXEC(IRCCEITIVE) 0239 12=ITIME(1) 0240 IF( 12-I1)1975,1980 0241 1975 12=12+1CC 0242 1980 IF((I2-I1)-90)1960,200 0243 200 CCNTINUE 0244 CO 2050 1=1,1CO 0245 CALL ADCCN(IFLOiW,O) 0246 CALL ACCCN(IPRES,3) 0247 CALL ACCCN(IBFLC,4) 0248 SFL0W=SFLOW+FLOAT(IFLOW) 0249 SPRES=SPRES+FLOAT(IPRES) 0250 2050 SBFLC=SBFLO+FLC4T(IBFLO) 0251 BUFLC=SEFLO/1CO. 0252 IRFLC=IFIX(SFLCW/IOC.) 0253 PRESS=SPRES/100. 0254 RETURN 0255 END 0256 END$
**** LIST END ****
















CHAPTER III

MATHEMATICAL MODEL


A. Basic Model


The simplest analysis of reaction kinetics for a flowing afterglow system may be accomplished by using a plug flow model. This model assumes that the buffer gas axial velocity, v (and the electron and ion axial velocities in the high pressure environment) is independent of radial or axial position in the reaction tube. In this simple model it is also assumed that the neutral reactant gas is injected uniformly throughout the flow tube cross-section at z=0, where the z-axis is the cylindrical axis of the flow tube. In addition, the diffusion of reactants and products in the reaction tube is not considered.

For net reactions of the type


e- + X2 - X- + X X2 = F2, Cl2, Br2 (22)



the rate equation becomes


d[X-]/dt = ke-] [X2] (23)



where the symbols within brackets represent the number densities of reactants and product and k is the bimolecular rate constant. In order to determine [X-] as a function of time, [e-] and 54 -









[X2] must first be evaluated. The rate equation for the electrons is


d[e-]/dt = -k[e-][X2] (24) If the assumption is made that [X2] >> [e-] for all t, then [X2] may be treated as a constant. Integrating Equation 24 then yields


[e-] = [e-]� exp{-k[X2 It) (25) where [e-o is the electron number density in the reaction tube at t=O (that is, at the neutral reactant gas injection port). Substitution of this result into Equation 23 yields the differential equation


d[X-]/dt = k[X2][e-� exp{-k[X 2it) (26) Integrating this equation gives the desired solution for the product ion number density


[X-] = [e-] {l - exp(-k[X2 It)} (27) The reaction time, t, written in terms of the reaction tube length, L, and the axial flow velocity, Vo, is


t - L/vo (28)


for the plug flow model. Equation 27 then becomes









[X-] = [e-l 0( - exp(-k[X2]L/vo)} (29)


Thus, the measurement of [X-] at the end of the reaction tube versus [X2] results in the determination of the rate constant k if the reaction tube length and the axial flow velocity are known. At this point it is useful to reiterate the assumptions made in the derivation of Equation 29:

1. the axial flow velocity, vo, is constant throughout
the reaction tube,

2. diffusion of reactants and products in the reaction
tube is unimportant,

3. the neutral reactant gas is injected uniformly in
a cross-section of the reaction tube at t=O (that is,
z=O) and

4. the neutral reactant number density is much greater
than the electron number density for all t>O in the
reaction tube.

Each of these assumptions will now be examined and accepted or modified on the basis of experimental evidence. The derivation of the model for the experimental system will then be altered to include any changes made in the basic assumptions.


B. Axial Flow Velocity


Determination of the axial flow velocity in the flow tube is necessary in order to calculate the reaction time


t - L/vo (28)


available to the electrons and halogen gas in the reaction tube. Two basic assumptions concerning the axial flow velocity










were made in the derivation of Equation 29

1. the axial flow velocity, vo, is constant throughout
the reaction tube and

2. in the high pressure environment present in the
reaction tube, ions, electrons and buffer gas move
down the tube with the same velocity profile.

If these assumptions are true, then the time required by any species to transit the reaction tube is given by


t = 7a2L/F (30) where a is the flow tube radius, L is the reaction tube length and F is the buffer gas volume flow rate.

The method illustrated in Figure 17 was used to determine whether Equation 30 could be used to calculate reaction times for the flowing afterglow experimental configuration containing a microwave discharge electron source. During normal operation of the flowing afterglow system, the neutral reactant gas injected into the flow tube reacts with electrons produced by the microwave discharge and forms negative ions, which are sampled by the mass spectrometer system. If a platinum probe is inserted into the afterglow and a positive potential applied to this probe as shown in Figure 17, electrons will be removed from the afterglow as they reach the probe. Thus, negative ions will not be formed downstream after the electrons already beyond the probe at the time of the potential application are consumed. If the potential applied to the probe is used to simultaneously trigger an oscilloscope sweep, then the ion current (at the scope vertical input) as a function of time








ION SIGNALTO SCOPE VERTICAL AXIS


REACTANT GAS


MICROWAVE POWER


P I



PUMP


Figure 17.


. BUFFER TION CHANNEL BUF, GAS


MICROWAVE PROBE DISCHARGE ~SOURCE


MKS
BARATRON 0
SCOPE
TRIGGER




SWITCH






Experimental Configuration for the Measurement of Transit Times for Ions in the Flow Tube










is displayed on the oscilloscope. This scope trace can be photographed with a Polaroid camera. Neglecting axial diffusion, it is expected that the ion signal versus time trace obtained in the manner described above would be a step function if the assumptions previously made are correct. A sample experimental trace is shown in Figure 18. Since the trace is not a step function and axial diffusion is not expected to result in a tailing of the magnitude observed in this trace, it is apparent that the radial velocity profile (that is, the axial flow velocity as a function of radial distance, r, in the flow tube) is not planar and also that radial diffusion of species present in the reaction tube is important.

A literature search previously revealed that due to frictional forces at the walls, the radial velocity profile for the viscous flow of a gas in a cylindrical tube is not planar but parabolic. Neglecting the axial velocity gradient (near zero in the present experiment), the radial velocity profile is given by46


v(r) = wvo(b - r2/a2) (31)


where


w = 2/(l + 5.52X/Pa) (32) and


b = 1 + 2.76X/Pa (33)


X is the mean free path (cm) at one Torr, P is the pressure (Torr)






I I I I I


5F


21-


I I I I I I I I


TIME (msec)


Figure 18.


Sample Trace Obtained in the Flow Tube


in the Measurement of Ion Transit Times









in the reaction tube and a is the flow tube radius (cm). In the present experiments 1 S P < 3 Torr of argon buffer gas. This yields 1.97 < w < 1.99 and 1.008 > b > 1.002. Thus, the radial velocity profile is approximately given by


v(r) = 2v0 (1 - r2/a2) (34)


where vo is the plug flow linear velocity. The ion signal versus time trace shown in Figure 18 may now be explained in terms of this velocity profile.

When a potential is applied to the probe at t=0, any

electrons downstream of the probe will continue to be carried down the tube in the flowing stream and will react with the reactant gas present in the reaction tube. The resulting ions are extracted through the orifice and detected by the quadrupole mass spectrometer system. Since the radial velocity profile of the buffer gas is of the form given in Equation 34, ions at the center of the flow tube will have the shortest reaction tube transit times while those nearer the walls will have the longest. As the ion density along the cylindrical axis of the reaction tube is depleted, ions diffuse from the areas where r>0. This accounts for the fact that the observed ion current as a function of time after the application of the blocking potential to the probe does not drop sharply to zero after the initial constant period and tailing occurs as shown in Figure 18.









Figure 19 shows the results of a series of measurements (closed circles) of negative ion reaction tube transit times (for r=O) as a function of the argon buffer gas pressure in the flow tube, using the technique just described, where the break in the ion signal versus time trace such as that shown in Figure 18 is taken as the transit time for ions from the probe to the sampling orifice. The upper solid line in Figure 19 represents the reaction tube transit times calculated from the measured buffer gas volume flow rate using the equation


t = L/v(r=O) = ia2L/2F (35)


where the factor of 1/2 arises because v(r=0) = 2vo. The ion transit times measured by the probe technique are seen to be smaller than those calculated from the buffer gas volume flow rate. This may be attributed to the geometry of the present flow tube when in the microwave discharge source configuration. The microwave discharge produces ions and electrons in a quartz tube with an inner diameter less than 1.12 cm. Buffer gas is pumped through this tube into the flow tube, which has an inner diameter of 2.57 cm. Due to this arrangement the buffer gas tends to stream through the center of the flow tube at a rate higher than predicted by a parabolic velocity profile. In addition, the velocity outside this central filament is less than expected. Given sufficient distance (that is, time), the radial velocity profile will become parabolic as the gas moves through the flow tube.47 This statement





































2.00 2.50


REACTION TUBE PRESSURE (Torr)


Figure 19.


Measured Ion Transit Times in the Flow Tube Versus Pressure for the Microwave Discharge Source Configuration


3.00










is illustrated in Figure 19 by the fact that as the reaction tube transit time increases, the values measured by the probe technique and those calculated from the buffer gas volume flow rate merge. This indicates that given sufficient time, the velocity profile, even with the microwave discharge source, will develop its parabolic shape. The flow tube in the flowing afterglow apparatus, however, is not sufficiently long to permit the parabolic profile to become fully developed when using the microwave discharge source. Therefore, the filament flow phenomenon must be taken into account in analyzing the data obtained using the microwave discharge source. Thus, Equation 27 becomes


[X-] = [e-]o{1 - exp(-k[X2It')} (36)


where t' is the ion reaction tube transit time measured by the probe technique described above.

As a check of the probe technique used to measure ion

reaction tube transit times, these parameters were also measured by an alternative probe technique. This procedure involved monitoring the current collected by a second probe (downstream from the blocking probe shown in Figure 17) as a function of time after application of the potential to the blocking probe. Two transit time measurements obtained in this manner are shown in Figure 19 as closed squares. The results of this double probe technique are seen to be in near agreement with the probe-ion signal technique discussed earlier.









In order to avoid the filament flow problem described above, previous researchers have found it necessary to make their flow tubes long enough to allow the parabolic velocity profile to develop48 or to smooth the buffer gas flow with a sintered glass disc placed in the flow tube upstream of the reaction region.46 In the present experiments the latter solution was employed. This necessitated the location of the electron source downstream of the sintered glass disc. Thus, at this point the apparatus was converted to the filament source previously described.

With the filament source installed in the flow tube,

ion transit times could easily be measured using the technique previously described with the exception that the blanking potential was no longer applied to a probe but to the filament. The circuit used to accomplish this is shown in Figure 20. With the double-pole double-throw switch in the upper position, a negative bias is applied continuously to the filament and the source operates in a continuous mode. With the doublepole double-throw switch in the lower position, the source operates in a pulsed mode at a rate determined by the square wave input at the PNP transistor base. Ion transit times may be determined by triggering an oscilloscope sweep on the negative slope of the square wave input. This negative pulse results in zero volts filament bias; that is, the source is switched to the "off" position from the "on" position. Thus, the ion signal output of the mass spectrometer system,






KEITHLEY AMMETER


FILAMENT BIAS










SQUARE
WAVE I N


-.
DDT


FILAMENT IN FLOW TUBE


I'
TO
I VARIAC


FILAMENT
TRANS FORMER


I


Figure 20.


Filament Source Configuration for the Measurement of Ion Transit Times in the Flow Tube


"1









applied to the vertical input of the oscilloscope, versus time trace is obtained similar to that shown in Figure 18. The oscilloscope sweep may also be triggered on the positive slope of the square wave input. This positive pulse results in a negative filament bias; that is, the source is switched to the "on" position from the "off" position. Ion transit times are then determined by the time required for the appearance of the ion signal after pulse application. Figure 21 shows the results of a series of transit time measurements (for r=0) with the filament source installed in the flowing afterglow system. The measurements were made on three different ions, triggering on both positive and negative square wave pulses as described above. Ion transit times calculated from the measured buffer gas volume flow rate assuming a parabolic velocity profile are also shown in Figure 21. The good agreement between transit times measured by the pulse technique and those calculated from the measured buffer gas volume flow rates indicates that the sintered glass disc installed in the flow tube is effective in smoothing the buffer gas flow, enabling a parabolic velocity profile to be established in the flow tube. The agreement also indicates that the ions and buffer gas move down the flow tube at the same velocity. For the moment it is also assumed that the electrons are at thermal energy. This assumption will be discussed later.

From the discussion above it is clear that for the flowing afterglow filament source configuration, Equation 29 must













+ F-,- PULSE A H2 0+, + PULSE o F-,+ PULSE V SF6, + PULSE 0 CALCULATED


0




0

0 A 0


4 +


O


+,6 +0 +


1.00


0 0


2.00
REACTION TUBE PRESSURE


3.00
(Tort)


Figure 21.


Measured Ion Transit Times in the Flow Tube Versus Pressure for the Filament Source Configuration


13.-


12.1-


1I.-


10. -


8.0 -


7.0I-


6.01-


5.0-


9.0-F









be modified to include the parabolic radial velocity profile. Thus, Equation 29 becomes


[X-] = [e-] {l - exp(-k[X2lLl2vo)} (37)


Consideration of the axial flow velocity radial profile has led to a modification of the basic model, derived in Section A, to account for the filament flow phenomenon with the microwave discharge source and the parabolic profile with the filament source. The kinetic equations relating the ion density [X-] to the rate constant, k, are then


[X-] = [e-]o{l - exp(-k[X2]t")} (36)


for the microwave source and


[X-] = [e-]0{l - exp(-k[X2]L/2vo)} (37)


for the filament source.


C. Radial Diffusion of Charged Species


The tailing observed in the ion signal versus time traces of the ion transit time measurements in the previous section indicates that radial diffusion is an important factor in the analysis of flowing afterglow reaction kinetics. Thus, the transport equation for negative ions produced by dissociative electron attachment in the flowing afterglow reaction tube becomes









2vo(l - r2/a2)a[X-]/az =


(D_/r)a(ra[X-]/ar)/ar + k[e-][X21 (38)


where the left side represents the time rate of change of the negative ion concentration, the first term on the right represents the negative ion radial diffusion loss rate and the second term, the negative ion production rate from the attachment reaction.48 D is the negative ion radial diffusion coefficient. However, before a solution for this equation can be found, a similar transport equation for the electron density must be solved


2v (l - r2/a2)3[e-]/3z


(De/r)3(rD[e-]/ar)/Dr - k[e-][X2] (39)



where the left side represents the time rate of change of the electron density, the first term on the right, the electron diffusion loss rate and the second, the electron reaction loss rate. D is the electron radial diffusion coefficient.
e
Equation 39 has been solved by Cher and Hollingsworth49 and its solution may be written


(e e-] [ R(r)Z(z) (40)
0


where









R(r) =


exp(- Xr2/Za2) F 1(1/2 - X/48, l;8Xr2/a2) (41)



Z(z) = exp(-Dex2z/2voa2 - k[X2]z/2vo) (42)


X2 = X2 + c ka2[X ]/De - C k2a4[X I2/D2 (43)
0 1 2 2 2 e


2 = 1 + ka2[X2 I/Dex2 (44)



and [e-]' is the electron density at r=O and z=0, a is the
0
flow tube radius and Xo (=2.7098), ei (=0.2372) and e2 (=0.00150) are empirical quantities determined from the solution of the equation


F (1/2 - X/40, 1;8a) = 0 (45)



a necessary condition in order for the density of the electrons to approach zero as r approaches a.49 F (1/2 - X/0, 10X) F 112 1, ;)

represents a confluent hypergeometric function. Now that a solution has been obtained for the electron density in the flow tube this solution must be substituted into Equation 38 and an expression for [X-] found. It is obvious at this point that obtaining an exact analytical expression for the negative ion number density is impossible due to the intractability of Equation 38 upon substitution of the expression derived for the electron number density.









At this point the assumption is made that since the present experiments measure only the axial variation of the reactants/ products, then only the solution of Equation 39 at r=0 is necessary. Therefore, Equation 40 becomes


[e-] = [e-]exp{-DezX2/2voa2 - (1 + C )k[X z/2v


e2k2a2[X 2]2z/2De v } (46)


where the first term in the exponential represents radial diffusion losses, the second reaction losses and the third coupling between reaction and diffusion. If we define [e-]0 as the electron density at r=O, z-L and [X2]=0, then


[e-]o [e-]oexp{-DeLX2/2voa2} (47)


and


[e-] = [e-] exp{-(l + 1 )k[X 2]L/2vo


�2k2a2[X2]2L/2DeVo} (48)



where L is the reaction tube length. This equation applies only to the electron density at r=0, that is, on the flow tube axis. Therefore, substitution of Equation 48 into Equation 38 and the subsequent solution to yield an expression [X-] = f(r,z) is meaningless. At this point it is assumed that


[X-] = [e-] - [e-]
o


(49)









that is, that the difference between the electron number density at r=0 and z=L with [X2]=0 and the electron number density at r=0 and z=L with [X2]#0 is due to the formation of negative ions, which undergo negligible radial diffusion in their transit through the reaction tube. Substitution of Equation 49 into 48 then yields


[X-] [e-]0 [l - exp{-(l + 1)k[X2]L/2vo


e 2k2a2[X ]2L/2DeVo}] (50)



The validity of this equation will be tested by measuring known reaction rates. Generally,


C2k2a2[X2]2L/2Devo " (1 + EI)k[X 2]L/2vo (51)



Thus, Equation 50 may be written


[X-] = [e-10{l - exp(-0.619k[X 2]L/vo)} (52)



Comparing this result (applicable to the filament source configuration) to Equation 29, it can be seen that correcting for a parabolic velocity profile and the radial diffusion of electrons yields a correction factor of 0.616, that is,


k - (1 + 0.616)ks (53)


where k is the actual rate constant and ks is that derived from data using the model outlined in Section A. This result









expresses the assumption used by Ferguson et al.48 in the reduction of experimental data where it is assumed


k (1 + a )k (54) i ai s



where the ai represent corrections to the rate constant obtained by the reduction of data with the simple model. These correction factors include the effects of a parabolic velocity profile, radial diffusion, non-uniform neutral reactant injection and axial diffusion. The largest correction factors by far are the corrections for the parabolic radial velocity profile and
48
radial diffusion. Axial diffusion corrections are usually negligible and will not be considered here.48

The inclusion of the radial diffusion of electrons in the mathematical model has yielded the equation


[X-] [e-] {1 - exp(-0.619k[X2]L/v )} (52)



for the filament source configuration.

Due to the lack of a parametric form for the radial velocity profile with the microwave discharge source configuration, no correction could be made to the model. In addition, the effect of the radial diffusion of electrons is expected to be less than that for the filament source configuration since the axial flow velocity at the center of the reaction tube, where the density of the charged species is highest, is much faster in the microwave source configuration; therefore, the electrons have less time to diffuse.









D. Inlet Effects


As pointed out by several authors, the effect of a point

source reactant gas inlet in a flowing afterglow is to drastically deplete the electron density in the center of the reaction tube due to the large neutral reactant density at r=0 and z=0. 46,48 Given sufficient distance (that is, time), this perturbation will correct itself as the mixture flows down the reaction tube. This self correction is accomplished through diffusion of electrons from r>0 to r=0 and diffusion of the neutral species from r=0 to the region r>O. This problem has been studied thoroughly by Ferguson et al.48 In their system this phenomenon results in a correction of about 30% (ai = -0.3) in the simple rate constant for an order of magnitude decrease in the primary ion signal. Since the radial diffusion of the electrons in the flow tube results in an axial density profile proportional to


exp{-D X2L/2v a2} (55)



comparison of the exponent in both the present experiments and those of Ferguson et al. will indicate whether point source injection of the neutral reactant is more or less of a correction in the present experiments. Thus,


[(X2/2)(LD/voa2)]C / [(X2/2)(LD/v a2)]F =


[L/Pvo a2] / [L/Pv a21F (56)










since D ep-1 where P is the flow tube pressure. The subcripts
e

C and F refer to the current apparatus and that of Ferguson et al., respectively. Inserting typical numerical values yields


(20/2 x 2.5 x 103 x 1.282) /
C


(60/0.5 x 8 x 103 x 42)F = 2.6 (57)



Therefore, radial diffusion in the current experiment should be faster and the perturbations produced by a point source should result in a smaller correction factor than in the experiments of Ferguson et al. For this reason no modification was made to the mathematical model for perturbations due to inlet effects.


E. Reactant/Electron Number Density Ratio


No actual determination of the electron density in the present experiments was made. However, previous researchers have found electron densities on the order of 107 to 1010 electrons/cm3 for flowing afterglow systems.48,50 Since one of the assumptions made in the derivation of models presented in the previous sections was that


[X2] >> (e-] (58)



for all t>0, it is important to determine whether this assumption is in fact true. An analysis of the models presented previously reveals that if the neutral density were not always greater










than the electron density, then the rate constants determined by the reduction of data using these models would be too small. The only experiments where this was expected to be a problem were those in which the attachment of electrons to sulfur hexafluoride was studied. In these experiments the sulfur hexafluoride number density was sometimes as low as 108 molecules/ cm3. However, reduction of the experimental data using a model which does not make the assumption expressed by Equation 58 above yields no significant difference in the rate constants obtained. Therefore, the assumption above was retained.


F. Ambipolar Diffusion


In an afterglow containing electron densities greater

than the order of 107 electrons/cm3, electrons diffuse to the walls of the flow tube at a rate several orders of magnitude slower than their free diffusion rate. This phenomenon, known as ambipolar diffusion, is due to the retarding potential exerted on the electrons by the positive ions present in the afterglow. When a gas, which attaches electrons to form negative ions, is injected into the afterglow, the electron diffusion rate is governed approximately by the equation51


Da = 2D+{ + [X-]/[e-]} (59)


where Da is the ambipolar diffusion coefficient, D+ is the positive ion free diffusion coefficient, [X-] is the number density of the negative ion formed and [e-] is the electron






78


number density. Substitution of this equation into the models derived previously, reveals that the rate constant calculated, assuming constant electron diffusion, will be smaller than the actual rate constant. This error is probably significant in electron attachment studies of the type presented here.
















CHAPTER IV

DATA REDUCTION


The product ion number density at the end of the reaction tube may be related to the product signal by the expression


[X-] = ci (60) where I is the product ion current and c is a coefficient which depends on the ion sampling efficiency, the transmission coefficient for the electrostatic lens system and quadrupole mass spectrometer and the gain of the electron multiplier used for ion detection. The coefficient c is a constant during a particular experiment. Equation 52 may now be written


I = {[e-]0/c}{ - exp(-O.619k[X2]L/v )} (61)



As the neutral reactant number density, [X21, approaches infinity (or in reality, a number density large enough to attach essentially all of the electrons in the reaction tube within a short distance of the reactant gas injection port), the product ion number density approaches a maximum, which may be written


[X-]. = cI. = [e-]0 (62)


Substitution of this result into Equation 61 yields the expression

< 79










I = IC{l - exp(-O.619k[X2 ]L/vo)} (6


If the product ion signal, I, is measured as a function of the reactant gas number density, [X2], and the maximum product ion signal, I., is determined, then a simple one parameter curve fit will yield the desired rate constant, k. In actual practice there are at least three complications:

1. the measured product ion signal includes a baseline,

2. the determination of I,, is difficult due to noise
in the ion signal and

3. there may be a significant error, AQ, in the determin
of the factor [X2]/vo.

Substitution of these errors into Equation 63 yields


ation


Im = I. + AI - Iexp{-O.619kL[X2]m/(v ) +


0. 619kLAQ}


(64)


where Im is the measured product ion signal, [X2] is the measured reactant gas number density and (vo)m is the measured buffer gas linear velocity (plug flow). Equation 64 may be written


(65)


y = PI - P2exp(-P3x)


where


P1 = T + AI


(66)


(67)


P2 i l 0exp(O.619kLAQ)


(63)


AI,










P3 = O.619kL/(vo)m (68)



and where y = I and x = [X2]m. Thus, a curve fit of measured ion signal versus reactant gas number density data yields the parameter P3 from which the desired rate constant, k, can be determined. Generally, AQ=O; therefore,


P1 -P2 = AI (69)



and


P2 I, (70)



Thus, the values obtained for the parameters P and P2 were checked by noting the approximate values of AI and I,. Typical values for the ion signal baseline, AI, and the maximum ion signal observed, I. + AI, may be obtained by looking at the data listed in Appendix IV.


A. Jacobian Matrix Technique As indicated above, the mathematical models derived in Chapter III generally result in an equation of the form


Y, = P1 - P2 exp(-P3x ) (71)


which relates the observed ion signal, y,, to the reactant gas flow, xi. In this equation the parameter P3 must be determined in order to calculate the rate constant, k, from the experimental observations.










The method used to find the parameters P. P 2 and P3

is an iterative least squares technique.52 The set of observations, Yi (n in number), are thought to be a function of the set of parameters, P (3 in number in this case).
J


= fi(PI,P2,P3,xi) =


P1 - P2 exp(-P3xi) i=l,n (72)



However, due to experimental errors and/or model inadequacies, there will be deviations defined by


di = Yi - fi(Pl'P2'P3'xi) i=l,n (73)



The least squares technique involves finding the set of parameters, Pj, such that


n 2
S = E d (74)
i=l i


is minimized. At this point the observations are linearized with respect to the parameters, P, by assuming a set of initial values, P , for the parameters and expanding in a Taylor series about the initial values, keeping only the first two terms.


di = Yj - fi(Pl'P0'P0'x.) +
i , il1 2' 3' 1


3 0
E (af /aPj (P -P0) (75)
J=l i p0
j









Defining the vector d (length n) as above and the vectors a (length n) and 6 (length m-3) by


aj = Yj - f (pO,pO,pO
1 1 2 3')





6- P - P0


(76)


(77)


and the matrix A (n x 3)


(78)


Aij = (afi/aP )Ipo



the deviation can be written in matrix notation as


d =a -A


(79)


S = d'd = (a' - A'6)(a - A6)


(80)


where d', a , respectively.


A and 6" are the transpose of d, a, A and 6, S is minimized if


as/m6 0 This yields


B6 = b


where B = A'A and b = A'a.


and


J=1,2,3


(81)


(82)









6 = B-ib (83)


then gives the change to be made in the initial parameters in order to minimize the sum of the squares of the deviation, that is, S. Thus, a new set of initial parameters is defined by


p1 = pO + 6 (84)


and the Taylor series expansion made about the new points P1. The entire process is then repeated until the iterations converge and parameters Pit P2 and P3 are determined.

Figure 22 shows the result of the application of the Jacobian matrix curve fit technique to actual experimental data. The open squares represent data points obtained in an experiment in which the dissociative attachment of electrons to fluorine was studied. The solid line defines the least squares fit obtained by fitting the data to an equation of the form


Y, = P1 - P2 exp(-P3 x ) (71)



Following the sample curve fit result is a listing of a version of the Jacobian matrix technique which allows all of the selected peaks (F- ion signal for instance) from a specific data file to be fit to the same parametric equation, such as that given above. The operator specifies the data file, whether or not to delete any experimental data points and selects the specific ion signal within that data file to be analyzed. The program then estimates the initial parameters PO, PO and P0 1 2 3




I I I I I


14'-


d-+ F2 - F-+F


1.2 I-


1.0 I-


0 0


0.8 F-


0.6 F


04 I-


. iII
0.8 1.6 2.4 32
FLUORINE FLOW (Xld5molecules/sec)

Figure 22. Dissociative Electron Attachment in Fluorine










COOl FTN,L
C002 PRCGRAV ALTO
C003 ******************************************************* C004 C* * 0005 C* PRCGRAM ALTO THIS PROGRAM FITS DATA, STORED IN * C006 C* THE SPECIFIED DATA FILE, TO A RATE EQUATION OF THE * C007 C* FORP GIVEN IN LINE 118 (IN THIS PROGRAM EITHER * 0008 C* EXPCNENTItLLY DECREASING DATA CR ASYMPTOTIC * C009 C* EXPCNENTIALLY INCREASING DATA) USING A JACCBIAN * 0010 C* MATRIX LEAST SQUARES TECHNIQUE. SOURCE IS STORED * 0011 C* ON CISC AS CTUA. * 0012 C* * 0013 ******************************************************** 0014 DIMENSION ZvECT(4A , ETRX(4,4),XVECT(4),BINV(4,4) 0015 I,XOBS(1CC)tYCBS(100),DELY(4),PARMT(4),IRRAY(640). 0016 2IFILE(3),NY(ICO),NX(IOO) ZY(ICO) 0017 ICNWD=lC2F
0018 IRCD=14
0019 WRITE(7,20)
0020 20 FORMAT(IX, INPUT FILE NAME 0021 READ(7,3C)(IFILE(I),I=I,3) 0022 30 FORMAT(3A2)
0023 C******************************************************** 0024 C* * 0025 C* LINES 32 THROUGH 37 ALLOW THE OPERATOR TO DELETE 0026 C* THE FIRST FEW DATA POINTS (IF THE EXPERIMENT * 0027 C* REQUIRES A PERIOD CF TIME TO ATTAIN STABILITY) AND * 0028 C* TO SELECT THE SPECIFIC ION SIGNAL DATA TO BE * 0029 C* REDUCED (CL-(35) INSTEAD OF CL-(37) FOR INSTANCE). * 0030 C* * 0031 ******************************************************** 0032 WRITE(7,43)
0033 43 FORMAT(IX, INPUT NUMBER OF STARTING DATA POINT ) 0034 READ(7,*)JJ
0035 WRITE(7,45)
0036 45 FORMAT(IXI, INPUT PEAK TO BE FIT 0037 READ(7,*)JJJ
0038 CALL EXEC(IRCD,ICNWE,IRRAY,IOIFILEO) 0039 NU=IRRAY(2)
0040 ICHAN=JJJ+l
0041 WRITE(6,48)(IFILE(I),I=1,3),ICHAN 0042 48 FCRMAT(tX, DATA FILEO ,2X,3A2/lX, MASS CHANNEL 0 0043 113/IX, Y=A-B*EXP(-C*X) CURVE FIT ?/I/X, RUN ,7X, 0044 2 A ,14X, B ,14X, C ,8X, K (T MEAS.) ,2X, K (T CALC. 0045 3) //)
0046 CC 1200 FM=1,NU
0047 N=5*PM-4
0048 CALL EXEC(IRCD,ICNWC,IRRAY,640,IFILEN) 0049 J=IRRAY(IO)
0050 CC 5C I=JJ,J
0051 K=75+7*I4JJJ
0052 II=1+1-JJ










0053 YCBS(II)=FLCAT(IRRAY(K))*(IC.**12)/(3276.4*(1C.** 0054 1(IRRAY(6)))) 0055 K=K-JJJ+I 0056 50 XCBS(II)=FLCAT(IRRAY(K-2))/3276.4 0057 *****************************************************c 0058 C* * 0059 C* LINES 63 THROUGH S2 MAKE INITIAL ESTIMATES OF THE 0060 C* PARAMETERS PARMT(1), PARMTI2) AND PARMT(3). * 0061 C* * 0062 ******************************************************** 0063 YPIN=I.E 20 0064 DC 55 I=l,J 0065 IF(YVIN-YOBS(I))55,53 0066 53 YVIN=YCPS(I) 0067 XPIN=XCeS(I) 0068 55 CONTINUE 0069 CC 60 I=1,J 0070 60 ZY(I)=YOES(I)-YMIN 0071 YPAX=-I.E+20 C072 CC 70 I=lJ 0073 IF(ZY(I)-YMAX)7C,65 0074 65 YMAX=ZY(I) 0075 XMAX=XCES(I) 0076 70 CCNTINUE 0077 IF(XMAX-XMIN)75,1CO 0078 75 PARMT(I)=YMIN 0079 PARMT(2)=-YVAX 0080 F=1 0081 77 IF(ZY(I)-0.5*YMAX)8C,90 0082 80 I=I+l 0083 GCTO 77 0084 90 PARMT(3)=ALOG(PARMT(2)/(PARFT(1)-YOBS(I)))/XOBS(I) 0085 CCTO 15C 0086 ICO PARMT(L)=YMAX+YMIN 0087 PARMT(2)=YMAX 0088 I'= 1 0089 110 IF(ZY(I)-,5*YMAX)12C,115 C090 115 1=1+1 0091 GCTO 11C 0092 120 PARMT(3)=ALCG(PARMTI2)/(PARMT(1)-YOBS(I)))/XOBSfI) 0093 150 F=IRRAY(0) 0094 N=3
0095 IL=O 0096 C******************************************************** 0097 C* 0098 C* LINES 107 THRCUGH 193 USE AN ITERATIVE LEAST 0099 C* SQUARES TECHNIQUE TO ARRIVE AT VALUES FOR THE 0100 C* PARAMETERS PARMT(1), PARMT(2) AND PARMT(3). IF THE 0101 C* CURVE FIT COES NOT CONVERGE AFTER 35 ITERATIONS, 0102 C* THE PRCCESS IS TERMINATED AND THE PROGRAM PROCEEDS * 0103 C* TO THE NEXT EXPERIMENT STORED IN THE SPECIFIED DATA * 0104 C* FILE.










0105 C* 0106 **************************************************** 0107 175 CC 210 I=1,4 0108 ZVECT(I)=0.C 0109 CC 210 J=1,4 0110 210 ePTRX(I,J)=C.0 0111 CC 5C0 I=1,V 0112 IF(AFS(PARMT(3)*XGBS(I))-85.5)260,250 0113 250 %RITE(7,255)YM 0114 1RITE(6,255)VV 0115 255 FORMAT(IX, NC FIT PCSSIBLE FCR RUN 14) 0116 GCTO 12CC 0117 260 CCNTINUE 0118 YPREC=PIRMT(I)-PARMT(2)*EXP(-PARMT(3)*XGBS(I)) 0119 CELY(1)=I.O 0120 CELY(2)=-EXP(-PARMT(3)*XOBS(1)) 0121 CELY(3)=PARVT(2)*XOeS{I)*EXP(-PARMT(3)*XCBS{L)) 0122 CEV=YCBS(1)-YPREC 0123 CC 200 K=1,N 0124 ZVECT(K)=ZVECT(K)+CELY(K)*DEV 0125 CC 300 J=ItN 0126 E1TRX(KJ)=BtTRX(K,J)4DELY(K)*CELY(J) 0127 300 CCNTINUE 0128 2C0 CONTINUE 0129 5CO CCNTINUE 0130 Nt\=N+I 0131 IF(NN-5)650,750 0132 650 CC 699 L=NN,4 0133 699 BPTRX(L,L)=I.O 0134 750 CCNTINUE 0135 CTMI=BMTRX(3,3)*BMTRX(4,4)-BNTRX(3,4)**2 0136 UTM2=BMTRX(2,3)*BMTRX(4,4)-BMTRX(2,4)*BMTRX(3,4) 0137 DTM3=BTRX(2t3)*MTRX(3,4)-BMTRX(3,3)*BMTRX(2,4) 0138 BTM4=BMTRX( ,3)*BMTRX(4,4)-BTRX(1,4)*BMTRX(3,4) 0139 CTM5=BMTRX(I3)*BMTRX(3,4)-BMTRX(1,4)*BMTRX(3,3) 0140 ETM6=BMTRX(l,3)*BMTRX(2,4)-BMTRX(1,4)*BMTRX(2,3) 0141 CTMNI=B!TRX(I,1)*(BTRX(2,2)*DTMI-BMTRX(2,3)*DTM2+ 0142 1PTRX(2,4)*CTV3) 0143 CTMN2=BTRX(1,2)*(BITRX(1,2)*OTM1-BMTRX(2,3)*DTM4+ 0144 I8MTRX(2,4)*CTM5) 0145 CTMN3=BITRX(13)*(BTRX(,2*DTM2-BMTRX(2,2)*OTM4+ 0146 IENTRX(2,4)*DTM6) 0147 CTMN4=BTRX(I,4)*(BVTRX(1,2)*DTM3-BMTRX(2,2)*CT,5+ 0148 18MTRX(2,3)*CTM6) 0149 DTMNT=CTMN1-CTMN2+DTMN3-CTMN4 0150 BINV(1,I)=B TRX(2,2)*OTM1-BFTRX 2,3)*DTM2+B TRX(2,4) 0151 I*CTM3 0152 BINV(1,2)=-EMTRX(1,2)*DTM1+BMTRX(2,3)*DT40153 1METRX(2,4)*CTM5 0154 BINV(1,3)=BMTRX(1,2)*DTM2-BMTRX(2,2)*DTM4+BPTRX(2,4) 0155 1*CTM6 0156 BINV(1,4)=-BMTRX(1,2)*DTM3+BMTRX(2,2)*DTM5-










0157 ePMTRX(2,3)*ETV6 0158 BINV(2,2)=BYTRX(,1)*CTMl-BITRX(l,3)*OTM4+ 0159 IBMTRX(1,4)*CTM5 0160 BINV(2,3)=-BMTRX(1,1)*DTM2+BTRX(1,2)*DTJ40161 IBeTRX(1,4)*CTP6 0162 EINV(2,4)=BMTRX(1,1)*CTM3-BMTRX(1,2)*DTt5+BMTRX(1,3) 0163 I*CTM6
0164 BINV(3,3)=BMTRX(I,1)*(BMTRX(2,2)*BMTRX(4,4)0165 1EPTRX2,4)*2)-ETRX(I1,2)*(BMTRX(1,2)*BMTRX(4,4)0166 2eM.TRX(2,4)*BMTRX(i,4))+BMTRX(1,4)*(BMTRX(I,2)* 0167 3BMTRX(2,4)-BTRX(l,4)*BMTRX(2,2)) 0168 BINV(3,4)=-BMTRX(1, 1)*(BMTRX(2,2)*BMTRX(3,4)0169 IBTRX(2,4)*MTRX(2,3) +BTRX(1,2)*(BMTRX(1,2)* 0170 28TRX(3,4)-BTRX(1,4)*BMTRX(2,3))-BMTRX(1,3)* 0171 3(PMTRX(1,2)*BMTRX(2,4)-BMTRX(1,4)*BMTRX(2,2)) 0172 BINV(4,4)=BMTRX(1,1)*(BMTRX(2,2)*BMTRX(3,3)0173 IEPTRX(2,3)**2)-EYTRX(1,2)*(BMTRX(1,2)*BtTRX(3,3)0174 2BMTRX(1,3)*MTRX(2,3))+HMTRX(1,3)*(BMTRX(1,2)* 0175 3BMTRX(2,3)-BTR�X(1,3)*BMTRX(2,2)) 0176 8INV(2,1)=BINV(1,2) 0177 BINV(3,1);BINV(1,3) 0178 BINV(3,2)=BINV(2,3) 0179 BINV(4,1)=BINV(1,4) 0180 BINV(4,2)=BINV(2,4) 0181 EINV(4,3):BINV(3,4) 0182 C0 800 I=1,N 0183 XVECT(I)=0.C 0184 CO 800 J=I,N 0185 80C XVECT(I)=XVECT(I)+(EINV(I,J)*ZVECT(J)/DTMNT) 0186 CC 850 I=1,N 0187 85C PARMT(I)=PARMT(I)+XVECT(I) 0188 IF(AES(XVECT(1))-0.O1)920,95C 0189 920 IF(AES(XVECT(2))-0..1)930,950 0190 930 IF(ABS(XVECT(3))-.CCO01)ICOC,950 0191 950 IL=IL l
0192 IF(IL-35)975,25C 0193 975 GCTO 175
0194 ******************************************************** 0195 C* * 0196 C* LINES 201 THRCUGH 220 CALCULATE A REACTION RATE * 0197 C* CONSTANT FROM THE RESLLT OF TFE CURVE FIT DCNE * 0198 C* ABCVE ANC CUTPUT TFE RESULTS. * 0199 C* * C200 ******************************************************** 0201 lGCO VSUBB=FLCAT(IRRAY(11))/32764. 0202 EMSBR=FLCAT(IRRAY(4))/ICO. 0203 PRESS=FLCAT(IRRAY(14))*FLOAT(IRRAY(5))/(3276400C.I 0204 CCNCF=(FLCAT(IkRAY42))*10.**(-IRRAY(3)))/100. 0205 TMEAS=FLCAT(IRRAY(1))/ICCCO. 0206 RLENT=IS.61 0207 XKI=(7.17*1C.**(-14))*PARMTI3)*VSUBB/(TMEAS*CONCF* 0208 1EFSBR*PRESS)






90



0209 XK2=((I.C26*1O.**(-9))*PARMT(3)*VSUBB**2)/(E'SBR* 0210 ICCNCF*RLENT*PRESS**2) 0211 IF(TVEAS) lOICIC 10,I1C20 0212 1010 XKI=O.C 0213 1C20 RITE(7,101)PM,PARVT(1),PARfT(2),PARMT(3),XKLXK2 0214 WRITE(6,1O15)M,PARMT(IIPARIT(2),PARMT(3),XK1,XK2 0215 1015 FORMAT(14,3X,E12.5,3XtEI2.5,3XLC2.5,3XE1O.3,3X, 0216 IElO.3) 0217 GCTO 12CC 0218 WRITE(7,1C50)XK1,XK2 0219 1C5C FCRMAT(2E20.4) 0220 1200 CCNTINUE 0221 END 0222 ENDS
**** LIST ENE ****




Full Text

PAGE 1

MEASUREMENT OF THERMAL ELECTRON DISSOCIATIVE ATTACHMENT RATES FOR HALOGEN GASES USING A FLOWING AFTERGLOW TECHNIQUE By GARY DONALD SIDES A DISSERTATION PRESENTED TO THE GRADUATE COUNCIL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA

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Copyright, 1975, by Gary Donald Sides

PAGE 3

ACKNOWLEDGMENTS The author wishes to express his appreciation to the many people who have contributed to the completion of this research. Special thanks are due Professor Robert J. Hanrahan, Chairman of his Supervisory Committee, whose tireless efforts on his behalf made this research possible. The author also thanks Dr. Thomas 0. Tieman, Co-Chairman of his Supervisory Committee, whose co-operation indeed made this dissertation possible. Special thanks are due Professor E.E. Muschlitz, Jr., who was instrumental in getting an assignment for the author at the Aerospace Research Laboratories. Thanks are also due Dean Miller for his technical assistance, Dr. B. Mason Hughes for his advice and computer programming assistance, Julius Becsey for the loan of his direct grid search subroutine, Dr. E. Grant Jones for reading this dissertation and suggesting improvements, and Alexis VanDenAbell for her administrative assistance. The author also appreciates the excellent support of the skilled machinists, draftsmen and glassblowers at the Aerospace Research Laboratories. In addition, the author wishes to express his gratitude to the Aerospace Research Laboratories and the United States Air Force for allowing this research to be completed. The author wishes to thank his wife, Sarah, both for typing the dissertation and for tolerating the many inconveniences caused by years of graduate study. iii

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TABLE OF CONTENTS Page ACKNOWLEDGMENTS iii LIST OF TABLES vi LIST OF FIGURES vii ABSTRACT ix CHAPTER I. INTRODUCTORY DISCUSSION 1 A. Electron Attachment 1 B. Discussion of Literature Data 5 1. Fluorine 5 2. Chlorine 8 3. Bromine 17 4. Summary of Published Data 21 C. Experimental Approach 23 CHAPTER II. DESCRIPTION OF THE FLOWING AFTERGLOW SYSTEM 26 A. Experimental Apparatus 26 B. Data Acquisition 41 CHAPTER III. MATHEMATICAL MODEL . ; 54 A. Basic Model 54 B. Axial Flow Velocity 56 C. Radial Diffusion of Charged Species 69 D. Inlet Effects 75 E. Reactant/Electron Number Density Ratio 76 F. Ambipolar Diffusion 77 CHAPTER IV. DATA REDUCTION 79 A. Jacobian Matrix Technique 81 B. Grid Search Technique 91 iv

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Page CHAPTER V. EXPERIMENTAL RESULTS 105 A. Microwave Discharge Source 105 1. Electron Energy 105 2. Electron Attachment in Sulfur Hexafluoride 106 3. Electron Attachment in Fluorine 110 4. Sulfur Hexafluoride Oxygen Negative Ion Charge Transfer Ill B. Filament Source 115 1. Electron Energy 115 2. Electron Attachment in Sulfur Hexafluoride 116 3. Electron Attachment in Fluorine 117 4. Electron Attachment in Chlorine 117 5. Electron Attachment in Oxygen 118 6. Electron Attachment in Bromine 121 CHAPTER VI. DISCUSSION OF RESULTS 128 A. Comparison with Published Data 128 B. Significance of the Results 132 C. Assumptions Made in the Derivation of the Mathematical Model 133 D. Suggestions for Modification of the Flowing Afterglow Apparatus and Further Research 134 APPENDIX I. ANALYSIS OF THE FLUORINE /ARGON MIXTURE 137 APPENDIX II. ELECTROSTATIC LENS SYSTEM 139 APPENDIX III. THERMALIZATION OF ELECTRONS BY ELASTIC COLLISIONS IN AN ARGON AFTERGLOW 145 APPENDIX IV. EXPERIMENTAL DATA 150 LIST OF REFERENCES 160 BIOGRAPHICAL SKETCH 164 v

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LIST OF TABLES Table Pa 8 e 1. Measured First Appearance Potentials (eV) for Dissociative Electron Attachment in Chlorine 14 2. Measured First Appearance Potentials (eV) for Dissociative Electron Attachment in Bromine 20 3. Measured First Appearance Potentials (eV) for Dissociative Electron Attachment in the Halogens 22 4. Thermal Electron Dissociative Attachment Rates 23 5. Rate Constants Determined in the Present Experiments ... 126 6. Comparison of the Present Results with Published Data .. 129 7. Electron Energy Versus Time Calculations for an Afterglow 149 8. Data Listings Key 150 vi-

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LIST OF FIGURES Figure Page 1. Potential Energy Diagram for Dissociative Electron Attachment to Diatomic Molecules 2 2. Potential Energy Diagram for Electron Attachment to Sulfur Hexafluoride 6 3. Electron Attachment Probability in Chlorine Versus the Pressure-Reduced Electric Field 9 4. Calculated Electron Attachment Thresholds Versus Experimental Thresholds Measured by Bradbury 11 5. Electron Attachment Probability in Chlorine Versus Electron Energy 12 6. Electron Attachment Cross-Section Versus Electron Energy for Chlorine and Bromine 18 7. Electron Attachment Coefficient Versus the PressureReduced Electric Field for Chlorine and Bromine 19 8. Flowing Afterglow Apparatus in the Microwave Discharge Source Configuration 27 9. Flowing Afterglow Apparatus in the Filament Source Configuration 29 10. Filament Emission Regulator Circuit 30 11. Buffer Gas Rotameter Calibration Curves 33 12. Buffer Gas Volume Flow Rate Versus Flow Tube Pressure 34 13. Reactant Gas Linear Mass Flowmeter Calibration 37 14. Comparison of Two Techniques Used to Measure the Reactant Gas Number Density 40 15. Computer-Interfaced Data Acquisition System 42 vii

PAGE 8

Figure 16. Magnetic Disc Data File Organization 17. Experimental Configuration for the Measurement of Transit Times for Ions in the Flow Tube 18. Sample Trace Obtained in the Measurement of Ion Transit Times in the Flow Tube 19. Measured Ion Transit Times in the Flow Tube Versus Pressure for the Microwave Discharge Source Configuration 20. Filament Source Configuration for the Measurement of Ion Transit Times in the Flow Tube 21. Measured Ion Transit Times in the Flow Tube Versus Pressure for the Filament Source Configuration 22. Dissociative Electron Attachment in Fluorine 23. Dissociative Electron Attachment and Br~ Formation in Bromine 24. SF^/SFg Ratio in the Microwave Discharge Source Configuration 25. F Ion Signal Versus the Partial Pressure of an Argon Metastable Atom Quenchant, Nitrogen, Injected into the Afterglow 26. Charge Transfer Between SF. and 0~ o Z 27. Dissociative Electron Attachment in Chlorine 28. Electron Attachment in Oxygen 29. Formation of Br in Bromine 3 30. Dissociative Electron Attachment in Bromine 31. Electrostatic Lens System 32. Electrostatic Lens Control Circuit 31. Electrostatic Lens Performance Page 45 58 60 63 66 68 85 104 107 112 114 119 120 123 124 140 142 143 viii

PAGE 9

Abstract of Dissertation Presented to the Graduate Council of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy MEASUREMENT OF THERMAL ELECTRON DISSOCIATIVE ATTACHMENT RATES FOR HALOGEN GASES USING A FLOWING AFTERGLOW TECHNIQUE By Gary Donald Sides June, 1975 Chairman: Robert J. Hanrahan Major Department: Chemistry Co-Chairman: Thomas 0. Tiernan Aerospace Research Laboratories A flowing afterglow apparatus was designed, constructed and used to measure thermal electron dissociative attachment rates in the halogen gases fluorine, chlorine and bromine. Electrons were produced in a high velocity buffer gas flow using either a microwave' discharge source or a filament source. The electrons and positive ions produced in the source were carried past a reactant gas injection port by the high velocity viscous flow of the buffer gas. The halogen gas injected at that port then reacted with the electrons to form halide ions. These ions were sampled at the end of the reaction tube by a quadrupole mass spectrometer. By monitoring the negative ion signal as a function of the halogen gas flow injected into the reaction tube, electron attachment rates could be deduced. The operation of the flowing afterglow system was checked by < ix

PAGE 10

measuring the thermal attachment rate for electrons in sulfur heaxaf luoride. The average value obtained for this rate constant "“8 3 was 3.9 ± 1.4 x 10 cm /molecule-sec. The average rate constants obtained for the rates of dissociative electron attachment in -9 fluorine, chlorine and bromine were 3.8 ± 1.2 x 10 , 3.7 ± 1.7 x 10 ^ and 1.1 ± 0.9 x 10 ^ cm^ /molecule-sec, respectively. Electrons produced in the source of the flowing afterglow system are rapidly thermalized in the high pressures present in the flow tube. Electron temperatures were estimated to be 300-600°K in the present experiments. The rate of the three-body attachment reaction Br + + Ar to form Br^ was —28 6 2 also measured and found to be 1.9 ± 1.0 x 10 cm /molecule -sec. A charge transfer reaction, SF^ + O 2 , and the three-body attachment of electrons to oxygen were also observed using the flowing afterglow apparatus. x

PAGE 11

CHAPTER I INTRODUCTORY DISCUSSION A. Electron Attachment Dissociative electron attachment to diatomic molecules is generally thought to proceed by a resonance mechanism in which the electron is first attached to the molecule to form a molecular ion complex. ^ The negative ion formed may then undergo auto-ionization (that is, ejection of the electron) and revert to the neutral molecular state or it may dissociate into an atom and an atomic ion. The sequence of steps in equation form are e" + AA t (AA )* -*• A + A (1) This reaction sequence may be discussed in terms of a potential energy diagram as shown in Figure 1. The Franck-Condon region is defined by the line ab. Electrons with an energy between E^ and E£ will be attached by the molecule to form the negative ion complex (AA )*. The nuclei then begin to separate, their energy following the upper potential curve. During the separation the negative molecular ion is subject to auto-ionization, a process by which it may revert to the neutral state with the ejection of an electron, possibly leaving the neutral molecule vibrationally excited. If the complex ion nuclei separate to 1

PAGE 12

(AA ) 2 c 0 ) S .c o CO 4J c o Vj 4J o IV w (V > <0 u o 03 CO 4J CO C -H 03 O 4J o o Pm 4J (V |M 3 00 A9U3N3 N0I19VU31NI NUCLEAR SEPARATION

PAGE 13

3 the radius R g without undergoing auto-ionization, then the negative ion becomes stable against auto-ionization and the ion dissociates. The fragments of dissociation, A and A, have a total kinetic energy between Eand E. . j 4 The rate of dissociative electron attachment will then depend not only upon the rate of electron capture to form the molecular negative ion but also upon the lifetime of this resonance state against auto-ionization and the time required for the nuclei to move a distance R g apart. The average lifetime of the resonance state against auto-ionization is written as -fi/T where T is the width (in energy units) for auto-ionization and 'h is Planck's constant divided by 2 tt. If T is the time required by the nuclei to separate to R=R S> then the dissociative attachment cross-section may be written as °DA = °C ex P[-fT/tf] (2) where is the electron capture cross-section and F is the width for auto-ionization averaged over the nuclear separation Rq ( r=r c at electron capture) to R g since T=r(R) and r(R g )=0 (that is, auto-ionization is no longer possible for R>R g ).^ For the halogen gases fluorine, chlorine and bromine, the electron affinities of the halide atoms are greater than the corresponding neutral molecule dissociation energies. This means that the molecular negative ion, formed by a two-body electron-halogen molecule collision, will be produced at an energy much greater than the dissociation energy of the ion. Thus, the ion formed will dissociate within one vibrational period.

PAGE 14

4 This will be the case whether the molecular ion is formed in a repulsive or an attractive state. In order for thermal electron dissociative attachment in the halogen gases to be possible, the molecular negative ion potential curve (repulsive or attractive) must intersect the neutral molecule potential curve in the Franck-Condon region. The discussion above indicates the mechanism by which electrons undergo dissociative attachment to the halogen molecules chlorine, fluorine and bromine, whose dissociative electron attachment rates were measured in the current research. In this research the rate of electron attachment to sulfur hexafluoride was also measured. Electron attachment to form a molecular negative ion, such as SF _ , may be explained by a 6 two-step mechanism in which the electron is first attached to 2 the molecule to form a molecular negative ion. However, the negative ion is vibrationally excited and may eject an electron through auto-ionization unless a process takes place to remove the excess energy. Since relaxation through vibrational transitions is a slow process, it is thought that collisional stabilization is the dominant relaxation mechanism if the pressure is not too low.^" In equation form the electron attachment to SF^ may be written SF 6 + e" X (SF^)* ^ SF“ (3) where M is the species removing the vibrational energy of (SF )* through inelastic collisions. If one considers the 6

PAGE 15

5 molecule SF as a diatomic molecule SF -F, then the electron 6 5 attachment mechanism may be explained in terms of the simple potential energy diagram in Figure 2. The Franck-Condon region is again defined by the line ab. Since the cross-section for the attachment of electrons to sulfur hexafluoride is a maximum for thermal energy electrons, ^ the potential curve for SF 6 must cross the minimum of the SF curve. Thus, electrons with o an energy between 0 and will be attached to SF^ to form vibrationally excited SF . If the vibrational energy is removed 6 by collisional stabilization, then a stable negative ion, SF , results. If the excited negative ion is not collisionally 6 stabilized, then ejection of the electron may occur. If the initial energy of the electron is between and E_^, then the negative ion formed may dissociate. ^ It has been shown that the ratio of SFT/SF in a flowing afterglow is independent of 5 6 r\ pressure. This would indicate that the (SF“)* complex probably 6 in 2 dissociates within a vibrational period (VL0 LJ sec) . It has also been shown experimentally that the ratio of SF /SF obtained by the attachment of electrons to sulfur hexafluoride can be used as a measure of the electron temperature or average electron energy 2,5 B. Discussion of Literature Data 1. Fluorine A thorough search of chemistry and physics literature failed to yield any experimental measurements or theoretical

PAGE 16

SF, + F 6 A9U3N3 NOI10Va31NI -F NUCLEAR SEPARATION

PAGE 17

7 estimates for electron attachment cross-sections, rates, coefficients or probabilities in fluorine. Due to the extreme reactivity and corrosive nature of this gas, most researchers seem reluctant to investigate its properties in kinetics instruments . The minimum appearance potential of F ions from the dissociative attachment reaction e " + F 2 £ (F“)* + F" + F (4) can be calculated from the known electron affinity of the fluorine atom, EA(F) = 3.62 eV,^ and the molecular fluorine dissociation energy, D(F 2 ) = 1.60 eV,^ using the equation A(F~) = D(F 2 ) EA(F) + K + E (5) where A(F”) denotes the appearance potential of F” ions and K and E represent the kinetic and excitation energies, respectively, of the products of the reaction. If K and E are zero for the dissociative attachment process, then A(F“) = 1.60 3.62 = -2.02 eV (6) Therefore, the reaction is exothermic and would be expected to have a zero energy threshold. This has been confirmed by g Burns who demonstrated that F~ ions are formed by electrons with zero energy and is consistent with the work of Thorbum, 9 who found that the appearance potential of F ions, produced by dissociative electron attachment to fluorine, was less

PAGE 18

8 than 2 eV, the lower energy limit of his electron source. In addition, DeCorpo and Franklin 10 have obtained an appearance potential of 0 ± 0.1 eV for F ions produced by dissociative electron attachment in fluorine. 2. Chlorine Though several investigations of the electron attachment mechanism in chlorine have been made, there is still considerable disagreement concerning the threshold value and the attachment t , ... . 9,11-17 cross-section versus energy behavior for this reaction. In addition, no thermal electron attachment reaction rates have been published. The electron affinity of chlorine, EA(C1) = 3.82 eV , ^ and the molecular dissociation energy, D(C1 2 ) = 2.48 eV, 7 can be used to calculate the minimum appearance potential for Cl ions in the dissociative attachment reaction, assuming K and E to be zero. A(C1”) = 2.48 3.82 = -1.34 eV (7) The reaction is exothermic and would be expected to have a zero energy threshold. Bradbury 11 used a drift tube method to measure electron attachment probabilities in chlorine/argon mixtures as a function of the pressure-reduced electric field, E/P, which is directly proportional to the average electron energy in the gas. His data are shown in Figure 3. He obtained a threshold of less than 1 volt/cm-Torr for dissociative electron attachment

PAGE 19

9 (0001 X ) AinieVQOUd J-N3SAIH0V1 .lv Figure 3. Electron Attachment Probability in Chlorine Versus the Pressure-Reduced Electric Field (After References 11 and 12)

PAGE 20

10 in chlorine. In order to determine the approximate energy of electrons corresponding to E/P = 1 volt/cm-Torr , the calculated dissociative electron attachment threshold energies versus the measured E/P thresholds for the dissociative attachment reactions studied by Bradbury are shown in Figure A. This plot indicates that the threshold for dissociative electron attachment in chlorine is in the range less than 0. 1-1.1 eV, the energy range corresponding to less than 1 volt/cm-Torr. The dashed lines indicate the range of energy values possible for a given measured threshold (measured in E/P units) . Although it is recognized that the average electron energy for a given E/P value is a function of the composition of the gaseous medium, the threshold estimate above should be reasonable since a variety of gaseous environments were used in this "calibration" plot. Bailey and Healey used a drift tube apparatus to determine the attachment probability as a function of the pressurereduced electric field, _E/P, for electrons in chlorine and carbon dioxide or helium mixtures. In addition, they were able to convert these data to attachment probability as a function of electron energy data. The resulting data, shown in Figure 5, indicate a threshold for the reaction of about 0.3 eV. Q Thorburn used a mass spectrometer to determine the appearance potential of Cl ions formed by the dissociative electron attachment reaction in chlorine. He found the appearance potential to be less than 2 eV, the minimum electron energy obtainable in his source. He also observed an appearance potential, A(C1 ) , at 4.4 ± 0.2 eV which he postulated could

PAGE 21

11 o > O zc CO 111 cc zc hI2: Ul X o £ 6 Q Ul or r> CO < UJ c (U e •H Vi 0) P, X w to 3 CO M 0) > to •o 1— I O X CO 0) H X E-i 4J c 0) E X o £ a x •o to Vi CO P3 4-1 4J , < XI C T 3 O CD Vi Vi 4-1 3 O CO 0) CO ££ T3 CO 0) T3 4-1 rH CO O i-l X 3 CO O 0) 1— t Vi 3£ 0) Vi 3 60 (A9) aiOHS3b'Hl 1N3WH0V11V aUlVinOIVO

PAGE 22

12 Figure 5. Electron Attachment Probability in Chlorine Versus Electron Energy (After Reference 12)

PAGE 23

13 be explained by dissociative electron attachment in chlorine in which one of the products, Cl” or Cl, was in an excited state. 13 Frost and McDowell used a mass spectrometer with a monoenergetic electron source and measured an appearance potential of 1.60 ± 0.05 eV for Cl ions in chlorine with a maximum at 2.4 eV. This value falls outside the energy range for the appearance potential, A(C1") , deduced from the Bradbury 11 data. Neither does it agree with the expected appearance potential of zero deduced by comparing the dissociation energy of molecular chlorine with the electron affinity of the chlorine atom. The resonance observed by Frost and McDowell is probably one in which the molecular ion is formed in an excited electronic state which then dissociates. This would explain the apparently high appearance potential obtained in their work. Frost and McDowell did not see the process producing Cl ions at 4.4 eV Q that Thorburn observed. Moe 1 ^ used an RPD electron gun in a trapped electron apparatus and observed four resonance peaks attributed to dissociative attachment in chlorine. These peaks were located at 0, 1.75, 3.07 and 5.9 ± 0.17 eV. The first resonance peak is due to dissociative electron attachment in which the molecular ion potential energy curve intersects the neutral molecule potential energy curve in the Franck-Condon region. The other three resonances are probably ones in which the molecular ion is formed in an excited electronic state which then dissociates. Note that the second resonance at 1.75 ± 0.17 eV is probably

PAGE 24

14 13 the same resonance observed by Frost and McDowell with a threshold at 1.60 ± 0.05 eV and a maximum at 2.4 eV. Dunkin et al. ^ have reported the qualitative observation of large dissociative electron attachment rates for chlorine in a flowing afterglow apparatus. This finding supports a zero energy threshold, since electrons in the high pressure helium afterglow are known to be near thermal energies. ^ Thus, there appears to be some disagreement concerning the energetics of the dissociative attachment of electrons to chlorine. Table 1 summarizes the observations to date of the first appearance potential for Cl ions produced by dissociative electron attachment in chlorine. Table 1 Measured First Appearance Potentials (eV) for Dissociative Electron Attachment in Chlorine A(C1~) Author (s) <0. 1-1.1 Deduced from Bradbury^ data 0.3 12 Deduced from Bailey and Healey data <2 Thorburn^ 1.6 ± 0.05 Frost and McDowell‘S 0 ± 0.17 Moe^ 'VO Dunkin et al.S These data show the disagreement concerning whether thermal electrons (^0.03 eV) will undergo dissociative attachment in chlorine.

PAGE 25

15 As was previously mentioned, Bradbury used a drift tube method to determine the attachment probability for electrons in chlorine/argon mixtures as a function of the pressurereduced electric field as shown in Figure 3. Extrapolating the measured attachment probabilities, h, to E/P=0 yields -4 h-5 x 10 at thermal electron energies. This agrees with a value for h=5 x 10~^ measured by Wahlin.^ Electron attachment cross-sections can be calculated from the observed attachment probabilities using the equation a = h/A^ (8) where A^ is the electron mean free path at one Torr and is the number of molecules per cubic centimeter per Torr. 18 Since Bradbury did not state the composition of the Cl /Ar 2 mixture used in his experiments, the cross-section was first calculated assuming the thermal electrons to be in 100% chlorine and then calculated assuming 100% argon (that is, much more argon than chlorine) , these concentrations representing the two possible extremes. A^ for thermal electrons in argon is 0.13 cm. The calculated cross-section for thermal electron dissociative attachment to chlorine is then 1.2 x lO ^ cm^. The mean free path for thermal electrons in chlorine at one i o Torr is approximately 0.0005 cm. This results in an attachment cross-section of 3.0 x 10 cm 4 . Thus, analysis of the Bradbury data yields a thermal dissociative electron attachment cross-section of 1.2 300 x 10 19 cm^. This corresponds to

PAGE 26

16 —12 3 a rate constant of 1.2-300 x 10 cm /molecule-sec for thermal energy electrons. 12 As was previously mentioned, Bailey and Healey used a drift tube apparatus to determine the attachment probability as a function of E/P for electrons in chlorine and carbon dioxide or helium mixtures. They also measured the electron mean free path, drift velocity and free path velocity as a function of E/P. These data enabled them to calculate attachment coefficients, cross-sections and rate constants as a function of E/P or electron energy. The attachment probability as a function of E/P is shown in Figure 3. The maximum in the Bradbury^ data is at 6 volts/cm-Torr while that in the Bailey and Healey data is at 11 volts/cm-Torr. The average electron energy in chlorine and carbon dioxide or helium mixtures for a given E/P is expected to be lower than that in a mixture of chlorine and argon, since electrons transfer energy more efficiently to carbon dioxide or helium than argon. Thus, the maximum in the Bailey and Healey data occurs at a higher E/P than the Bradbury data, since the average electron energy is directly proportional to E/P. Bailey and Healey also obtained the attachment probability as a function of electron energy; these data are shown in Figure 5. As previously stated, these data yield a threshold for dissociative attachment near 0.3 eV and a maximum at 1.5 eV. The Bailey and Healey data may also be converted to the attachment cross-section as a function of electron energy and to the attachment coefficient as a function

PAGE 27

17 of E/P. These data are shown in Figures 6 and 7, respectively, and as stated above illustrate a significant attachment crosssection for electrons at energies as low as 0.3 eV. Bozin and Goodyear^ measured attachment coefficients in pure chlorine as a function of the pressure-reduced electric field. They obtained these data by observing the variation of pre-breakdown ionization currents with distance between parallel electrodes for E/P between 70 and 150 volts /cm-Torr. Their results are shown in Figure 7. In the E/P regions in which the Bozin and Goodyear and the Bailey and Healey data overlap, the attachment coefficients measured by the latter are much less than those measured by Bozin and Goodyear. Bozin and Goodyear interpret this disagreement as being partially due to the neglect of the effects of ionization ignored by Bailey and Healey. 3. Bromine There is general agreement among researchers that the dissociative attachment of electrons to bromine is a zero energy threshold process. This is expected in view of the fact that the electron 21 affinity of the bromine atom, EA(Br) = 3.49 eV, is larger 22 than the molecular dissociation energy, DCBr^) = 1.97 eV. The minimum appearance potential for Br” ions from the reaction can then be calculated from A(Br") = 1.97 3.49 = -1.52 eV (9) assuming K and E to be zero. Thus, the reaction is exothermic

PAGE 28

ATTACHMENT CROSS-SECTION (X IO l8 cm 2 ) 18 ELECTRON ENERGY (eV) Figure 6. Electron Attachment Cross-Section Versus Electron Energy for Chlorine and Bromine (After References 12, 23 and 24)

PAGE 29

19 O O O O CVJ O o o CO o
PAGE 30

20 and a zero energy threshold is not surprising. Table 2 summarizes the first appearance potentials measured for the bromineelectron reaction. All of the data listed in this table are consistent with a zero energy threshold for dissociative electron attachment in bromine. Table 2 Measured First Appearance Potentials (eV) for Dissociative Electron Attachment in Bromine A(Br ) Author (s) <0.7 23 Deduced from Bailey et al. 0.03 ± 0.03 Frost and McDowell‘S 0.05 ± 0.17 Moe ^0.03 24 Deduced from Truby 23 Bailey et al . used their drift tube apparatus to investigate electron attachment in bromine and helium or carbon dioxide mixtures. The resulting attachment coefficients versus pressurereduced electric field data are shown in Figure 7. Since they also measured the electron free velocity and drift velocity in these mixtures, the attachment coefficients may be converted to attachment cross-sections. These data are shown as a function of energy in Figure 6. 13 Frost and McDowell observed a maximum Br ion current due to the dissociative attachment of electrons in bromine at 0.03 eV with the ion signal dropping to zero at 0.72 eV.

PAGE 31

21 Moe^ used the trapped electron technique mentioned above and noted dissociative electron attachment resonance peaks at 0.05, 0.98 and 3.30 ± 0.17 eV. The first peak is due to attachment in which the potential energy curve for the molecular ion intersects the neutral molecule potential energy curve in the Franck-Condon region while the other peaks are due to attachment yielding molecular ions, which dissociate, in higher energy states. Razzak and Goodyear 25 measured attachment coefficients in pure bromine as a function of the pressure-reduced electric field using the same method employed for Bozin and Goodyear's 17 chlorine studies. The data obtained by them are shown in Figure 7. The coefficients obtained are again higher than the corresponding measurements by Bailey et al. 25 2 A Truby used a microwave cavity technique to determine the rate constant for dissociative attachment of electrons in bromine at 296°K. He obtained a value of k = 0.82 x 10“ 12 cm /molecule-sec. This corresponds to a value for the attachment cross-section of 0.80 x 10 -1 ^ cm 2 . 4. Summary of Published Data Table 3 summarizes dissociative electron attachment appearance potential measurements, either published or deduced from published data (for references refer to the preceding discussion) , for the halogens.

PAGE 32

22 Table 3 Measured First Appearance Potentials (eV) for Dissociative Electron Attachment in the Halogens Gas Appearance Potentials Fluorine 0, <2, 0 ± 0.1 Chlorine <0. 1-1.1, 0.3, <2, 1.6 ± 0.05, 0 ± 0.17, ^0 Bromine <0.7, 0.03 ± 0.03, 0.05 ± 0.17, M).03 Appearance potential measurements indicate that both fluorine and bromine have a zero energy dissociative electron attachment threshold as expected; however, there is some disagreement in the case of chlorine. The measurement of the rate of thermal energy electron attachment in chlorine would help settle the controversy. Table 4 summarizes thermal electron dissociative attachment rate constants, either published or calculated from published data, for fluorine, chlorine and bromine. These data illustrate the need for further halogen thermal electron dissociative attachment studies. Not only are there no data for fluorine but there are also no definitive measurements for chlorine since the rates shown were extrapolated from data for which the electron energy is greater than thermal. In addition, there is a factor of eighteen disagreement between the rate measurement for bromine and a value extrapolated from the data of Bailey et al.

PAGE 33

23 Table 4 Thermal Electron Dissociative Attachment Rates Molecule k (cm 1 /molecule-sec) Author (s) Fluorine none Chlorine 1.2-300 x 10 -12 Extrapolated from Bradbury 11 <6 x 10 -12 Extrapolated from Bailey and Healey 12 large Dunkin et al. 1 ^ Bromine 1.5 x 10* 11 23 Extrapolated from Bailey et al. 0.82 x 10 -12 Truby 2 ^ C. Experimental Approach In view of the absence of rate data for the attachment of thermal electrons to the halogen molecules, an apparatus was designed and constructed to obtain this information. A flowing afterglow technique was selected for these experiments after a review of the methods which have been used to measure thermal electron attachment rates. The flowing afterglow method was selected primarily because of the ease with which 2 thermal electrons are produced in the afterglow. In addition, this technique has been used previously to measure a thermal 2 electron attachment rate. The present experiments were performed in three stages 1. the design and construction of the flowing afterglow apparatus, 2. the use of this apparatus to measure known reaction rates in order to determine whether the apparatus was functioning

PAGE 34

24 properly and 3. the use of the apparatus to measure thermal electron attachment rates for the halogens. The reactions used to check out the flowing afterglow apparatus were e" + SF J (SFp* SF(3) 0 0 0 and SF, + or > SF“ + 0„ (10) 6 2 6 2 Both of these reactions were selected because their rates 2 26 had been measured using a flowing afterglow technique. ’ In addition, the thermal electron attachment rate for sulfur hexafluoride has been measured using a variety of experimental techniques. 2,27-30 During the course of experimental measurements in the flowing afterglow apparatus, another known reaction rate, that of the 0 9 0 2 + e“ t (Op* 0 ~ (ID reaction was also determined as a further check of experimental procedure. 31 ’ 32 Once the initial tests of the experimental technique were completed, the thermal electron attachment rates for the reactions e" + F 2 t (Fp* F“ + F (4) e" + Cl 2 t (Cip* Cl" + Cl ( 12 )

PAGE 35

25 e“ + Br 2 Z (Br“) * -*• Br + Br ( 13 ) were determined. In addition, the reaction rate for Br + Br^ + Ar -* Br“ + Ar ( 14 ) was determined in the course of the experiments.

PAGE 36

CHAPTER II DESCRIPTION OF THE FLOWING AFTERGLOW SYSTEM A. Experimental Apparatus The flowing afterglow apparatus in the microwave discharge source configuration is shown in Figure 8. Electrons are produced by a 2450 MHz microwave discharge (approximately 2 watts) in argon buffer gas in a quartz tube with an inside diameter of 1.1 cm. The microwave power supply 33 is coupled to the buffer gas by an Evenson cavity 3 ^ and the microwave power is monitored by a microwave power meter 33 (not shown) . The buffer gas flow is measured by a rotameter 36 (not shown) and a linear mass flowmeter. 3 ^ The buffer gas pressure is measured at the center of the reaction tube by a capacitance 38 manometer. Electrons produced in the active discharge are rapidly thermalized in the high pressure environment (1 to 4 Torr) and flow past the reactant gas injection port, where a gas such as fluorine may be introduced into the afterglow. The reactant gas flow is monitored by a linear mass flowmeter capable of measuring argon flows over the range 1 to 225 atm-microliters/ sec . 3 ^ Negative ions formed in the reaction tube (19.6 cm in length) are sampled through a 0.23 mm orifice, 0.076 mm in length, located on the tip of a stainless steel 26

PAGE 37

REACTANT GAS SOURCE 27 v 60 t-i <0 X U W •H a v 5 u o 0> X to 3 4J « u rt a o. < o iH 60 U 0) 60 e p* 00 ai 3 60 •H Source Configuration

PAGE 38

28 cone. The cone is maintained at +4 to +13 volts with respect to ground in order to extract negative ions from the flowing afterglow at the end of the reaction tube. The ions extracted are focused by a cylindrical electrostatic lens system into the lens elements of an ionizer. These elements then focus the ions into a voltage-scanned quadrupole mass spectrometer.^® The ions are then mass resolved by the quadrupole filter and detected by an electron multiplier. A preamp-electrometer (not shown) amplifies the resulting signal and provides analog outputs for computer and oscilloscope inputs. The flow tube is pumped by a 1000 liter/minute rotary pump.^ A charcoal trap in the pump line converts fluorine to carbon tetraf luoride in order to prevent mechanical pump degradation. A molecular sieve trap in the pump line prevents back diffusion of hydrocarbons from the mechanical pump. The flowing afterglow apparatus in the filament source configuration is shown in Figure 9. The basic difference between this configuration and that shown in Figure 8 is the removal of the microwave source and the substitution of a filament electron source. In addition, a sintered glass disc was installed upstream of the source in order to smooth the buffer gas flow through the flow tube. Also, at this point an automatic flow control system^ was installed so that the reactant gas flow rate could be controlled by a computer during an experiment. The filament source is shown in detail in Figure 10. The filament is a thoriated-iridium ribbon^ which is spot-welded to hermetic feedthroughs mounted in the

PAGE 39

REACTANT GAS SOURCE 29 Figure 9. Flowing Afterglow Apparatus in the Filament Source Configuration

PAGE 40

PROGRAMMABLE 30 Figure 10. Filament Emission Regulator Circuit

PAGE 41

31 flow tube walls. The anode is at ground potential and mounted approximately 1.3 mm from the filament. Filament current is supplied by a remotely programmable power supply. ^ Electrons emitted by thermionic emission from the filament are accelerated to the anode by the -45-volt negative bias applied to the filament. These electrons produce secondary electrons by ionization of the buffer gas in the flow tube. The secondary electrons are then swept down the flow tube by the axial velocity of the buffer gas and thermalized by elastic collisions in the high pressure environment. Filament emission is monitored by a microammeter. The filament emission control circuit contains operational amplifiers #1 and #2 which provide the necessary voltage to the input of the programmable power supply. The emission current causes a voltage drop across a 10 kft resistor. This voltage drop is applied through a 50 kfl resistor to the inverting input of operational amplifier #1. This technique provides feedback stabilization of the emission current. Operational amplifier #3 acts as a comparator to prevent the voltage input to the programmable power supply from exceeding the limit set by the 10 kft potentiometer. This prevents the passage of excess current through the filament (that is, prevents filament destruction) . The buffer gas generally used in these experiments was argon, the flow rate typically being 10-25 atm-cm 3 /sec. Two methods were employed to monitor the buffer gas flow in these

PAGE 42

32 studies. Initially, the buffer flow was measured with a rotameter, using both sapphire and stainless steel floats. Calibration curves at 20 psig (regulator gauge pressure) for the rotameter are shown in Figure 11. These curves were obtained using a bubble meter calibration method. Use of the rotameter for measuring flow rates has several disadvantages which severely limit its accuracy and utility. These include the dependence of the calibration on temperature and gas pressure, the poor dynamic range, the difficulty in accurately reading the meter, and the lack of an electrical signal output, which is needed for automated readout devices. Therefore, a linear mass flowmeter was used to measure flow rates for all experiments presented in this report. The flowmeter used to measure buffer flow permits monitoring of flow rates up to 155 atm-cm^/sec with an accuracy of approximately ±0.1% of full scale. The calibration of this meter remains constant over a pressure range 1 psia (absolute pressure) to 150 psig. In addition, the meter provides a 5-volt output signal at full scale for use with a readout device. The buffer gas linear mass flowmeter was not calibrated in this laboratory but was calibrated by the manufacturer.-^ Figure 12 is a plot of buffer gas flow versus pressure in the flow tube. The buffer gas flow was calculated from the relation F = f (T/273.15) (760/P) (15)

PAGE 43

25.0 33 o cvi o o cri o o ID o o to o z 5 < UJ tr or UJ H UJ 2 £ o u. (oss/oo-uiio) MOU N09HV Figure 11. Buffer Gas Rotameter Calibration Curves

PAGE 44

BUFFER GAS FLOW (liters/sec) 34 FLOW TUBE PRESSURE (Torr ) Figure 12. Buffer Gas Volume Flow Rate Versus Flow Tube Pressure

PAGE 45

35 3 where f is the buffer gas flow rate in atm-cm /sec, T is the gas temperature (°K), and P is the gas pressure (Torr) at the center of the reaction tube. The agreement between the data obtained using the rotameter with sapphire float and that obtained with the linear mass flowmeter is obvious. The buffer gas flow measured by the rotameter with stainless steel float and the linear mass flowmeter exhibit poorer agreement. The buffer gas flow rate is maintained constant by regulating the backing pressure behind a fixed leak. The stability of the buffer gas flow has been checked by monitoring the linear mass flowmeter output as a function of time. The observed drift in the voltage output at a given flow rate was approximately 0.007 volt/hour. This corresponds to approximately 0.1% of full scale per hour and is negligible during a typical experiment. The derivation of the expression relating the linear mass flowmeter signal output to the buffer gas axial velocity (bulk flow velocity) is given below. The buffer gas flow in 3 atm-cm /sec is given by f = V b (10000/5)(273.15/294.26)(M b /60) (16) where is the voltage output of the linear mass flowmeter (5-volt output, full scale, corresponds to 10000 standard 3 cm /sec (SCCM) of air) and is a factor specific for the buffer gas in use. Therefore, the expression relating the 3 buffer gas flow in cm /sec to the bulk flow axial velocity may be written

PAGE 46

36 v Q = F/ira 2 = 2.583 x 10 4 M^/Pira 2 (17) where P is the pressure in Torr at the center of the reaction tube and a is the flow tube radius in centimeters. If argon or helium is the buffer gas, then v Q = 7.15 x 10 3 V b /P ( 18 ) since a = 1.283 cm for the flow tube used in the current experiments and M b = 1.43 for argon or helium. The reactant gas flow rate was monitored with a linear mass flowmeter for which full scale deflection corresponds to 5 SCCM of air. A monel transducer was used with this flowmeter in order to permit monitoring of corrosive gases. In the experiments reported here, the flowmeter was calibrated for argon since most reactant gas mixtures used consisted of at least 99.8% argon, and thus, the thermal conductivity of the mixture is essentially that of argon. Conversion factors supplied by the manufacturer allow the calculation of gas flow for other gases or mixtures of gases. A typical calibration plot is shown in Figure 13 (data points and solid line) . Calibration curves measured over a six-month period were found to differ by less than 2 / (slope difference) . The full scale flow measured for argon agrees to better than 2% with that calculated by use of a conversion factor given in the flowmeter manual. The dashed line shown in Figure 13 is the manufacturer's calibration. It is concluded, therefore, that the reactant gas flow rates

PAGE 47

37 MASS FLOWMETER OUTPUT (volts) Figure 13. Reactant Gas Linear Mass Flowmeter Calibration

PAGE 48

38 are accurate to within 2%. The mass flowmeter has been found to be linear over the flow regime from 1 to 225 atm-microliters/ sec, which corresponds to a 10-volt output from the flowmeter. Since the flowmeter operation depends on the mass flow of the gas to change the temperature along a heated conduit (which in turn is dependent upon the heat capacity of the gas) , the flowmeter calibration is independent of pressure over a j, wide range. The calibration curve shown in Figure 13 was obtained over the range 2 to 20 psig, and no variations with pressure were observed. From the measured reactant gas flow, the number density of the reacting species in the reaction tube can be calculated. If argon is the diluent and buffer gas, then the number density of the reactant in the flow tube, calculated from measured reactant and buffer gas flows, is given by "lMF = 1.61 x 10 13 V r C f P/V b (19) where is the fractional concentration of the reactant gas and is the voltage output of the linear mass flowmeter used to monitor the reactant gas. As a check against this method of determining the reactant gas number density, the change in pressure in the reaction tube may be monitored as the reactant gas flow is varied, and the number density can then be calculated independently of the linear mass flowmeter signal. Thus, from the ideal gas law <

PAGE 49

39 n AP = Ap ( N A / RT ) ( 20 ) or n AP " 3 * 22 13 x 10 AP ( 21 ) if argon is used for these comparisons where is Avogadro's number, R is the international gas constant and T is the gas temperature (assumed to be 300°K) . The pressure change, AP, is measured in units of millitorr. Figure 14 gives a comparison of the number density of the reactant gas in the flow tube at 3 Torr buffer gas pressure (corresponding to 0.87 volts output from the buffer gas linear mass flowmeter) as calculated by the two methods noted above. The agreement is within at least 9% over the full range of reactant gas flow, thus indicating that the use of the linear mass flowmeter technique to determine reactant number density is satisfactory. The measurement of the partial pressure of the reactant gas mixture during an actual experiment is not feasible, since this corresponds to only about 14 millitorr for full scale flow and thus a small drift in reaction tube pressure during the experiment would introduce considerable error. Such drift probably accounts for the difference observed in the two number density measurement techniques compared above, especially since the deviations observed correspond to a pressure of about one millitorr on a buffer gas total pressure background of 3000 millitorr.

PAGE 50

LMF NUMBER DENSITY (I0 l4 cm~ 40 Figure 14. Comparison of Two Techniques Used to Measure the Reactant Gas Number Density

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41 B. Data Acquisition The data acquisition system ultimately developed during the course of this research is shown in Figure 15. The system was designed around a 24K, 16-bit minicomputer and its peripheral 45 devices. Analog signals proportional to experimental parameters such as reactant and buffer gas flows, reaction tube pressure, ion signal and ion mass were converted to digital signals by a 14-bit analog-to-digital converter. A relay register was used to advance the mass programmer-peak switching hardware. A 12-bit digital-to-analog converter provided the remote programmed input signal necessary to control the automatic flow system hardware. A cathode ray terminal was used to give the operator input/output capabilities. A storage oscilloscope allowed the operator to display ion signal versus reactant gas flow data at the end of an experiment. The raw data for each experiment were stored on a magnetic disc system to be reduced at a later time. Once the flowing afterglow system is in the operational mode (traps filled, buffer gas flow set, the desired filament emission current obtained and so forth), a single experiment consists of little more than running the program AFGLO whose outline and listing are at the end of this chapter. Program AFGLO is loaded into the core of the minicomputer from the magnetic disc, where all data acquisition, reduction and storage files are located, by entering a directive at the teletype keyboard. At this point the operator moves to the cathode ray terminal

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42 £ Figure 15. Computer-Interfaced Data Acquisition Syst

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A3 and inputs experimental parameters (sampling orifice potential, reactant gas concentration, reactant gas linear mass flowmeter multiplier, the capacitance manometer full scale pressure, the electrometer input resistor value, the number of mass programmer channels used and the A/D converter rate) , operating limits (the reactant gas flow stability time, the reactant gas upper flow limit, the number of data points desired and the number of runs desired) and the data file name. Program AFGLO then reads sector zero of the data file to determine three pieces of information: the next sector available in the file for the storage of experimental data and two calibration constants (slope and intercept) necessary for the operation of the automatic flow control system. The D/A converter voltage necessary to obtain the reactant gas upper flow limit is then applied to the programmable input of the automatic flow controller. The reactant gas flow is then monitored until it has been within ±0.1 volts of the desired flow for a period of time greater than the. reactant gas flow stability time (generally 15 or 20 seconds) . At this point the ion intensity of peak #1 is obtained and then the quadrupole is switched through the remaining peaks measuring the ion signal intensity of each. The reactant gas flow, buffer gas flow and buffer gas pressure are also measured at this point. The reactant gas flow is then decremented by an amount determined by the number of data points desired and the upper reactant gas flow limit (the lower limit is always 0.05 volts for

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44 decrement purposes). If the desired reactant gas flow is greater than 0.02 volts at this point, then the D/A converter output is decremented and the data point acquisition cycle repeated. If the desired reactant gas flow is less than 0.02 volts, then the data acquisition process is complete. The average values for the buffer gas flow and the buffer gas pressure during the experiment are then determined and the experimental data and input parameters are stored on a magnetic disc in the data file specified above. A plot of the ion signal of primary interest versus reactant gas flow for the experiment is also displayed on a storage oscilloscope. The configuration of a magnetic disc data file is shown in Figure 16. The number preceding each stored parameter is the word number within a specific sector. Each data file consists of 501 fixed point sectors; each sector consists of 128 fixed point words. Sector 0 of the data file is used to store parameters needed for each experiment such as the next sector available for data storage, the number of experiments stored in the data file and the slope and intercept calibration constants relating the 12— bit D/A converter output voltage to the reactant gas flow obtained. Sectors 1 through 500 allow the storage of 100 sets of experimental data, 5 sectors per experiment. The first 80 words of each block of 5 sectors (one experiment) are reserved for the storage of experimental parameters such as the reactant gas concentration, orifice potential and so forth. Words 81 through 640 of each <

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SECTOR 0 45 •u p. OJ o CO 4 .P a> iH 1-1 cd Pp Q) rv W CO CM CO o CO 3 4-1 60 4J u 3 3 CD Cl) 4J cd .P a o a a •H 3 3 p CO cd rH 4-) o • CO 0 3 3 rH 2 CM 3 rQ 4H • 6 3 3 • CO • • 3 • X rH cd m ON 3 r^. U rH 60 rH rH P. M 3 u 3 3 a P 4H o cd p 3 O P u 3 3 4-1 M cd 4-1 3 CO U O 4-1 3 CO 3 u CO 3 P cd rH i — 1 CO 4J P P. 0 3 *H c X CO • •H • 3 • 3 • Q) o O 3 00 3 NO J-i rH Oh rH 00 rH P. P O 4J 3 o "3 a 3 3 •H 3 3 M 4-1 rH 3 U x 3 U X 3 3 •H 3 rH 3 3 3 *H a 3 3 3 • J> • P rH 3 rH 4-1 4-1 3 P fr. O 3 3 4-1 Pp a 4-J 0) •rl <> H 3 rH rH • P a cd •H p 3 o O X O • P. 3 CO 3 4h X 3 4-1 • 3 a rH 3 3 rH a • • • 3 • rH CO r-m 4H 0\ 4J rH rH Hts 21. mass of 22. mass of 23. mass of 24. orifice peak 4 peak 5 peak 6 potential

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> Pn o 44 rH *H rH 4-1 CO g -w 4J csi G P O 4-1 cd u • G m > 44 •u •u -H rH *H rH •H CM to CO CO G U G •U a 4-> G CX a O. v Pn rH 4J 44 4-1 •H r-i •H CM to CO •U rH G 4-1 G 44 o G P g a Cd u 4-1 4J a) a G v >s 4-1 U •H O •H o CO 00 CO 00 c G G 4-1 0) 4J 4-1 P 4J P G G •H CM *H vp . A! • AS G 00 G CM 4J C4 G rH P rH P Pn Pn 4J 44 •rH O •H O CO 00 to 00 G G a> 4J G 44 4J P 44 p G G •H rH iH in • AS • AS 00 G t'' G CM G CM G o rH Pi rH P o in VP m Pi Pj pj o O * * * o H H H CJ CJ CJ W > W W CO o Pn CO CO 1 — J 44 144 •rl O CO 00 4J O G CJ 00 G 44 G 44 P G 44 C t-i p •H sf • G • A! CM 44 vp G CM G CM G rH X) rH P Pn 44 iH O to oo G G 44 44 P • G •h m • • AS • m G CM G rH P Figure 16. Magnetic Disc Data File Organization

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experimental 5-sector block are used to store reactant gas flow versus ion signal data points (up to Since this data file is fixed point, some parameters (for example, reactant gas per must be converted to digital form in such all significant figures. 80 per experiment) . floating point cent concentration) a way as to preserve

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OUTLINE OF PROGRAM AFGLO input experimental parameters, operating limits and data storage file V read from sector 0 of the specified data file: the next available sector and automatic flow control calibration constants V output voltage from D/A converter to remote input -^•of automatic flow control to obtain the desired reactant gas flow V monitor reactant gas flow until within ±0.1 volts of the flow desired for the period of time specified V using the relay register, switch the quadrupole through the desired masses while measuring the ion signal intensity for each mass 1 measure the reactant gas flow, buffer gas pressure and buffer gas flow i maintain a sum of the buffer gas pressure and buffer gas flow measurements decrement the reactant gas flow, reactant gas flow desired <0.02 volts? M/ yes determine the average buffer gas flow and buffer gas pressure measured during the experiment I store the experimental data on magnetic disc in the file specified above Nl/ plot the ion signal versus reactant gas flow data of primary interest on the storage oscilloscope

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CC01 CC02 C CO 3 C004 0005 C 006 COO 7 CC08 CC09 0010 0011 0012 0013 0014 CO 1 3 CO 16 0017 0018 0019 C02C 0021 0022 0023 C02 4 0025 C026 0027 0028 0029 C03C 0031 0032 0033 0034 0035 0036 0037 0038 0039 0040 0041 0042 0043 0044 0045 0046 0047 C048 0049 0050 0051 0052 49 FTN , L PROGRAM AFGLC C* * c* SOURCE PROGRAM IS GSFAG. WHEN LOADING, ATTACH THE * c* FILES EADRV, CCNCE AND CAQR FOR THE CALLS ACCCN, * c* RELAY AND CAQ , RESPECTIVELY. WHEN LOADING, ATTACH * c* THE FILES CDPTR ANC CCPLR FOR THE CALL PLCTR. * c* * c* PARAMETER CHANNEL MULTIPLIER * c* REACTANT FLOW 0 1 $ c * ION SIGNAL 1 1 * c* UQN SIGNAL 2 10 * c* PRESSURE 3 ICO * c * PUFFER FLOW 4 10 * c* MASS 5 10 c* PEAK SWITCHING 10 (RELAY) * c* * DIMENSION NX(80)»NY(8C) COMMON IRRAY (64 0 ) , IFILE( 3) , JRRAY( 10) , ION< 6) I CNW C 1 C 2 B CALL RELAY ( 10 » 0 ) DC 25 1=1,640 25 I BRAY ( I ) = 0 C* * C* LINES 32 THROUGH 110 REQUIRE THE OPERATOR TO INPUT * C* EXPERIMENTAL CONDITIONS AND LIMITS. * C * * WRITE{7,60) 60 FORMAT! IX, INPUT ORIFICE POTENTIAL (VOLTS) ) READ(7,*)P0TEN IRRAY! 2 4 ) = IF IX! PGTEN*10. ) WRITE!7»70) 70 FORMAT! IX, INPUT REACTANT GAS CONCENTRATION { ) ) READ ( 7 » * ) RCCNC 75 IF(RCCNC-1G0. )8C,10C 8C RCCNC=RCCNC*1Q. IRRAYI3 ) = I R R A Y ( 3 ) + l GOTO 75 100 IRRAY(2 )= I F IX(RCCNC ) WRITE(7»125) 125 FORMAT ( IX, INPUT REACTANT GAS LMF MULTIPLIER ) READ(7,*)RGMUL IRRAY (4 )=IFIX(RGMUL*1C0. ) WRITE(7, 150 ) c* * C* EXPERIMENTAL DATA IS STORED ON DISC IN THE FILE * C* GIVEN HERE. *

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50 0053 0054 0055 0056 0057 0058 0059 0060 0061 C 06 2 0063 0064 0065 0066 0067 0068 0069 0070 0071 0072 0073 0074 0075 0076 0077 0078 0079 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 G09 5 0096 0097 0098 0099 0100 0101 0102 0103 0104 $ 15C FORMAT (IX, INPUT DATA FILE NAME ) READI7, 175) ( IFILEII ) , 1= 1 , 3 ) 175 FORMAT ( 3 A 2 ) WRITE ( 7, 200 ) 2 0 0 FORMAT ( IX, INPUT 6ARATRQN FULL SCALE (MICRONS) ) READ ( 7 , * ) IRR AY ( 5 ) WRITE(7,225) 225 FORMAT (IX, INPUT ELECTROMETER RESISTOR (5,7 OR 9) ) READ ( 7, =f ) IRRAY ( 6 ) WRIT£(7»235) 235 1 F USEC T ) 1X ’ INPUT NUFBER CF MASS PR °GRAMMER CHANNELS WRITE(7,240) 2 4 C FORMAT ( IX, INPUT ACC RATE (CPS) ) READ ( 7 » * ) I R R AY ( 8 ) WRITE(7,245) 245 FORMAT { IX , INPUT REFLO APC STABILITY TIME (SEC) ) c* * C * Ap C STABILITY TIME IS TEE TIME WITHIN WHICH THE * C* REACTANT GAS FLOW MUST BE BETWEEN THE PRESCRIBED * C* LIMITS BEFORE A DATA POINT IS TAKEN. * C* C* ******* ********%***********$$$$$$*$%$ READ (7, * ) IRRAY ( 9 ) NCSEC=IRRAY(8)*IRRAY(9) 265 WRITE(7,275) 275 FORMAT! IX, INPUT REACTANT GAS UPPER FLOW LIMIT 1 (VOLTS ) ) I RCD= 14 CALL EXEC( I RCD, ICNWC,JRRAY,10,IFILE,0) C * * C* SLOPE AND YINTC ARE CALIBRATION CONSTANTS FOR * C* THE AUTOMATIC REACTANT GAS FLOW CONTROL SYSTEM. * C * * C ***** ******* ***** * *£* *****$$* ** *c $$*.$$$$$*$£*£££ SLOPE = FLCAT ( JRR A Y ( 3 ) )/lCCCO. YINTC=FLCAT(JRRAY(4))/1C0. V=UFL IM*SLOPE+Y INTC CALL CAC(V) C* C* C* C* c* C * * AT THIS POINT THE C/A CONVERTER SETS THE REACTANT * GAS FLOW AT THE DESIREC UPPER LIMIT BY APPLYING V * VOLTS TO THE REMOTE PROGRAMMING INPUT GF THE * AUTOMATIC FLOW SYSTEM. * WRITE! 7 ,300 )

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0105 0106 0107 0108 0109 0110 0111 0112 0113 0114 0115 0116 0117 0118 0119 0120 0121 0122 012 3 0124 0125 0126 0127 0128 0129 0130 0131 0132 0133 0134 0135 0136 0137 0138 0139 0140 0141 0142 0143 0144 0145 0146 0147 0148 0149 0150 0151 0152 0153 0154 0155 0156 51 3CCFORMAT ( IX » INPIT NUMBER DATA POINTS DESIRED (80 MAX 1 ) ) R E A D ( 7 * * ) I R R A Y ( 1C) WRITE(7,325) 325 FORMAT ( IX* INPUT NUMBER OF RUNS DESIRED ) READ ( 7 » * ) NRUNS C* * C* AT THIS POINT THE AUTOMATIC DATA ACQUISITION * C* SYSTEM TAKES OVER. * C* * CO 9 CO NN=1, NRUNS 6FSUM = C . C PRSUM=0.0 CO 350 K K = 1 ,6 35C ION { KK ) =C CO 375 K K= 8 1 » 64 C 375 IRRAY (KK ) = 0 V=UFL IM*SLOPE+Y INTO CALL CAC(V) CESFL = UFL IM CALL STAPC(NCSEC»CESFL) K-81 4CC CALL CATA(BUFLO, IRFLG, PRESS, K) IRRAY (K ) = IRFLG IRRAY(K4l) = ICN( 1 ) IRRAY(K42) = I0N(2 ) IRRAY(K43 ) = ION ( 3 ) IRRAY(K+4) = I0N(4 ) IRRAY (K45 )= IOM 5 ) IRRAY(K46) = I0N( 6 ) BFSUM=8FSUM4EUFLC PRSUM=PRSUM4pRESS K=K 4 7 CESFL=CESFL-(UFL IM-C. 05 ) /FLOAT ( IRRAY ( 10 ) 1 ) IF(DESFL-C.02)5CC,45C 45C V = DESFL*SL0PE4Y INTO CALL CAC(V) CALL STAPC(NCSEC,CESFL) GOTO 40C 5CC IRRAY ( U) = IFIX( BFSUM/FLOAT ( IRRAY ( 10) ) ) IRRAY(14) = IFIX(PRSUM/FL0AT( IRRAY(IO) ) ) N = J R R A Y ( 1 ) JRRAY(2 ) = JRRAY( 2 )4l J RR AY { 1 ) = JRR AY ( 1 )45 IRRAY(17)=JRRAY(2) I RCD = 1 5 C****** **************************************** ********** C * * C* AT THIS POINT THE CATA FOR ONE EXPERIMENT IS * C* TRANSFERRED TO THE MAGNETIC DISC SYSTEM AND STORED *

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0157 0158 0159 0160 0161 0162 0163 0 16 A 0165 0166 0167 0168 0169 0170 0171 0172 0173 0 17 A 0175 0176 0177 0178 0179 0180 0181 0182 0183 0184 0185 0186 0187 0188 0189 0190 0191 0192 0193 0194 0195 0196 0197 0198 0199 0200 0201 0202 0203 0204 0205 0206 0207 0208 52 C* IN THE DATA FILE SPECIFIED ABOVE. * C* * CALL EXECI IRCD, I CNW C , I RR AY , 640 , IFlLEtN) CALL EXEC( IRCD, ICNWC,JRRAY, 10* I F I LE , 0 ) £*******$£*«*$*$*****«***$**$**$**$$***$**$*$£$$** **$$$*$ C* $ C* LINES 169 THROUGH 180 NORMALIZE THE ION SIGNAL OF * C* INTEREST VERSUS REACTANT GAS FLOW AND PLOT THE DATA * C* CN A STORAGE CSC I LLGSCCPE . * C ^ $ MAX=0 N = 8 1 + ( I R R A Y { 1CJ-1 )*7 CO 600 1=81, N, 7 I F ( IRRAY ( 1+2 )~MAX )6CC, 550 550 MAX = IRRAY ( I + 2 ) 600 CONTINUE DC 700 1 = 81, N, 7 J=( 1-74)77 NX(J)=IFIX(4C95. AFLOAT! IRRAY( I ) >732764. ) 7C0 NY{ J) = I FIX (4 095. *0.9*FLOAT( IRRAY! 1 + 2) ) /FLOAT (MAX) ) N= I RR AY ( 10) 9CC CALL PLCTR(NX,NY,N) GCTO 265 END £******$«$**$** ** 44 *$*$**$**$*$$*****$*** $**#**$$***$***$ C* $ C* SUBROUTINE STAPCO THIS SUBROUTINE DETERMINES WHEN * C* THE REACTANT GAS FLOW HAS BEEN WITHIN THE DESIRED * C* LIMITS FOR THE PERIOD OF TIME PRESCRIBED ABOVE BY * C* THE INPUT REFLG STABILITY TIME . CONTROL IS THEN * C* RETURNED TC THE MAIN PROGRAM. * C* # C****£$***$*$ ***$**** S*********************************** SUBROUTINE S T AP C ( NCS EC , C ESF L ) 1CC0 N =0 1050 CALL ACCOM IFLCW,0) REFLC = FLOAT( IFLCW J/3276.4 IF(REFLC-CESFL+C.10)1C0G,11CC 1 ICO IF(REFLC-CESFL-C. 10 >1200,1000 1200 N=N+ 1 I F ( N-NCSEC ) 1C5C , 130C 1300 RETURN END c* * C* SUBROUTINE CAT AO THIS SUBROUTINE MEASURES THE * C* BASELINE AND ICN SIGNALS FOR UP TO FIVE MASSES, THE * C* BUFFER GAS FLOW ANC THE REACTION CHANNEL PRESSURE * C* FOR A GIVEN REACTANT FLOW, WHICH IS ALSO MEASURED. * C* *

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02C9 02 1 C 0211 0212 0213 0214 0215 0216 0217 0218 0219 0220 0221 0222 0223 0224 0225 0226 0227 0228 0229 0230 0231 0232 0233 0234 0235 0236 0237 C23 8 0239 0240 0241 0242 0243 0244 024 5 0246 0247 024 8 0249 0250 0251 0252 0253 0254 0255 0256 **** 53 £****$*$*$*$*$*************$***$*** SUBROUTINE CATA(BUFLC,IRFLO,PRESS) CCRMCN IRRAYI64C), IFILE(3)» JRRAY ( 10) , ION (6) CORMCN I T I M E ( 5 ) SEFLC=C .0 SPRES = 0 .0 SFL0lft = 0 .0 N CHA N = I R R A Y ( 7 ) CO 2CC0 J = 1 , NCFi AN IFIK-82 ) 1350 , 14CC 1350 CALL ACCCNI IRRAY { J+17 ) , 5) 14C0 SIONS=C.C CALL ACCCN ( ICNS , 1 ) I F { ICNS — 3113) 18CC, 15C0 1 5C0 CC 1600 1=1, ICC CALL ACCCNI ICNS , 1 ) 1 6C0 S IONS = S ICNS + FLOATI ICNS ) S IONS = S ICNS/ ICC. GCTG 1950 l 8 C 0 CC 1 9CG 1 = 1, ICO CALL ACCCNI ICNS, 2) 19C0 SIONS=S ICNS+FLCATI ICNS) S ICNS = S ICNS/ 1C0C. 1950 ICNI J)= IFIXI SIGNS ) CALL RELAY I 10 , 1 ) CALL RELAY(1C,0) I RC 0 E= 1 1 CALL EXECI IRCCE, IT I N E ) 1 1= I T IME 1 1 ) 1960 CALL EXECI IRCCE, ITINE) 12= I T IME ( 1 ) IF! I 2I 1 ) 1975,1980 1975 I2=I2+1CC 1980 I F { ( I2-I1)-90)1960,2CCO 2C00 CCNTINUE CO 2050 1=1 , ICO CALL ACCCN I IFLCfc ,0 ) CALL ACCCNI IPRES,3) CALL ACCCNI IBFLC ,4) SFLCW=SFLOW+FLGAT I I FLOW) SPRES = SPRES + FLGAT( I PRES ) 2050 SBFLC = SEFLO + FLCATI IBFLO ) BUFLC=SEFLO/ ICO. IRFLC=IFIXI SFLCW/IOC. ) PRESS=S PRES/ 100. RETURN ENC ENC $ LIST ENC ****

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CHAPTER III MATHEMATICAL MODEL A. Basic Model The simplest analysis of reaction kinetics for a flowing afterglow system may be accomplished by using a plug flow model. This model assumes that the buffer gas axial velocity, Vq (and the electron and ion axial velocities in the high pressure environment) is independent of radial or axial position in the reaction tube. In this simple model it is also assumed that the neutral reactant gas is injected uniformly throughout the flow tube cross-section at z=0, where the z— axis is the cylindrical axis of the flow tube. In addition, the diffusion of reactants and products in the reaction tube is not considered. For net reactions of the type e" + X 2 X" + X x 2 = F 2 , Cl 2 , Br 2 (22) the rate equation becomes d[X“]/dt k[e-][X 2 ] (23) where the symbols within brackets represent the number densities of reactants and product and k is the bimolecular rate constant. In order to determine [X“] as a function of time, [e~] and 54

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55 [X 2 ] must first be evaluated. The rate equation for the electrons is d [e ]/dt = -k[e“][X 2 ] (24) If the assumption is made that [X 2 ] » [e ] for all t, then [X 2 ] may be treated as a constant. Integrating Equation 24 then yields [e~] = [e ] Q exp{-k[X 2 ]t} (25) where [e ] 0 is the electron number density in the reaction tube at t=0 (that is, at the neutral reactant gas injection port) . Substitution of this result into Equation 23 yields the differential equation d[X“]/dt = k[X 2 ][e~] o exp{-k[X 2 ]t) (26) Integrating this equation gives the desired solution for the product ion number density [X-] = [e ] Q {l exp(-k[X 2 ]t)} (27) The reaction time, t, written in terms of the reaction tube length, L, and the axial flow velocity, v Q , is t = L/v q (28) for the plug flow model. Equation 27 then becomes

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56 [X“] = [e-] Q {l exp(-k[X 2 ]L/v 0 )} (29) Thus, the measurement of [X ] at the end of the reaction tube versus [X 2 ] results in the determination of the rate constant k if the reaction tube length and the axial flow velocity are known. At this point it is useful to reiterate the assumptions made in the derivation of Equation 29: 1. the axial flow velocity, v Q , is constant throughout the reaction tube, 2. diffusion of reactants and products in the reaction tube is unimportant, 3. the neutral reactant gas is injected uniformly in a cross-section of the reaction tube at t=0 (that is, z=0) and 4. the neutral reactant number density is much greater than the electron number density for all t>0 in the reaction tube. Each of these assumptions will now be examined and accepted or modified on the basis of experimental evidence. The derivation of the model for the experimental system will then be altered to include any changes made in the basic assumptions. B. Axial Flow Velocity Determination of the axial flow velocity in the flow tube is necessary in order to calculate the reaction time t = L/v q (28) available to the electrons and halogen gas in the reaction tube. Two basic assumptions concerning the axial flow velocity

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57 were made in the derivation of Equation 29 1. the axial flow velocity, v , is constant throughout the reaction tube and 2. in the high pressure environment present in the reaction tube, ions, electrons and buffer gas move down the tube with the same velocity profile. If these assumptions are true, then the time required by any species to transit the reaction tube is given by t = Tra 2 L/F (30) where a is the flow tube radius, L is the reaction tube length and F is the buffer gas volume flow rate. The method illustrated in Figure 17 was used to determine whether Equation 30 could be used to calculate reaction times for the flowing afterglow experimental configuration containing a microwave discharge electron source. During normal operation of the flowing afterglow system, the neutral reactant gas injected into the flow tube reacts with electrons produced by the microwave discharge and forms negative ions, which are sampled by the mass spectrometer system. If a platinum probe is inserted into the afterglow and a positive potential applied to this probe as shown in Figure 17, electrons will be removed from the afterglow as they reach the probe. Thus, negative ions will not be formed downstream after the electrons already beyond the probe at the time of the potential application are consumed. If the potential applied to the probe is used to simultaneously trigger an oscilloscope sweep, then the ion current (at the scope vertical input) as a function of time

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REACTANT ION SIGNALTO GAS SCOPE VERTICAL AXIS I MICROWAVE 58 o : UJ u. u. D m V) < o Ul Ll) Figure 17. Experimental Configuration for the Measurement of Transit Times for Ions in the Flow Tube

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59 is displayed on the oscilloscope. This scope trace can be photographed with a Polaroid camera. Neglecting axial diffusion, it is expected that the ion signal versus time trace obtained in the manner described above would be a step function if the assumptions previously made are correct. A sample experimental trace is shown in Figure 18. Since the trace is not a step function and axial diffusion is not expected to result in a tailing of the magnitude observed in this trace, it is apparent that the radial velocity profile (that is, the axial flow velocity as a function of radial distance, r, in the flow tube) is not planar and also that radial diffusion of species present in the reaction tube is important. A literature search previously revealed that due to frictional forces at the walls, the radial velocity profile for the viscous flow of a gas in a cylindrical tube is not planar but parabolic. Neglecting the axial velocity gradient (near zero in the present experiment) , the radial velocity profile is given by^ v(r) = wv Q (b r 2 /a 2 ) (31) where w = 2/(1 + 5 . 52\/Pa) (32) and b = 1 + 2.76A/Pa (33) X is the mean free path (cm) at one Torr, P is the pressure (Torr)

PAGE 70

60 CO CO in to eg in m eg o
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61 in the reaction tube and a is the flow tube radius (cm) . In the present experiments 1 < P < 3 Torr of argon buffer gas. This yields 1.97 < w < 1.99 and 1.008 > b > 1.002. Thus, the radial velocity profile is approximately given by v(r) = 2v q (1 r 2 / a 2 ) (34) where v Q is the plug flow linear velocity. The ion signal versus time trace shown in Figure 18 may now be explained in terms of this velocity profile. When a potential is applied to the probe at t=0, any electrons downstream of the probe will continue to be carried down the tube in the flowing stream and will react with the reactant gas present in the reaction tube. The resulting ions are extracted through the orifice and detected by the quadrupole mass spectrometer system. Since the radial velocity profile of the buffer gas is of the form given in Equation 34, ions at the center of the flow tube will have the shortest reaction tube transit times while those nearer the walls will have the longest. As the ion density along the cylindrical axis of the reaction tube is depleted, ions diffuse from the areas where r>0. This accounts for the fact that the observed ion current as a function of time after the application of the blocking potential to the probe does not drop sharply to zero after the initial constant period and tailing occurs as shown in Figure 18.

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62 Figure 19 shows the results of a series of measurements (closed circles) of negative ion reaction tube transit times (for r=0) as a function of the argon buffer gas pressure in the flow tube, using the technique just described, where the break in the ion signal versus time trace such as that shown in Figure 18 is taken as the transit time for ions from the probe to the sampling orifice. The upper solid line in Figure 19 represents the reaction tube transit times calculated from the measured buffer gas volume flow rate using the equation t = L/v(r=0) = ira 2 L/2F ( 35 ) where the factor of 1/2 arises because v(r=0) = 2v Q . The ion transit times measured by the probe technique are seen to be smaller than those calculated from the buffer gas volume flow rate. This may be attributed to the geometry of the present flow tube when in the microwave discharge source configuration. The microwave discharge produces ions and electrons in a quartz tube with an inner diameter less than 1.12 cm. Buffer gas is pumped through this tube into the flow tube, which has an inner diameter of 2.57 cm. Due to this arrangement the buffer gas tends to stream through the center of the flow tube at a rate higher than predicted by a parabolic velocity profile. In addition, the velocity outside this central filament is less than expected. Given sufficient distance (that is, time), the radial velocity profile will become parabolic as the gas moves through the flow tube.^ 2 This statement

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63 o o ro O in cvi O o cvi o to CO to UJ a: a. uj oo O Z O I— o < UJ tr u o VM ID U 3 CO tn (0 0) 0) O g W •H 3 H O CO 4-1 •H 0) CO 60 e w « OS Wt X H O CO C *rl O O M (0 X) > OS OS M 3 to m o Ov 0) C4 3 60 i-t Pu ( 09 SUJ) 3 SAj IX 1ISNVH1 3sni NOI10V3a

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is illustrated in Figure 19 by the fact that as the reaction tube transit time increases, the values measured by the probe technique and those calculated from the buffer gas volume flow rate merge. This indicates that given sufficient time, the velocity profile, even with the microwave discharge source, will develop its parabolic shape. The flow tube in the flowing afterglow apparatus, however, is not sufficiently long to permit the parabolic profile to become fully developed when using the microwave discharge source. Therefore, the filament flow phenomenon must be taken into account in analyzing the data obtained using the microwave discharge source. Thus, Equation 27 becomes [X~] = [e _ ] 0 {l exp(-k[X 2 JO} (36) where t' is the ion reaction tube transit time measured by the probe technique described above. As a check of the probe technique used to measure ion reaction tube transit times, these parameters were also measured by an alternative probe technique. This procedure involved monitoring the current collected by a second probe (downstream from the blocking probe shown in Figure 17) as a function of time after application of the potential to the blocking probe. Two transit time measurements obtained in this manner are shown in Figure 19 as closed squares. The results of this double probe technique are seen to be in near agreement with the probe-ion signal technique discussed earlier.

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65 In order to avoid the filament flow problem described above, previous researchers have found it necessary to make their flow tubes long enough to allow the parabolic velocity 48 profile to develop or to smooth the buffer gas flow with a sintered glass disc placed in the flow tube upstream of the reaction region. ^ in the present experiments the latter solution was employed. This necessitated the location of the electron source downstream of the sintered glass disc. Thus, at this point the apparatus was converted to the filament source previously described. With the filament source installed in the flow tube, ion transit times could easily be measured using the technique previously described with the exception that the blanking potential was no longer applied to a probe but to the filament. The circuit used to accomplish this is shown in Figure 20. With the double-pole double-throw switch in the upper position, a negative bias is applied continuously to the filament and the source operates in a continuous mode. With the doublepole double-throw switch in tne lower position, the source operates in a pulsed mode at a rate determined by the square wave input at the PNP transistor base. Ion transit times may be determined by triggering an oscilloscope sweep on the negative slope of the square wave input. This negative pulse results in zero volts filament bias; that is, the source is switched to the "off" position from the "on" position. Thus, the ion signal output of the mass spectrometer system,

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KEITHLEY AMMETER 66 O < Filament Source Configuration for the Measurement of Ion Transit Times in the Flow Tube

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67 applied to the vertical input of the oscilloscope, versus time trace is obtained similar to that shown in Figure 18. The oscilloscope sweep may also be triggered on the positive slope of the square wave input. This positive pulse results in a negative filament bias; that is, the source is switched to the "on" position from the "off" position. Ion transit times are then determined by the time required for the appearance of the ion signal after pulse application. Figure 21 shows the results of a series of transit time measurements (for r=0) with the filament source installed in the flowing afterglow system. The measurements were made on three different ions, t*'i88 er i n 8 on both positive and negative square wave pulses as described above. Ion transit times calculated from the measured buffer gas volume flow rate assuming a parabolic velocity profile are also shown in Figure 21. The good agreement between transit times measured by the pulse technique and those calculated from the measured buffer gas volume flow rates indicates that the sintered glass disc installed in the flow tube is effective in smoothing the buffer gas flow, enabling a parabolic velocity profile to be established in the flow tube. The agreement also indicates that the ions and buffer gas move down the flow tube at the same velocity. For the moment it is also assumed that the electrons are at thermal energy. This assumption will be discussed later. From the discussion above it is clear that for the flowing afterglow filament source configuration, Equation 29 must

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REACTION TUBE TRANSIT TIME (msec) 68 13. 12 . II. + F~PULSE A H 2 0 + , + PULSE F", + PULSE V SF~,+ PULSE O CALCULATED 10 . O H? 9.0 8.0 + ° A O 7.0 A, 6.0 5.0 + + o + + ^ 1d + O O + a o + o + -Q _l 1.00 2.00 3.00 REACTION TUBE PRESSURE (Ton) Figure 21. Measured Ion Transit Times in the Flow Tube Versus Pressure for the Filament Source Configuration

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69 be modified to include the parabolic radial velocity profile. Thus, Equation 29 becomes [X-] = [e"J o (l exp(-k[X 2 ]L/2v D )} (37) Consideration of the axial flow velocity radial profile has led to a modification of the basic model, derived in Section A, to account for the filament flow phenomenon with the microwave discharge source and the parabolic profile with the filament source. The kinetic equations relating the ion density [X ] to the rate constant, k, are then [X ] = [e ] 0 U exp(-k[X 2 JO} (36) for the microwave source and [X~] = [e“] 0 (l ~ exp(-k[X 2 ]L/2v Q )} (37) for the filament source. C. Radial Diffusion of Charged Species The tailing observed in the ion signal versus time traces of the ion transit time measurements in the previous section indicates that radial diffusion is an important factor in the analysis of flowing afterglow reaction kinetics. Thus, the transport equation for negative ions produced by dissociative electron attachment in the flowing afterglow reaction tube becomes

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70 2v q (1 r 2 / a 2 ) 3 [ X ] / 3 z = (D_/r)3(r3[X-]/3r)/3r + k[e"][X 2 ] (38) where the left side represents the time rate of change of the negative ion concentration, the first term on the right represents the negative ion radial diffusion loss rate and the second term, the negative ion production rate from the attachment 48 reaction. D_ is the negative ion radial diffusion coefficient. However, before a solution for this equation can be found, a similar transport equation for the electron density must be solved 2v o (l r 2 /a 2 ) 3 [e“]/9z = (D e /r) 9 (r9[e“]/9r)/9r k[e _ ][X 2 ] (39) where the left side represents the time rate of change of the electron density, the first term on the right, the electron diffusion loss rate and the second, the electron reaction loss rate. is the electron radial diffusion coefficient. Equation 39 has been solved by Cher and Hollingsworth^ and its solution may be written [e ] = [e ]gR(r)Z (z) (40) where

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71 R(r) = exp(-BXr 2 /Za 2 ) F (1/2 A/43, l;3Ar 2 /a 2 ) (41) Z(z) = exp(-D e A 2 z/2v Q a 2 k[X 2 ]z/2v Q ) (42) A 2 = A 2 + £i ka 2 [X 2 ]/D e e 2 kV[X 2 ] 2 /D 2 (43) 3 2 = 1 + ka 2 [X 2 ]/D e A 2 (44) and [e ]' is the electron density at r=0 and z=0, a is the flow tube radius and A Q (=2.7098), e (=0.2372) and e ^ (=0.00150) are empirical quantities determined from the solution of the equation F (1/2 A/43, 1;3A) = 0 (45) a necessary condition in order for the density of the electrons 49 to approach zero as r approaches a. ^F^(l/2 A/43, 1 ; 6A) represents a confluent hypergeometric function. Now that a solution has been obtained for the electron density in the flow tube this solution must be substituted into Equation 38 and an expression for [X~] found. It is obvious at this point that obtaining an exact analytical expression for the negative ion number density is impossible due to the intractability of Equation 38 upon substitution of the expression derived for the electron number density.

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72 At this point the assumption is made that since the present experiments measure only the axial variation of the reactants/ products, then only the solution of Equation 39 at r=0 is necessary. Therefore, Equation 40 becomes [e~] = [e _ ] "exp{-D zX 2 /2v a 2 (1 + e. )k[X]z/2v o e o o 1 2 o e 2 k 2 a 2 [X 2 ] 2 z/2D e v o > (46) where the first term in the exponential represents radial diffusion losses, the second reaction losses and the third coupling between reaction and diffusion. If we define [e“] as the electron density at r=0, z=L and [X 2 ]=0, then [e“] Q = [e“]^exp{-D e LA 2 /2v 0 a 2 } (47) and [e~] = [e'] Q exp{-(l + e i )k[X 2 ]L/2v Q £ 2 k 2 a 2 [X 2 ] 2 L/2D e v 0 ) (48) where L is the reaction tube length. This equation applies only to the electron density at r=0, that is, on the flow tube axis. Therefore, substitution of Equation 48 into Equation 38 and the subsequent solution to yield an expression [X“] = f(r,z) is meaningless. At this point it is assumed that [X ] = [e“] [e~] o ( 49 )

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73 that is, that the difference between the electron number density at r=0 and z=L with [X^ ] = 0 and the electron number density at r=0 and z=L with [X 2 ]^0 is due to the formation of negative ions, which undergo negligible radial diffusion in their transit through the reaction tube. Substitution of Equation 49 into 48 then yields [X"j = [e “] o [1 exp{-(l + e i )k[X 2 ]L/ 2 v o e 2 k 2 a 2 [X 2 ] 2 L/ 2 D e V o }] (50) The validity of this equation will be tested by measuring known reaction rates. Generally, £ 2 k 2 a 2 [X 2 ] 2 L/2D e v o « (1 + £l )k[X 2 ]L/2v o (51) Thus, Equation 50 may be written [X ] = [ e — J 0 { 1 ~ exp(-0.619k[X 2 ]L/v Q )} (52) Comparing this result (applicable to the filament source configuration) to Equation 29, it can be seen that correcting for a parabolic velocity profile and the radial diffusion of electrons yields a correction factor of 0.616, that is, k = (1 + 0.616)k g ( 53 ) where k is the actual rate constant and k„ is that derived s from data using the model outlined in Section A. This result

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74 expresses the assumption used by Ferguson et al.^ i n t h e reduction of experimental data where it is assumed k (1 + Z a )k i i s (54) where the a^^ represent corrections to the rate constant obtained by the reduction of data with the simple model. These correction factors include the effects of a parabolic velocity profile, radial diffusion, non-uniform neutral reactant injection and axial diffusion. The largest correction factors by far are the corrections for the parabolic radial velocity profile and radial diffusion. ^ Axial diffusion corrections are usually negligible and will not be considered here.^® The inclusion of the radial diffusion of electrons in the mathematical model has yielded the equation for the filament source configuration. Due to the lack of a parametric form for the radial velocity profile with the microwave discharge source configuration, no correction could be made to the model. In addition, the effect of the radial diffusion of electrons is expected to be less than that for the filament source configuration since the axial flow velocity at the center of the reaction tube, where the density of the charged species is highest, is much faster in the microwave source configuration; therefore, the electrons have less time to diffuse. [X ] = [e ] {1 exp(-0. 619k[X 0 ]L/v )} o L o (52)

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75 D. Inlet Effects As pointed out by several authors, the effect of a point source reactant gas inlet in a flowing afterglow is to drastically deplete the electron density in the center of the reaction tube due to the large neutral reactant density at r=0 and z=0. 46 ’ 48 Given sufficient distance (that is, time), this perturbation will correct itself as the mixture flows down the reaction tube. This self correction is accomplished through diffusion of electrons from r>0 to r=0 and diffusion of the neutral species from r=0 to the region r>0. This problem has been studied thoroughly by Ferguson et al. 4 8 In their system this phenomenon results in a correction of about 30% (a.^ = -0.3) in the simple rate constant for an order of magnitude decrease in the primary ion signal. Since the radial diffusion of the electrons in the flow tube results in an axial density profile proportional to exp{-D X 2 L/2v a 2 } (55) comparison of the exponent in both the present experiments and those of Ferguson et al. will indicate whether point source injection of the neutral reactant is more or less of a correction in the present experiments. Thus, [(x2/2)(LD e /v o a 2 )] c / [ (X 2 /2) (LD £ /v o a 2 ) ] ? = [L/Pv Q a 2 ] c / [L/Pv Q a 2 ] F (56)

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76 since D ^P -1 where P is the flow tube pressure. The subcripts e C and F refer to the current apparatus and that of Ferguson et al. , respectively. Inserting typical numerical values yields (20/2 x 2.5 x 10 3 x 1.28 2 ) / C (60/0.5 x 8 x 10 3 x 4 2 ) 2.6 (57) F Therefore, radial diffusion in the current experiment should be faster and the perturbations produced by a point source should result in a smaller correction factor than in the experiments of Ferguson et al. For this reason no modification was made to the mathematical model for perturbations due to inlet effects. E. Reactant /Electron Number Density Ratio No actual determination of the electron density in the present experiments was made. However, previous researchers have found electron densities on the order of 10 2 to 10^ o 48 50 electrons /cnr for flowing afterglow systems. ’ Since one of the assumptions made in the derivation of models presented in the previous sections was that [X 2 ] » [e“] (58) for all t>0, it is important to determine whether this assumption is in fact true. An analysis of the models presented previously reveals that if the neutral density were not always greater

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77 than the electron density, then the rate constants determined by the reduction of data using these models would be too small. The only experiments where this was expected to be a problem were those in which the attachment of electrons to sulfur hexafluoride was studied. In these experiments the sulfur g hexafluoride number density was sometimes as low as 10 molecules/ cm 3 . However, reduction of the experimental data using a model which does not make the assumption expressed by Equation 58 above yields no significant difference in the rate constants obtained. Therefore, the assumption above was retained. F. Ambipolar Diffusion In an afterglow containing electron densities greater than the order of 10 7 electrons/cm 3 , electrons diffuse to the walls of the flow tube at a rate several orders of magnitude slower than their free diffusion rate. This phenomenon, known as ambipolar diffusion, is due to the retarding potential exerted on the electrons by the positive ions present in the afterglow. When a gas, which attaches electrons to form negative ions, is injected into the afterglow, the electron diffusion rate is governed approximately by the equation 51 D a = 2D + {1 + [X ] / [e“] } (59) where D a is the ambipolar diffusion coefficient, D + is the positive ion free diffusion coefficient, [X ] is the number density of the negative ion formed and [e ] is the electron

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number density. Substitution of this equation into the models derived previously, reveals that the rate constant calculated, assuming constant electron diffusion, will be smaller than the actual rate constant. This error is probably significant in electron attachment studies of the type presented here.

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CHAPTER IV DATA REDUCTION The product ion number density at the end of the reaction tube may be related to the product signal by the expression [X-] = cl (60) where I is the product ion current and c is a coefficient which depends on the ion sampling efficiency, the transmission coefficient for the electrostatic lens system and quadrupole mass spectrometer and the gain of the electron multiplier used for ion detection. The coefficient c is a constant during a particular experiment. Equation 52 may now be written I “ { [e — ] Q /c } { I exp(-0. 619k[X 2 ]L/v o > } (61) As the neutral reactant number density, l^], approaches infinity (or in reality, a number density large enough to attach essentially all of the electrons in the reaction tube within a short distance of the reactant gas injection port), 'the product ion number density approaches a maximum, which may be written [X ] 0o = cIqo = [e"] Q (62) Substitution of this result into Equation 61 yields the expression 79

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80 I = ijl exp (-0. 619k [XjL/v )} (63) If the product ion signal, I, is measured as a function of the reactant gas number density, [X 2 ]| and the maximum product ion signal, I^,, is determined, then a simple one parameter curve fit will yield the desired rate constant, k. In actual practice there are at least three complications: 1. the measured product ion signal includes a baseline, Al, 2. the determination of I^ is difficult due to noise in the ion signal and 3. there may be a significant error, AQ, in the determination of the factor [X 0 ]/v . z o Substitution of these errors into Equation 63 yields I “ loo + AI Iooexp{-0.619kL[X o ] / (v ) + m Z m o m 0.619kLAQ} (64) where I is the measured product ion signal, [X„] is the measured m z m reactant gas number density and (v ) is the measured buffer o m gas linear velocity (plug flow). Equation 64 may be written y = Pjl ~ P 2 exp(-P 3 x) (65) where P x = !«, + AI (66) P2 = looexp(0. 619kLAQ) (67)

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P, = 0.619kL/(v ) (68) j o m and where y = I and x = [X„] • Thus, a curve fit of measured m 2 m ion signal versus reactant gas number density data yields the parameter from which the desired rate constant, k, can be determined. Generally, AQ^O; therefore, P x P 2 = AI * (69) and P 2 = Ico (70) Thus, the values obtained for the parameters P^ and P^ were checked by noting the approximate values of Al and la,. Typical values for the ion signal baseline, AI, and the maximum ion signal observed, I^ + AI, may be obtained by looking at the data listed in Appendix IV. A. Jacobian Matrix Technique As indicated above, the mathematical models derived in Chapter III generally result in an equation of the form y ± * p i “ p 2 exp(-P ;J x i ) (71) which relates the observed ion signal, y^, to the reactant gas flow, x^. In this equation the parameter P^ must be determined in order to calculate the rate constant, k, from the experimental observations.

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82 The method used to find the parameters P^, P^ and P^ 52 is an iterative least squares technique. The set of observations, y^ (n in number) , are thought to be a function of the set of parameters, P. (3 in number in this case). *1 ’ £ 1


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Defining the vector d (length n) as above and the vectors a (length n) and 6 (length m=3) by 83 *i £ i (P °l' P 2' P W (76) and (77) and the matrix A (n x 3) (78) the deviation can be written in matrix notation as d = a A (79) and S = d"d = (a' A'6')(a Afi) (80) where d', a', A' and 6' are the transpose of d, a, A and 6, respectively. S is minimized if 3S/36j = 0 j=l,2,3 (81) This yields B6 = b ( 82 ) where B = A' A and b = A' a.

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84 “ B h (83) then gives the change to be made in the initial parameters in order to minimize the sum of the squares of the deviation, that is, S. Thus, a new set of initial parameters is defined by P 1 » P° + 6 (84) and the Taylor series expansion made about the new points Pj. The entire process is then repeated until the iterations converge and parameters P^, P^ and P^ are determined. Figure 22 shows the result of the application of the Jacobian matrix curve fit technique to actual experimental data. The open squares represent data points obtained in an experiment in which the dissociative attachment of electrons to fluorine was studied. The solid line defines the least squares fit obtained by fitting the data to an equation of the form y ± = “ p 2 exp(-P x ± ) (71) Following the sample curve fit result is a listing of a version of the Jacobian matrix technique which allows all of the selected peaks (F ion signal for instance) from a specific data file to be fit to the same parametric equation, such as that given above. The operator specifies the data file, whether or not to delete any experimental data points and selects the specific ion signal within that data file to be analyzed. The program then estimates the initial parameters P°, P° and P°

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85 0 ! c •H U O 3 tH c u c o o CO CO •H Q • CM CM 0 ) M 3 00 H

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CC01 C002 COG 3 0004 0005 C006 CG07 0008 0009 OOIC con 0012 0013 0014 0015 0016 0017 0018 0019 0020 0021 0022 0023 0024 0025 0026 0027 0028 0029 0030 0031 0032 0033 0034 0035 0036 0037 0038 0039 0040 0041 0042 0043 0044 0045 0046 0047 0048 0049 0050 0051 0052 86 FTN,L PROGRAM AUTO c* * C* PROGRAM AITOO THIS PROGRAM FITS DATA, STORED IN * C* THE SPECIFIED CATA FILE, TO A RATE EQUATION OF THE * C* FORM GIVEN IN LINE 118 (IN THIS PROGRAM EITHER * C* EXPONENTIALLY DECREASING CATA OR ASYMPTOTIC * C* EXPONENTIALLY INCREASING CATA) USING A JACOBIAN * C* MATRIX LEAST SQUARES TECHNIQUE. SOURCE IS STORED * C* ON CISC AS CTU A . * C* * C**$**$****$*:fr$*******$*$** ******$***** ******$***£****$** DIMENSION ZVECT(4 ), BMTRX(4, 4) » XVECT14) ,BINV(4,4) 1 ,XCBS( ICC) ,YCBS( 100 ),CELY(4) ,PARMT(4) , IRRAY (640) « 2 I FILE ( 3 ) ,NY( ICO ) ,NX ( 100) ,ZY{ ICO ) ICNWD= 1 C2B IRCD= 14 WRITE ( 7 »20 ) 20 FORMAT (IX, INPUT FILE NAME ) R EA D ( 7 » 3 C ) ( IFILEf I ), 1 = 1,3) 30 FORMAT ( 3A2) C*****************^***# * *** * *$ **:{<** *******$******** C 4 ^ C* LINES 32 THROUGH 37 ALLOW THE OPERATOR TO DELETE * C* THE FIRST FEW DATA POINTS (IF THE EXPERIMENT * C* REQUIRES A PERIOD OF TIME TO ATTAIN STABILITY) AND * C* TO SELECT THE SPECIFIC ION SIGNAL CATA TO BE * C* REDUCED ( CL— (35) INST EAC OF CL-(37) FOR INSTANCE). * C* * WPITE(7,43) 43 FORMAT ( IX , INPUT NUMBER OF STARTING DATA POINT ) READ ( 7, * ) J J W R I T E ( 7 ,45) 45 FORMAT ( IX , INPUT PEAK TO BE FIT ) R EAD ( 7 , * ) J J J CALL EXEC ( IRCD, ICNWC, IRRAY, 1C, I FILE, 0) NU= IRRAY (2 ) ICHAN=.J JJ+1 WRITE (6,48) ( IFILE( I ), 1=1,3) , ICHAN 48 FORMAT ( IX, CATA FILEC ,2X,3A2/1X, MASS CHANNEL 0 , 1I3/1X, Y=A-B*EXP (-C*X ) CURVE FIT ///IX, RUN ,7X, 2 A , 14X , B , 14X , C , 8X , K (T MEAS.) ,2X, K (T CALC. 3 ) // ) CC 1200 MM=1,NU N = 5 * M M 4 CALL EX EC (IRCD, I CNWC , IRR AY, 640, I F ILE , N ) J=IRRAY ( 10) CO 5 C I = JJ,J K = 7 5 +7$ I + JJ J I I=I + 1-JJ

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0053 00 5 4 0055 0056 0057 0058 0059 0060 0061 0062 0063 0064 0065 0066 0067 0068 0069 0070 0071 007 2 0073 0074 0075 0076 0077 0078 0079 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 0095 0096 0097 0098 0099 0100 0101 0102 0103 0104 87 VCBS( II ) = FLO AT ( IRRAV(K) ) * ( 1 0 . ** 1 2 ) / ( 3276 . 4* ( 10. ** 1 < IRRAY ( 6 ) ) ) ) K = KJ J J + 1 50 XCBS ( II ) = FLOAT { IRRAY (K2) )/ 3276.4 £*$********$*****$*****************$************:{:****$*** C* * C* LINES 63 THROUGH 92 MAKE INITIAL ESTIMATES OF THE * C* PARAMETERS PARMT(l), PARMT12) AND PARMT ( 3 ) . * C* * 0 ******************************************************** YMIN=1. E + 20 CO 55 1=1, J I F( YM IN-YOBS ( I ) ) 55, 53 53 YMIN=YCeS(I) XMIN=XCES( I ) 55 CONTINUE CO 60 1=1, J 60 Z Y ( I ) = Y06 S ( I J-YMIN YMAX=— 1.E + 2Q CO 70 1=1, J I F { Z Y ( I )-YMAX)7C,65 65 YMAX=ZY ( I ) XMAX=XCES ( I ) 7G CONTINUE IF(XMAX-XMIN)75, ICO 75 PARMT ( 1 ) = YM IN PARMT ( 2 )=-YM AX 1 = 1 77 I F ( Z Y { I )-0.5*YMAX)8C,90 80 1=1+1 GOTO 77 9 0 PARMT ( 3 ) = ALGG (PARMT (2) /(PARMT! 1 ) — YOB S ( I ) ) )/XOBS( I) GOTO 150 ICO PARMT ( 1 ) = YMAX + YM IN PARMT ( 2 ) =YM AX 1 = 1 110 IF(ZY( I )-.5*YMAX) 120,115 115 1=1+1 GOTO 110 120 PARMT ( 3 )=ALCG (PARMT (2 ) / (PARMT ( 1 )-YOBS( I ) ) )/XGBS( I ) 150 M = IRRAY ( 10) N = 3 I L=0 C#:.}:**}}:^**#***** $***#:$*;{(;(<* $*>}!:(:****$**** **********£******* 0 * * C* LINES 107 THROUGH 193 USE AN ITERATIVE LEAST * C * SQUARES TECHNIQUE TO ARRIVE AT VALUES FOR THE * C* PARAMETERS PARMT(l), PARMT12) AND P ARM T ( 3 ) . IF THE * C* CURVE FIT COES NOT CONVERGE AFTER 35 ITERATIONS, * C* THE PROCESS IS TERMINATED AND THE PROGRAM PROCEEDS * C* TO THE NEXT EXPERIMENT STORED IN THE SPECIFIED DATA * C * FILE. *

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0 1C5 Cl 06 0107 0108 0109 0110 0111 0112 0113 0114 0115 0116 0117 0118 0119 0120 0121 0122 0123 012 4 0125 0126 0127 0128 0129 0130 0131 0132 0133 0134 0135 0136 0137 0138 0139 0140 0141 0142 0143 0144 0145 0146 0147 0148 0149 0150 0151 0152 0153 0154 0155 0156 88 O * 175 CG 210 1=1,4 ZVECTf I )=C.C CC 210 J = 1 » 4 210 E RTRX { I » J ) =C . 0 CC 500 1=1, R 1 F ( A 8 S ( PARMT ( 3 ) *XCBS { I ) ) — 85 5)260, 250 250 WRITE(7,255)RM KRITE(6,255)RR 255 FORMAT (IX, NC FIT POSSIBLE FCR RUN ,14) GCTG 12CC 260 CONTINUE YPREC = PARMT ( 1 )P ARM T ( 2 ) *EXP (-PARMTI 3 ) *X0BS ( I) ) CELY ( 1 ) =1 .0 CELY(2)=-EXP(-PARMT(3)*XGBS{ I) ) CELY(3)=PARRT(2)*XOeS(I ) *EXP (-PARMT ( 3)*XCBS { l ) ) C EV = YCB S ( I ) -YPR E C CG 200 K= 1 , N ZVECT (K )=ZVECT(K)+DELY(K)*DEV CG 300 J= 1 * N ERTRX(K,J)=BRTRX(K,J)+DELY(K)*DELY{J) 300 CONTINUE 2CC CONTINUE 500 CONTINUE N N = N + 1 I F ( NN-5 ) 650 , 75C 650 CG 699 L=NN,4 699 BRTRX(L,L)=1.0 750 CONTINUE CTM1=BMTRX(3,3)*BMTRX(4,4)-BRTRX(3,4)**2 CTM2=»BMTRX(2,3)*BMTRX(4»4)-BNTRX(2,4)*BMTRX(3,4) DTM3=BRTRX(2,3)*EMTRX(3,4)-BMTRX(3,3)*BMTRX (2,4) DTM4 = BMTRX ( 1 , 3 ) * BMT RX ( 4 , 4 )BHTRX ( 1,4 ) #BMTRX 13,4) CTM5=BMTRX(l,3)*BMTRXt3,4)-BKTRX(l,4)*BMTRX{3,3) CTM6 = BMT RX ( 1,3 ) * BMT RX ( 2 , 4 ) -BRTRX ( 1 , 4 ) TRX { 2 , 3 ) DTMN1=BRTRX (1,1 )*( BN TRX ( 2 , 2 ) *DTM 1-BMTRX { 2 , 3 ) *CTM2+ 18RTRX(2,4)*CTR3 ) CTMN2 = BRTRX( 1,2)*(BMTRX(1,2 ) *DTM 1-BMTRX ( 2 , 3 ) *DTN4 + 1BMTRX (2 ,4 )*CTM5 ) CTMN3 = BMTRX ( W3 )*( BNTRX ( 1,2) *DTM2— BMTRX (2,2 )*DTM4+ 1BNTRX(2,4)*CTN6) CTMN4 = BMTRX ( 1,4 ) *( BPTRX ( 1 , 2 ) *DTM 3-BM TRX { 2 , 2 ) *DTM5+ 1BMTRX(2,3 )*CTM6 ) DTMNT=DTNN1-CTMN2+DTMN3-DTMN4 E INV ( 1 , 1 )=BNTRX ( 2 , 2 ) *DTM 1-BMTRX ( 2,3 ) *DTM2+BMTRX ( 2 , 4 ) 1 *DTM3 B INV ( 1, 2 )=-BMTRX { 1, 2 ) *0TM 1 + BMTRX ( 2,3 ) *DTM41BMTRX(2,4)*CTM5 B INV ( 1 , 3 ) = BMTRX ( 1 , 2 ) *DTM2-BMTRX ( 2 , 2 ) *DTM4+8MTRX(2»4) 1 *CTM6 BINV ( 1, 4 ) =-BMTR X ( 1, 2 ) *DTM3+BMTRX{ 2,2 ) *DT M 5-

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0157 0158 0159 0160 0161 0162 0163 0164 0165 0166 0167 0168 0169 0170 0171 0172 0173 0174 0175 0176 0177 0178 0179 0180 0181 0182 0183 0184 0185 0186 0187 0188 0189 0190 0191 0192 0193 0194 0195 0196 0197 0198 0199 0200 0201 0202 0203 0204 0205 0206 0207 0208 89 1BMTRX(2,3)*CTN6 8INV(2»2)=BMTRX(1,1 ) *CTM 1-BMTRX ( 1,3)*DTN4+ 1 BNTRX { 1,4 )*CTN5 BINV ( 2, 3)=-BMTRX ( 1, 1 ) *DTM2 + BMTRX l 1, 2 )*DTK41 ENTRX ( 1,4)*CTM6 EINV(2,4)=BNTRX(1,1 )*CTM3-BMTRX { 1»2)*DTN5+8NTRX ( 1 , 3 J 1*CTM6 eiNV(3,3)=BKTRX(l,l)*(BMTRX(2,2)*BMTRX(4,4)lBMTRX(2,4)**2)-eMTRX( 1 , 2 ) * ( 8MTR X { 1 , 2 ) *BMTRX ( 4 , 4 ) 2BMTRX ( 2 ,4 ) *BMTRX ( 1 , 4 ) ) +BMTRX { 1 , 4 ) * ( BMTRX { 1 , 2 ) * 3BNTRX{2»4)-BNTRX( 1 , 4 ) *BMTRX ( 2 , 2 ) ) BINV(3,4)=-BMTRX(1, 1)*(BMTRX(2,2)*BMTRX(3,4)1BMTRX(2,4 )*BMTRX (2, 2 ) )+BMTRX( 1,2)*(BMTRX (1,2)* 2BMTRX(3,4)-BMTRX(1,4)*8MTRX(2,3) )-BMTRX( 1,3)* 3 { BMT RX { 1, 2 ) *BMTRX ( 2 ,4 J-BMTRX ( 1 , 4 ) *BM TRX { 2 , 2 ) ) BINV(4,4) = RMTRX( 1, 1 ) * ( BMTRX ( 2 , 2 ) *8MTRX ( 3 , 3 ) ieRTRX(2, 3 )**2 ) — B MTR X ( 1,21*1 BMTRX ( 1 , 2 ) *BM TRX ( 3 , 3 ) 2 BMTRX ( 1 , 3 )*8MTRX (2, 3 ) ) +BMTRX ( 1 , 3 ) * { BMTRX ( 1 , 2 ) * 3BMTRX(2,3)-BNTRX< 1,3 )*8MTRX(2,2 ) ) E INV ( 2 i 1 ) =B I N V ( 1,2) BINV(3, 1 ) tB I NV ( 1,3) BINV(3,2)=BINV(2,3) BINV (4, 1 ) = B I N V ( 1,4) BINV (4, 2)=BINV( 2,4) EINV(4»2)=BINV(2,4) CC 800 1=1, N X VECT ( I )=0.C CO 8 C 0 J= 1 » N 80 0 XVECT ( I ) = X V EOT ( I ) + (EINV( I , J ) *ZV EC7 ( J ) /DTMNT ) CC 850 1=1, N 850 PARMT ( I ) = PARRT( I ) + XVECT ( I ) IF(A.BS( XVECT (1) )-0. 01)920,950 920 I F { A ES ( XVECT ( 2) )-0. 01)930, 950 9 30 IF ( ABS( XVECT ( 3) )-G.CC01 ) 1000,950 9 50 I L= I L+ 1 I F ( 1L— 35)975, 25C 975 GCTO 175 c* * C* LINES 201 THROUGH 220 CALCULATE A REACTION RATE * C * CONSTANT FROM THE RESLLT OF THE CURVE FIT OCNE * C* ABC VE ANC CUTPUT TFE RESULTS. * C* * 1CC0 V SUB E= F LC AT ( IRRAYl II) )/32764. EMSBR = FLCAT< IRRAY(4))/1C0. PRES S = FLC AT ( IRR AY ( 14) )* FLOAT! IRRAYl 5) ) / ( 327640CC. I CCNCF= l FLOAT ( IRR AY 12)1*10. **(-IRR AY <3)))/lC0. TMEAS = FLCAT ( IRRAYl 1 ) )/iCCC0. RLENT=I9.61 XKI = (7. 17*10. **(-14) ) *PARKT { 3 )*VSUBB/ ( TMEAS*CONCF* IEMSB REPRESS )

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0209 0210 0211 0212 0213 0214 0215 0216 0217 0218 0219 0220 0221 0222 $*** 90 XK2=( ( l.C26*10.**(-9) )*PARMT(3)*VSU8B**2)/(EMSBR* 1CCNCF*RL£NT*PRESS**2) IF(TNEAS) 1010,1010, 1020 1010 X K 1 = 0 . C 10 20 WRITE (7 , 1015 ) MM , PARRT ( 1 ) , P ARMT ( 2 ) , P ARMT ( 3 ) , XK1 , XK2 WRITE16, 1 0 1 5 ) M M , P A R K T ( 1 ) , P A R N T ( 2) ,PARMT (3) , XK1 ,XK2 1015 FORMAT (I4,3X,E12.5,3X,E12.5,3X,E12.5,3X,E1Q.3,3X, 1E10. 3) GOTO 1 2 C C WRITE(7,1C50)XK1,XK2 1 C 50 FORMAT ( 2E2C .4 ) 1200 CONTINUE END END $ LIST END ****

PAGE 101

91 and fits the specified ion signal of experiment 1 to the parametric form given in line 118. When convergence of the fit is obtained, the results are then combined with other experimental parameters stored in the data file and a reaction rate constant is calculated. The program then curve fits the remaining data and calculates corresponding rate constants for each experiment. B. Grid Search Technique The Jacobian matrix technique described in the previous section has one major disadvantage. Since it uses a Taylor series expansion to linearize the parametric equation with respect to the parameters P 1 , P and P , it is possible for the iterations performed in the program to diverge if the initial guesses for the parameters are too unreasonable. A more powerful technique (albeit slower) , which avoids this 53 difficulty, is a direct grid search procedure. Using this technique the equation y ± = P 1 ~ P 2 exp(-P^x^) (71) may be written y i = Af(C,xJ + B (85) where A = -P„, B = P . C = P and 2 1 3 f(C,x) = exp(-Cx) (86) In this form A and B are linear parameters and C is a non-linear <

PAGE 102

92 parameter. An estimate is then made of the initial value of the parameter C and a one-dimensional grid of step size AC constructed around this initial guess, C o » Once the initial estimate C Q is made, initial estimates for the parameters A and B may be found by a linear least squares curve fit of the experimental data to the equation The sum of the squares of the deviations for each grid point can then be calculated. If a minimum does not fall within the grid, then it is increased in size until a minimum is captured. The grid is then shifted to center on the minimum and reduced in size until the location (that is, values of A, B and C) of the minimum sum of the squares of the deviations is known. Each manipulation of the grid (expansion, contraction or shift) is accompanied by a new estimate of the linear parameters and the calculation of the sum of the squares of the deviations at each grid point. This technique may be easily extended to fit data with more than one non-linear parameter. When a metastable quenchant is added to the argon afterglow, the bromine system reduces to the equations y • = A f (C ,x. ) + B •'l o o’ i o ( 87 ) Br 2 + e t (Br )* + Br“ + Br ( 13 ) Br~ + Br + Ar Br" + Ar 2 3 ( 14 )

PAGE 103

93 The kinetics equation describing the Br ion behavior is then [Br ] = (k^/ (k^ k 1 )}[e"] o (exp(-k i [Br 2 ]t) expC-k^ [Br^] t) } (88) where k^ = k 2 [Ar]. In parametric form this may be written I = A{exp(-ax) exp(-bx)} + B (89) where B is the baseline and I is the Br ion signal. Listed on the following pages is a version of the direct grid search technique used to fit the Br signal to Equation 89 above. A sample curve fit result is shown in Figure 23. The open squares represent experimental data obtained in the study of the two reaction sequence listed above. The solid line is the curve fit result obtained by fitting the Br ion signal to Equation 89.

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94 C0C1 F TN4 , L 0002 PROGRAM 8RFIT CCC 3 £$*$$$*$$***£ 0004 C* * C005 C* PROGRAM ERF ITC TFIS PROGRAM USES THE DIRECT GRID * 0006 c* SEARCH TECHNIQUE TO FIT THE BRION SIGNAL TO AN * 0007 c* EQUATION OF THE FORM Y= A* ( EXP ( -AA*X J-EXP ( -BB*X ) ) +B . * 0008 c* RATE CONSTANTS FOR THE REACTIONS BR2 + E~ = BR+ * 0009 c* BR AND BR+ ER2 + M = BR3+ M ARE THUS OBTAINED. C010 c* SOURCE IS STCREC AS TIFRB. ATTACH GRIDA V.HEN * 0011 c* LOADING. * 0012 c* * 0013 c* * $ $ * $ £ £ $ $ 2 ^ $={t >)c #3j: £ $ :{c # $ >}: $ 0014 DIMENSION IRRAY ( 640 ) , IF I L E ( 3 ) 0015 COMMON N , X 0 8 S ( ICC) *YGBS( ICO) 0016 COMMON A » B 0017 EXTERNAL SURGE 0018 ** 0019 c* 0020 c* STATEMENTS 27 THROUGH 46 ALLOW THE OPERATOR TO * 0021 c $ CHOOSE THE CATA FILE, RUN NUMBER, PEAK NUMBER AND * 0022 c* TO DECIDE WHETHER TO CELETE THE FIRST FEW DATA $ 0023 c* POINTS . * 0024 c* * 0025 0026 ICNWC= 1C2B 0027 WR I T E ( 7 , 20 ) 0028 20 FORMATtlX, INPUT FILE NAME ) 0029 R EAD ( 7 , 30 ) ( I F I L E ( I) ,1 = 1,3) 0030 30 FORMAT ( 3 A 2 ) 0031 35 WR1TE(7,40) 0032 40 FORMAT ( IX, ENTER RUN NUMBER ) 0033 READ! 7, * )M 0034 WRITE(7,42) 0035 42 FORMAT ( IX , INPUT PTS AT LOW VOLT. END OF EXPT TO 0036 1CELETE ) 0037 READ! 7, * ) IDLTE 0038 N = 5*f/-4 0039 I RC D= 14 0040 CALL EXEC ( IRCD, ICNWC, IRRAY, 640, I F IL E , N ) 0041 WRITE(7,43) 0042 43 FORMAT ( IX , INPUT NUMBER OF STARTING DATA POINT ) 0043 READ(7,*)JJ 0044 WRITE! 7,45) 0045 45 FORMAT ( IX, INPUT PEAK TO BE FIT ) 0046 READ!7,*)JJJ 0047 IRRAY! 10 ) = IRRAY! 10 )IDLTE 0048 J = I R R AY { 10) 0049 CO 50 I=JJ,J 0050 K = 75+7* I + JJ J 0051 I I = I + 1-JJ 0052 YOBS! II)=FLCAT(IRRAY(K))*(10.**12)/(3276.4*(10.M*

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0053 005 A 0055 0056 0057 0058 0059 0060 0061 0062 0063 0064 0065 0066 0067 0068 0069 CC70 0071 0072 0073 0074 0075 G076 0077 0078 0079 0080 008 1 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 0095 0096 GC97 0098 0099 0100 Old 0102 0103 0104 95 5 0 1 ( I R R A Y ( 6 ) ) ) ) K=KJ J J + 1 XGBS( II )= FLOAT ( IR RAY (K-2) 1/3276.4 60 I RR A Y ( 10 ) = IRRAY ( 10J + 1-JJ WRITE(7,60) FORMAT ( IX, INPUT ESTIMATES FOR AA AND BB ) 65 READ(7,*)AA,8B KRITE(7,65) FORMAT ( IX, INPUT AASTP AND BBSTP ) READ ( 7 , * ) AASTP, EESTP N = I RRAY ( 10) C* * C* SUBROUTINE SERCH CONTROLS THE GRID CONSTRUCTED * C* AROUND THE NON-LINEAR PARAMETERS AA AND BB < THAT * C* IS, CONTROLS THE EXPANSION, CONTRACTION AND SHIFT * C* OF THIS GRID.) * C* * 0 ************$***£$ ’S-'#******^#*###***^**##:#* CALL SERCH (SUMDE, 1 . E13 , A ASTP , BBSTP , 0. ,AA,BB*0.,S) V\RITE(6,3)A,8,AA,B8,S WRITE(7,3)A,B»AA»BB,S 3 FORMAT ( 5 E 14 . 4 ) C* * C* LINES 83 THROUGH SC COMPUTE THE RATE CONSTANTS FROM * C* THE CURVE FIT PARAMETERS AA AND BB OBTAINED ABOVE * C* AND EXPERIMENTAL PARAMETERS STORED IN THE DATA FILE.* C* * $£***$**$$*$*£****$ *****$«****$$*=}:*$***$********:!'$*=!:* 1000 VSUBB=FLCAT( I RRAY( 1 1 ) 1/327 64. EMS BR = FLCAT (IRRAY(4))/1C0. PRESS=FLOAT( IRRAYI 14) )* FLOAT! IRRAYI5) )/( 32764000.) CCNC F= ( FLOAT (IRRAYI 2) )*10.**{-IRRAY( 3) ))/100. RLENT==19.61 XK1=( (1.01*10. **( — 9) )*AA*VSUBB**2 )/( EMSBR*CCNCF * 1RLENT*PRESS**2) XK2=BB*XK1/A A WRITE(6,1G50)XK1,XK2 VtRITE(7» 1050)XKl,XK2 1050 FORMAT ( 2E20.4) GOTO 35 END c* * C* FUNCTION SLMDE USES A LINEAR LEAST SQUARES * C* TECHNIQUE TO CALCULATE THE LINEAR PARAMETERS A AND * C* B AND THE SUM OF THE SQUARES OF THE DEVIATIONS AT * C* EACH GRID POINT. * C* * C***$*$*$**£**$**S***4 ***$*********** *#$**$*$**$****:$** FUNCTION SUMDE( A A,8B,DUMY)

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0105 0106 C 1 07 0108 0109 0110 0111 0112 0113 0114 0115 0116 0117 0118 0119 0120 0121 0122 0123 0124 0125 0126 0127 0128 **** 96 DIMENSION F X ( IOC ) COMMON N,XOeS(lCC),YCBS(100) COMMON A,B FN = N SUMX=0 . SUMX Y = C . SUMX2=0 . SUMY-O. CO ICO J=l,N F X ( J )=EXP {-AA*XCBS( J) )-EXP(-BB*XCBS( J) ) SUMX = SUM X+FX ( J ) SUMXY=,SIMXY + FX{ J )*YCBS( J ) SUMX2=SUMX2+FX( J )**2 ICO SUMY=SUMY+YCBS( J ) CET=FN*SUMX2-SUMX**2 A = ( FN*StMXY-SUMX*SUMY)/OET B=( SUMX2*SUMY-SUMXY*SUMX ) /DET SUMDE=G. CG 101 J= 1 » N CALC=A*FX ( J ) +B 1C1 SUMOEtSUMCE+(YGBS(J )-CALC ) **2 RETURN END ENDS LIST END ****

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C001 0002 0003 C0Q4 0005 0006 0007 C008 0009 0010 0011 0012 0013 0014 0015 0016 0017 0018 0019 C02C 0021 0022 0023 0024 0025 0026 0027 0028 0029 0030 0031 0032 0033 0034 0035 0036 0037 0038 0039 0040 0041 0042 0043 0044 0045 0046 0047 0048 0049 0050 0051 0052 97 F T N4 , L SUBROUTINE S ERC F ( FUNCM , STEP L I , X S TEP , YSTEP Z STEP , X , 1Y,Z, VALUMI ) C* * C* FUN CM IS TFE USER CODEC FUNCTION SUBROUTINE. MUST * C* BE DECLARED EXTERNAL IN THE MAIN PROGRAM. PUNCH * C* MUST HAVE THREE ARGUMENTS. IF THE FUNCTION HAS * C* LESS THAN THREE VARIABLES, DUMMY ARGUMENTS MUST * C* REPLACE THE INACTIVE ARGUMENTS. STEPLI IS A * C* PRE-DETERM INEC LOWER LIMIT FOR THE CESIRED ACCURACY * C* IN THE VARIABLES CN RETURN. XSTEP, YSTEP AND ZSTEP * C* ARE INITIAL STEP INCREMENTS OF THE VARIABLES. THE * C* MINIMUM SEARCH BECOMES INACTIVE IN A PARTICULAR * C* DIRECTION IF THE CORRESPONDING STEP INCREMENT IS * C* MACE ECUAL TO ZERC IN THE CALL STATEMENT. THESE * C* QUANTITIES CN RETURN EECOME THE FINAL ACCURACIES OF * C* THE VARIABLES. X, Y AND Z ARE THE INITIAL GUESS * C * VALUES FOR THE INDEPENDENT VARIABLES. IN RETURN * C* X, Y AND Z ARE THE VALUES OF THE VARIABLES AT THE * C* MINIMUM AND VALUMI IS THE VALUE OF THE FUNCTICN AT * C* THE MINIMUM. FI IS TFE FIRST FUNCTION VALUE ON * C* RETURN, ITERA IS THE TOTAL NUMBER OF ITERATIONS ON * C* RETURN, KFLAT IS RETURNED 1 IF AFTER 10 CONSECUTIVE * C* ITERATIONS THE FUNCTICN DID NOT CHANGE, MINE IS * C* RETURNED 1 IF TRUE MINIMUM WAS FOUND AND IF KSTGP * C* IS SET TO 1 OUTSIDE THE PROGRAM, THE MINIMIZATION * C* STCPS. * C* * £*%%%**%***%********$ t*********************************** DIMENSION XC(7),YD{7)»ZD(7) , VAL UEC ( 7 , 7 , 7 ) I TER A^O KST0P=0 NCENC=0 KP1 = C K P2 = 0 K P3 = 0 KFLAT=0 M I N I =0 M I N P E R = C KREP=0 J XF 1 =0 J YF 1 =0 J ZF 1 =0 J XFU = 0 JYFU-0 J ZFU =0 XSTEPF=C. YSTEPF=C. Z STE PF= C . 10C0 CONTINUE ABSX=ABS(X)

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G053 0054 0055 0056 0057 0058 0059 0060 0061 0062 0063 0064 0065 0066 0067 0068 0069 C07C 0071 0072 0073 0074 0075 0076 0077 C 07 8 0079 0080 0081 0082 0083 0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 0095 0096 0097 0098 0099 0100 0101 0102 0103 0104 98 A8SY = ABS ( Y ) A BS Z = AB $ (Z ) J XM = 4 JYM=4 J ZM = 4 IF(XSTEP+A8SX.NE.A8SX)XSTEPF=XSTEP IF(YSTEP+ABSY.NE.ABSY)YSTEPF=YSTEP IF(ZSTEP+ABSZ.NE.ABSZ)ZSTEPF=ZSTEP IFtKPl.NE.O )XSTEPF=XSTEPK IF(KP2.NE.0 )YSTEPF = YSTEPK IF(KP3.fsc.0 )ZSTEPF = ZSTEPK IF{XSTEP + ABSX.EG.A8SX«.ANC.YSTEP + ABSY.EQ.ABSY.AND. 1ZSTEP+ABSZ.EG.ABSZ)G0T0 1017 ITERA=ITERA+1 I F( XSTEP + ABSX. EC. ABSX )G0 TO 201 IF( YSTEF+ABSY.EC .A8SY )G0 TO 202 I F { ZSTEP + ABSZ.EG .ABSZ )GG TO 203 CC 301 J= 1 » 7 XD( J)=X4FL0AT!J-4)*XSTEP Y 0 ( J )=Y + FLCAT ( J 4 ) * Y S 1 E P ZD(J)=Z+FL0AT(J-4)*ZSTEP CC 302 JX = 1 » 7 X=XD ( JX ) CC 302 JY = 1 » 7 Y=YD ( JY ) CC 302 J Z= 1 1 7 Z=ZDl JZ ) VALUED(JX,JY,JZ ) =FUNCM ( X , Y , Z ) VALUEC=VALUEC(4»4f4 ) V ALUP I = V ALU EC ( 1, 1,1) I FL AT = 0 CC 304 J X= 1 * 7 DO 304 J Y = 1 t 7 CC 304 J Z= 1 , 7 IFIVALUPI.LT. VALUED! JX, JY, JZ) )GC TO 304 J XM= J X JYM= JY JZM=JZ I F( V ALUM. GT. VALUED! JX, JY,JZ> ) IFLAT = 0 IFLAT=IFLAT+1 IF! IFLAT.GT. 1)GC TO 303 JXF 1= JXF J YF 1 = J Y P J ZF 1 = J Z P X 1= X D ( J XP ) Y 1=YC ( JYP ) Z1=ZC( JZP) JXFU= JXP JYFU=JYP J ZFU = JZP XU=XC ( JXP ) YU=YC! JYP)

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0105 0106 0107 0108 0109 0110 0111 0112 0113 0114 0115 0116 0117 0118 0119 0120 0121 0122 0123 0124 0125 0126 0127 0128 0129 0130 0131 0132 0133 0134 0135 0136 0137 0138 0139 0140 0141 0142 0143 0144 0145 0146 0147 0148 0149 0150 0151 0152 0153 0154 0155 0156 ZU=ZC( jzn VALUN1=VALUEC(JX,JY,JZ) 304 CONTINUE X = XD( JXN ) Y = YD { JYN ) Z = ZO( JZP ) I F ( I FL A T . EQ . 1 ) GC TO 1001 X = . 5*( X 1 + XU ) Yt.5*(Y1+YU) Z=. 5* ( Zl + ZU ) GO TO 1CC1 2C1 JJ=1 A =Y B = Z ABSA=AESY AfiSB=ABSZ ASTEP-YSTEP ESTEP =. ZSTEP GO TO 2 C 4 202 J J = 2 A = X B = Z ABSAAESX ABS8=A6SZ A STE P=;X STEP B ST EP= ZSTEP GC TO 204 203 J J = 3 A = X B=Y ABSA= AESX AESB=A8SY ASTEP=;XSTEP B STE P = Y ST EP 204 I F ( ASTEP+ABSA.EG.ABSA)GO TO 104 IF( BSTEP + ABSB.EC .ABSB ) GO TO 101 CO 205 J = 1 1 7 XD(J)=A+FLCAT(J-4)*ASTEP 205 Y0( J )=B+FLGAT ( J— 4 )* ESTEP CG 206 JX = 1 » 7 A=XD( JX ) CG 206 JY=1,7 B=YD ( JY ) LF( JJ.EC. 1)VALUEC( JX, JY , 1)=FUNCB(X, A,B) I F ( J J. EC. 2) VALUED ( JX, JY,1 )=FUNCN(A, Y,B) 2 06 I F { J J.EQ.3) VALUED! JX, JY, 1)=FUNCB( A f 8*Z) V ALUEC=VALUEC (4 ,4, 1 ) VALUi v I = VALUED( 1 * 1 » 1 ) I FL AT = 0 CG 208 JX= 1 * 7 CO 208 J Y= 1 1 7 IF( VALUBI.LT. VALUEOtJX, JY,1) JGO TC 208

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0157 0158 0159 0160 0161 0162 0163 0164 0165 0166 0167 0168 0169 0170 0171 0172 0173 0174 0175 0176 0177 0178 0179 0180 0181 0182 0183 0184 0185 0186 0187 0188 0189 0190 0191 0192 0193 0194 0195 0196 0197 0198 0199 0200 0201 0202 0203 0204 0205 0206 0207 0208 J AN = J X J BN = J Y IF1VALUNI.GT .VALUED(JX,JY»1 ) ) I F L AT = 0 I FL AT= I FLAT + 1 I F ( IFLAT.GT. 1 )GC TO 207 J AF 1 = J AN JBF1=JBN A1 = XC< JAN ) B 1 = YC (JEN) 207 J AFU = J AN J BFU = J BN AU=XD( JAN) BU=Y0( JEN ) VALUNI=VALUED( JX, JY, 1) 208 CONTINUE GC TC ( 209,210,211) , JJ 209 JYN= JAN J ZN= J BN Y = XD ( JYN ) Z=YDl JZN) YSTEP^ASTEP ZSTEP=8STEP X ST E P = C . JYF1=JAF 1 JZF1 = JBF l JYFU= J AFU JZFU=JBFU I F ( I FLAT. EC. 1 ) GC TO 1001 Y=.5*( Al+AU) Z=.5*( Bl+BU ) GC TC 1001 210 J XM = J AN J ZM= J BN X=XO( JXN) Z=YD( JZN ) XSTEP=ASTEP ZSTEP=BSTEP YST E P = 0 . JXF1=JAF 1 JZF1=JBF1 JXFU= JAFU J ZFU = J B FU I F ( IFLAT .EQ. 1 )GC TO 1001 X =. 5*{ Al + AU) Z = . 5*( E 1 + BU ) GC TC 1CC1 211 J XN = J AN J YN = J BN X = XO( JXN ) Y=YD( JYN ) XSTEP=ASTEP YSTEP^BSTEP

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C209 0210 0211 0212 0213 0214 0215 0216 0217 0218 0219 0220 0221 0222 0223 0224 0223 0226 0227 0228 0229 0230 0231 0232 0233 0234 0235 0236 0237 0238 0239 0240 0241 0242 0243 0244 0245 024 6 0247 0248 0249 0250 0251 0252 0253 0254 0255 0256 0257 0258 0259 0260 Z STE P = 0 . JXF1=JAF1 JYF1=JBF1 J XFU = J A FU JYFU=JBFU I F ( IFLAT.EQ. 1 ) GC TO 1001 X=.5*(A1+AU) Y = . 5 * ( e 1 + 8U ) GC TC 1CC1 101 GC TC ( 103,102, 102) , JJ 102 A = X ABSA=ABSX ASTE P = X STEP J J J= 1 GC TC l C 6 103 A=Y A BS A = AB SY ASTEP=YSTEP J J J = 2 GC TC 1 C 6 104 GC TC ( 105,105, 1C3) , JJ 105 A = Z ABSA=ABSZ AST EP = ZST EP J J J = 3 106 CO 107 J= 1 » 7 107 XD( J )=A+FLCAT (J-4)*ASTEP DC 108 JX = 1 , 7 A =XD ( JX ) I F< JJJ. EC. 1 )VALUED( JX,1 ,1 ) =FUNCF ( A , Y , Z ) IF{ JJJ. EQ. 2) VALUED ( JX,1, 1 ) = FUNCIY ( X , A , Z ) 108 I F{ JJJ . EG. 3 )VALUED( JX, 1 , 1 ) = FUNCM ( X, Y , A ) VALUEC = VALUED{4, 1, 1 ) VALUE 1 I = VALUEC (1,1,1) 1 FL AT = 0 DC 110 JX=1 , 7 IF{VALUFI.LT.VALUED(JX,1,1) )GG TO 110 JAM= JX IF(VALUNI.GT.VALUED( JX, 1,1) ) I FLAT=0 IFLAT=I FLAT+1 IF ( I FLAT .GT . 1 )GC TO 1C9 JAF 1= J AF A 1= X D ( J A F ) 109 J AFU = J A F AU=XC ( J A F ) VALUFI=VALUEC(JX,1,1) 110 CONTINUE GC TC (111, 112, 113) ,JJJ 111 J XF= JAM X=XD ( JXF ) XSTEP=ASTEP Y ST E P = 0 .

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0261 0262 0263 0264 0265 0266 0267 0268 0269 0270 0271 0272 0273 0274 0275 0276 0277 027 e G279 028 0 0281 0282 0283 0284 0285 0286 0287 0288 0289 0290 0291 0292 0293 0294 0295 0296 0297 0298 0299 0300 0301 0302 0303 0304 0305 0306 0307 0308 0309 0310 0311 0312 102 Z STE P = C . J XF l = J A F 1 J XFU = JA FU I F { IFLAT.EQ. 1)GC TO 1001 X=. 5* ( Al + AU ) GO TO 1CCI 112 J Y M = J A M Y = XD( JYM ) YSTEP=ASTEP X ST E P = 0 . ZSTEP=0. JYF1=JAF1 JYFU= JAFU I F { IFLAT.EQ. 1 ) GO TO 1001 Y = .5=MA1 + AU ) GO TC 1C01 113 JZM= J AM Z=XD { JZM ) ZSTEP=ASTEP XSTEP = G . Y ST E P = G . JZF1=JAF1 JZFU=JAFU I F ( I FLAT .EQ. 1 )GC TO 1001 Z=.5*( A14AU ) GO TC ICC! 1001 I F ( ITERA.EQ.1)F1=VALUEC IFIVALUMI.LT. VALUECIGO TC 1CC3 I F ( I FLAT .GT . 1 ) GO TO 1006 I F { KSTCF.EQ. 1)GC TO 1017 1002 XSTEP=. 5*XSTEP YSTEP=.5*YSTEP ZSTEP=.5*ZSTEP M IN I = 1 KPREP=0 I F ( XSTEP.GT.STEPLI.CR.YSTEP.GT.STEPLI.OR.ZSTEP.GT. 1 STEPL I ) GOTO 1016 GO TC 1017 1003 K P 1 = 0 K P2 = 0 KP3 = C I F { JXM. EG. l.OR. JXM.EQ.7 .OR. JYM.EQ.l.OR. JYM.EQ.7.0R. 1JZM.E0.1.0R.JZM.EQ.7)G0T0 1004 GO TC 1 C 1 6 1004 M INP ER= 1 KREP=KREP+1 IFIKREP.GT. 1 )G0 TG 1005 J XM 1 = JXM JYM1= JYM JZMI^JZM GO TC 1 C 16 1C 05 I F ( JXM1.EC.JXM.AND. JYM1.EC. JYM. AND. JZM1.EC. JZM) GOTO

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0313 0314 0315 0316 0317 0318 0319 0320 0321 0322 0323 0324 0325 0326 0327 0328 0329 0330 0331 0332 0333 C334 0335 0336 0337 0338 0339 0340 0341 0342 0343 0344 0345 0346 0347 0348 0349 0350 0351 0352 0353 $ $$ 5 != 103 11008 KREP=0 GC TC 1016 1CC6 I F ( M IN I . EQ . I ) GO TO 1C10 I F ( MINPER.EG.l ) GC TC 1007 XSTEPF=XSTEP YSTEPF=YSTEP ZSTEPF=ZSTEP KFLAT=KFLAT+1 IF(KFLAT.EQ.10)GC TC 1017 1007 KREP=KREP+1 1008 I F ( JXF1.EQ. 1«CR«JXFL.EQ. 7. OR.JYFl.Ea. l.CR.JYFU.EQ. 1 7 . OR « J Z F 1 . EG • 1 . OR • J ZFU • EQ • 7 ) GOTO 1009 y in i = i GC TC 1 C 1 6 10C9 FKREP=KREP I Ft JXF1 .EG. l.GR . JXFU.EQ.7)XSTEP=XSTEP*FKREP IF(JYF1.EC.1.GR.JYFU.EQ.7)YSTEP=FSTEP*FKREP IFUZF1.EC. l.GR. JZFl,EQ.7)ZSTEP = ZSTEP*FKREP GC TC 1 C 1 6 1010 I F ( JXFl.EQ.l.AN0.JXFU.EG.7)GG TO 1013 1011 I F { JYF1 .EG. l.ANC.JYFU.E0.7)GC TO 1014 1012 IF( JZF1.EG. l.AND.JZF0.EG.7)GG TO 1015 GO TC 1 C C 2 1013 KP1=KP1+1 I Ft KP1. EG. 1 ) XST EPK = XSTEP IF(KP1.EC.3)XSTEP=0. GC TC 1 C 1 1 1014 KP2=KP24l IFtKP2.EC. 1 ) YSTEPK = YSTEP IF(KP2.EG.3)YSTEP= r 0. GC TC 1 C 1 2 1015 KP3 = KP3+ 1 IF(KP3.EC.1)ZSTEPK=ZSTEP IF(KP3.EG.3)ZSTEP=0. GC TC 1 CC2 1016 GO TC 1CC0 1 C 1 7 IFtXSTEPF.GT.C. )XSTEP = XSTEPF IFtYSTEPF.GT.O. )YSTEP = YSTEPF IFtZSTEPF.GT.O. )ZSTEP = ZSTEPF RETURN LIST END ****

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10 A

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CHAPTER V EXPERIMENTAL RESULTS As previously mentioned, experiments using the flowing afterglow apparatus with both a microwave discharge source and a filament source have been carried out. Thus, the experimental results will be presented under these two headings. The rate constants measured in the present experiments are summarized in Table 5 at the end of this chapter. A. Microwave Discharge Source 1. Electron Energy Several authors have shown that electrons are rapidly 2 5 thermalized in a flowing afterglow environment. * An approach to the problem, given in Appendix III, indicates that the electrons should indeed be rapidly thermalized, under the present experimental conditions, by the time (1-3 msec) they reach the reactant gas injection port from their source in the microwave discharge. The only experimental procedure used to actually estimate electron temperatures in the flowing afterglow was based on the measurement of the ratio of SF^ to SF7 ion currents when SF, was injected at the neutral reactant o 6 port. This ratio has been shown by other investigators to 105

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106 2 3 5 be strongly dependent on electron energy. ’ * The results of the present measurements are illustrated by Figure 24. Since the ratio, SF~/SF~, is known to be independent of pressure 5 6 in the pressure regime of Figure 24, the variable ratio observed must reflect changes in electron energy in the reaction tube as the pressure is varied. The energy variation observed is probably a result of the change in experimental conditions influenced by flow tube pressure. These conditions include electron collision frequency, electron diffusion losses, buffer gas axial velocity and the microwave discharge coupling efficiency. In any event the SF7/SFT ratios measured here indicate an 5 b average electron temperature of approximately 400°K or 600°K depending on whether the ratios are compared to the data of c 2 Chen and Chantry or Fehsenfeld, respectively. 2. Electron Attachment in Sulfur Hexafluoride In order to determine whether attachment rates measured with the flowing afterglow system in the microwave source configuration are reliable, the total attachment rate of electrons to sulfur hexafluoride was measured. This reaction has previously been studied by several investigators,^ ^ including Fehsenfeld^ —7 3 who reported an attachment rate constant of 2.1 x 10 cm J / molecule-sec measured in a flowing afterglow with helium buffer gas at a temperature of 289°K. The total attachment rate for this reaction was found by Fehsenfeld to be constant over a range of several hundred degrees.

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107 CD CM to CM UJ DC CO O (/) W £ CL UJ CO h5 O
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108 The rate for the attachment reaction is so large that 100% SF^ cannot be injected into the afterglow without quenching it, that is, immediately attaching all free electrons. Thus, mixtures of SF^ with argon, which were in the concentration range 0.1 to 0.001% SF^, were used in these experiments. In the experiments utilizing the microwave discharge source the total product ion signal (the sum of SF“ and SF”) o • 5 was monitored as a function of the sulfur hexafluoride flow into the afterglow. The resulting data, listed in Appendix IV, were reduced using the filament flow model derived in Chapter III Section B. The average value obtained for the total attachment —8 3 rate constant for SF, was 4.2 ± 1.1 x 10 cm /molecule-sec. b In order to make accurate kinetic measurements in a flowing afterglow system, downstream sources of electrons must be removed in order to ensure that all electrons in the flow tube have the same time to react with the injected gas; that is, no electrons should be produced downstream of the reactant gas injection port. One possible source of electrons in the reaction tube is Penning ionization which can occur with rare gas metastable atoms. In the case of argon metastables, this reaction Ar m + X -* Ar + X+ + e” (90) is possible if the ionization potential of X is less than the energy of the argon metastable. This is not a problem in the SF^ + e~ reaction studies since the energies of the argon metastables, 11.54 and 11.72 eV,^ are less than the ionization potential of sulfur 55 hexafluoride, 16.15 eV.

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109 Another possible mechanism for the production of electrons Cf. C *7 by metastables has been suggested by Biondi. * The reaction Ar m + Ar m -* Ar + Ar + + e" (91) is energetically possible since IP(Ar) < 2E(Ar m ). Because of the possibility of this metastable-metastable reaction, experiments were conducted in which nitrogen was injected into the afterglow, upstream of the reaction tube. The added nitrogen removes metastables by the reaction Ar ( 3 P„) + N (X X Z ) -*• N (C 3 ir ) + Ar^S) (92) 2 2 g 2 u o followed by radiative emission of the excited nitrogen product (C 3 ir B 3 n ) . The rate of this quenching reaction has been O measured and found to be high (0.3 x 10""^® cm 3 /molecule-sec) . Thus, the injection of even a few millitorr of nitrogen into the afterglow should deplete the metastable concentration by several orders of magnitude before the reactant gas is injected. The data listed in Appendix IV include experiments in which nitrogen was injected as a metastable quenchant. Considering the scatter in the data, there is no significant difference in the average electron attachment rate constant calculated —8 from experiments using the quenchant (k = 4.6 ± 1.3 x 10 cnr/molecule-sec) and that obtained from experiments not using ~*8 3 the quenchant (k= 3.9 ± 0.9 x 10 cnr/molecule-sec) . Thus, it does not appear that the metastable-metastable reaction is an important source of electrons in the present experiments.

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110 3. Electron Attachment In Fluorine As previously stated, fluorine and electrons undergo a dissociative attachment reaction to form a negative ion and an atom e" + F t (F“)* + F“ + F (4) The experimental data obtained in the study of this reaction are listed in Appendix IV. The data were reduced to rate constants using the filament flow model derived in Chapter III Section B. The average value obtained for the bimolecular rate constant for the dissociative attachment of electrons to fluorine in a series of seven measurements is 4.6 ± —9 3 1.2 x 10 cm /molecule-sec. A 0.065% fluorine in argon gas mixture was injected into the afterglow in order to determine the dissociative electron attachment reaction rate for fluorine. The mixture was specified to be nominally 0.1% fluorine by the manufacturer. An analysis to determine more accurately the fluorine concentration was carried out as described in Appendix I. Q Since the ionization potential of fluorine, 16.6 eV, is greater than the energy of the argon metastable. Penning ionization is not expected to be a downstream source of electrons. In order to show that metastables were not interfering with the measurement of the fluorine electron attachment rate through some other mechanism, the following simple experiment was

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Ill devised. A constant flow of fluorine was injected into the reaction tube and the resulting F ion signal was continuously monitored as a function of the partial pressure of the metastable quenchant, nitrogen, injected upstream into the afterglow. If the metastables constitute an important downstream source of electrons, then the injection of nitrogen upstream from the reaction tube should drastically reduce the F ion signal by removing metastables at a rate k = 0.3 x 10 -10 cm 3 /molecule-sec as discussed previously. Figure 25 is a log plot of the resulting F ion signal versus the partial pressure of nitrogen. It is seen that the F ion signal decreases at a rate corresponding A 3 to k 10 cnr /molecule-sec, approximately four orders of magnitude smaller than the quenching rate of the metastables by nitrogen. Thus, it does not appear that argon metastables interfere with the measurement of the fluorine electron attachment rate. 4. Sulfur Hexafluoride Oxygen Negative Ion Charge Transfer In the process of checking out the flowing afterglow system, the rate of the charge transfer reaction SF 6 + 0 -+ SF+ 0 2 (10) was measured. The rate coefficient for this reaction was determined by Fehsenfeld^ in a flowing afterglow system to be 7 x 10 cm /molecule-sec. This charge transfer reaction is particularly suitable for checking out a flowing afterglow system since the rate is so slow that pure sulfur hexafluoride

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"ION SIGNAL (arbitrary units) 112 N 2 PRESSURE (millitorr) Figure 25. F Ion Signal Versus the Partial Pressure of an Argon Metastable Atom Quenchant, Nitrogen, Injected into the Afterglow

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113 may be injected into the afterglow in order to study the reaction. Thus, this eliminates errors in making reactant/diluent mixtures. In addition, the reaction rate has been previously measured in a similar flowing afterglow system. In making these measurements, helium was used as the buffer gas and oxygen was injected into the afterglow both to remove helium metastables and to produce 0~ ions. The helium metastables were removed by Penning ionization He m + 0 2 -* He + 0+ + e" (93) C >2 ions were then formed by the attachment of electrons to oxygen 0 2 + e t (ID Sulfur hexafluoride was injected into the afterglow downstream from the oxygen inlet port and the decay of the 0~ ion signal was monitored as a function of the SF, flow rate as determined D by a linear mass flowmeter. The data obtained are listed in Appendix IV. Using the filament flow model derived in Chapter III Section B, the data listed in Appendix IV yield an average rate constant of 3.7 ± 0.4 x 10 '*' 1 cm'Vmolecule-sec , indicating better than a factor of two agreement with the Fehsenfeld result. In one experiment, illustrated in Figure 26, both the 0 and SF ion signals were monitored as the SF, flow Z o 6 rate was varied. The solid lines are the least squares curve fit results. The rate constants obtained from the SF and 0”

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114

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115 ion signals were 3.1 x lCT 11 cm 3 /molecule-sec and 3.8 x 10 -11 cm 3 /molecule-sec , respectively. The agreement between the two values indicates the feasibility of obtaining rate constants from the appearance of ion signals. A Cl ion signal was observed in the afterglow in the charge transfer experiments. The Cl" originates from a residual impurity in the afterglow. Since Cl has a higher electron affinity than SF^, it should not undergo charge transfer with the molecule and the Cl signal should remain constant throughout the experiment provided that sampling conditions are constant. This is precisely what was observed as shown in the data listed in Appendix IV. B. Filament Source 1. Electron Energy When sulfur hexafluoride was injected into the flowing afterglow apparatus in the filament source configuration, the SF” signal levels were so low that they could not be extracted from the noise (^5 mV) . Even for experiments in which the system sensitivity was fairly high (^5 volts SF“ signal) , no SF“ signal could be observed. Therefore, it is assumed that the SF~/SF“ ratio is on the order of 10 -5 . This corresponds to an average electron energy of 300°K or 350°K depending on whether this ratio is compared to the data of Chen and Chantry 5 or Fehsenfeld, 2 respectively. Since the flow time between the filament source and the reactant gas injection

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116 port is on the order of 1-3 msec, the calculations in Appendix III are still applicable. These calculations indicate a rapid * thermalization of electrons in a high pressure flowing afterglow. The lower electron energy estimate for the filament source configuration compared to the microwave source configuration is not unreasonable since a microwave discharge results in a greater heating of the buffer gas with which the electrons 48 are in thermodynamic equilibrium. In addition, the incidence of superelastic collisions between electrons and metastable atoms, which tend to increase the average electron energy, is greater in a microwave discharge afterglow due to the 58 higher metastable atom densities. 2. Electron Attachment in Sulfur Hexafluoride A series of nineteen determinations of the rate of attachment of thermal electrons to sulfur hexafluoride were made using the flowing afterglow system in the filament source configuration. These data are summarized in Appendix IV. The average value _ q q obtained for the rate constant, k, was 3.8 ± 1.8 x 10 cm'/ molecule-sec using the reaction tube transit times calculated from the measured buffer gas flows assuming a parabolic radial velocity profile and 3.5 ± 1.7 x 10 ® cm^/molecule-sec using the reaction tube transit times measured by the probe technique described in Chapter III Section B. It has been shown that flowing afterglows with a filament source have a lower metastable atom density than those with a microwave discharge source.

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117 Therefore, no experiments were done in which a metastable quenchant was injected into the afterglow since the experiments with a microwave discharge source configuration indicated that argon metastable atoms were not a significant downstream source of electrons. 3. Electron Attachment in Fluorine The study of dissociative electron attachment in fluorine, using the filament source, yielded a rate constant, k, of -9 3 3.1 ± 1.2 x 10 cm /molecule-sec using the reaction tube transit times calculated from the measured buffer gas flows assuming a parabolic radial velocity profile and 3.1 ± 1.2 x l(f 9 cm 3 / molecule-sec using reaction tube transit times measured by the probe technique discussed in Chapter III Section B. The experimental data obtained in the study of this reaction are listed in Appendix IV. A sample of the data obtained in the study of electron attachment in fluorine with the flowing afterglow system in the filament source configuration is shown in Figure 22. 4. Electron Attachment in Chlorine The dissociative attachment rate of electrons in chlorine was measured in the flowing afterglow using the filament source. Both the Cl (m/e = 35) and the Cl (m/e = 37) isotopes were monitored in these experiments. The rate constants obtained for the dissociative attachment of electrons in chlorine were

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118 3.7 ± 1.8 x 10“ 9 cm^/molecule-sec for the Cl (m/e = 35) isotope and 3.7 ± 1.7 x 10 9 cm^/molecule-sec for the Cl (m/e = 37) isotope. The data obtained are listed in Appendix IV. Figure 27 illustrates the results of a typical chlorine experiment. The solid lines are least squares fits for this experiment. 5. Electron Attachment in Oxygen Upon the injection of oxygen into the flowing afterglow reaction tube, 0^ was formed by the attachment process °2 0 2 + e" t (0 2 )* * 0“ (11) A plot of the 0” ion signal versus the oxygen partial pressure in the reaction tube is shown in Figure 28. The solid line represents a hand drawn curve fit. Reduction of these data to a rate constant yields k = 2.2 x lO ^ cm^/molecule^-sec. The reaction 0 2 + e“ + 0" + 0 (94) 59 has a threshold of approximately 3 eV. Since only a very small 0“ signal (two orders of magnitude less than the 0~ signal) was observed when oxygen was injected into the reaction tube in the present experiments, it is assumed that the electron energy distribution contains no significant high energy tail. The 0~ signal observed may be due to the diffusion of very small amounts of oxygen upstream to the filament region where electron energies greater than 3 eV occur.

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119 v c •H M O rCM 0) >-< s 00 i-t CHLORINE FLOW (XIO° molecules/sec)

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120 o E w cc Z) V) c n LU cc D. OJ o Figure 28. Electron Attachment in Oxygen

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121 6. Electron Attachment in Bromine The study of electron attachment in bromine is complicated by the occurence of three reactions when bromine is injected into the afterglow e" + Br 2 t (Br~)* -> Br~ + Br (13) Ar m + Br 2 -* Br+ + Ar + e (95) Br~ + Br. + Ar ->• Br" + Ar (14) 2 3 The injection of a metastable quenchant, such as nitrogen, into the afterglow eliminates the need to consider the Penning ionization process. The data observed in experiments then depend on the two reactions shown as Equations 13 and 14. The study of the bromine-electron reaction system, shown above as Equations 13 and 14, was performed in three steps 1. the injection of high concentrations of bromine so that only the second reaction need be considered in the reduction of data, 2. the injection of dilute bromine such that only the electron attachment reaction is important and 3. the injection of intermediate concentrations of bromine and reducing the data assuming both reactions to be important. The techniques above apply to the case where k^, the attachment rate constant, is on the order of k 2 [Ar], the pseudo secondorder rate constant for Equation 14 (hereafter known as kp .

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122 Figure 29 illustrates the data obtained using the technique of step 1. The solid line represents the least squares curve fit obtained for the Br signal. The rate of bromine injection was so rapid that only the reaction Br" + Br 2 + Ar -*• Br~ + Ar (14) was observed. The average rate constant k', determined from the observation of the Br" signal, is 1.2 ± 0.3 x 10 -11 cm 3 / molecule-sec. The observation of Br“ in one experiment yielded a rate constant k 2 equal to 0.48 x 10 -11 cm 3 /molecule-sec. The Br^ ion was at the upper mass limit for the mass spectrometer used in the present experiments. Observation of this signal was difficult and inaccurate. Figure 30 illustrates the technique for which the bromine injection rate was so small that only the reaction Br 2 + e~ t (Br“)* + Br + Br (13) need be considered. The solid line represents the least squares curve fit obtained for the Br” signal. The average rate constant, k^, obtained for these experiments is 1.0 ± 0.9 x 10 -*--*cm-V molecule-sec. Figure 23 illustrates the data obtained for which both the electron attachment reaction and the Br“ formation reaction were important. In these experiments the average rate constants obtained were 1.5 ± 1.2 x 10 -11 cm 3 /molecule-sec for k^ and

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123 io N; O in o o N; 6 m ro o 60 •H BROMINE FLOW (XIO mo!ecu!es/feec)

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124 01 c ft B o M « C m 0) M 2 to ft pt, BROMINE FLOW (X ld 7 molecules/sec)

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125 1.4 ± 0.8 x 10~H cm^/molecule-sec for k^. The solid line is the least squares curve fit obtained for the Br~ signal. The average value obtained for in all of the experiments was 1.1 ± 0.9 x 10 cm /molecule-sec. The average value — 11 1 for k 2 was found to be 1.2 ± 0.6 x 10 X ' L cni /molecule-sec . Since all of the experiments were done with the buffer gas pressure at approximately 2 Torr, the average rate constant, k', when converted to a third order rate constant, k 2> yields a value for k 2 of 1.9 ± 1.0 x 10“^ cm^/molecule^-sec.

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Rate Constants Determined in the Present Experiments 126

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127 -a TJ 3 u a d d d 0) a 0 0 *H rH 0) vi p 0 0 0 'w' 0 0 M V-/ VI 0 O CO o 0 3 rQ •H 3 a 0 0 a) os B 0 0 0) 0) 3 0 xd vi CO 0 P rH d d VI rH VI iH 0 0 a 0 0 •H •H cO 0 d rP i •H *H > a a tH •x) > Vi 3 p a T) 0 0 "d a) O 0 o 0 0 Vi Vi (1) Vi 0 HH d r0 O u B 00 XI Xd B O 00 tH 0 P rO M 0 Vi vi 0 a) •H 0 0 H rC Xd ai -h u co 3 r0 O P 0 00 00 vi d 0 O Vi £ CO o a > •H •H d 0 > X3 CO rH •H 0 Xd rd •h a 0 VI 0 P xd •H 0 vi a 0 Dr -H CO 0 ai ja 4J 0 u P P VI VI VI u u s 0 rH 0 0 0 d d d 0 X 0 -H 0 0 0 0) co a 0 tc! vi o\ CM ON m CM 0 CJ X3 0 d • • • • • • 1 0 3 o rH O 0 rH rH 4h 3 0 a O 3 40 -H +1 +1 +1 +1 +1 +1 Vi 1 Vi m 03 xd O 3 o in rH 04 CM ON VI VI O CV • • • • • • • •H -0X rH rH rH tH 0 CM rH d 3 3 3 xd m VI H rH d rH M •H XI 3 3 <3 d H 3 3 3 Vi + Vi VI O 3 d 3 HH 1 CO 3 Vi u H 03 bO 3 04 CQ m VI >4 CL 0 d X a 0 + t 3 O 3 m VI VI CO 1 M 03 O 1 u <3 d vj d 0 PQ 0 0 0 + O VI H CO t d VI CM 3 3 3 X) CM Vi VI | 3 d J-i PQ 3 x: rH 3 CQ n 0 3 + 3 T3 + rH VI 3 3 1 rH VI Xd 0) 1 Vi <3 3 H 3 0 « 3 XJ

PAGE 138

CHAPTER VI DISCUSSION OF RESULTS A. Comparison with Published Data Table 6 compares the average rate constants obtained for reactions studied in the present research with those published or extrapolated (EXT) from data publisned in chemical literature. The rate constants presented in Table 6 are in units of cm 3 / molecule-sec except those for three-body electron attachment to oxygen and the three-body Br~ formation, the rates for f) o which are in units of cm /molecule -sec. The electron temperature in the flowing afterglow was estimated in Chapter V to be in the range 300-600°K. The first three reactions listed were investigated in order to determine whether rate constants measured in the present flowing afterglow apparatus are reliable. The rate constant measured for the attachment of electrons in sulfur hexafluoride is approximately a factor of six smaller than the rate constant measured by Fehsenfeld in a flowing afterglow apparatus and by other researchers using various techniques. Thus, it appears that rate constants for electron attachment measured in the present experiments may be low by this factor of six. As discussed in Chapter III Section F, the major reason for 128

PAGE 139

Comparison of the Present Results with Published Data 129 a o o cd 0)
PAGE 140

130 o mo to rO 3 M H o\ CM I O iH X on CM oo CM I o fH X O • rl +1 CT\ M <3 + CM U 1 CO PQ u m + + 1 CO M M PQ <3 + + CM CM M pq PQ CM + + I I U M

PAGE 141

131 this low rate constant is probably the change in the electron diffusion rate as negative ions are formed in the afterglow. The measurement of the three-body attachment of electrons to oxygen yielded a rate constant in agreement with the data published by Pack and Phelps. The SF^/O" charge transfer reaction studied yielded a rate constant within a factor of n £ two of the Fehsenfeld result. Thus, it appears that the flowing afterglow apparatus used in the present experiments yields electron attachment rate constants within a factor of six and charge transfer rates within a factor of two. As was discussed in Chapter I Section B no electron attachment rate data have been published for fluorine. The present results represent the first measurement of this rate constant. Attachment to chlorine for thermal electrons has been qualitatively observed by Dunkin et al. ^~* to be large. The present experiments certainly agree with that observation. The rate constant measured is larger than the estimates extrapolated 11 12 from the data of Bradbury and Bailey and Healey. This is probably due to poor estimates of the mean free path at thermal energies of electrons in the gases used in their experiments. The value of the mean free path is necessary in order to convert measured attachment probabilities to rate constants. The thermal electron attachment rate measured for bromine agrees well with the value extrapolated from the data of 2 Q Bailey et al. The rate constant obtained in the present experiments is a factor of thirteen larger than that obtained by Truby^ in a static afterglow experiment.

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132 The rate of the three-body formation of Br~ in which argon is the third body has not been reported. This rate may be compared to that measured by Truby^ for Br~ formation in which bromine is the third body. B. Significance of the Results Dissociative electron attachment is currently being investigated due to the application of this technique to the development of chemical laser systems. For example, in the HF chemical laser F atoms react with hydrogen to yield vibrationally excited HF F + H 2 > H + HF (v « 2,3) (96) which produces the population inversion necessary for lasing. ^ Current research has focused on efficient mechanisms for the production of F atoms necessary to initiate this reaction. Electron beam techniques are currently being used to dissociate fluorine (and other fluorine atom containing compounds) in order to produce the required F atom concentrations. In the process some of the fluorine is ionized, producing electrons, and those electrons and electrons from the primary beam may be thermalized in the relatively high pressures used in the laser systems. These electrons can then rapidly attach to fluorine to produce F atoms at a rate measured in the current research. Thus, it is now possible for laser engineers to estimate the importance of dissociative electron attachment in fluorine in the operation of an HF chemical laser system.

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133 In addition, the importance of the dissociative attachment of thermal electrons in chlorine in the HC1 chemical laser £ O system may be estimated. No previous data for the thermal attachment of electrons to chlorine have been reported. The measurement of the rate of dissociative attachment of thermal electrons in bromine confirms the previously reported fact that the rate of this reaction is much slower than that for chlorine, fluorine or iodine. Thus, the application of this technique as a source of bromine atoms in an HBr laser is not expected to be feasible. C. Assumptions Made in the Derivation of the Mathematical Model Several assumptions were made in the derivation of the mathematical models used to reduce the experimental data, obtained in this research, to rate constants. Further comment concerning the accuracy of these assumptions is certainly in order. It was assumed that electrons, ions and buffer gas should move down the reaction tube at the same rate in the high pressures present in the flow tube. Figure 21 shows this assumption to be true for ions and buffer gas in the flow tube. The determination of the electron temperature in the reaction tube yielded values on the order of 300-600°K which indicates that the electrons are not being accelerated down the flow tube by small electric fields present in the tube. In addition. <

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134 in the high pressure environment in the reaction tube the electrons should suffer many collisions with the buffer gas and move down the flow tube at the same rate. In view of the standard deviations (30-90%) obtained for rate constant measurements presented in this research, the neglect of inlet effects is probably justified since corrections for this effect would change the rate constants obtained by . 48 only about 20% (1.62k ->\L.32k ) at most. Thus, no corrections s s for inlet effects were made. The change in the electron diffusion rate as negative ions are formed in the afterglow is probably the major reason for the low rate constant obtained in the present research for the attachment of electrons in sulfur hexafluoride. The only way to correct for this effect is to include this phenomenon in the transport equation for electrons in the reaction tube and to reduce the experimental data using numerical techniques. D. Suggestions for Modifications of the Flowing Afterglow Apparatus and Further Research There are several modifications of the flowing afterglow apparatus which could be made in order to improve the performance of the system. In the present design, fluctuations in the ion signals obtained may in part be due to the charging of surfaces in the flow tube, particularly the cone on which the ion sampling orifice is located. The present system configuration does not allow the cone to be easily removed

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135 for cleaning since both the electrostatic lens system and the flow tube are attached to the same flange as the cone. In addition, in the present experimental configuration the buffer gas is not pumped smoothly over the cone but at a somewhat oblique angle to the orifice axis. This may prevent the sampling from being viscous and make the ion signal behavior versus reactant gas flow somewhat dependent on potentials applied to the sampling orifice. The flow tube should be redesigned such that the ion sampling is truly a viscous process. Another source of signal fluctuations in the present experiments may be charged surfaces present on the lens elements between the sampling orifice and the quadrupole. Most of these lens elements could be eliminated and the distance between the sampling orifice and the quadrupole shortened considerably. This would eliminate many unnecessary lens elements and should improve the transmission of the lens system. One problem also noted in the present research was the diffusion of reactant gas from the dead volume between the injection port and the reactant gas leak valve. This appeared to be significant at small reactant gas flow rates and probably caused the relatively large baseline observed in the chlorine and bromine experiments. One solution to the problem would be to maintain a constant carrier gas flow through the dead volume. This would constantly flush the reactant gas line. There are many interesting research topics which can be pursued with the flowing afterglow apparatus. There is at

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136 present a continuing interest in the measurement of the rate of thermal electron attachment to molecules containing halogen atoms and the possible applications of these measurements in the development of chemical lasers. In addition, during the course of the present research halogen-negative ion reactions such as C *2 + Br^ ** Br + products (97) were observed. Many reactions of this type are energetically possible and represent an area of halogen negative ion chemistry still unexplored.

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APPENDIX I ANALYSIS OF THE FLUORINE/ ARGON MIXTURE The fluorine/argon mixture obtained from Matheson Gas Products was specified to contain approximately 0.1% fluorine. In order to minimize errors in the determination of the rate of dissociative electron attachment, an analysis of the fluorine/ argon mixture was made. The technique employed to determine fluorine was a wet chemical procedure in which fluorine is precipitated as triphenyltin fluoride. ^ The fluorine/argon mixture was bubbled through a 0.025 M solution of sodium hydroxide at the rate of about 0.8 atm-cnP/sec (1 bubble/sec) for a total of 64 hours. The fluorine reacts with water to form HF and ozone. The HF is then neutralized by the NaOH, resulting in a sodium fluoride solution. The flow of the mixture was monitored continuously with the reactant gas linear mass flowmeter and the flow rate versus time was r 4 recorded on a strip chart recorder. Integration of the resulting data indicated that the fluorine content was extracted from 3.743 x 10^ atm-cm^ of the mixture. The resulting sodium fluoride solution was then diluted to 200 ml. in a volumetric flask, and 25 ml. aliquots of this solution were analyzed by precipitating the fluorine as triphenyltin fluoride. The precipitate was 137

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138 then filtered with a 0.45 micron miilipore filter and weighed. The basis for this technique is that triphenyltin fluoride is highly insoluble in ethanol and water. Triphenyltin chloride is the precipitating reagent and is soluble in a 60-70% ethanol/ water solution. Thus, a solution of triphenyltin chloride is added to a solution of sodium fluoride to precipitate triphenyltin fluoride, which can be filtered, dried at 110°C, and weighed. The average weight of triphenyltin fluoride obtained from the aliquots analyzed was 0.1002 ± 0.0045 gram. Upon application of the appropriate factor (0.05153) to convert from triphenyltin fluoride to fluoride, the average per cent fluorine by volume in the fluorine/argon mixture was found to be 0.065 ± 0.003%. Therefore, the assumption that the nominal value given by Matheson (0.1%) was correct would have resulted in an error of about 50% in the attachment rate coefficient determined.

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APPENDIX II ELECTROSTATIC LENS SYSTEM The electrostatic lens system used to focus ions from the flowing afterglow reaction tube into the quadrupole mass spectrometer system is shown in Figure 31. The lens system was designed from published guidelines for electron optics. ^ Cylindrical lens elements are mounted on sapphire rods, and potentials are applied to them to produce fields (labeled lens #1, lens //2 and lens #3), between the lens elements, which focus the ions. Figure 31 illustrates that there are four cylindrical lens elements (separated by spacers) at different potentials. The actual lenses are the electrostatic fields between these lens elements. The eight-inch flange on which three of the lens elements are mounted is also a cylindrical lens elements. The sampling cone is also mounted on the eight-inch flange. Since the flange and cone form one lens element in the system, they are isolated from the vacuum housing by using a Teflon ring seal and nylon bolts. One of the cylindrical elements is primarily wire mesh, which facilitates pumping of the gas from that region. Electrical potentials are applied to the lens elements through a hermetic seal mounted on the flange. Figure 8 shows the location of the electrostatic lens system in the flowing afterglow apparatus. 139

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140 SAMPLING ORIFICE V / HERMETIC SEAL Figure 31. Electrostatic Lens System

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141 Figure 32 illustrates the electrostatic lens control circuit. This is basically a voltage divider allowing positive or negative potentials to be applied to the lens elements. A digital panel meter is used to monitor the potentials applied to the lens elements. Switches A through F are part of a six-pole quadrupolethrow function switch. In position 1 the digital panel meter displays the potential applied to the lens element selected by switch G. Positions 2 and 3, respectively, allow the digital panel meter to be used as either a 200-volt or a 2-volt voltmeter. Position 4 disconnects the panel meter from the voltage divider circuit. The power supply^ output is grounded at center potential, allowing ±75 volts to be applied to the lens elements. The 8 mfd capacitors provide an AC ground for the circuit, decreasing the ripple superimposed on the DC output of the circuit due to AC pickup. In general, the potentials on the lens elements are adjusted for maximum ion signal. Typical potentials are +10, +20, +45 and +20 volts for the sampling cone, lens element #1, lens element #2 and lens element #3, respectively, when sampling negative ions from the afterglow. Figure 33 illustrates the response of the observed ion signal (F~ in this case) to variations in the potentials (up to 25 volts) applied to the lens elements. Each curve was obtained by initially adjusting all lens elements for maximum ion signal and then varying the potential for a given element. An important fact to note here is that no ion signal is obtained until the sampling cone potential is at least +4 volts. This is due to the fact that

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3.2 MSI 142 C3 be: o in co H O CL _J U1 X . n ft ft C\J LU o u. ir o in Figure 32. Electrostatic Lens Control Circuit

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143 (sijun ^D-UjqjD) 1VN9IS NOI

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144 the plasma is positive with respect to ground and the negative ions must be extracted by a positive potential. The small potentials applied to the sampling orifice should have no accelerating effect on the electrons in the high pressure environment of the reaction tube.

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APPENDIX III THERMALIZATION OF ELECTRONS BY ELASTIC COLLISIONS IN AN ARGON AFTERGLOW Calculations were made to ascertain whether electrons in an active microwave discharge can be assumed to have been reduced to thermal energies (that is, to approximately the average energy of the buffer gas) within the period between their removal from the active discharge and their arrival at the point at which the neutral reactant gas is injected into the reaction tube (1 to 3 msec). These calculations were based on the following assumptions: 1. The electron energy in the active discharge was assumed to conform to a Maxwell-Boltzmann distribution with a temperature corresponding to an energy of 10 electron volts (approximately 175 volts/cm-Torr°' for argon). 2. The argon buffer gas energy distribution was assumed to be Maxwell-Boltzmann, with a temperature of 300°K at all times. 3. The fraction of the energy lost per elastic collision with an argon atom by an electron was given by the relation^® f (E) = (8/3)[mM/(m + M) 2 ] [ 1 T/T ] (98) m where m and M are the masses of the electron and atom, respectively, and T and T represent the temperature of the atoms and electrons, respectively. 4. Inelastic electron-atom collisions were not considered. 145

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146 The history of an electron with energy E q at t=0 in an argon buffer gas can be derived as follows. The changes in the energy of the electron upon suffering elastic collisions with argon are given by E = [1 f(E)]E Jo E = [1 f (E) ] 2 E 2 o E 3 = [1 f(E)] 3 E o E n( t) = f 1 " f(E)] n(t) E Q (99) or ln[E n(t) /E Q ] = n(t)ln[l f(E)] (100) where n(t) is the total number of elastic collisions suffered by the electron. Using the approximation ln[l f (E) ] = -f (E) + l/2f (E) 2 l/3f (E) 3 ... (-l) i t" 1 f(E) i (101) and dropping all but the first term, since f(E) << 1, reduces Equation 100 to ln[E n(t) /E o ] = -n(t)f (E) ( 102 )

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147 The total number of collisions may be calculated from the expression n(t) = A v(t)dt (103) where V(t) is the electron-atom collision frequency, which changes with respect to time by virtue of the fact that the electron energy, and thus the velocity, changes with respect to time. This assumes that the mean free path for an electron undergoing elastic collisions in argon is independent of electron energy. The mean free path used in these calculations was X e =10 meters for an argon pressure of 2.5 Torr. We can now write v ( t) (2E/m) 1/2 (104) v(t) = v(t)/X = (2E/m) 1/2 /A (105) e e n(t) = / fc [(2E/m) 1/2 A ]dt (106) o e In [E/E ] = f(E)/X (2E/m) 1/2 dt (107) o e o where v(t) is the electron velocity and E is a function of time. The value f(E) may be written f (E) = (8/3)[mM/(m + M) 2 ][l kT/E] (108) where k is the Boltzmann constant and kT is the average energy of the argon atoms at 300°K (0.026 eV) . We then have

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148 ln[E Q /E] = (8/3)[mM/(m + M) Z ] [1 kT/E] [1/A ] (2E/m) 1/2 dt e o (109) or In [E /E] = (8/3) [mM/(m + M) 2 ] [1/A ] [2/m] 1/2 [1 kT/E] E 1/2 dt (HO) The integral may be approximated and the equation written in the form ln[E /E] = (8/3) [mM/(m + M) 2 ] [1/A ][2/m] 1/2 [1 kT/E]E 1/2 t (HI) This equation gives a correct value for E at time t only if t is sufficiently small that the fraction kT/E and the term 1/2 E do not change appreciably during that interval. To extend the useful interval to which this equation may be applied, it can be written in the form In [E /E] = (8/3) [mM/(m + M) 2 ] [1/A ][2/m] 1/2 t/At . l [1 kT/E. JET, At 3-1 j-i (112) where At is a time increment which is small, such that the change in the fraction of energy transferred per collision

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149 and the collision frequency can be considered constant during this interval. A Hewlett-Packard 2116C computer was used to calculate energy versus time data based on Equation 112. These data are shown in Table 7. Table 7 Electron Energy Versus Time Calculations for an Afterglow E(eV) t(msec) 10 0 5.6 0.01 0.52 0.1 0.029 1 0.026 2 0.026 3 Therefore, the electrons are reduced to thermal energy by elastic collisions in an argon afterglow in a period of the order of 1-2 msec.

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APPENDIX IV EXPERIMENTAL DATA LISTINGS The experimental data obtained in the present experiments are tabulated at the end of this appendix. Data obtained for which the resulting rate constants are greater than two standard deviations from the mean are not included in the listings. Table 8 provides a key to the data listings at the end of this appendix. Table 8 Data Listings Key Reaction Studied Electron Source Number of Experiments Page Electron Attachment in SF 6 microwave 22 153 SF 6 °2 Charge Transfer microwave 4 154 Electron Attachment in F 2 microwave 7 155 Electron Attachment in SF 6 filament 19 156 Electron Attachment in F 2 filament 21 157 Electron Attachment in C1 2 filament 16 158 Electron Attachment in Br 2 filament 20 159 In order to present the experimental data on a reasonable number of pages, the ion signal versus reactant flow results 150

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151 were fitted to an equation of the form (113) using an orthogonal polynomial technique. 69 In this equation y represents the observed ion signal in picoamps and x represents the reactant gas flow in raolecules/sec. Thus, by substituting the coefficients presented in the data listings for a given experiment into Equation 113 and knowing the maximum reactant gas flow during that particular experiment, the experimental data may be regenerated. All of the experimental data listings follow the same format. The type of electron source used and the reaction studied are given at the top of each page. Each experiment is summarized in two lines. The first line, reading from left to right, contains seven pieces of information: the experiment 3 number, the buffer gas flow in atm/cm -sec, the buffer gas pressure in Torr, the measured reaction tube transit time in msec, the sampling cone potential in volts, the metastable atom quenchant pressure in Torr and the maximum reactant gas flow in molecules/sec. The metastable atom quenchant used in the present experiments was nitrogen except in the SFg (>2 charge transfer experiments in which oxygen was used. Three dashes appearing within the first line indicate that the measurement corresponding to the location of the dashes was not performed. The second line, reading left to right, lists the coefficients (a through g) obtained using the

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152 orthogonal polynomial curve fit technique. Dashes appearing in the second line indicate a less than sixth order curve fit. The coefficients presented in the listings reproduce the data very well except for three experiments noted by asteriks beside the experiment numbers. The ions monitored in the present experiments are the product ions shown at the top of each page of the data listings. In the SF^ 0^ charge transfer experiments the ion was monitored. In experiment 3 the coefficients tabulated in the second and third lines correspond to the SF^ and 0 ^ ion signals, respectively. In experiment A the coefficients tabulated in the second and third lines correspond to the 0 and Cl ion signals, respectively. In the chlorine data listings the coefficients tabulated in the second and third lines of each experiment correspond to the Cl (m/e = 35) and Cl" (m/e = 37) ion signals, respectively. In the bromine data listings the coefficients tabulated in the third line of experiment 2 correspond to a Br^ ion signal.

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153 MICRGWAVE SCLRCEO 1 747E+01 2 664E+01 3 736E+C0 4 282E+01 5 375E+01 6 694E+C1 7 335E+02 8 196E+02 9 263E+C2 10 31 1E+02 11 1018+02 12 972E+01 13 102E+02 14 118E+02 15 264E+01 16 1096+02 17 223E+01 18 478E+Q1 19 138E+02 20 160E+02 21 820E+00 22 25 1 E + 00 25.1 355E-11 25.0 549E-1 1 25.2 454E-1 1 25.0 306E-1 1 24.8 295E-1 1 24.8 1 36E-1 1 23.9 993E-12 2 3.8 832E-12 24.3 21CE-1 1 24.6 165E-1 1 24.5 608E-1 1 24.4 470E-1 1 24.1 361E-1 1 24.2 332E-1 1 23.9 228E-11 24. 1 308E-11 25.0 304E-11 25.0 -149E-1 1 24.8 398E-11 24.7 408E-1 1 24.6 688E-12 24.4 695E-12 SF6 + E2. 14 -382E-25 2.15 -634E-25 2.12 -600E-25 2. 16 -406E-25 2.15 -378E-25 2. 10 970E-25 2.06 -264E-26 2.C8 -228E-26 2.08 -854E-26 2.13 -682E-26 2.12 -740E-25 2.13 -613E-25 2.11 -390E-25 2. 14 — 406E-25 2.08 480E-25 2.11 -916E-27 2.16 805E-25 2. 17 1C0E-23 2.11 -448E-25 2.11 -469E-25 2.08 216E-24 2.07 157E-24 =; SF6235E-39 435E-39 433E-39 29 IE-39 256E-39 2 6 5 E— 3 8 319E-41 291E-4 1 160E-4C 131E-4C 468E-39 4C6E-39 188E-39 2 66 E39 -184E-38 -918E-39 275E-38 -7C7E-37 294E-39 3C7E-39 -891E-38 -567E-38 3.8 -620E-54 4.2 -171E-53 5.2 167 E53 5.2 -U2E-53 5.2 8 82 E54 5.2 269E-52 3.9 -188E-56 3.9 -182E-56 4.5 149E-55 5.1 -126E-55 5.4 1 54 E53 5.4 1 32 E53 4.3 -808 E5 5 4.3 -9C9E-54 4.6 219E-52 4.6 130E-52 4.7 -436E-5 1 4.7 232E-50 5.2 1C9E-53 5.2 1C9E-53 5.5 163E-51 5.5 8 89 E52 .COO 147E-68 .COO 348E-68 .000 325E-68 .050 217E-68 .050 145E-68 .0 00 -123E-66 • COO 535E-72 .020 551E-72 .COO 672E-71 .020 5866-71 .COO 245E-68 .020 182E-68 .COO -2G0E-68 .020 151E-68 .COO -1 ICE-66 .020 -685E-67 .COO 1 15E-64 .020 -362E-64 .COO 211E-68 .000 197E-68 .000 -143E-65 -COO -661E-66 512E+12 -103E-83 3856+12 -281E-83 354E+12 -245E-83 367E+12 -165E-83 386E+12 -873E-84 1866+12 210E-81 290E+13 -583E-88 2796+-13 -636E-88 187E+13 -115E-86 183E+13 -1C4E-86 3490+12 -141E-83 296E+12 -507E-84 268E+12 427E-83 5476+12 — 965E-84 222E+12 200E-81 225E+12 124E-81 640E+1 1 -897E-79 6406+11 212E-78 360E+12 -165E-83 4596+12 -139E-83 934E + 1 1 4 84 £—80 1C8E+12 189E-80

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154 NICRGWAVE SCLRCEO SF6 + C 2= SF6+ 02 1 106E+02 2 941E-01 3 347E+00 912E-01 4 771E-01 469E+01 2 7.0 -249E-L5 27.0 -1 12E-17 26.3 2S1E-16 -109E-17 27.7 -982E-18 -667 E1 7 2.35 457E-32 2.35 527E-35 2.31 122E-33 490E-35 2. 3C 520 t— 3 5 8436-34 -496E-49 -1C7E-52 237E-51 -94 IE-53 -132E-5 2 -275E-51 13.5 251E-66 13.5 73 9 E— 71 13.1 -166E-69 648E-71 11.7 133E-70 265E-69 . 320 -46 IE-84 .320 . 310 . 300 215E+15 315E+15 572E+15 582E+15

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155 NICRCWAVE SCURCEC 1 1I8E+02 2 822E+01 3 7026+01 4 781E+01 5 133E+01 6 387E+01 7 105E+01 26.5 267E-12 26.5 1 16E-12 26.5 -146E-12 25.6 64 1 E — L 2 29.6 213E-12 25.6 -150E-12 25.6 1 16E-12 F2 + E2.30 -3536-27 2.30 394 E27 2.30 128E-26 2.50 -573E-27 2.50 706E-26 2.5C 798E-26 2.50 799E-26 = F+ F 4.0 -157E-42 4.0 — 168E-4 1 4 . C -278E-41 4.0 -156E-41 4.0 -5586-40 4.0 -523E-4C 4.0 -6 2 4 E40 8.9 842E-57 8.9 284E-56 8.9 278E-56 10.2 645E-56 10.2 169E-54 10.2 151E-54 10.2 195E-54 .000 -726E-72 .COO -184E-7 1 .000 -134E-71 .COO -676E-71 .COO -229E-69 .COO -2C6E-69 .000 -277E-69 155E+13 156E-87 1556+13 437E-87 155E+13 253E-87 1C2E+13 234E-86 698E+12 114E-84 606E+12 1C6E-84 554E+12 147E-84

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156 FILAMENT SCURCEO 1 146E+0C 2 * 124E-01 3 328E+00 A 213E+00 5 415E+00 6 319E+00 7# 175E+01 8 107E+01 9 159E+01 10 166E+01 11 125E+01 12 95 1E + 00 13 808E+00 1 A 768E+00 15 454E+00 16 633E+00 17 416E+00 18 198E+00 19 603E-01 13.7 428E-13 13.6 1CCE-12 2C.2 465E-13 6.8 84SE-13 6.7 275E-13 13.0 232E-12 13. 1 -745E-13 13.2 969E-13 12.1 128E-12 19.9 125E-12 6 . 1 145E-12 1C. 9 34CE-12 1C. 9 281E-12 10.8 280E-12 11.4 491E-12 11.3 3 03E— 1 2 17.3 257E-13 18.6 258E-13 17.1 661E-13 SF6 + E1.47 -137E-26 1.48 -766E-26 1.92 -137E-26 . 97 -236E-26 .96 -401E-27 1.48 -664E-26 1.45 293E-26 1.43 433E-27 1.39 -227E-26 1.89 -312E-26 .88 -316E-26 1.27 -152E-25 1.26 -108E-25 1.26 -115E-25 1.30 -327E-25 1.30 -148E-25 1.32 146E-24 1.75 -263E-27 1.6 7 16 2 E— 26 = SF66.5 243E-40 6.5 31CE-39 6.1 225E-4C 8.3 349E-4C 8.3 416E-41 6.6 9 6 3 E4 0 6.6 -383E-40 6.5 -734E-40 6.4 2C6E-40 5.7 399E-4G 8.6 343E-40 7.0 42 2 E39 7.0 242E-39 7.0 261E-39 7.0 1 17E-38 7.0 39CE-39 4.9 -218E-37 1C9E-41 204E-4C 8.9 -230E-54 9.0 -590E-53 8.9 -201E-54 9.9 -270E-54 9.9 -272E-55 9.9 -653E-54 226E-54 130E-53 -9C6E-55 -267E-54 198E-54 -682E-53 -321E-53 -339E-53 -215E-52 -540E-53 128E-5C 10.7 -110E-56 10.7 -116E-54 .COO 1C8E-68 .COO 513E-67 .COO 916E-69 .COO 104E-68 .COO 927E-7G .CCO 138E-68 .COO -o 1 6E-69 .COO -905E-68 .COO 171E-69 .COO 892E-69 .COO 584E-69 .COO 562E-67 .COO 236E-67 .COO 234E-67 .COO 1 92E-66 .COO 373E-67 .COO -333E-64 .COO -364E-71 .COO 17 IE6 9 165E+12 -199E-83 1C6E+12 -165E-81 147E+12 -164E-83 214E+12 -158E-83 258E+12 -122E-84 129E+12 2C3E-83 247E+12 619E-84 146E+12 222E-82 235E+12 -853 E -85 231E+12 -1 17E-83 228t+12 -690E-84 IC9E+12 -179E-81 1C9E+12 -741E-62 110E+12 -664E-82 946E + 1 1 — 659E-81 955E+1 1 -1C4E-81 366E+11 321E-78 294E+12 657E-86 148E+12 445E-84 * PCCR CURVE FIT

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157 FILAMENT 1 450E+CG 2 228E-0L 3 503E+G0 4 595E+00 5 109E+00 6 693E-0L 7 843E-02 8 318E-01 9 176E-C1 10 106E-01 11 107E-C1 12 303E-01 13 517E-02 14 154E-01 15 124E-01 16 174E-01 17 452E-01 18 517E-01 19 226E+00 20 226E+0Q 21 1 12E+00 SCIKCEO 11.0 246E-13 22.1 92CE-14 12.8 218E-13 12.9 206E-13 13.1 429E-14 13.1 357E-14 13.2 273E-14 13.3 3 13E-14 13.3 242E-14 13.3 2 13E-14 13.2 355E-14 13.0 4 38 E14 12.6 271E-14 12.3 287E-14 12.0 30 IE-14 11.9 344E-14 12.1 452E-14 12.1 4 15E-14 13.4 821E-14 13.2 113E-13 13.0 66 IE-14 F2 + E= 1.28 -519E-28 2. CO -192E-28 1.46 -442E-28 1.46 -436E-28 1.48 -104E-28 1.47 -600E-29 1.48 -391E-29 1.46 -742E-29 1.47 -455E-29 1.49 -213E-29 1.48 -583E-29 1.47 -727E-29 1.42 — 518E-29 1.41 -566E-29 1.41 -608E-29 1.40 -681 E— 29 1.40 -120E-28 1.40 -119E-23 1.48 -599 E -29 1.47 -262E-28 1.4 7 8 12 E— 29 F+ F 7.4 543E-43 5.7 2C7E-43 6.4 429E-43 6.5 453E-43 6.8 145E-43 6.8 5 5 IE44 6.8 3C6E-44 6.8 1 C 1 E4 3 6.8 439E-44 6.8 1C9E-44 6.8 463E-44 6.8 68CE-44 7.2 513E-44 7.2 571E-44 7.2 612E-44 7.2 678E-44 7.2 167E-43 7.2 18 IE-43 7.2 -335E-43 7.2 251E-43 7.2 -763E-43 -289E-58 -U3E-58 -209E-58 -238E-58 12 . 7 1 1 CE 12.7 -271E-59 12.8 -129E-59 12.8 -748E-59 12.8 -219E-59 12.0 30 3 E60 12.0 1 94 E— 59 12.0 342 E— 59 18.1 -286E-59 15.9 -3C2E-59 18.2 -320E-59 17.0 -356E-59 15.8 122E-58 15.4 -143E-58 17.0 828E-58 17.1 1 34 E— 59 17.1 146E-57 .COO 75CE-74 .000 30 IE— 74 .000 492E-74 . COO 608 E74 .000 424E-74 .000 668E-75 .000 272E-75 .000 280E-74 .000 543E-75 .COO 488E-76 .000 4 04 E75 .COO 863E-75 .000 7C2E-75 . COO 787E-75 .000 834E-75 .000 944E-75 .000 452E-74 .000 563E-74 .000 -708E-73 .000 -170E-73 .000 -1 17E-72 327E+13 -750E-90 316E+13 -3C7E-90 349E+13 -447E-90 322E+13 -559E-90 193E+13 -647E-90 287E+13 -641E-91 383E+13 -223E-91 194E+13 -417E-90 286E+13 -524E-91 290E+13 -43 3 E92 3C8E+13 -323E-91 288E+13 -8556-91 286E+13 -721E-91 291E+13 -791E-91 287E+13 -852E-9 1 289E+13 -989E-91 192E+13 -667E-90 194E+13 -862E-90 115E+13 211E-88 1 13E + 13 758E-89 1 13E + 13 341E-88

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158 FILARENT SCURCEO CL 2 + E= CL+ CL I 8.0 1.01 _ _ _ 11.0 . COO 6C3E+13 141E+01 176E-14 -142E-29 529E-45 -850E-61 4C3E-77 1 22E-93 4 34 E + 00 489E-15 3 94 E30 146E-45 -241E-61 126E-77 233E-94 2 11.2 1.26 — 1 1 .0 .COO 3536+13 220E+01 471E-14 -692E-29 54 IE-44 -230E-59 5C0E-75 -430E-91 557E+00 1 13E-14 -162E-29 129E-44 -566E-60 127E-75 -112E-91 3 11.2 1.24 — 11.0 .000 2966+13 1896+01 718E-14 1406-28 139E-43 -729E-59 188E-74 -190E-90 560E+C0 1 79E-14 -315E-29 292E-44 -144E-59 358E-75 -351E-91 4 11.1 1.25 — 11.0 .CCO 358E+13 2086+01 468E-14 -588E-29 395E-44 145 E59 273E-75 -2C4E-91 5816+00 153E-14 -213E-29 159E-44 -650E-60 134E-75 -1C9E-91 5 11.0 1.25 — 11. C .COO 3546+13 175E+01 829E-14 -138E-28 113E-43 -484E-59 1C1E-74 -836E-91 498E+00 220E-14 -344E-29 275E-44 -1 16E-59 246E-75 -2C5E-91 6 12.9 1.40 — 10.9 .COO 370E+13 380E+00 166E-13 -271E-28 217E-43 -899E-59 184E-74 -149E-90 102E+C0 433E-14 -697E-29 5 5 6E-44 -230E-59 472E-75 -381 E— 9 1 7* 12.8 1.39 — 10.9 .COO 368E+13 6 1 6 E + C 0 174E-13 -238E-28 16CE-43 -571E-59 103E-74 -756E-91 153E+00 442E-14 -569E-29 363E-44 -124E-59 22GE-75 -157E-91 8 12.7 1.38 — 10.9 .CCO 371E+13 456E+C0 196E-13 -315E-28 246E-43 -996E-59 2C0E-74 -158E-90 113E+-C0 475E-14 76 7 E~ 29 599E-44 -241E-59 485E-75 -382E-91 9 19.6 1.87 — 11. C .COO 370E+13 441E+00 5 1 IE-14 210E-29 -604E-44 352 E— 59 -849E-75 747E-91 929E-01 1 ICE-14 6 60 E30 -15CE-44 842 E60 -198E-75 171E-91 10 19.6 1.86 — 11.0 .COO 365E+13 395E+00 495E-14 166E-29 -567E-44 369E-59 -943E-75 866E-91 814E-01 104 E14 538E-30 149E-44 923E-60 -236E-75 218E-91 1 1 27.5 2.35 — 11.0 .COO 365E+13 601E-01 799E-15 428E-30 29CE-45 -4C3E-60 124E-75 -124E-91 171E-01 21CE-15 512E-31 872E-46 -891E-61 250E-76 -231E-92 12 13.2 1.40 — 11.0 .CCO 351E+13 450E+C0 857E-14 144E-28 1 18E-43 -506E-59 1C6E-74 -881E-91 1 1 1E + 00 2 3 7 E 1 4 -405E-29 337E-44 -144E-59 3C5E-75 -252E-9 1 13 13.4 1.41 — 11.0 .COO 359E+13 557E+C0 138E-13 -225E-28 18CE-43 -746E-59 154E-74 -125E-90 158E+00 382E-14 -628E-29 50 8 E44 -214E-59 448E-75 -370E-91 14 13.3 1.41 — 11.0 .COO 355E+13 426E+00 135E-13 -223E-28 1 8 2 E4 3 -773E-59 162E-74 -134E-90 121E+00 37CE-14 6 05 E29 49 IE-44 -208 E59 439E-75 -3646-91 15 13.3 1.41 — 1 1.0 .COO 354E+13 379E+C0 134E-13 -221E-28 181E-43 -7706-59 163E-74 1 35 E— 9 0 112E+00 37GE-14 -597E-29 483E-44 -204E-59 432E-75 -3596-91 16 20. 2 1.88 — 11.0 .COO 362E+13 200E+00 247E-14 279E-29 -475E-44 2 59 E— 59 -622E-75 554E-91 553E-01 66CE-15 708E-30 -1 16E-44 619E-60 -145E-75 1276-91 * PC CR CURVE FIT

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159 FILAMENT SCURCEO 3R2 + E= BR+ BR 1 33.6 2. Cl 10.1 .050 219E+16 106E+01 -125E-17 9C0E-36 -2C6E-54 — — — 2 33.0 2. CO — 10.1 .050 214E+16 822E+C0 -725E-18 40 IE-36 -886E-55 — — — 217E-01 961E-19 -579E-37 127E-55 — — — 3 31.5 1.91 — 10.0 .050 181E+16 399E+C0 -765E-18 5926-36 -152E-54 — — 4 31.4 1.93 — 10. c .050 341E+15 176E-02 177E-17 -785E-36 -967E-53 126E-70 — — 5 3 2.3 1.93 — 10.0 .050 293E+15 609E-03 ^ 4 3 E1 8 4 63 E35 193E-52 -1C2E-69 — — 6 32.0 1.94 — 10.C .050 297E+15 10LE-02 222E-18 875E-35 -289E-52 355E-70 — — 7 31.9 1 .94 — 10.0 .050 3396+15 117E-01 -502E-18 22 1 E— 34 -1C3E-51 149E-69 — — 8 31.8 1.97 — 10. C . ICO 214E+15 202E-02 186E-18 119E-34 -62 4 E5 2 108E-69 175E-89 — 9 31.0 1.86 — 10. C .050 542E+15 826E-02 532E-17 -209E-34 319E-52 -165E-7C — — 10 3 C . 7 1.85 — 10. c .050 533E+15 132E-01 53CE-17 -289E-34 622E-52 -462E-70 — — 11 31.3 1.89 — 10.0 .050 526E+15 433E-02 392E-2C 245E-35 66CE-53 437E-71 — — 12 31.2 1.94 — 10. C .100 578E+15 205E-02 528E-18 3086-35 -963E-53 721E-71 — — 13 31.5 1.93 — 10.0 .100 582E+15 127E-03 9G6E-18 729 E36 -625E-53 597E-71 — — 14 31.5 1.89 — 10. C .050 424E+15 122E-01 916E-18 445E-35 -254E-52 290E-70 — — 15 32.1 1.94 — 10.0 .050 527E+15 12 IE— 02 829E-18 145E-37 -579E-53 664E-71 — — 16 32.0 1.98 10. C . 100 523E+15 535E-02 467E-18 147E-35 -723E-53 686E-71 — — 17 33.3 2.05 — 10.0 .150 3C9E+15 485E-02 872E-18 -1406-34 12CE-51 -421E-69 518E-87 — 18 32.4 1.9 7 — 10. C . 100 524E+15 108 E— 02 718E-19 427E-36 -1C1E-54 -538E-72 — — 19 32.1 1.97 — 10.0 .100 627E+15 179E-02 455E-19 123E-35 -263E-53 169E-71 — — 20 25.1 1.61 — 10. C . 100 650E+15 174E-03 164E-18 265E-35 -840E-53 657E-71 — —

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LIST OF REFERENCES 1. H.S.W. Massey, E.H.S. Burhop and H.B. Gilbody, Electronic and Ionic Impact Phenomena , Vol. II, Clarendon Press, Oxford, 1969. 2. F.C. Fehsenfeld, Journal of Chemical Physics, 53 , 2000 (1970). 3. W.M. Hickam and R.E. Fox, Journal of Chemical Physics, 25 , 642 (1950). 4. Fehsenfeld (see reference 2) believes SF^ to be formed by the attachment of electrons to sulfur hexafluoride to yield SF~ in a repulsive state M).43 eV above the SF^ ground state. 5. C.L. Chen and P.J. Chantry, Bulletin of the American Physical Society, 15 , 418 (1970). 6. H.O. Pritchard, Chemical Reviews, 52 , 529 (1953). 7. T.L. Cottrell, The Strength of Chemical Bonds , Butterworth ' s Scientific Publications, London, 1954. 8. J.F. Burns, Carbide and Carbon Chemicals Company, K-25 Plant, Report K-1147 (1954). 9. R. Thorbum, Proceedings of the Physical Society of London, 72, 122 (1959). 10. J.J. DeCorpo and J.L. Franklin, Journal of Chemical Physics, 54, 1885 (1971). 11. N.E. Bradbury, Journal of Chemical Physics, 2 _, 827 (1934). 12. V.A. Bailey and R.H. Healey, Philosophical Magazine, 19 , 725 (1935). 13. D.C. Frost and C.A. McDowell, Canadian Journal of Chemistry, 38, 407 (1960). 14. H-K Moe, Dissertation Abstracts International, 30 , 158-B (1969). 15. D.B. Dunkin, F.C. Fehsenfeld and E.E. Ferguson, Chemical Physics Letters, 15 , 257 (1972). 160

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161 16. H.B. Wahlin, Physical Review, 19, 173 (1922). 17. S.E. Bozin and C.C. Goodyear, British Journal of Applied Physics, 18, 49 (1967). 18. L.B. Loeb , Basic Processes of Gaseous Electronics , University of California Press, Los Angeles, 1960. 19. O.J. Orient, Canadian Journal of Physics, 43 , 422 (1965). 20. E.W. McDaniel, Collision Phenomena in Ionized Gases , John Wiley and Sons, Inc., New York, 1964. 21. G. Herzberg, Atomic Spectra and Atomic Structur e, Dover Publications, New York, 1944. 22. G. Herzberg, Spectra of Diatomic Molecules , D. Van Nostrand Company, Inc., New York, 1950. 23. J.E. Bailey, R.E.B. Makinson and J.M. Somerville, Philosophical Magazine, 24, 177 (1937). 24. F.K. Truby, Physical Review A, 4^, 613 (1971). 25. S.A.A. Razzak and C.C. Goodyear, Journal of Physics D, 2 _, 1577 (1969). 26. F.C. Fehsenfeld, Journal of Chemical Physics, 54, 438 (1971). 27. B.H. Mahan and C.E. Young, Journal of Chemical Physics, 44 , 2192 (1966). 28. C.E. Young, UCRL Report No. UCRL-17171, 1966. 29. E. Chen, R.O. George and W.E. Wentworth, Journal of Chemical Physics, 49., 1973 (1968). 30. F.J. Davis and D.R. Nelson, Chemical Physics Letters, _3, 461 (1969). 31. L.M. Chanin, A.V. Phelps and M.A. Biondi, Physical Review, 128 , 219 (1962). 32. J.L. Pack and A.V. Phelps, Journal of Chemical Physics, 44 , 1870 (1966). 33. Model PGM-10, Raytheon Company, Manchester, New Hampshire. 34. Evenson Cavity, Opthos Instrument Company, Rockville, Maryland.

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162 35. Model 725.3, Opthos Instrument Company, Rockville, Maryland. 36. Model 1355, Brooks Instrument Division, Emerson Electric Company, Cincinnati, Ohio. 37. Model All-10000, Hastings-Raydist, Hampton, Virginia. 38. Model 77H-300, MRS Instruments, Inc., Burlington, Massachusetts. 39. Model All-5, Hastings-Raydist, Hampton, Virginia. 40. Model 162-8, Extranuclear Laboratories, Inc., Pittsburgh, Pennsylvania. 41. Model 1375B, Sargent-Welch Scientific Company, Springfield, New Jersey. 42. Series 216, Granville-Phillips Company, Boulder, Colorado. 43. Made to specifications by Electron Technology, Inc., Kearny, New Jersey. 44. Model LCS-CC-01, Lambda Electronics Corporation, Melville, New York. 45. Model 2116C, Hewlett-Packard, Palo Alto, California. 46. R.C. Bolden, R.S. Hemsworth, M.J. Shaw and N.D. Twiddy, Journal of Physics B, 45 (1969). 47. S. Dushman and J.M. Lafferty, Scientific Foundations of Vacuum Technique , John Wiley and Sons, Inc., New York, 1962, 48. E.E. Ferguson, F.C. Fehsenfeld and A.L. Schmeltekopf , Advances in Atomic and Molecular Physics, 5_, 1 (1969). 49. M. Cher and C.S. Hollingsworth, Advances in Chemistry Series, 80, 118 (1969). 50. A. Redfield and R.B. Holt, Physical Review, 82 , 874 (1951). 51. F. Kaufman, Advances in Chemistry Series, 80 , 29 (1969). 52. R.F. Curl, Jr., Journal of Computational Physics, 6_, 367 (1970). 53. J.C. Becsey, L. Berke and J.R. Callan, Journal of Chemical Education, 45^, 728 (1968) . 54. M. Bourene and J. Le Calve, Journal of Chemical Physics, 58, 1452 (1973).

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163 55. J.L. Franklin, J.G. Dillard, H.M. Rosenstock, K. Draxil and F.H. Field, National Standard Reference Data Series, 26 _, 1 (1969). 56. M.A. Biondi, Physical Review, 82_, 453 (1951). 57. M.A. Biondi, Physical Review, 88_, 660 (1952). 58. D. Smith, C.V. Goodall and M.J. Copsey, Journal of Physics B, 1 , 660 (1968). 59. J.F. Paulson, Advances in Chemistry Series, 58_, 28 (1966). 60. F.K. Truby, Physical Review A, 4_, 114 (1971). 61. D.I. Rosen, R.N. Sileo and T.A. Cool, IEEE Journal of Quantum Electronics, OE-9 , 163 (1973). 62. J.V.V. Kasper and G.C. Pimentel, Physical Review Letters, 14, 352 (1965). 63. N. Allen and N.H. Furman, Journal of the American Chemical Society, _54, 4625 (1932). 64. K.R. Spangenburg, Vacuum Tubes , McGraw-Hill, New York, 1948. 65. Model AN2510-1B, Analogic, Wakefield, Massachusetts. 66. Model C150-.08, Deltron, Inc., North Wales, Pennsylvania. 67. V.E. Golant, Soviet Physics-Technical Physics, 680 (1959). 68. A.M. Cravath, Physical Review, 36 , 248 (1930). J.W. Bright and G.S. Dawkins, I and EC Fundamentals, 4^, 93 (1965). 69.

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BIOGRAPHICAL SKETCH Gary Donald Sides was born October 5, 1947, in Tuscaloosa, Alabama. He graduated from Holt High School in Holt, Alabama, in June, 1965. He received his Bachelor of Science in chemistry from the University of Alabama in June, 1969. He received his Master of Science in chemistry from the University of Florida in June, 1971. In July, 1971 he entered the United States Air Force as an officer and was stationed at Wright-Patterson Air Force Base where he has worked since that time as a research chemist at the Aerospace Research Laboratories. During this time he pursued his degree of Doctor of Philosophy from the University of Florida. He was married to the former Sarah Ann Smith in May, 1968 and they have one son. 164

PAGE 175

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. A j) Robert J. Hahrdtrhn, Chairman Professor of Chemistry I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Thomas 0. Tiernan, Co-Chairman Aerospace Research Laboratories I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. E.E, Muschlitz, Jr. Professor of Chemistry

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I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy. Richard A. Blue Professor of Physics This dissertation was submitted to the Graduate Faculty of the Department of Chemistry in the College of Arts and Sciences and to the Graduate Council, and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy. June, 1975 Dean, Graduate School