FUNDEMENTAL STUDIES AND APPLICATIONS OF LASER-ASSISTED IONIZATION IN A HYDROGEN - OXYGEN - ARGON FLAME BY King-Chuen Lin A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemistry 1982 ABSTRACT FUNDEMENTAL STUDIES AND APPLICATIONS OF LASER-ASSISTED IONIZATION IN A HYDROGEN - OXYGEN - ARGON FLAME BY King—Chuen Lin Laser-enhanced ionization (LEI) is an application of the optogalvanic effect in flames. A laser is used for resonant excitation of an analyte. Excited atoms subsequently undergo collisional ionization and are detected as ions. This provides considerable enhancement over ground state collisional ionization. Dual laser ionization (DLI) is similar to LEI, but involves two lasers to produce the analyte ions in flames. In our DLI technique, an Nz- laser pumped dye laser is used to resonantly excite an alkali analyte to a higher electronic state and then the ultraviolet N2 laser serves to further promote the excited analyte population into the ionization continuum. Alternatively, collisions in the atmospheric pressure flame may result in ionization of the analyte following the dye laser excitation. The ions produced are collected by a pair of voltage-biased nichrome wires suspended inside the flame, and the signal is . I . o King-Chuen Lin _ processed by a boxcar integrator. This thesis convers two main tOpics: (l) flame and ion properties probed by DLI, and (2) the relative merits of the DLI and LEI techniques. The first subject includes flame temperature determination by DLI, through the measurement of ion mobility and diffusion coefficients (Chapter V). This is the first time that the Optogalvanic effect has been used to measure flame temperature. A current- and voltage-dependent formulation has been derived to characterize the ion production by the laser and to estimate the ion density in the flame (Chapter VI). On the second subject, two theoretical models based on quantum mechanical methods (Chapter III) and rate equations (Chapter IV) have been studied and compared with the experimental results. Insight is gained with regard to ionization mechanisms, the spectral and temporal profiles of ionization, the relationship of ionization and fluorescence, and the relative enhancement of DLI over LEI. In addition, optimal use of DLI, based on the energy levels of the analyte, has been investigated (Chapter VII). Finally suggestions for the future develOpment of DLI are proposed (Chapter VIII). To Dad, to Mom, and to Jueichi' ii ACKNOWLEDGEMENTS Thanks, my Lord. Accompany me in my life; carry me through the difficult pathes, and provide me with peace and abundance. I would like to express my deepest appreciation to my advisors,Stanley R. Crouch, George E. Leroi and Paul M. Hunt for their intellegent advice and helpful discussions over all the aspects of the thesis. Without their joint direction and patience, this thesis would not have been accomplished. I amindebted in C.A. van Dijk for his valuable suggestion in my research, and in the group fellows for their friendship. I wish to thank Jo Kotarski for her help with figures and slides in the thesis, Manfred Langer for his excellent work on vapor cells. Appreciation is due to the department of chemistry, Michigan State University and National Science Fundation for their finacial support since 1978. The industry research fellowship provided by SOHIO during the sumer of 1982 is also acknowledged. I am deeply grateful for Rick Hallgren and his family. Their great help, spiritual encouragement and deep friend- ship with my family always warm up Jueichi'sand my hearts. The Jones, my host family, deserve appreciation for their kindness and friendship. Nor can I forget the friends in iii 'pvl 0‘ -v W -' I »-- ...' u. . O Chinese Christian fellowship of Michigan State University; their concerns and helps had accompanied me for past years. I wish to express my sincerest thanks to my parents for their support and for remaining so close when so far away, to my wife, Jueichi, for her love, understanding and putting up with me. iv I... H \ u... - \ u‘~ \‘; Chapter TABLE OF CONTENTS LIST OF TABLES. . . . . . . . LIST OF FIGURES . . . . . . . CHAPTER A. C. (HEQTER B. C. CHAPTER III - EXPERIMENTAL AND THEORETICAL STUDIES OF DUAL LASER IONIZATION OF SODIUM IN AN H2 - o A. I - INTRODUCTION. . . Overview. . . . . . . 1. Laser-Enhanced Ionization 2. Current LEI Development. 3. Dual Laser Ionization Historical. . . . . . 1. 2. 3. The Optogalvanic Effect (OGE) Ionization SpectroscoPy with Thermionic Diode Detection Resonance Ionization Spectroscopy (RIS) (DLI). (LEI) Organization of the Dissertation. II - EXPERIMENTAL . . Instrumentation . . . 1. 2. 3. 4. 5. Laser Source . . . Flame Cell . . . . Optical'Detection. Ionization Detection Signal Processing. Reagents. . . . . . . Procedure . . . . . . Introduction. . . . . -Ar FLAME. page 14 16 18 21 21 26 40 46 49 50 59 60 63 63 In. . - u . . nub F b A a 90- at. h . 1... \ub a E. F. CHAPTER Experimental. . . . . . . . . . . . . . Theoretical O O O O O O O O O O O O O O l. 2. Multiphoton Ionization in a Two-Level Atomic System. . . . . . . Application to Sodium. . . . . . . . Results 0 O O O O O I O O O O O O O O O Multiphoton Ionization in the Flue O O O O O O I O O O O O O O O 0 Measurement of the Dye Laser Profile by DLI . . . . . . . . . . . 3. Dependence of the Ionzation Profile on Dye Laser Power . . . . . Discussion. . . . . . . . . . . . . . . Conclusion. . . . . . . . . . . . . . . IV - RATE EQUATION APPROACH TO A THREE-LEVEL SYSTEM FOR DUAL LASER IONIZATION AND LASER—ENHANCED IONIZATION. . . . . Introduction. . . . . . . . . . . . . . Theoretical Basis . . . . . . . . . . . 1. 2. General Solution . . . . . . . . . . Special Case . . . . . . . . . . . . Results and Discusstion . . . . . . . . 1. 2. 3. 4. 5. 6. 7. Effects of K on ni and n2. . . . . . Nonsteady State Versus Steady State. n. and n with Respect to Spectral Ifradiange . . . . . . . . . . . . . Temporal Profiles for Ionization and Fluorescence . . . . . . . . . . . . Laser Pulse Duration . . . . . . . . Continuum to Ground State Coupling . Nonsteady State Versus Steaday State for Different Laser Pulse - Duration . . . . . . . . . . . . . . Conclusion. . . . . . . . . . . . . . . vi 65 67 67 .70 76 76 81 83 86 97 99 99 101 101 113 116 119 128 131 134 139 145 148 153 mu.‘ '1 p.- 0.0» 'J 5“ E. ".‘ I-l CHAPTER V - FLAME TEMPERATURE DETERMINATION A. B. C. D. E. DUAL LASER IONIZATION . . . . Introduction. . . . . . . . . . . Experimental. . . . . . . . . . . Theoretical . . . . . . . . . . . Results . . . . . . . . . . . . . Discussion. . . . . . . . . . . . CHAPTER VI - ALTERNATIVE APPROXIMATIONS D. BASED ON THE EQUATION OF CONTINUITY . . . . . . . . . Introduction. . . . . . . . . . . Theoretical Basis . . . . . . . . Results and Discussion. . . . . . Conclusion. . . . . . . . . . . . CHAPTER VII - THE EFFICACY OF DLI IN AN A. B. C. D. H2 - O2 - Ar FLAME. . . . . Introduction. . . . . . . . . . . Experimental. . . . . . . . . . . Results and Discussion. . . . . . 1. Ion Background . . . . . . . . 2. Sodium Ionizaiton with BS - 4D Two-Photon Resonance Excitation 3. One- or Two-Photon Resonance meitation O O O O O O O C O O 4. Na + SS Two-Photon Absorption and 3P + SS One-Photon Absorption. mnCIQSi-on- O »- O O I O O O I O O 0 CHAPTER VIII - SUGGESTIONS FOR FUTURE A. B. DEVELOPMENT OF DLI . . . . Summary . . . . . . . . . . . . . PrOposal for DLI Development. . . 1. DLI - diabnosis of Spectral and Temporal Information Regarding Excited Sates. . . . . . . . . vii 155 155 159 165 168 173 177 177 178 186 194 197 197 200 202 202 212 217 220 224 229 229 230 230 2. Re-examination of Sensivity and Selectivity of DLI. . . . . . . . . . . 3. Saturation Dual Laser Ionization. . . . 4. DLI in Vapor Cell versus DLI in Flames Flames I O O O O O O O O O O O O O O I I REF EREN CE S I O O O O O O O O O O O O O I O O 0 O 0 APPENDIX A - TWO-STEP LASER-ASSISTED IONIZATION OF SODIUM IN A HYDROGEN-OXYGEN- ARG ON PM 0 O O O O O O I O O O I O A. Introduction . . . . . . . . . . . . . . . B. Experimental . . . . . . . . . . . . . . . C. Results and Discussion . . . . . . . . . . D. Conclusion . . . . . . . . . . . . . . . . E. Appendix . . . . . . . . . . . . . . . . . APPENDIX B - PHOTOIONIZATION CROSS SECTION BY QUANTUM DEFECT METHOD . . . . . . . . viii 236 237 238 242 254 254 255 259 278 279 283 R1 ~'l A ‘. oh u Table LI S T OF TABLES Comparison of Detection Limits . . . . . . Specifications of Nitrogen Laser . . . . . Parameters Concerning Sodium in the Special Case . . . . . . . . . . . . . . . A Comparison of Flames Temperatures for Similar H /0 /Ar Flames Obtained by Line-Revegsa and Dual Laser Ionization (DLI) Techniques. . . . . . . . Comparison of Parameters for Photoionization Cross Section Calculation ix Page 27 117 172 286 Figure 1 LIST OF FIGURES Block diagram of laser-induced ionization apparatus . . . . . . . . . Block diagram of experimental set-up for DLI . . . . . . . . . . . Diagram of flowing nitrogen system for N2 laser . . . . . . . . . . . . . . . Dependence of dye laser power ( o ) and sodium ionization ( ) on N2 pressure in N2 laser tube. . . . . . . The wavelength range of various organic dyes pumped by a 337.1 nm, N2 laser (Molectron). . . . . . . . . . . . . . Block diagram of the Hansch-type dye laser. . . . . . . . . . . . . . . The output power distribution of dye laser (Rhodamine 6G) with respect to wavelength . . . . . . . . . . . . . . Measurement of the effective cross section of beam waist of N2 laser along X axis ( the direction parallel to the optical table, but perpendicular to the laser beam . . . . . . . . . . . . . . Page 0 O O O 30 32 34 36 the 38 I un-upa ' r .n‘na- c ‘b Figure 9 10 11 12 13 14 15 16 17 Page Block diagram of gas flow system in an H2- 02- Ar flame. . . . . . . . . . . . . . . 41 The concentration dependence of thermal emission of Sodium atom in an Hz- 02 -Ar flame. . . . . . . . . . . . . . . . . . . . 47 Comparison of spatial profile of ionization obtained by time-integrated analysis and by time-scanned analysis, respectively. . . . . . . . . . . . 56 The comparison of temporal profiles of ionization obtained by time-scanned analysis and by time—integrated analysis, respectively. . . . . . . . . . . . . 57 Multiphoton ionization rate calculation of DLI case: Na(3$k) + hm (5890 A -+ Na(3P 1 3/2’ 0 + — + hw2(3371 A)-+ Na + e . . . . . . . . . . . 74 Multiphoton ionization rate calculation of O LEI case: N3(3$8) + hml (5890 A) + Na(3P3/2) O .- + 2hw1(5890 A) -+ Na++ e . . . . . . . . . . 7s Dye laser power dependence measurement of LEI. . . . . . . . . . . . . . . 77 N2 laser power dependence measurement of DLI, with constant dye laser power (arbitrary units). . . . . . . . . . . . 79 Enhancement ratio of DLI to LEI versus detuning wavelength . . . . . . . . 30 xi :- nuvc ..I~D . to C. “a 7) Q- t?" Figure 18 19 20 21 22 23 24 25 26 27 28 29 Page Comparison of DLI and LIF profiles. . 82 Dependence of sodium DLI profile on dye laser power. . . . . . . . . . . . . . .. . 84 Ratios of DLI profiles. . . . . . . . . . . . 85 Dependence of DLI on the dye laser power. . . . 87 Dependence of LIF on the dye laser power (arbitrary units) . . . . . . 90 Dependence of LIF on the dye laser power (arbitrary units) . . . . . . 91 Dependence of DLI on dye laser power (arbitrary units) . . . . . . . . . 92 DLI profile ratio from dee = 5.0 MW/cm2 and dee=2.4MW/cm2......... 96 Three-level energy diagrams for (a) LEI and (b) DLI. . . . . . . . . . . . . . 102 Temporal profiles of ionization in DLI with spectral irradiance of 5 x 10"10 W/cm2 Hz and various K values. . . . . . . . . . . . . . . . . 120 Temporal profiles of ionization in LEI with spectral irradiance of S x 10-10 W/cm2 Hz and various K values. . . . . . . . . . . . . . . . . . . . 122 Temporal profiles of excited state population density (fluorescence) in DLI with spectral irradiance of xii u u.‘ ’- — ,.H.ov C. '8 'v Figure 30 31 32 33 34 35 36 37 10 5 x 10' W/cm2 and various K values 0 O O O O O O O O O O O O O O O O O 0 Temporal profiles of excited state population density (fluorescence) in LEI with spectral irradiance of 5 x 10-10 W/cm2 Hz. . . . . . . . . . . . . . . . . . Comparison of temporal profiles of ionization in DLI for the nonsteady state case and the steady state case. . . . Comparison of temporal profiles of ionization in LEI for the nonsteady state case and the steady state case. . . . Comparison of power dependence of ionization for DLI and LEI. . . . . . . The NZ laser power dependence of ionization in DLI. . . . . . . . . . . . . . Comparison of power dependence of fluorescence for DLI and LEI . . . . . . . . The relationship of temporal Profiles for ionization, expressed by ni/nT , and fluorescence, expressed by n2/nT ' 1n DLI. O O O O I O O O- O O I O 'O O O O The relationship of temporal profiles for ionization, expressed by ni/nT and I Page . 124 . 126 . 129 . 130 . 132 , 133 . 135 137 fluorescence, expressed by n2/nT, in LEI. , , , 138 xiii I '.o- v; ,,1.uv . ,0‘ .1 .o‘ .0- ! p Figure Page 38 Comparison of ionization in DLI induced by a nsec pulsed laser and by a nsec pulsed laser. . . . . . . . . . . 141 39 Comparison of ionization in LEI induced by a nsec pulsed laser and by a nsec pulsed laser. . . . . . . . . . . 143 40 The effect of different continuum relaxation processes on the power dependence of ionization in DLI . . . . . . . . 146 41 The effect of different continuum relaxation processes on the power dependence of ionization in LEI . . . . . . . . 147 42 Comparison of the power dependence of ionization in DLI nonsteady state case and the steady state case for different laser pulse durations. . . . 149 43 Comparison of the power dependence of ionization in LEI for the nonsteady state case and the steady state case for different laser pulse durations . . . . . . . . 151 44 Schematic of probe configuration. . . . . . . . 161 45 Asymmetric sensitivity of DLI apparatus to ion siganl . . . . . . . . . . . . 162 46 Sample strip-chart recorder tracings for the Na+ ion signal produced by the dual laser apparatus . . . . . . . . . . . . . . . . . . . 164 xiv .\-‘V‘ _ ..Iocv . 0. CI '0 'o (v. c“ Figure 47 48 49 50 51 52 53 54 55 56 57 58 2 Ion lifetime g as a function of db . . Ion lifetime g as a function of reciprocal probe bias voltage . . . . Model of ionized particles disturbed by a negative biased probe. A plot of sodium ion signal vs. negative bias voltage on the bottom probe. . . . . . . . . . . . . A plot of ion signal vs. the reciprocal of interprobe distance A plot of ionization vs. the reciprocal of interprobe distance. . .'. . . . . A plot of ionization vs. reciprocal of interprobe distance . . A plot of ionization vs. reciprocal of interprobe distance. . . . . . . . . . Floating potential vs. distance from bottom probe to ionizing beam. . . . . Energy schemes for sodium and lithium DLI. . . . . . . . . . . . . . Ion signals obtained when the dye laser is tune through the two-photon (ZS + 3D) excitation of Li . . . . . . Lasing at 6154 A plus boradband emission (over m 100 A range) produced by a Rhodamine B tunable dye laser. . . . . . . . . . . XV Page 169 171 , 182 , 188 190 192 193 195 203 205 207 ‘.'.’: O U .o'o. a On ‘1 'l ‘4 ‘c ’- '- .O‘ Figure Page 59 Ion signals obtained for the energy scheme of Figure 56(c) [Na(38 + SS) two-photon excitation] under various experimental conditions. . . . . . . . 209 60 Relative ionization from Na as a function of the power of broadband lasing from Rhodamine 6G, at constant N2 laser power . . . . . . . . . . . . . . . . 211 61 Dye laser power dependence of sodium ionization with two-photon resonance excitation (38 + 4D) . . . . . . . . . . . . . 213 62 Na ion spectra from DLI with 3P SS one-photon one-photon excitation, case(d) of Figure 56, 6154 A indicates the ion peak induced by the 3PL5 + 58% transition . . . . . . .'. . . . . . . . . . . 222 63 Dye laser power dependence of sodium . . . . .. 223 ionization with one-photon absorption (3P3/2+SS). 64 Spectra of (a) lithium DLI and (b) lithium LEI (x 200) with 23 + 2P excitation . . . . . . . . . . . . . . . . . . 227 65 a. Partial energy level diagram of sodium . . . . . . . . . . . . . . . . . 233 b. Block diagram of an experimental set-up for temporal profile measurement by DLI. . . . . . . . . . . . . 239 xvi Figure '66 67 68 69 70 71 72 73 Page Block diagram of the experimental set-up for DLI in a vapor cell. . . . . . . . . 239 The ion signal of Na in a uartz cell, induced by DLI with the dye laser tuned across the 35 + 3P transition. . . . . . . . . . . . . . . 241 Experimental arrangement for simultaneous observation of laser assisted ionization and laser induced fluorescence. . . . . . . . . . . 256 Ionization siganl ( ) and ratio of ionization signal to sodium solution concentraiton ( ) vs. sodium solution concentration . . . . 261 Profile of ionization signal ( ) and fluorescence signal ( ) obtained by scanning dye laser across the 351/2 + 3P3/2 (589.0 nm) Na transition . . . . . . . . . . . . 265 Dependence of ionization and fluorescence signals on Ar content of flame . . . . . . . . . 270 Dependence of ionization signal on probe voltage for various sodium solution concentration. . . . . . . . . . . . . . . . . . 271 Ionization profiles obtained by scanning the dye laser across the Na(3S-* 4D) two-photon transition. . . . . . . . 276 xvii 9. '~. .—. 6.. s ~§\. CHAPTER I INTRODUCTION A. Overview A-l Laser-enhanced Ionization (LEI) Laser-enhanced ionization (LEI) is a technique to detect analytes in a flame by forming ions with the aid of a laser. Based on the Boltzmann distribution, collisional ion formation in a flame is much less favored from ground state analytes than from excited analytes. Therefore, the laser is employed in the LEI technique to promote an analyte to a higher energy state, so that collisional ionization becomes more efficient. The collisional rate constant is enhanced by decreasing the energy defect between the ionization continuum and the discrete state. Actually, while investigating the photoionization of alkali elements, Mohler et a1., early in 1925, observed Cs ions produced by irradiation of a Cs sample with a wavelength corresponding to the principal series lines of Cs atoms (1). This phenomenon is often called the 5 r..- a... Own. a..‘ u .' .“ “v. ....I 1H 9. ‘Q ; rl' - 5 u I optogalvanic effect. With the advent of powerful lasers, this effect was first applied to analytes in a flame in 1976, and the technique is now more aptly called LEI (2-4). The atmOSpheric pressure flame used as an atomic reservoir is similar to those used in other analytical atomic spectIOSCOpic techniques. Electrostatic probes have been utilized to detect positive ions and electrons generated in a gas discharge since the 1920's (5). Surprisingly, an instrument consisting of a radiation source (laser), an analyte reservoir (flame), and an ion detector (electrostatic probe), led to a dramatic rediscovery of the optogalvanic effect. LEI differs from conventional flame spectroscopic methods (such as absorption, emission and fluorescence) and other laser-induced optical methods (such as laser-induced fluorescence) in at least two characteristics. First, LEI involves the continuum states of analytes, whereas other optical methods deal solely with the discrete states; second, an ion detector (electrostatic probe) is employed in LEI, whereas an optical detector (e.g. photomultiplier tube) must be used in the others. Based on these Specific characteristics, LEI has been developed as a new, powerful technique in the area of flame Spectroscopy. For example, Table 1 compares the detection limits of LEI to those of other optical nethods. It can be seen that LEI shows superior sensitivity in trace metal analysis for many elements Table 1 . Comparison of Detection Limits (ng/m1)* ele- laser ment LEI FAAa FAEb FAFC FAFd Ag 1 1 2 0.1 4 Ba 0.2 20 1 --- 8 Bi 2 50 20000 5 3 Ca 0.1 1 01 20 0.08 Cr 2 2 2 5 1 Cu 100 1 0.1 0.5 1 Fe 2 4 5 8 30 Ga 0.07 50 10 10 0.9 In 0.006 30 0.4 100 0.2 K 1 3 0.05 --- --- Li 0.001 1 0.02 --- 0.5 Mg 0.1 0.1 5 0.1 0.2 Mn 0.3 0.8 1 l 0.4 Na 0.05 0.8 0.1 --- 0.1 Ni 8 5 20 3 2 Pb 0.6 10 100 10 13 Sn 2 20 100 50 --- T1 0.09 20 20 8 4 *Taken from G.C.Turk, J.C. TrawEL'J.R. DeVoe and T.C. O'Haver, Anal. Chem. g1, 1890 (1979). aFlame atomic absorption. bFlame atomic emission. cFlame atomic fluorescence, conventional light sources. dLaser induced flame atomic fluorescence. (6-8). A-2 Current LEI Development Most LEI research has been carried out by scientists at the National Bureau of Standards (NBS) since 1976; the publications have been recently reviewed (2). Briefly, the mechanism of LEI is as follows: the analyte, nebulized into a flame, is first excited by a dye laser tuned to resonance with a selected excited state; then, the excited atoms are ionized mainly by collisions with foreign gases in the flame. The collision-dominated process is the principal pathway to ionization following resonant excitation of the analyte with a us pulsed flash lamp-pumped dye laser (4). LEI, as a new powerful ionization spectroscopy, shows several advantages over other optical methods: (1) LEI is free from certain optical interferences, such as scattering of the laser light, stray light and flame background emission. (2) The efficiency of ion detection can be much higher than that for photon detection; i.e. one ion produced from one atom can in principle be detected by a simple ion probe detector, whereas the quantum efficiency of photomultiplier tube is < 0.50 (3). There are no solid angle restrictions as in fluorescence u;': . . .0-4 I-‘ o‘n-‘fiov a 'IPAA u...‘ I do. I ."oo" has... .-..I ‘ .‘_.- o.~-: a.“ , ‘ A I....v c‘. . .- . a :3“ U . .'.‘ where photons are emitted isotropically. (4) Local dynamics in the flame can be monitored by LEI by positioning the probes and laser beam, but the averaged dynamics are viewed by fluorescence. (5) LEI is free from post-filter effects. Current developments in LEI can be divided into three main subjects: (1) Trace metal analysis: this is the major application of LEI. Various approaches have been used to optimize LEI for the detection of trace elements. At present more than 20 species have been measured; detection limits for some elements are as low as 0.001 part per billion (ppb) (e.g. Li) (6-8). The approaches to improving LEI include: (a) use of different types of lasers (CW, pulsed, atomic resonance-line lasers) and dual-dye laser combinations (each dye laser being resonant with a particular atomic transition, and the two lasers sharing a common intermediate state) to upgrade the sensitivity and the selectivity of LEI (6-12). (b) employment of various energy schemes including single photon, two-photon, stepwise and thermally nonresonant processes in efforts to extend the applicability of LEI (6,8,10,12). (c) utilization of various probe configurations and probe shapes in order to increase the ion collection efficiency (4, 13-14). (2) Electrical interferences in LEI: although the LEI technique is free from many optical interferences, it is affected to some extent by electrical interferences that originate from thermal ionization of the analyte and matrix species and from combustion reactions in the flame (7,8,11). Flame composition, easily—ionized matrix components, bias voltage applied to the electrodes, probe shapes and laser position with reSpect to the probes have all been found to affect the LEI signal (7-8, 11, l4-15). (3) Extension to molecular LEI: investigations in this field have been carried out mainly by another division at NBS. Oxide molecules in a CZHZ/air flame can be ionized collisionally or ionized by two photons with resonant irradiation of a dye laser. The ionization process depends on the energy defect between the ionization threshold and the resonantly excited state (16-18). The LEI spectra of oxide molecules were shown to be identical to one photon absorption spectra from the ground state to the resonant intermediate state. Furthermore, the intensity and the resolution (e.g. for the NO molecule) were reported to be better than those from laser-induced fluorescence (16-18). Clearly, LEI can complement conventional optical spectroscopy, not only in trace metal detection, but also in structure elucidation. However, a disadvantage of molecular LEI lies in its restricted applicability; only oxides and a few other molecules (e.g. C2, CH) can exist in flames. There are a few additional papers related to the fundamentals of LEI. Mallard and Smyth obtained ion o I. I‘ ‘ .. ‘1‘ I... .U' v-lvv - o.- I I ‘d’I . IItqnh - -\\ ucvuvvu “A. .‘ .UV‘. .‘. .. n .“0 O. ‘H. mobilities in CZHZ/air and CO/O2 flames, by measurement of the laser-pulse to the ion-arrival time gap (19). A simple three-level system of LEI has been developed to describe the ion signal production by neglecting relaxation processes from the ions (20). The temporal and spatial behaviors of ions produced by LEI in an Hz/air flame have been investigated in terms of a unique imaging method (21). From the above brief review, it is obvious that LEI is not as mature as most optical Spectroscopic methods (e.g., fluorescence, emission). The major reason is because of its relatively recent discovery and the small number of groups involved in LEI development at this time; however, it has a very promising future. A-3 Dual Laser Ionization (DLI) Dual laser ionization (DLI) is similar to LEI, but employs two lasers in producing the analyte ions in flames. In our laboratory, the two beams are formed by (a) directing an N2 laser-pumped dye laser beam and (b) reflecting a portion of the N2 pumping laser collinearly into the same area of an Hz-OZ-Ar flame. The detailed experimental set-up is described in Chapter II. The idea to use two beams to produce ions in a '- RA 4 233-tr, I .a~~. . 'v-d UH“. c v C I r. . ' " "c ..'..I U». ‘Oin'qao .' I ‘ “'vtuuu s " "“‘a': n U \ ., ‘VAQHA. '6‘ .‘. ‘v‘ a 'VI. I h c 4 a,“ . .. u‘“ a..: ‘. . 0 7. |.. . . at 0'0“...» " a " uh» 4‘. . l I U a" ‘k': I‘ I 51.5,, b“. u u C a I n. l.‘ ' In .‘el‘ 5 F . ‘0 1 I I 0 'n ‘n‘ . 'b"\h V‘: . fl \ ‘ M I.I -: s..a \ ‘ ~ I .t \ P flame was first triggered by T.F. George (U. of Rochester) in a departmental colloquium in 1980 where he discussed a laser-assisted collisional ionization model. However, the method utilizes a two-step process as had been suggested previously by various authors (22,23). Our results demonstrate that the nonresonant N2 laser can interact Significantly with the excited analyte population produced by the tunable dye laser, and thus can enhance ion production. Briefly, in our DLI technique, the dye laser is used to resonantly excite the analyte to a higher energy state. Then the ultraviolet, N2 laser (1 = 3371 A) serves as the ionizing beam to further promote a portion of the excited analyte population into the ionization continuum. Alternatively, collisions in the atmospheric pressure flame may result in ionization of the analyte following the dye laser excitation. This is the ionization pathway that occurs in atomic LEI. Because the collisional ionizaiton rate for species present in the excited state is nearly an exponential function of the energy defect between the continuum and the excited state, it can predominate over photoionization if the energy defect is small. Likewise, photoionization can predominate for large energy defects. Thus the energy defect, which depends on the particular excited level, determines which process is dominant. The experimental results and calculated predictions are presented in Chapter VII. Moreover, the photoionization process in DLI differs from that of the so-called multiphoton ionization spectroscopy (MP1) which is carried out in a low pressure cell. The former requires only on photon from the N2 laser to achieve ionization; however, MPI involves absorption of N (N _>_2) photons from the laser source, and "thus requires a more intense laser field to achieve ionization. B. Historical B-l The Optogalvanic Effect (OGE) The irradiation of a gas discharge or a flame by light at a wavelength resonant with a transition of the analyte may induce a variation of the impedance which can be detected as a voltage change across the discharge tube or the flame. The rediscovery of this effect with laser irradiation was achieved at NBS in 1976 (3, 24-25). In fact, the OGE was first observed by Mohler et al. and Penning (1, 26-27). Mohler detected Cs ions with a thermionic diode upon irradiation of the Cs with wavelengths correSponding to the principal series lines (1). Penning found the current across the discharge tube changes when radiation from another similar discharge tube 10 was incident (26,27). This was the first observaiton of the OGE in a discharge with a resulting current change in response to the absorption of radiation. Following Penning's observation, several analogous experiments were carried out by various groups (28-32). Although the OGE was first observed over 50 years ago, the potential of the phenomenon as a detection method was recognized only since its rediscovery by Green et a1. (3, 24-25). Green et a1. first applied the OGE in hollow cathode tubes to lock a CW dye laser to several characteristic atomic transition frequencies. The voltage change across the discharge tube was used to monitor the wavelength instead of conventional optical detectors (33). The OGE results make many weak resonance and excited state transitions available for frequency locking (33). King et al. used a similar technique to calibrate the output of a laser and to determine the laser band width (34). Keller et al. calibrated wavelengths emitted by species in a hollow cathode discharge tube through OGE measurements. The correspondence between laser-induced voltage changes and emission intensities permits the establishment of an atlas of emission lines, useful for cmtogalvanic wavelength calibration (35). Stephens demonstrated that the OGE detector is capable of showing selectivity towards atomic resonance radiation (36). Smyth et a1. investigated a possible ionization mechanism for an spectroscopy in a neon discharge (37,38). The OGE has — 11 been observed in the discharge of such gas lasers as the He-Ne laser, the xenon laser and the carbon dioxide laser (39-43), and in the subnormal glow discharge of commercial indicator lamps (44). The OGE Spectra of molecules (N82, N02, N2) in a discharge excited with a tunable CW dye laser were first reported by Feldmann (45). His results show that optogalvanic spectroscopy is a simple and sensitive method for the detailed study of the Spatial and velocity distribution of plasma atomic and molecular species which cannot be detected by fluorescence spectroscopy without background radiation. Zare and coworkers, reported the OGE in a pure iodine discharge upon irradiation with a CW dye laser (46). The resulting B-x spectrum of 12 closely resembles the laser-induced fluorescence (LIF) excitation spectrum when the laser beam is off the center line of the discharge axis. In addition, I lines (neutral and ionic) were also found. High-resolution spectroscopy on single-photon transitions has been performed using Doppler-free intermodulated optogalvanic spectroscopy (47). Doppler-free two photon optogalvanic spectra (TOGS) in a dc discharge tube were reported by Goldsmith et a1., who claimed that the method provides a simple and powerful alternative to fluorescence detection of two-photon transition. The result shows TOGS may provide a practical means Of observing Doppler-free two photon transitions 12 from nonmetastable or from metastable states (48). Ausschnitt et al. reported multiphoton OGE detection of hydrogen and deuterium in a discharge plasma (49). Beenan et al. observed an OGE signal in pulsed hollow cathode discharges (50). The signal in the pulsed mode was increased by factors of 1.7 to 650 over that in a CW mode. Keller et al. used the laser-induced impedance change in a uranium hollow cathode discharge for standard spectroscopic measurements, for determination of oscillator strengths, for measurement of the electron temperature of the discharge, for isotope ratio analysis and for information about the Sputtering process (51). Bridges characterized the OGE in cesium, argon, neon, hydrogen and mercury gas discharge plasmas. The polarities, magnitude and saturation of the induced-voltage changes were determined (52). Optogalvanic double-resonance Spectroscopy was proposed by Vidal as a new method of state-selective spectroscopy applicable to plasma discharges (53). Engleman and Keller irradiated a hollow cathode discharge with two lasers with wavelengths corresponding to different optical transitions in which a common intermediate energy level is involved (54). Their experiments indicated that the induced impedance changes are useful for determining and confirming spectral assignments and for studying energy transfer. 13 Atomic Rydberg states are usually detected by (l) fluorescence, (2) field ionization, (3) collisional ionization in a Space charge limited diode, and (4) photoionization. The field ionization method, in particular, has been used in many experiments involving high-lying states of atomic beams, because the Rydberg states can be easily ionized by a dc electric field, and the ions and the electrons thus produced can be counted almost without loss (55). Bridges first reported a study of the Rydberg states of cesium with the optogalvanic effect and CW laser excitation (52). Camus et al. used the technique to study Rydberg states of barium, with J values ranging from O to 5, using a two-step pulsed laser excitation, starting form the 5d653D1'2’3, metastable levels populated by the discharge (56). Delsart et al. reported the optogalvanic detection of krypton Rydberg states under two-step pulsed laser excitaiton, starting from either the 2P2, or the 2P3 intermediate level. These states were populated by the first-step N2 laser-pumped dye laser (57). They have obtained information about the nd [3/2]2 and nd [7/2]3 levels, for values of n not accessible to their analogous Kr Rydberg state study with field ionization detection (57,58). The magnitude of the OGE is dependent on the Inagnitude of the ionization rates of levels whose populations are perturbed by the laser. Based on this, ILawfler developed a linear steady state analytical model of 0"”- '...o- 0.. o n .\ v... - '5 . I: 9“ 14 the OGE by a rate equation approach applied in a positive column on the 587.6 nm He transition (59). This review of optogalvanic effect in discharges shows only a few examples of this promising technique. Compared with OGE in discharges, the OGE in flames (LEI) is still in its initial stages of development. B—2 Ionization Spectroscopy with Thermionic Diode Detection It is hard to clearly distinguish each laser-induced ionizaiton technique. Techniques are typically classified on the basis of the ionization process (collisional or photoionization), the sample type (atom or molecule), the atomization system (discharge, flame, vapor cell, or supersonic nozzle beam) and the detection system (thermionic diode, proportional counter, ionization chamber, electron multiplier or mass Spectrometer). These types of ionization spectroscopy are closely related; several of them are discussed in subsections 8-2, 8-3 and B-4. Mohler was the first scientist to use a thermionic diode to detect ions. As noted earlier, he monitored the concentration of the cesium ion when the vapor was irradiated with wavelengths of the principal series (1). Because of its high sensitivity, the thermionic diode has 15 been popularly adapted to measure ion formation (59-61). Typically the thermionic diode contains a plate anode and a dc-heated filament electron source. The amplification 5 to 106, (comparable to that factor is in the range of 10 of photomultiplier tubes); it is ascribed to the trapping of ions within the space charge potential well (62). In a space-charge detector, all the ions created are detected, whereas sample fluorescence emitted isotropically is Often detected only over a small solid angle. The current pulse of the thermionic diode are much longer than the excitation laser pulses or the emitted light pulses in a fluorescence experiment. Thus, a fast electronic system is not needed. Marr and Wherrett employed such a detector with a mercury irradiation of Cs to study the ionization potential of Csz, the ionization processes leading to Csz+ and Cs+, and the molecular absorption cross section of Cs (62). 2 Thermionic diodes have also been employed in the investigation of Rydberg states. Aymar et al. used two-photon absorption spectroscopy with an N2 laser-pumped dye laser and thermionic diode detection to obtain new data on the even-parity J = O and J = 2 levels of neutral barium. The energies of the 6snslS0 series (16 i n S 61), the 6sndlD2 series (15 S'n 5 81) and the 6snd3D2 series (15 5, n §_30) have been determined (63). Multiphoton ionization of alkali metals with space charge detection 16 has been investigated by Collins et al. (64). B-3 Resonance Ionization Spectroscopyi(RIS) RIS, pioneered by scientists at the Oak Ridge National Laboratory is a photoionization method in which atoms are promoted to an intermediate state with laser(s) radiation and then converted into ion pairs by absorption of photons from precisely tuned laser(S) (22). The electrons produced can be detected either by a pulsed ionization chamber or by a proportional counter. The former is used only as an analog device with a lower limit of sensitivity of approximately 200 electrons; the latter may be used as either a digital or an analog device with a sensitivity of one electron (65,66). With current laser technology, it is possible to saturate specific transitions and to convert each atom to a positive ion and a free electron. With the aid of a proportional counter the R18 technique was employed to 19 detect a single CS atom in the presence of 10 Ar atoms and 1018 CH4 molecules (67). Similar experiments were carried out to detect a single xenon atom and a single lithium atom (68,69). Several other applications of RIS, such as photo-dissociation of salts, collisional line broadening measurement, identification of Rydberg states, CA. a .- b-- I. on. I p“ o.) .h . \'. Q 17 gas amplification fluctuations in proportional counters, and studies of atomic diffusion in the counter have been reported (69-75). P. Lambropoulos has also contributed experimental and theoretical results in the field of atomic multiphoton ionization spectroscopy (76,77). Another branch in this field is being studied in France by Lompre, Mainfray, Manus et al. (experimentalists) and Gontier, Trahin, Crance et a1. (theorists) (78-84). In several studies of the multiphoton ionization of atoms, factors such as spatial effects (including the ac stark effect, the enhancement effects, and the effective order of nonlinearity) and temporal properties have been investigated (78-84). B-4 Multiphoton Ionization Spectroscopy (MP1) In order to avoid confusion with the fields reviewed in subsection B-3, only molecular multiphoton ionization Spectroscopy is discussed here. The research groups of Johnson (85,86) and Petty (87) were the first to show that multiphoton ionization spectroscopy (MP1) with a proportional counter or an electron multiplier detection can be a powerful tool to study multiphoton transitions of normal molecules. To date, MPI has been used primarily to discover and identify new electronic states. Examples ‘fi. 7'- I .- I... II. I‘. “In 18 include: iodine, benzene, ammonia, alkanes, amines and polyenes -- where new states can be predicted theoretically, but were not previously observable because of the unfavorable selection rules (87-93). In addition, MP1 can provide a means of probing excited-state repulsive potentials (94). With MP1, the ionization spectra of the molecules cooled in a supersonic nozzle have been obtained; this greatly simplifies rotational and vibrational structure (95-97). The first studies of multiphoton ionization in effusive molecular beams, with mass analysis to provide identification and relative abundances of the fragmentations, were carried out by Bernstein and coworkers (98,99). From an analysis of the MP1 process one can estimate the photon numbers absorbed by the resonant intermediate state (98,99). C. Organization of the Dissertation This thesis contains eight chapters and two appendices. This introductory chapter and the following experimental chapter are general in nature. Theoretical and model treatments, experimental results and applications follow. Chapter III considers the mechanism of ion production in DLI. The detailed multiphoton ionization 19 profiles of DLI and LEI with respect to the detuning wavelength are compared with a theoretical model derived from time-dependent perturbation theory. This simplified analysis must be modified somewhat to account for the experimental observations. DLI and LEI are considered on a more phenomenological basis in Chapter IV through a rate equation approach. The temporal relationship between ionization and fluorescence for the optogalvanic effect in a flame is theoretically described. The predictions have not yet been tested experimentally. In addition, a comparison is made of the enhancement of ionization and fluorescence in DLI to those in LEI, respectively, and of the impact of prolonged irradiation on both DLI and LEI. The rate equation approach can be applied successfully to many aspects of DLI diagnosis. Chapter V treats the use of DLI to determine flame temperatures. This is the first time that the optogalvanic effect has been applied to measure flame temperatures. Information on ion mobilities and diffusion coefficients in a flame is also provided. Chapter VI presents further consideration of the behavior of ions in the field of the electrostatic probes. An attempt is made to relate DLI to the probe theories, which have been developed primarily for the diagnosis of gas discharges. A simple model is used to characterize the regions including charged particle sources, sheath and 20 probe. The behavior of saturated ion current in the field of the probe is described, and ion densities are estimated. Chapter VII considers the efficacy of the DLI technique. The domination of collisional ionization or photoionization following promotion of the analyte to an excited state can be controlled by selection of the excited state which is in resonance with the tunable dye laser. An examination of which process prevails is made for various selected excited states of sodium and lithium. The results are in agreement with the calculations. Energetic considerations for the optimum application of DLI are discussed. Suggestions for future development of the DLI technique are presented in Chapter VIII. The DLI-based diagnosis of the temporal and spectral occurrence of excited states is proposed. Also, the possibility of DLI saturation studies and the applicability of DLI in a vapor cell are presented. Appendix A deals with some basic characteristics of DLI and presents our first experimental results (obtained jointly with C.A. van Dijk and F.M. Curran). Appendix B deals with the calculation of the photoionization cross section of atom based on the quantum defect method. The calculated results by different numerical methods agree with Peach's table of related parameters (100). u». t‘h CHAPTER I I EXPERIMENTAL A. Instrumentation The basic block diagram of a laser-induced ionization apparatus is depicted in Figure l. A laser source irradiates the sample and excites the atoms (or molecules); this is followed by absorption of additional photons or by collisions to yield ions. Alternatively, sample ions can be generated by direct multiphoton processes from the ground state. The resulting ions are then collected or counted by an ion detector. Following amplification, the ion signal is recorded by a readout device such as a strip-chart recorder, an oscilloscope or a computer data acquisition system. In resonance ionization Spectroscopy (R18) and the multiphoton ionization (MP1) technique, the sample is introduced in a vapor cell. Typical ion detectors are proportional counters, mass Spectrometers, thermionic diodes and electron multipliers (22,62,86,98). By contrast, in laser-enhanced ionization (LEI) the sample is introduced into a flame and biased electrostatic probes are employed 21 22 [ laser }._1"£"'_.LsamplejJ ion {detector] 1 I Eecorder It amplifier Figure 1. Schematic laser-assisted ionization apparatus. 23 as ion detectors (2-4). Signal processing devices are typically boxcar integrators and lock-in amplifiers for pulsed lasers and CW lasers, respectively. The dual laser ionization (DLI) apparatus used in this research is analogous to that used in LE1, and is illustrated in Figure 2. The DLI apparatus includes three major components: (1) the light source, composed of a pulsed N2 laser-pumped tunable dye laser, with the N2 laser radiation utilized as the second, non-tunable beam; (2) a flame cell as an atom-reservoir, providing a selected concentration of metal atoms; (3) the detection and readout system. The latter includes a pair of biased nichrome wires and a current-to-voltage conversion device for ionization detection, a monochromator (with photomultiplier tube) located at an angle of 900 with respect to the incident light for fuorescence measurement, and a strip-chart recorder and an oscilloscope used as readout devices. The LEI technique was first developed as a potential trace analysis technique at the Naitonal Bureau of Standards (NBS) (2-3); the NBS workers employed a flashlamp-pumped, s pulsed dye laser or a CW dye laser. The choice of a ns pulsed N2 laser-pumped dye laser in these experiments was predicated on the following factors: 1. The ns pulsed laser source had not been used in Previous LEI experiments, and was available in our laboratory, Rf [/‘\ - - BOXCAR I \‘ + 7315553 INTEGRATOR ‘ , N2 LASERJ=::I‘ I I:::DNElJfiifll ‘ 7 I _ FROM NZLASER QED 4’ [NANCE Figure 2. Block diagram of experimental set-up for DLI. 25 2. Dual laser ionization may offset the lower ion population induced by a ns pulsed dye laser, as compared to that induced by ails source. For example, the simple equation n~ kAt (n is the ion density, k the ionization rate constant and At the laser pulse duration) predicts that the ion population obtained from a 10 ns pulsed laser is less by about two orders of magnitude than that obtained from 1 us pulsed laser, if both lasers have the same power density (W/cm2 ). Thus the N2 laser-pumped dye laser leads to lower sensitivities in the LEI technique. However, the DLI method may actually show analytical sensitivity superior to that of LEI. 3. Time-resolution of the ion signal can be measured with a ns pulsed laser, and studies Of the dynamics of ion behavior are possible. During the DLI experiment (see Figure 2), the N2 laser-pumped dye laser was focused in the center of an Hz-Oz-Ar flame. A portion of the N2 laser beam was split off and reflected with a flat mirror into the opposite side of the flame. Both beams are collinearly focused in the same region. The path lengths and lenses were adjusted for maximum temporal and spatial overlap of the two laser pulses at the burner. The ionization signal was detected with a pair of biased,~0.9mm diameter nichrome wires. These probes were mounted on micrometer-driven transition stages and located in the vicinity of the beam path. The signal from the probes were processed by a boxcar averager 26 with gated integrator; data were recorder on an x-t recorder. The fluorescence emitted by the sample was spectrally resolved by a monochromator placed at an angle of 900 with respect to the incident laser radiation to minimize the interference of elastically scattered radiation. Following the monochromator, a photomultiplier tube was used to detect the fluorescence. Both the ionization and fluorescence signal could be Observed on a storage oscilloscope (Model 564 Tektronix, Inc., Beaverton, OR). A-l Laser Sources Pump Laser The laser used to pump the tunable dye laser was an N2 laser with output at 3371 A° (Model 0.5 - 150, NRG, Inc., Madison, WI). When the N2 laser is fired repetitively (10-60 HZ), a train of short pulses (each0: Sns FWHM) irradiate a fluorescent dye in the cavity of the tunable dye laser. The general characteristics of the N2 laser are given in Table 2. During the operation of the N2 laser, the flow of prepurified grade nitrogen (Airo Inc., Montvale, N.J.) is controlled by a high quality pressure 27 Table 2. Specifications of Nitrogen Laser Repetition Rate: Peak Power at 60 Hz: Pulse Dration: Average Power at 60 Hz: Power Requirement at 120 volts, Beam Divergence: 60 Hz: 1 - 60 Hz 0.5 MW 5 nsec FWHM 150 mW 10 amp 3.8 mrad x 10.7 mrad 28 regulator (also Airco) having both high and low pressure gauges; the low pressure gauge is used to set the pressure in the Spark gap, which normally operates in the pressure range of 20 to 28 psi. The following N2 passes through the Spark gap, then through the laser tube where the pressure is adjusted to be about 70 Torr by a needle valve. A filter dryer is located between the Spark gap and the laser tube in order to remove any carbon that may be released in the spark gap. A diagram of the flowing nitrogen system is shown in Figure 3. A water on-off valve is located on the input Side of the power supply. This interlock protects against operation of the laser without water cooling. The conditions used in the experiment maintain the laser tube pressure at 70 Torr, the pressure in the spark gap at 25 psi, and the repetition rate of the laser at 20 Hz. These conditions provide satisfactory output power and stable peakéto-peak ratio. The pressure in the N2 laser tube affects the output power of the N2 laser, and thus that of the dye laser; subsequently, it also affects the sensitivity of ionization induced by the N2 laser-pumped dye laser. The ionization signal, and the power output Of dye laser versus N2 pressure in the laser tube are shown in Figure 4. 29 emuaem .o .HmmmH .QEDQ Esoom> .m «Momma .O “mason Essom> em xm>am> mapmwc .m «Hmwup 3mm xumom .O «Houmanmmu .m «wauuon «z .<. 2 How Emumhm somouuwc de3OHm mo Emummflo N .m muoowm Output Power of Dye Loser (on) Figure 4. O) A 0‘. N 45 ()1 LO 6. 4. Ionization (cu) 1 U" .13 1.4.1 50 55 SO 65 7O 75 Pressure of N2 Loser Tube (Torr) Dependence of dye laser power (0) and sodium ionization (11) on N2 pressure in N2 laser tube. The ionization signal of sodium is related to the dye laser power. Sodium ions are produced by dual laser ionization (DLI) with the dye laser tuned to a transition of the 385 + 3P3 level of sodium. The concentration of sodium 18 10 ppm (ug/ml). e a ‘.I Ub-ou 0.. .i. .h. NI .0. x I‘- e. x 9‘ s 31 ‘ —— (b) N2 Laser—Pumped Dye Laser The dye laser was first discovered by Sorokin and Lankard in 1966 in describing the stimulated emission from a fluorescent organic dye in liquid solution and by Schafer et al. in realizing the tunability of such a source (101,102). Since then, the dye laser has been highly developed. It offers a Simple and versatile method for generating tunable, coherent radiation over a broad range from the ultraviolet to the infrared. Several properties of optically pumped dye lasers are described below: (1) frequency range: The output tuning range of a dye laser, usually pumped by a fixed wavelength laser, depends mainly on the particular dye or dye mixture used in the laser. This range may vary from several nanometers to over a hundred nanometers. Figure 5 depicts the wavelength ranges for various dyes when pumped by an N2 laser. (2) spectral width: The linewidth (FWHM) of the Simplest dye laser configuration is on the order of 5 nm. This width can be reduced dramatically by adding a spectral resolution element, such as a prism, a diffraction grating, an interference filter or a O Fabry-Perot etalon. For example, a linewidth of 0.01 A for an N2 laser-pumped dye laser was obtained by using a 32 0N0 ova Och www.c- vvpé. thO 00.: 00.2 + 9P8 mun wZ.N<>> mus. wZ.N mo mason sumcwam>m3 one .o coo owm one 9.... oov, . m 9.39% _: mz§m© voopmmn on» no OchoHoEO ma Hopuoomu Dunno ofluum m .sumcwaw>m3 on “common :ufi3 Awe mcflsoponm. momma who mo cowusbwnunwp HTSOQ uaovno one .5 munofim av £92925 nmmm mnmm 00mm En nvmn 9mm nmhm 09.0 093 + I 36 8mm F- “D In) QT ID a; (no) JaMOd (ndmo 37 peak energy ~160 DJ) at 5890 A and~85 KW (or peak energy...v 300 ,uJ) at 5787 A can be achieved. In order to increase the power density of the laser, a lens with 15 cm focal length was set at an appropriate position between the front mirror and the flame. The cross section of the beam waist focused by the lens was measured with a 50(1m pinhole moved in three dimensions by a micrometer-driven translation stage. At first the pinhole was moved along the Z axis, the direction of the laser beam, and fixed at the position with the maximum output power as measured by the joulemeter; then the pinhole was moved in the x and Y directions, respectively. A Spatial profile of output power against the X (or Y) axis was obtained, as shown in Figure 8. By multiplying the full width at half maximum (FWHM) of the Gaussian profiles Obtained in the X and Y axes, respectively, an effective cross section of the beam waist (cmz) was estimated. The focal area of the dye laser through the lens was determined to be (1.0 I 0.3) x 10-3 cm2; Similarly, the focal area of the N2 laser through a quartz lens was determined to be (2.01:0.4) x 10"4 cm2. Although we may take full advantage of the high output power, the Short pulse duration and the small spectral linewidth of the N2 laser-pumped dye laser in these experiments, several disadvantages exist: (1) The tunable frequency range of each dye is small. In order to excite different elements, many .0‘ O r (9 <3 (.0 r . Loser Power (0.0.) .Figure 8. , J 38 1 1 1 I 1 l 'IOO 0 I00 200 X axis (pm) l '200 Measurement of the effective cross section of beam waist of N2 laser along the X axis (the direction parallel to the optical table, but perpendicular to the laser beam). Aljoulemeter is used to monitor the power output of N2 laser by irradiation through a 50 um pinhole moving along thex axis. The pinhole is positioned by a micrometer-driven translation stage. Fu11 width at half maximum (FWHM) of the laser beam is estimated to be 220 um. 39 different dyes must be used and an appropriate optical alignment is required to maintain a maximum output power for each dye. (2) Each dye solution has a finite lifetime. Degradation of the dye solution and a consequent reduction in output power were noted during long-term experiments. The ouput power of the dye laser also depends on temperature. Peters et al. pointed out that at temperatures higher than'nzo 0C, the peak power of Exciton C460 drops to~70% of the original power and the divergence angle of the laser beam increases by '913% (108). Fortunately, this effect is small for the dye solutions selected in our experiments. (3) High intensity radio frequency interference (RFI) is generated, which introduces noise into other electronic devices operated in the vicinity. For this reason, two rf chokes, consisting of several wire turns around a ferrite core, were soldered into the high-voltage power line of the N2 laser. Both the laser and the chokes were placed inside a grounded Faraday cage, consisting of 0.5 mm copper plating. These measures substantially decreased the RFI from the N2 laser discharge. (4) Large pulse-to-pulse variations of about 10% in the laser output. (5) A significant background of broad band lasing from each dye solution is generated (see Figure 7). Such lasing may interfere with the ionization Signals, 40 especially those induced by the DLI process; fortunately, the wavelength range of broad band lasing is invariant and several hundred A away from the selected wavelength. By selecting carefully the baseline, we may avoid its interference with the DLI Signal. This is discussed in detail in Chapter VII. A-2 Flame Cell The laminar flow, premixed, HZ-Oz-Ar flame utilized in the experiments is illustrated in Figure 9. Prepurified grade gases: 02,H2 and Ar, are controlled by dual pressure regulators, having high and low pressure stages. After passing through the pressure gauge, each gas is divided into two branches which form the inner and mantle flames, reSpectively. By adjusting a control valve to provide a predetermined setting on each calibrated flowmeter, a selected flow rate (l/min) for each gas can be obtained. For each branch of the flame, O2 and Ar are premixed first in a mixing chamber fitted with a safety spring; the subsequent gas mixture then mixes with H2 in another chamber prior to reaching the burner head. In this way, spontaneous combustion of H2 and O2 inside the mixing charmer can be safely avoided. The atomdc analyte is introduced into the inner flame by carrying its salt 41 02 Ar H2 CY L CYL (DILLENT GAS) (FUEL GAS) HPR ' HPR CV CV PM PM Spr MC we MC V! 8 F f Figure 9. .Block diagram of gas flow system in an Hz-Oz-Ar flame. CYL, high pressure cylinder; HPR, high pressure regulator; CV, capiliary valve; FM, flow meter; Spr, sprayer; MC, mixing chamber; WB, washing bottle; .‘ B, burner house. 42 solution out of a pneumatic nebulizer with Ar gas (see in Figure 10) before mixing with other gases. The mantle flame has the same composition as the inner flame, but contains no metal salt. The laminar premixed HZ-Oz-Ar flame is one of the most important premixed flames (109,110). Two important properties of the flame are: (1) Low flame background emission, and low temperature resulting in less ionization interference. (2) A high quantum yield for fluorescence, because 2) the quenching cross section of Ar is very small (< 2 A (111). Essentially, laminar premixed flames are less turbulent, less audibly noisy and have less flame flicker than turbulent flames, in which each flame gas is introduced separately and mixed above the burner head (112). Accordingly, the HZ-OZ-Ar flame results in less electrical interference from ionized combustion products in ionization experiments, and provides an intense signal with high Signal-to-noise ratio for fluorescence measurements. The burner of the flame is of the Meker type; the gases reach the burner head through 631 circular holes of 0.5 mm diameter and 5 mm length, arranged in concentric circles with a 2 mm interval between sucessive rings. The diameter of the inner flame is 15 mm, and the height of the primary combustion cones is approximately 2 mm. The burner head is cooled by a water jacket (113). I” II) I 0'54 Soul 0 mt vi.- a A? g U. Q ‘Dn ' II o ‘Uu. :‘a - W.‘ so '5 g 9 I" 43 In comparison to the ultrasonic nebulizer or the Hieftje-Malmstadt type nebulizer (114), the homemade pneumatic nebulizer used in this work produces larger droplets and less spatial resolution, which may result in optical scattering or imcomplete vaporization of solvent or solute. Nevertheless, DLI and LEI suffer no optical interference from flame background or stray light. Thus the disadvantage of the nebulizer is negligible in ionization experiments. The mantle flame prevents entrainment of air and smooths the radial temperature distribution of the inner flame. The effect of the mantle flame on the ionization signal is insignificant. However, if the mantle flame is of higher temperature than the inner flame, energy transfer to the inner flame can occur, which results in a disturbance of local thermodynamic equilibrium. Thus the mantle flame should be as identical in temperature to the inner flame as possible. Strictly speaking, in a flame or other high temperature plasma, it is impossible to reach true thermodynamic equilibrium because the flame radiates heat to the environment, undergoes secondary combustion at the flame boundaries and undergoes convection; these processes lead to a net transfer Of heat, mass and radiation within the flame. However, even though these transfers occur within the flame gases, it is still possible to maintain a I‘loca1" thermodynamic equilibrium as long as the transfer rates are small compared with the 44 'rates of equipartitioning of energy over the different energy forms. In a laminar premixed flame the region of a local thermodynamic equilibrium can be extended over a considerable portion of the flame gases; in contrast, the local equilibrium region is very small in the turbulent flame (115,116). When the inner and mantle flame have the same flow rate of H2, 02 and Ar (equal to 1.0 l/m, 0.5 l/m and 3.2 1/m, respectively), the temperature was determined by the DLI method to be about 2100 K, which satisfactorily agrees with that obtained by line reversal methods in Similar flames. Flame temperature measurement by the DLI technique is described in detail in Chapter V. In all atomic flame spectrometric methods, a sample solution is aspirated into the flame to produce an atomic vapor. There are five basic steps occuring throughout the process: (1) solution transport: In the initial step, the solution is carried from a container into the nebulizer. (2) droplet formation: The salt solution is broken into droplets after reaching the nebulizer; the size of the droplets formed decreases as the solution uptake rate increases. (3) solvent evaporation: The solvent evaporates from the droplet to leave a salt particle (This step may be completed with a chamber type nebulizer, such as Pneumatic and ultrasonic nebulizers, before the analyte 45 reaches‘ the flame.). The rate of solvent evaporation depends on several factors: the size of the droplet, the characteristics of the solvent, the number of solvent droplets per cubic centimeter and the flame characteristics. (4) solute evaporation: The remaining salt mist evaporates at a rate dependent on the size of the salt particles, the number of salt particles, the characteristics of the salt particles and the flame characteristics. (5) atomization: The final step is the production of atomic vapor after the solution is introduced into a flame. The free atom fraction is the ratio of the concentration of analyte species in the form of atoms to the combination of analyte in all forms such as ion, oxide and hydroxide. A general expression relating atomic concentration N in the flame gases to the analyte concentration C0 in the solution sprayed into the flame is (112,127): N = (6 x 10 ) Qt at 2T Here F indicates the solution transport rate (cm3/sec); e is related to the sprayer efficiencye Spray :8 is the free atom fraction; 9 and the degree of solute vaporation £8015 is the statistical weight of the ground state; Qt is the flow rate of unburnt gases into the flame; ef is the 46 expansion factor for the flame gases; ZT is the normalized electronic partition function. The atomic concentration N is a linear function of the analyte concentration over a wide concentration range. This is demonstrated in Figure 10 for thermal emission vs. sodium concentration in sodium chloride solutions; the deviation from linearity around 200 ppm is mainly due to the decrease in sprayer efficiency ( ), as the analyte concentration eSpray increases, or to self-absorption. A-3 Optical Detection The optical detection system used in these experiments consists of a filter/grating double monochromator (Model EU 700-56, GCA,Mcpherson), coupled to a photomultiplier tube (Model EU 701-30, GCA, Mcpherson), located at an angle of 900 with respect to the incident laser beams. The analyte fluorescence from the flame is focused by a lens onto the entrance slit of the monochromator. The resolution element is a plane diffraction grating. (48 mm x 48 mm ruled area;lineS/mm = 1130, blaze 1: 2500 A ). The monochromator has an assembly of eight filters with controlled Spectral transmittance characteristics,which provide a preliminary stage of wavelength discrimination. This feature serves to reduce IOOO - Thermal Emission (cu) 47 a—Figure 10. IO :00 (000 No Concentration (pg/ml) The concentration dependence of thermal emission of sodium atom in an Hz-O -Ar flame. An RCA11P 28 photomultiplier tube (no filters) is used as detector. The applied voltage is 700 V. The thermal emission signal tends to deviate from the linearity when the sodium concentration becomes >100 ug/ml due to self-absorption and nebulizer ineffiCiency. 48 higher order diffracted radiation and stray light, resulting in higher purity of the measured fluorescence signal. The spectral band pass of the monochromator is 2‘3 when a lOOum slit width and 1 mm slit height are employed. It is possible to reach 0.3 A spectral resolution with a 5 um slit width and l m slit height (118). A photomultiplier tube (RCA, 1P 28A) was set right behind the exist slit to detect the incident radiation already spectrally resolved by monochromator. The photomultiplier tube (PMT) typically has a wide linear dynamdc range of about 106 or more (112,119); nonlinear reSponse ensues as the photomultiplier approaches saturation, which is caused by Space charge limitations at the last few dynodes, and by finite photocathode resistivity effects (120). The nonlinear behavior can be easily checked by inserting a set of neutral density filters in front of the entrance slit of monochromator. The bias voltage between the anode and photocathode was set to -800 volts. The output current of the PMT was converted to a voltage and processed by a boxcar integrator. The output of the boxcar was read out on a strip chart recorder. b\ .5. 49 A-4 Ionization Detection The alkali metal ions produced in the flame by the DLI or the LEI technique are collected by a pair of voltage biased nichrome wires suspended inside the flame, about 10 mm above the burner head in order to avoid the combustion zone close to the burner head. The probe current passes through an electronic circuit formed by a preamplifier and a high-pass filter. The resulting voltage output is the input to the boxcar integrator for signal processing. The nichrome probes (“-0.9 mm in diameter) are inexpensive and resist satisfactorily the high temperature environment of the flame. The probes last several hundred hours. The disadvantage Of using nichrome probes results from analyte contamination, which grows gradually on the probe surface upon continued use. Leaching from the probe may lead to significant electrical interference upon the ionization signal when different analytes are introduced into the flame. Therefore, probes are changed often to avoid this interference. The nichrome wires were positioned parallel to one another in a plane perpendicular to the burner head. The probes were typically 4-10 mm apart. The bottom probe was placed about 10 mm above the burner head, and was mounted on a micrometer-driven translation stage with a positional accuracy of 10.01 mm; the top probe was also mounted on an .«u '.1 .‘1 'il a p... 3'55. \ {D 50 electrode holder and was movable in three dimensions by tuning an adjustment knob. The ionization sensitivity was found to have an unsymmetrical response to the probe voltage polarity. Superior sensitivity was achieved when the bottom probe was biased negative with respect to the top probe and located closer to the irradiated area. A detailed discussion of the ion behavior in the field of the probes is given in Chapter VI. The advantage of using metal wires to collect the ions is one of convenience and economy. Such electrodes are suitable for high temperature flames, although different ionic species cannot be distinguished. However, by using a high resolution laser source, the DLI technique can compensate for this disadvantage. A-S Signal Processing The output signal from the ion detector or the photomultiplier tube is the input to a dual channel boxcar averager (Model 162-164, Princeton Applied Research Corp., Princeton, N.J.) for signal processing. A boxcar averager can increase the signal-to-noise ratio by repetitive sampling of the signal-plus-noise with a gate at the appropriate time after a trigger pulse. It is advantageous to employ a boxcar averager to manipulate a signal induced 1) :- I" coal 30:1 Aha! on.“ g - ._’ p ~‘o ~ ~ I"‘- ..l- . 6 ADA 1.. ‘ .“ h“ ‘ C N ‘v I ') ( (I. C" rat _ &-¢ '0' 51 by a pulsed, low duty cycle excitation source, since the gate of the boxcar opens only when triggered by the signal, and the background noise is measured for the very short gate duration time. The boxcar averager was triggered synchronously by radio frequency noise produced when the N2 pumping laser is fired. There is a delay of‘~45 ns before the boxcar aperture opens to manipulate the signal. The lifetime of ions produced by the laser pulse is on the order of us. Hence it is not necessary to employ a delay line to prevent the signal from appearing prior to the gate. However, the lifetime Of atomic fluorescence is on the order of us; in this case, a delay line is useful. Since no impedance transformer device is employed at the output of photomultiplier tube to maintain the "true" Signal throughout the delay line, the fluorescence profile will be distorted to some extent (121). Since the fluorescence profile is not a major emphasis of this work, this distortion was neglected. The dual channel boxcar averager main frame (model 162) is equipped with one model 164 gated integrator and one model 163 sampled integrator which incorporates a Tektronix S-2 sampling head. The gate width of the model 164 provides a continuously variable sampling gate from 5 ns to 5 ms width. In contrast, the model 163 utilizes a selection of plug-in sampling units to obtain nonadjustable sampling gate widths ranging from 75 ps to l 52 ns (122). Consequently, the model 163 is preferably employed to sample a fast signal such as ns fluorescence decays. However, for time-integrated Signals or for longer decay times, the model 164 is preferred because its variable gate width can be adjusted to obtain a maximum signal-to-noise ratio. Accordingly, the model 164 gated integrator was employed to manipulate all the ionizaiton decays, on the order of us, and the time-integrated ion signal and fluorescence Signal in these experiments. Although a baseline sampling gate, associated only with the model 163, would be useful to eliminate the distortion caused by baseline drift on time-scanned signals, such distortion seemed negligible in these experiments. The sampling gate of both the model 163 and the model 164 can be positioned anywhere along the signal waveform, or it can be time-scanned across all or a portion of the signal by adjusting the initial dial. For averaging at a fixed point in time, hereafter called single-point analysis, the gate was located SO as to encompass the peak maximum. There are two modes, exponential averaging and sum averaging, incorporated in the model 164. When operating in the sum averaging mode, the result of each integration is added linearly to the previous values until output overload occurs. The output in this mode is simply the average of N repetitions; for white noise the signal-to-noise ratio should improve withvfil The mode is 53 only employed in single-point analysis. The summing mode is analogous to linear integration with an analog integrator. When the exponential averaging mode is chosen, the output Signal asymptotically approaches G times the input signal, where G is a gain factor. When the output level reaches G times the input level, there is no further change in the output signal, no matter how many repetitions of the input signal occur. Accordingly, it is considered to be the average of 2TC/AD repetitions of the input Signal, where TC is the selected model 164 time constant and AD is the selected aperture duration. The Signal-to-noise ratio achieved by this mode is (2TC/AD)]‘/2 The exponential mode is analogous to low-pass filtering with an RC filter. The exponential mode can be used in both Single- point analysis and time-scanned analysis. For the latter with the model 164, the minimum scan time (MST) is determined by I ’5 MST = 5 [(SPTC)2 + (OTC)2] x 57333 (2) where the Signal processing time constant (SPTC) is selected by the main frame time constant switch, the observed time constant (OTC) is computed by dividing the selected model 164 time constant by the product of the aperture duration times the repetition rate; ADR is the aperture delay range and the value of AD is the aperture 54 duration. For example, for one of the experimental conditions used here, the repetition rate was 20 Hz, the ADR was 50 us, the AD was 0.5 us, the SPTC was 100 11s and the time constant of the model 164 was 10 us. The minimum scan time was thus estimated as 500 sec. The spectral profile of ionization is obtainable with single-point analysis by averaging the portion of signal within the gate, then varying the laser wavelength across the signal profile. The temporal profile of ionization can be obtained by time scanning the boxcar gate across a portion or all of the ionization decay. Single-point analysis and time-scanned analysis are related to each other; that is, the Spectral profile of ionization can be Obtained by time-scanned analysis and the temporal profile can be obtained by single-point analysis. For each point (or wavelength) on the spectral profile of ionization, there is a corresponding temporal decay obtainable by scanning the gate width across the pulse formed at each different wavelength. The time can be integrated on a strip chart recorder at each wavelength; a gain G is related to the resulting area and time- integrated value obtained from single-point analysis. The area integration can be computed by applying cubic Spline interpolation to several selected known points to derive a decay function associated with the temporal profile Obtained experimentally. A computer program DCADRE (from the IMSL routine library) was utilized to integrate the '\ 55 function. Figure 11 shows a comparison of the area integrated spectral profile to the time-integrated profile for the ionization of sodium induced by DLI with 381/2 - 3P1/2 absorption. The methods are in satisfactory agreement. A significant error encountered with cubic spline interpolation is caused by the difficulty in selecting data around the maximum; however, manipulation of several sets of data may compensate for this drawback. On the other hand, the sampling gate can be positioned along the inization signal waveform by adjusting the initial dial, as mentioned earlier. For example, if the aperture delay range (ADR) is 50 us, and the intial dial is set at 10%, then the aperture delay is 5 us; that is, the aperture opens after 5 us delay within ADR. Consequently, it is possible to obtain a temporal profile of the ionization signal by serially positioning the aperature at points on the input waveform, then averaging the intensity at each point. By varying the value of the initial dial, the relative position of each average value carried by single-point analysis along the waveform of the pulse can be counted. A comparison of the temporal profile of ionization estimated by such a method with that obtained by time-scanned analysis is also given in Figure 12. The lifetimes of the ionization signal obtained by single point analysis are 3.2 10.2 us and 3.6i 0.2ps under the conditions of ADR = 20 us, AD = 5 us, and ADR = SOUS, AD = Sus, respectively. The results are in Ionization(a.u.) U! o Figure 11. -6 -4 -2 O 2 406 Dutuning Wavelength (A) Comparison of spatial profile of ionization obtained by time-integrated analysis and by time-scanned analysis, respectively. The Signals by time-scanned analysis are normalized with respect to the signals by time-integrated analysis. (.) denotes data processed by time-scanned analysis. (0) denotes data processed by time-integrated analysis. The analyte is 100 ug/ml Na. Na+ is produced by DLI with the dye laser tuned to the transition of the BSk-t3Pg level of sodium. Figure 12. 57 The comparison of temporal profiles of ionization obtained by time-scanned analysis and by time- integrated analysis, respectively. (4): (i) : (¢): (I): signal processed by time-scanned analysis; lifetime (T1) = 3.3 I 0.3 ns. signal processed by time-integrated analysis; aperture range = 20 us, aperture duration = 5 us; T2 = 3.2 I 0.2 us. signal processed by time-integrated analysis; aperture range = 50 us, aperture duration = 5 us; T3 = 3.6 t 0.2 vs. function of e‘x used to compare to the other three curves. The analyte is 100 ug/ml Na. Na+ is produced by DLI with the dye laser tuned to the transition of the 3Sk-+3P3/2 level of sodium. 58 #55 £3 530. 9o. 8 O -N A m m .0 _N 3 .0 .0 NO 3 a . . . . . _ . . in .N . . .0- . a. AM 0 ... d.» u L m e .m , m m . d\\/ 1 .2 . 4 n x .m z A .. / 1 / , /*l [I u / . . . N I/ I -Uli. . o p p p p p ’ llh' +lllpl "Ilnbu - 0 .0 NO we no no mo .3 mo mo .00 59 good agreement with the lifetime of 3.3 i0.3 us obtained by time-scanned analysis. B . Reagents Solutions made from reagent grade sodium chloride and lithium chloride (Baker analyzed reagent, Phillipsburg, N.J.) were used to liberate free alkali metal atoms in the flame. The reasons that alkali metals were chosen in the DLI and LEI experiments are as follows: (1) Because the ionization potentials of alkali elements are small (< 5.5 ev), they are sensitive to LEI by an N2 laser-pumped dye laser although it is harder to obtain a detectable ionization signal than by a 'us flashlamp-pumped dye laser, as described earlier in this chapter. In order to obtain some fundamental comparisons between DLI and LEI signals, it is useful to choose elements that are sensitive in the LEI technique. (2) Alkali elements have been‘well characterized in flames and other hot vapors. Diffusion and mobility coefficients, collisional ionization cross sections, oscillator strengths and other parameters are known. Rhodamine 6G, Rhodamine B, Rhodamine 101 and DCM were used as laser dyes. They were obtained from the Exciton Chemical Co. The first three laser dyes were u . A\w 60 -3 mole/1 in ethanol solution; the prepared 5 x 10 concentration of DCM in DMSO was also 5 x 10"3 mole/l. As the concentration of laser dye is changed, the profile of output power versus wavelength may shift significantly. By taking advantage of this property of the laser dye, a maximum output power in the desired wavelength region may be obtained. C. Procedure The data reported here are mainly temporal profiles and Spectral profiles of alkali ionization Signals obtained by time-scanned analysis and single-point analysis. In order to obtain reliable data, precise system alignment is required prior to any data acquisition. Briefly, the experimental procedure was as follows: (1) After 10-20 minutes of warm-up time, the dye laser was first adjusted to maximum output power by slight adjustments of the optical components of the entire dye laser device. Detected by the joulemeter, the output power and peak-to-peak stability were Observed on the oscilloscope. The calibration of laser wavelength and Spectral profile (a Gaussian profile is expected) is made bY deflecting part of the beam to the 61 monochromator-photomultiplier-strip chart recorder system. (2) The burner head was fixed at the position where the dye laser beam and N2 laser beam from the opposite direction have maximum temporal overlap by examination with a photodiode set on the burner head. (3) By moving a Sheet of paper over the burner head, the focused beams of the dye laser and the N2 laser were aligned to have a maximum overlap of their beam waists inside the inner flame. (4) A pair of nichrome wires was mounted in the electrode holders, the position of the bottom probe was precisely set by moving a micrometer-driven translation stage. The two probes were suspended parallel to one another, separated by 4-10 mm, in the vicinity of the laser beams; the bottom probe was placed at a distance of about 10 mm above the burner head. (5) The HZ-Oz-Ar flame was ignited and the salt solution was nebulized into the inner flame. It is important to follow the correct procedure to ignite the flame in order to prevent any danger. The Ar gas of the inner and mantle flames was first turned on by adjusting the flow meters. Then the H2 was sent through the flame system. The gaseous mixture of Ar and H2 was burned before turning on the 02 gas flow. Finally, the flow rate of each gas was adjusted to the appropriate setting on the flow meter. To turn off the flame, the reverse procedure was followed 62 (6) An appropriate aperture delay range and aperture duration were selected to provide a reliable output with maximum Signal-to-noise ratio. CHAPTER III EXPERIMENTAL AND THEORETICAL STUDIES OF DUAL LASER IONIZATION OF SODIUM IN AN HZ-Oz-Ar FLAME A.Introduction Laser-assisted ionization of gaseous atoms and molecules can yield detailed information about excited electronic states as well as provide an extremely sensitive method of analysis. Experimental techniques employed in the development of this field have included, for example, resonance ionization Spectroscopy with a proportional counter for ion detection(22), and multiphoton ionization spectroscopy with detectors such as electron multiplier thermionic diodes or mass spectrometers (64,99,123). Several theoretical models have been advanced which deal with the multiphoton and collisional steps involved in the process (124-129); perturbation theory and density matrix formalisms are often applied to the multiphoton ionization case. Laser-assisted ionization has also been applied to 63 64 metal vapors in analytical flames, and results in a remarkable improvement in trace element sensitivity in many cases. This form of the optogalvanic effect has been termed laser-enhanced ionization (LEI) (2). In addition to being more sensitive than conventional flame fluorescence spectroscopy, LEI is free from such optical interferences as stray light, self-absorption, and flame background (7,130). However, the complex parameters of the flame sampling system such as gas composition, nebulizer efficiency, and free atomic fraction - all of which influence the ionization signal - make fundamental studies of ionization in a flame difficult. Accordingly, no theoretical treatment of LEI has been reported heretofore. We have extended LEI of atoms in flames to include simultaneous irradiation by two different, collinear laser beams (131), a technique that we call dual laser ionization: DLI. The technique, described in section B, has been applied to alkali metal analytes, and we report here studies involving sodium solutions nebulized into a premixed Hz-Oz-Ar flame. We also introduce a theoretical model for the steps leading to ionization, and compare our eXperimental results to calculated predictions. In DLI multiphoton ionization can dominate over collisional ionization as the major analyte ionization process. In section C we derive equaitons for the multiphoton ionization rate - previously obtained by Geltman (124) by time-dependent perturbation theory - in matrix notation. I - a... ah- ... . . a . . . 1.4 .3. z. is . a . .. \m a. .p n n. .3 Av :- 3— :- -.. a: an. o u . o :o in c s o a sun p. on .o a“ ow an 0 :- SJ. I.— hs ..u u. Ix ,.s u o o o .n u i on o p on. . o o e . o t e: .6 a . s ..- n...- I . Q «‘1‘ .R‘ 53! \ 65 The experimental results are reported and compared to those given by the theoretical model in section D. The discrepancies are attributed to inadequacies of the model when it is applied to partial saturation of the initial analyte excitation step. An empirical formula is proposed to reconcile the results, as discussed in section E. B.Experimental The experimental set-up for two-step, laser-assisted ionization in flames has been described in the previous chapter. Briefly, ions produced in the interaction region (1 cm above the Maker burner head) were collected by a pair of biased nichrome wire probes suspended parallel to one another, 1 cm apart, inside the flame. The probe current passed through a load resistor, and the resulting voltage was the input to a boxcar integrator (PARC Model 162 - 164). Signals were monitored with an oscilloscope (Model 564 Tektronix, Inc., Beaverton, OR), and the output was diSplayed on a strip chart recorder. A grating/filter double monochromator (Model Eu-701-30, GCA, Mcpherson ACTON, MA), followed by a photomultiplier module (Model Eu-701-30, GCA, Mcpherson), positioned at an angle of 900 to the incident beam, was used to measure fluorescence from the flame/laser 66 interaction region. Rhodamine 6G was employed in the home-made Hansch-type dye laser, which was pumped by a 5 ns pulsed nitrogen laser (Model 0.5 - 150, NRG, Inc., Madison, W1). A convex glass lens focused the tunable dye laser radiation onto a (1.0 i 0.3) x 10.3 cm2 area in the center of the flame. LEI was measured when the output of the dye laser was tuned to various resonances in the Na Spectrum. For DLI measurements, a fraction of the N2 pump laser output was reflected to the opposite side Of the flame, and focused by a quartz lens onto a (2.0 i 0.4) x 10'4cm2 area so that maximum overlap Of the beam waists was effected.The optical elements were arranged to ensure that the two laser beams were also temporally coincident. A power meter (Model J3-05, Molectron Corp., Sunnyvale, CA) was used to measure the output power of the two lasers. Most data reported here were obtained with a dye laser power density of 50 MW/cm2 and an N2 laser power density of 80 MW/cmz. The dye laser radiation was attenuated by insertion of neutral density filters between it and the flame. A set of calibrated filters was employed to vary the N2 laser power density in a similar manner. In order to maintain constant conditions, the power density of each laser was checked frequently during the course of an experiment. The flame gas consisted of H2, 02, and AI in selected proportion. The components were well mixed prior .A - (a-I - “. '0‘ i .. -:" ~._ 'A - o.-' s A - b. . ‘ Q 5 ‘. 67 to passing through the burner head, and a sheath of identical composition was used to shield the inner flame within which ionization was induced. The sodium solution was carried from a pneumatic nebulizer by the Ar gas; the concentraton of the solution nebulized was 100 ppm Na throughout this work, except during the ionization profile measurement and the laser induced fluorescence (LIF) measurement, for which a 10 ppm concentration was employed. In addition to Na+ produced following resonant excitation of sodium in the flame, the broad band dye laser output in the 570 - 580 nm region can yield a significant sodium ion signal. This background signal has been substracted from the laser-induced ionization signals reported here. C. Theoretical C-l Multiphoton Ionization in a Two-level Atomic System Multiphoton ionization is Often treated in terms of time-dependent perturbation theory (77). We shall assume that this mechanism dominates the DLI process, and introduce matrix notation to develop an expression for the multiphoton ionization rate, analogous to Geltman's derivation (124). In time-dependent perturbation theory, the 68 Hamiltonian H can be expressed semiclassically as O H = H + Hint (1) Hint = ZEcos wt , (2) where Hols the unperturbed Hamiltonian of the atom, Hint represents interaction with the radiation field, 2 is the atomic displacement, and E and w represent the amplitude and frequency of the field, respectively. We assume that the laser radiation is monochromatic and linearly polarized. The SchrOdinger equation can then be written (h = 1) iiléiLEl = (H0 + ZE cos wt) W(r,t) (3) The wavefunction can be expanded in terms of eigenfunctions, ¢j(r) of the zeroth-order Hamiltonian (132), giving for a two-level system 2 \Hr,t) = z aj (t) 9:] (r) eXPI -iejt 1. (4) i=1 where aj(t) is a time-dependent COUpling coefficient andsj is an eigenvalue of Ho. Substitution into the SchrOdinger equation gives . 2 im = z: a- (t)zij E cos wt exp[ iwijt 1: (5) dt j___1 1 where zij = < ¢i(r)|Z|¢3(r)>, the dipole matrix element 69 between the unperturbed eigenfunctions, and wij = mi - wj, the energy difference between levels i and j. In matrix notation, Equation (5) can be written .d a1(t 0 Z exp[iw t]) 135(a2(t))= (Z12 exp[ -iw12t] 12 0 12 xa1(t)> a2(t) Ecost mt . (6) One can define a matrix b as (b1 (U) eXPl inlt] 0 b(t) = = b2(t) 0 exp[ inzt] a t 1( )) (7) where ni is a function of the detuning energy. Substitution of Equation (7) into Equation (6) followed by application of the rotational wave approximation (133,134) gives (11(b (M)= %(-:1 2123 exPI i(w-m21)t] exp[i(nl- n2)t] 1? b2 (1:) EexPI-i(w- 621)] exPI-i(n1- n2)t] '-2n2 b (t) - x 1 (8) bzm We call the square matrix in Equation (8) 0 , and introduce a matrix C to diagonalize it: 1 0 C-lfl C = A =(1 ) (9) 0 12 _ 70 Then from Equation (8) -iAt b(t) = c exp[ 2 1 c'1 10(0) , (10) where we set the initial time equal to 0. Sustitution of Equation (10) into Equation (7) provides the solution to the coupled differential Equations (5). C-2 Application to Sodium Consider the case: + .- Na(3Sk) +'nw1 + Na(3P3/2) +‘nw2(or + Zhwl) + Na + e . When the dye laser (with energy‘hol) is tuned across the 381/2-3P3/2 transition a ground-state sodium atom may absorb a photon and reach the 3P3/2 level; subsequent absorption of a photon from the N2 laser ( hwz) provides sufficient energy to reach the ionization continuum. We treat this case as a two-level atomic system, neglecting coupling between the 3P3/2 and 3Pl/2 levels. Thennl = 0, and setting n2 =(n-w215A we find 0 z E 0 = 12 1 21231 '2A (11) 71 By setting the secular determinant of 52 equal to zero we obtain the diagonal matrix A, - 2 2 2 g A + As [A + 21231] 0 ”A - [A2 + 222E2 ]% (12) 1 1 From Equations (9) and (12), the transform matrix C is found 1 Q /1 C = 12 2 (13) A1/‘212 1 I s g _ 2 2 2 a where 012 leEl andxl'z A i [A + 212 E1 ] . Substitution of Equations (12) and (13) into Equation (10) and application of the initial condition, b1(0) = all gives exp[-illt/Z] b = B ‘(14) exp[-ixztlzl I where B = 4L— 1 -11/A2 2 2 _ 1 A+ (A + 912)15 'A + (A2 + 912)% 2(A2 + 0&2)? (15) 912 ’912 72 The related transition probability can be eXpressed as = 2 2 2 912/2(A + 912) _ (16) If the two laser beams are linearly polarized and parallel, we obtain for the rate of multiphoton ioization induced by simultaneous absorption = 2 2 4 2 2 j=1 21f (17) where S2k ='§ zzizzk/(“zz ' w) (18) In Equation (17) E1 and E2 are the electric fields of the dye laser and the N2 laser, respectively. 22k is the first-order dipole matrix element for the transition from the 3P3/2 level to continuum level k, where k is the l quantum number of an allowed continuum state; since |2> = lag/2>, k can be kd3/2, kds/2 or ka/Z for linearly polarized radiation (77). 52k is a matrix element of the second order solution, since two additional dye photons are required to promote sodium from |2> to the continuum. The first term of Equation (17) represents three-(dye) photon ionization; i.e. it covers Na(3$1/2) + hgl + Na(3P3/2) +-2hw1 + Na+ + e”, the multiphoton case of LEI, - U... .QA s... .’F Q \ ‘AV~ 'M‘» 73 neglecting, however, the contribution of collisional ionization. The second term covers additional ionization due to DLI, again ignoring collisional contributions to the ionization rate. In our calculations, matrix elements for discrete-to-discrete state transitions are estimated on the basis of the Bates-Damgaard approximation (135), and those for discrete-continuum transitions are obtained by the quantum defect method (100). The same treatment was applied by Geltman (124). We have repeated one case calculated in reference (124), Na(3Sl/2) + Zhw + Na(581/2) + ha, -> Na+ + e-, and obtained very good agreement. Theoretical calculations of the ionization rate as a function of the detuning energy have been performed on the basis of Equation (17) for two cases: (a) DLI (ignoring the negligible contribution from the E1 term under these conditions) : Na(35%) +‘hw1(589rmn .. Na(3P ) + 11.02037 run) -> Na+ + e’ 3/2 (b)LEI (where the E2 term in the equation is absent) : Na(388) +‘hw1(539 nm) + Na(3P3/2) + Zhwl (589 nm) + Na+ + e' The results are shown in Figures 13 and 14, reSpectively. We omit treatment of the case: Na(3Sl/2) + 25 w2(337 nm) +Na+ + e-, since no detectable signal was experimentally observed when the dye laser beam was blocked. The experimental and calculated results will be compared in the next section. Ionization Rate (5") Cal) 6. l0 1 74 J l 1 41 .1 J ‘l5 Figure 13. -IO -5 O 5 IO l5 Detuning Wavenumber (cm") Multiphoton ionization rate calculation of DLI case: Na(3$k) + _hw1 (5890 A).+ Na(3P3/2) + hw2(3371 X) + Na+ e' a) dee = 50 NW/cmfi b) sze = 5 MW/cm2 ; = h c) dee O. S MW/cmé ; in ea case PN2 = 80 MW/cmz. A-Imhv Eunv~$ Pbfiv‘hnbkisn5Avs hyavuhvs‘uuvsuu Calculated ionization Rate (5") K) r 75 lO-°/”‘” \ K) ' -i0 -5 o 5 no :5 Detuning Wavenumber (cm") Multiphoton ionization rate calculation of LEI case: 0 Na(3$k) + hw1(5890 A) -+ Na(3P3/2) + 2hw1(5890 i) + .. e-Na + e ; 2 a) Pd = 50 MW/cm ; b) dee = S MW/cmz; c) Page = 0.5 MW/cm2. 76 D. Results D-l Multiphoton Ionization in the Flame Enhanced ionization of sodium in the flame under the influence of the dye laser alone (LEI) could occur through resonance absorption to the 3P3/2 state, followed by interactions with two additional photons as required to reach the ionization continuum ( case (b) above ). The LEI signal was measured as the dye laser power was attenuated by an order of magnitude. The power dependence is shown logarithmically in Figure 15, where a slope equal to one is obtained. Thus three-photon ionization is not the predominant mechanism for LEI under our conditions. Rather, collisions between the resonantly excited sodium atoms and the other components of the flame gas must provide the energy necessary for ionization. Indeed, collisional interactions among the components have been invoked previously to account for both conventional and laser-induced ionization in flames (4,136). As noted in our previous paper (131), when the N2 laser beam is permitted to impinge on a flame already under 381/22' 3P3/2 resonance excitation by the dye laser, the ionization signal tincreases by about two orders of 77 .H "macaw a no: mafia one .moaaom soon so com: mafia: mumuuenami .qu mo usaEmHsmmoE mocmpcammo Hmzom Hanna who .mamuzmfim 330d .68.. go oamko m a m N ._ u . d . . u q _ a . -m .m -v .m .m L .m .m .o. uouozguoi 78 magnitude. The dependence of the DLI signal on the N2 laser power is shown in Figure 16; it is linear over almost two decades of laser power. (The fall-off at high power levels is probably due to partial saturation.) This result indicates that DLI occurs by a multiphoton pathway, case (a) above. The ratio of ionization signals from DLI and LEI depends strongly on the wavelength of the dye laser beam. It is plotted as a function of detuning wavelength in Figure 17. The maximum DLI enhancement is obtained at the resonance wavelength, and the ratio drops quickly on either side. This observation may be understood in terms of resonant multiphoton ionization (81), where the relatively long lifetime of the intermediate stationary state (~17 nsec for the 3P state of Na (121)) facilitates absorption of an additional photon after the initial excitation. The corresponding lifetimes of the virtual states involved as intermediates in non-resonant multiphoton absorption are on the order of 10'15 sec. Alternatively, the results shown in Figure 17 can be interpreted in terms of the total, generalized two-photon cross section, which is larger at the resonance wavelength than off-resonance. 79 .Hm3om noes um ummoxw .mmsmu Hm3om on» no umos usonmoounu .H u amoam a mm: mafia one JAmuflca mumuuflnumv szom momma who pcaumcoo nufl3 .HAQ mo ucwEmHDmmmE mocmcswmmp mason momma NZ 8on 38.. N2 m9 m2 0. .l1 - - .wH ousmflm 9 uouozguoi 80 .COfiuwmsauu «\mmm + mmm on» amouom cocoa mw3 nomad who on» no hamumcumufla cmusmmmE mHmS mamcmfim qu can HAG .K ommm u numcmaw>m3 mosMCOmmm .numamam>m3 mcficsuoo msmnw> Ham on HAG mo Gavan usaEmocassm .nH musoflm, e5 £82903 9.8.50 m m N _ O T s d4 - . N... JII... O. {I (11 (I. 'rI (I 81 D-2 Measurement of the Dye Laser Profile by DLI The Spectral profile of laser-induced atomic fluorescence in a flame involves a convolution of the laser and atomic profiles (137). Since the full width at half-maximum (FWHM) of a broad-band dye laser is much larger than that of an atomic line, the resulting fluorescence profile can be taken as a measure of the laser profile. The DLI signal across the 381/2 -» 3P3/2 resonance was monitored as a function of dye laser power. The FWHM dropped from about 0.8 g at high power to a constant value of 0.5 X at powers below 0.5 MW/cmz. The normalized DLI profile is shown in Figure 18, where it is compared with the profile obtained by measuring the 3P3/2-r 351/2 fluorescence under the same experimental conditions. The results are essentially coincident; the minor deviations may be caused by the small error in determining the resonant wavelength. Thus the FWHM of the ionization profile in the flame is also limited by the dye laser. Similar conclusions have been drawn for low-density vapor cell systems (138,139). 82 .Emm OH H coflumuucmocoo oz .mmm + «\mmm u hHA mac SofipOm moumowocwmm>u50 cognac “NEU\32 mo.o u m can «so\zz om u m sues mflemoum Han Esaoom mmumOfloch o>uso oflaom .moafimoum mHA can HAD mo conflummeou .mH musmeh 3.532925 92.580 OW ON 0.. 0.. . who AW 0%. O..- m..- Ohmwa- .. O. .. ON 1 on " Laue. . Om L om . on .. 0m 4 om .. 00. 00902310! PGZHDWJON 83 D-3 Dependence of the Ionization Profile on Dye Laser $3323. The breadth of the ionization profile from DLI in the flame may depend on many factors: laser power, sodium concentration, flame gas composition, configuration of the two laser beams, probe voltage, geometry of the interaction zone in relation to the probe electrodes, etc. Consequently it is difficult to make a quantitative investigation of an individual ionization profile in the flame, with which to compare the results of theoretical calculations. However, noteworthy changes are observed in the DLI profile when the dye laser power is altered, which we attribute to this parameter, alone. These are depicted in Figure 19, where the integrated signal from the boxcar averager (in arbitrary units) is plotted versus the detuning energy for dye laser powers of 50, S and 0.5 MW/cmz. Relative ion populations may be obtained from ratios of such ionization profiles. Multiphoton ionization rates, which are linearly proportional to the ion populations (140), may be calculated via the formalism outlined in section C. Experimentally determined ionization ratios are compared with predicted values, calculated according to Equation (17), in Figure 20. The deviation is significant. An implicit assumption of the model upon which the K h-Ivv Ii! Uhh\i\I§ i\in 84 103 - IO- tion (cg) 0- 1 oniza L. L l l .4 i 45 -IO -5 o 5 . IO :5 Detuning Wavenurnber (cm”) Figure 19. Dependence of sodium DLI profile on dye laser _ 2 _ 2 power. a) dee — 30 MW/cm , b) dee - 5 MW/cm , = . = 2 ' c) dee 0.5 MW/cm , PN2 80 MW/cm in each case . 85 ..Nso\zz v.~\o.q~ who .usosmsonnu NEU\32 cm H m .Umumasoamo H II .Hmucwfiflnmmxw n < . Eo\zz m.vH\o.v~ ‘ map N m An .wmumaoono H II .Hmucmsflummxm n O \ wmc A. .EotmnEBmBB 8.5.8 m. 0. m - O 0.. O... m... m at .. . . m Am .mmawmoum HAD mo mowumm .ow Gunmen CV 01405 uonozguol ND F» GD (5) we oumum poueoxm asp scum :Owuoom mmono coaucwwsow souonmio3u one .Essceucoo an» zooms on msouogm momma amp Hmsofluwooa 03» onwsoou pan» naumHmsm mo mouaum coueoxo UMMflanm on oouoenummu me mfimnom one .qu 3. can Hun .3 now mfimummwo .25me Hm>maimouns .wm musmflm _. w . a a. a...“ sum as... a. «4‘ awe“ Tam N . - - m - . - v. a. m v. 3. .VNWXII I... I U; 30 .n _w.. .0 "V“. 0.80; 0231 I Cant fl vu‘b say CCES an v.$ This 6‘. .. mat fleas ‘ ; ‘ ..m; .LUJ pumping N2 laser in the DLI technique introduces the photoionization rate constant R in Figure 26b, which is the only difference between the two models. The laser-assisted collisional system studied by George showed that the interaction between laser radiation and particles may lead to a change in the collisional ionization rate constant; i.e. the effects of laser radiation and collisions are not independent of one another (156,157). This possible perturbation is neglected in the models presented here. Prior to reaching a general solution of the system, several assumptions must be made: 1. No coherent effect is produced in the system, so that the rate equations can be safely used instead of the density matrix formulation. We shall estimate the limitation imposed by this assumption in Section C. 2. The cross section for two-photon ionization through virtual states is very small in comparison with the cross sections of the other processes present in Figure 26. Therefore, we neglect the radiative rate constant from state 2 to the continuum caused by absorption of two additional dye laser photons, and the photoionization rate constant from the ground state to the continuum caused by absorption of two photons from the N2 laser. (This assumption is made in dealing with the special cases of Na (BS-+3P) in Section B-2). 3. The rate constants applicable to LEI are not disturbed by the addition of the N2 laser used in DLI. O D A. V“ a 1 a 'v I 104 4. The laser radiation density is spatially homogeneous. 5. The population distribution in states other than the three states considered in the models is neglected. Based on the scheme shown in Figure 26, a set of rate equations for the LEI case can be written: dni = k .n - KIL .3?— 21 2 l (1) 9’12 Ta? : 3120111 +Kni - (13210 + A21 + k21 + kZim2 (2) 9.11.1. . .. . dt ”321" 1' A21 + k21’nz B12U n1 (3) 1 = n1,+ 112 + ni . (4) For simplicity, the population densities n1, n2 and ni above are taken relative to the total population density n But for clarity ni/nT and nz/nT are used in T. the figures instead of ni and n2, respectively. The other -1 symbols used in Equations (1-4) are k (s ), the 13 collisional rate constant from state i upward to state j or deexcitation rate constant from i state downward to j 1 state; K (s- ), the relaxation rate constant, as a sum of radiative, radiationless and recombination rate constants monitored from the continuum; Bi.(cm2Hz/Wsec), the J Einstein absorption or stimulated emission coefficient; A21(s-1), the Einstein Spontaneous emission coefficient and U (W/cmZHz), the spectral irradiance of the laser. Substitution of Equation (4) into Equation (2) {any 'uC'. v 7.. ~3LG~ the s i‘e R; u 1a; 106 yields I an - at - BIZU + (K— B U)n-"(B 12 1 9U + Z)n where 12 2 z (5) 9 = l +-gl 9'2 (6) Z = A + k 21 2 + k . 1 21 ' (7) If the system is in thermodynamic equilibrium, the relation between B12 and B21 18 Blzgl=B2192 (158); gi IS the statistical weight of the ith state. In the following we divide the discussion into several cases, including the steady state (dnz/dt 3”- 0) case, and the nonsteady state case, with laser profiles that are step functions or rectangular pulse functions. . ’b (a) Steady State with anZdt — 0 Under steady state conditions, Equation (5) yields _ Ble + (K - B12U)ni n - 2 . Blng + z , (8) The spectral irradiance U(t) is assumed to be a unit step function o rt rt A |v CO (9) h I”! ‘ “3‘6- . a W34; Hi "1‘ “:5tu r r h5av .94 107 If Equation (6) and (7) and the boundary condition: ni(0) = 0, are substituted into Equation (1), the solution ni(t) of the first order differential equation yields - E _ “Mt) ni(t) - M (1 e ' (10) where M = K _ k21(K -‘312U°) (11) 312 gU° + z and N = kZiBIZU° (12) BlZgU° + Z Equation (10) describes the temporal behavior of the ion population density under steady state conditions. We shall discuss the validity to the laser pulse duration in using the steady state approximation to describe the ion behavior. Typically, a boxcar integrator is experimentally employed to process the signals generated by a pulsed laser. For simplicity, we consider the gain factor to be unity and assume the gate function in a boxcar is 1 0 < t 5 T 0 elsewhere Multiplying the gate function h by ni(t) and dividing the I Q 3 108 integrated result by the aperture duration T yields the averaged population density'fi'i as follows: _ 1 T ni = 4L ni(t) at] (14) Substitution of ni (t) in Equation (10) into Equation (14) gives -11 1 _N_ -MT.. 5. - M + T[: 2 (e 1% (15) (b) Nonsteady State (Analytical) Solution As long as a short laser pulse is employed, nonsteady state conditions should be considered because the laser pulse duration is not long enough for a steady state population to be reached. It is not difficult to obtain the analytical solutions for ni(t) and n2(t) from Equations (1-4). A complete solution of the coupled differential equations gives: n.(t) = C e-elt + C e-EZt + n. 1 1 2 1" (16) t + C e-82t + n -s nzit) = C e 1 4 2P 3 Where 109 _ l, ' 81,2 - 2 {(K + B129U + Z) + / 2 ~ (K+ Blng-I-Z) -4[K(K+ 131ng +2) - kZi(K-B12U)]}' (17) n. and n2 indicate the particular solutions of Equations 1P P (l) and (2), respectively. The results are n. = 12 21 lp e1E2 (18) B UK n. = 12 The coefficients C1, C2, C3 and C4 are not linearly independent of one another, because ni and n2 are coupled to each other in Equations (1-2). By susbtituting Equation (16) into either Equation (1) or Equation (2), one obtains = - 6 C3 k2.1 C1 1 (19) C =£-—62C 4 kZi 2 The values of Cl and C2 can be obtained by applying the boundary conditions: n(0) = nio and n2(0) = n20 to Equation (16). That leads to “10 3 C1 I C2 + nip (20) n = —— C + C + n 20 kZi 1 . k2i ) 2 2p A I In L45 \v H I 155'; no: 110 The solutions for C1 and C2 are: 21 C = X( _ ) - Y( _ ) 1 El 82 £1 £2 k21 K - £1 (21) C2=Y(E-€)-X(€-€) 1 2 1 2 r where X = n0 - nip (22) Y = n20 ‘ n2p At t = 0, the initial population densities ni0 and 1120 of the continuum and the excited state can be obtaind by solving Equations (1-2) with the steady state assumption (without spectral irradiation (11)). The results are: k21k12 n . =- 12 + k21 + k2i) + k21(k12 ' K) 10 K(k (23) 11 = K 1:12 20 K(k12 + k21 + k2i) + 1:210:12 - K) Equation (16) describes the temporal behavior of the population density of the continuum and excited state, reSpectively. Similarly, the averaged population densities '51 and '3} processed by the boxcar integrator can be 111 obtained according to Equation (14). (c) Rectangular Function for Spectral Irradiance Here we assume the Spectral irradiance U is a rectangular function: Uo 0 i t i T U = (24) O elsewhere Although the rise time of the laser profile is never equal to zero, the rectangular function assumption is closer to the experimental conditions observed with pulsed laser radiation than in the unit step» function assumption. As ‘the laser is turned on, the resulting population density for a specific level is the same as that. discussed. in cases (a) and (b) above. The laser irradiiates the system for T sec., then its Spectral irradiance falls to zero. Consequently, the population dnesity has a different distribution after T sec from that with spectral irradiance U . For the steady state case (a), the temporal behavior of the relative ion population density at times larger than T follows kZiK ni(t) = nil? exp[ (—z— - K) (T - t) 1, (25) 112 where niT indicates the population density at time T, and t is the time after the spectral irradiance falls to zero. For the nonsteady state case (b), by solving Equations (1-4) without spectral irradiance, one obtains = ' -s t ' -e t ni(t) Cle 1 + Cze ' I o (26) = -s t ' -s t n2(t) C3e l +C4e 2 ' where ' _ 1 - I z ‘ 21,2 - 1- [ (K+Z)+ /(K+2) + 4(Kk2i- KZ)] (27) and K- s' ' C5 =_'l—k. C31 21 (28) l c' =-——-2—K " e c' 4 k21 2 Equation (26) are analogous to those obtained in Equation (16); they describe the temporal behavior of hi and 112 after the laser is off. The coefficients C'1 and C'2 can be obtained by applying the boundary conditions ni(T) = niT and n2(T) = n2T to Equation (26). The results are: K - s k c 2 21 C =[n.( )-n ] 1 1T k21 2T (6i - 6;) exp(-siT) (29) _ eI k . C5 = [ 112,1, - (374)111'1'] , . 21 I 21 (£1 - 62) exp(-62T) For convenience, we take the same period of time 113 for both the laser spectral irradiance and the boxcar gate function to obtain the averaged population density; i.e. if the rectangular spectral irradiance pulse is 5x10"9 sec long, the aperture duration of the boxcar is also 5x10"9 sec. We shall compare the effects of laser pulse duration on both DLI and LEI in Section C on this basis. The equations derived above are suitable for the LEI system. As mentioned previously, the difference between the DLI and LEI schemes in Figure 26 is that a photoionization rate constant R, a function of the N2 laser power, is added to the former. Hence, by using 1(-+ k2i instead of k2i' we may still use the related equations in the above cases to describe the DLI system. B-2 Special Case Because the sensitivities of DLI and LEI have been compared for sodium (131), we use sodium here as an example. The sodium atoms in the premixed Hz-Oz-Ar flame are first excited to the 3P3/2 state by dye laser photons. Then sodium ions are produced by collisions in the LEI system, or by photoionization with an N2 laser in the DLI system, as shown in Figure 26. The pulse durations of dye laser and the N2 laser are both assumed to be 5 nsec. The collisional deexcitation rate constant k21 can 114 be estimated on the basis of equation (30), k21 =l gxa Gab Vab (30) where Xa is the particle density of foreign gas a in the flame (159). In our case the burnt gases contain 80% Ar and 20% H20 in the Hz-Oz-Ar flame (146). Cab is the collisional quenching cross section of species b by gas a (here species b indicates sodium), and Vab is the velocity of species a relative to Species b, and can be expressed i " .. /.§_}5_'I'.._ (31) Vab - uabTr ' h where k is Boltzmann's constant, T is the temperature in as K, and “ab is the reduced mass of species a and b. In our case, the flame temperature is NZlOO K (146). The collisional excitation rate constant k21 may be obtained directly from k12 using Equation (32), A312 =k 'g'_2'eXP(-F)I (32) k 21 91 12 where {W12 is the energy difference between the 381/2 and the 3P3/2 state. Similarly, the collisional ionization rate constant k21 from the 3P3/2 state is given by (147) __ — -AE -/kT 1:21 — gxa °ab* vabe 21 (33) 115 where cab, is the collisional ionization cross section of sodium atoms in the 3P3/2 state with the burnt gases in the flame and AE:2i is the energy defect between the 3P3/2 state and the continuum. The relationship between 821 and A21 is expressed as (158) 3 2hv21 A21 = To 1321 (34) where c is the velocity of light,\)21 is the frequency of the transition between the 381/2 and the 3P3/2 states, and h is the Planck's constant. The photoionization rate constant R from the 3P3/2 state to the continuum can be estimated in terms of the photoionization cross section of sodium by (153), R = °¢ I _ (35) where ¢ is the photon flux in photons/(cmzsec). The total energy of one dye photon (at 5890 i resonant with 3133/2 state) plus one N2 laser (at 3371 2) is greater than the ionization energy for sodium by 0.014 Rydberg. The photoionization cross section a (3P3/2 state to continuum with 6 =0.014 Rydberg) was calculated to be 3.5 x 10’18 cm2 by Aymar et al. (145). If we assume a power density of 80 MW/cm2 for the N2 laser, the photoionization rate constant is 8.6 x 1088-1. A5 :. vUA-A. C ‘I .36 Qch nu. . ".‘N‘ vw. ‘ 0 116 Table. 3 shows the values of the various cross sections, coefficients and rate constants used in the calculations. The relaxation rate constant K is assumed to be in the range of 104 to 10103.1. Such an assumption is reasonable, because the experimental results for the lifetime of Na+ are on the order of usec (146). We shall compare the effects of the relaxation rate constant from the continuum to the 3133/2 state, K(i -> 2), and from the continuum to the 381/2 state, K(i + l), on the ion population density in the next section. C. Results and Discussion Eberly and Daily have come to identical conclusions in examining the validity of the rate equation approach to laser excitation (153,154). Eberly used an equation related to the Rabi frequency and transition rate to examine limitations of the rate equation formulation (153). That is 92 P = '17 (36) where P is the transition rate under laser excitation, 9 15 ‘the Rabi frequency and F is the absorption line width. Only when P < (2 (or I' > 0 ), does one have a smooth 117 .HNmH. mocwummmu mom He. .mCONHMHaono How uxwu mom Am. .AmvH. mocmummmu mom Am. .AHmH. mocmuwmmu can .Hmav wocmnmmmu ca pmmmsomwv mm3 commwu may m2 XIMZHH «Hesscflucoo a.m\mmm.xu « emeEsscwucoo pcsoum “0mm .Hd u x. umcofiuomm mmouo downwaflcofl HMGOflmflHHOU How AHwH. mocmummmu 00m .mCOfluomm mmouo mcwnocwsv How AowH. mocmummmn mmm Adv eHeH I eeH H no N + H a2 a e.m TeH x m.m H .oumee N eeH x e H eHH NN H .Hmoo N NemeN.e meH x N.H me.e He.e A H + N 22 age meH x N.N N + H Eszcwucoo nun .m3\NmNso. H.N.Hub.m N N\m NHa .H-m.HNa 3-9%.. ANea..oao&a .Neso a $5 $55.2 -azf. an "N Am. Hes .m. .N. .H. xmm uH mmmu Hmflommm may :a Esfioom mcficumocoo mumumEmumn .m menus 118 monotonic population flow through the atomic levels; i.e. the rate equation formulation is valid under such conditions. Otherwise, population pulsations may occur at the Rabi frequency (155). Similarly, Daily pointed out that the rise time of the laser radiation must be longer than the collisional dephasing time in order to use the rate equation approach. Obviously, the former is related to the Rabi frequency; the latter is related to the absorption line width. We may estimate the Rabi frequency in the flame in comparison with the transition rates to examine the validity of the rate equation approach used in the system. The Rabi frequency of resonant radiation is defined as 93 ESE (37) h where d is the transition dipole matrix, E is the amplitude of the laser field and ‘h is the Planck's constant divided by 2n. The dipole matrix is related to the natural decay rate (Spontaneous emission rate) by (163) d = (-——3h E3)!5 ABA (38) 21 32“ 21 . where Ais the transition wavelength. The amplitude of the laser field can be eXpressed as _ 1 p, 15 w E- (ES-ET) ' (39) t U39 .‘CM' " US ”I a {lull wil N) 1¥ no, “Lu, 1 .39 h 9 Me: an; H1 RA sun: LIN A-u .II.‘ ‘ .5 119 where 6. is the permittivity of free space, and Pa /A indicates the power density of the laser radiation. Therefore, with a power density of 40 MW/cm2 (the dye laser power used in the special case B-2),$2 is estimated -1 as 1.6x1012 sec . The transition rates used in the system are less than lolosec-l, satisfying the inequality P <9 Obviously, under the conditions which apply to LEI and DLI, the rate equations employed here are valid. C-l Effects of K on ni and n2 The relaxation process of a sodium ion depends on several factors such as the recombination rate, the radiative deexcitation rate, diffusion, and mobility. 'For simplicity, we treat the relaxation process from the continuum as a parameter K. As shown in Figures 27-30, the temporal behavior of fluorescence and ionization with respect to various K values indicates that K has a significant effect on the decay of ionization, which falls faster with increasing K values. A large K value may cause the ion population density to be low in both DLI and LEI, because the ionization probability is offset by a strong deexcitation probability. Also a large K seems to result 1“ a. short rise time for the ion population density. On tljei other hand, the excited state population density in 120 Figure 27. Temporal profiles of ionization in DLI with 10 W/cm2 Hz and various K values. A: K = 106 s-l; B: K = 108 5.1; C: K = 10108-1 spectral irradiance of 5 x 10- (From equation (16) to (26) ). 121 I I I 1 T j 1 p )- - A I- 8 cl )- 41 , r d D - l 4 4 4 5.0 7.5 I0.0 l2?) l5.0 l7.5 T x IO9 (sec) Figure 28. 122 Temporal profiles of ionization in LEI with -10 spectral irradiance of 5 x 10 ‘ W/cmZHz and various K values. A: K = 106 5.1; B: K = 108 3'1; c: K = 1010 s’1 (Fr°m Equations (16) and (26) ). 123 2.5 5.0 7.5 I0.0 T x I09(sec) I [2.5 I50 I75 124 Figure 29. Temporal profiles of excited state population density (fluorescence) in DLI with spectral irradiance of 5 x 10-10 W/cm2 Hz and various K values. A: K = 1010 5.1; B: K = 108 3’1; C: 125 + I I 1 T I I '- d )- .. r- «I b d A - 4 )- N I- u - -( D B I D )- u C )- c- 1 2.5 5.0 7.95 (0.0 Tx IO (sec) (2.5 ’ (5.0 (7.5 126 FigureZHL.Temporal profiles of excited state population density (fluorescence) in LEI with spectral irradiance of 5 x 10' 0 W/cmZHZ; the profiles are identifal to each YSher for K = 106 s' K = 108 s' and K = 10 s'1 (from Equation (16) and (26) ). 127 u) q q cl '62 l l 1 L 4__ 1 A 2.5 5.0 7.5 IQO l25 I50 I75 Tx IO9 (sec) 128 LEI is independent of the K values, in the range of 104 to 1010 . That is different from the results of DLI, as can be seen by comparing Figure 29 to Figure 30. A larger K may offset the immediate fall of excited state population density in DLI during the period of laser radiation. Such a fast falling tendency is casued by the strong radiative coupling between the excited state and the continuum with the addition of the N2 laser. C-2 Nonsteady State versus Steady State Figures 31-32 show a comparison of the temporal behavior of the ion population density under steady state conditions (an/dt 3 0) and nonsteady state condition for both DLI and LEI. For the larger K values, the ion population density can be treated simply by the steady state case during the laser pulse; i.e. as K increases, the results based on the nonsteady state become approximately the same as those based on the steady state assumption. The K value is related to the lifetime of the ion population; hence after the laser radiation is off, n. 1 falls faster with a larger K value. 129 I __‘__.:=éq===:..4 . I ‘ - ——————— 1101213 - 1“‘—;ET“ ‘~313 ' p—i. .. “T -| _ I0 ' d b d b \ \ )- \ " \\ "on 5 s / \ o 0 C3 “\ . " \ -2 I I0 2.5 5.0 795 (0.0 |2.5 Tx|O(sec) Figure 31. Comparison of temporal profiles of ionization in DLI for the nonsteady state case and She steady state caseO A: K = 104 3‘1; B: K = 10 5‘1; and C: = 10 8‘1; the spectral irradiance is 10' W/cmZHz. l0 130 I I I I r I )- I- -I b I- I q) )- .- b I I- d m 808. - — ’ ’ - ull" .' -' —— ’ / / / - / - / I- d I- / q " / 3.8. - /”/’ - ~ ~ ~ ~ -I / ‘ \nonss. s x- - \ - J I n L 1 I 7.5 l0.0 (2.5 l5.0 Tx I09 (sec) 2.5 51.0 Figure 32. Comparison of temporal profiles of ionization in and the steady LEI for the noniteady state casg ’1 3'1; spectral case. A: K 10 s ; B: K = 10 irradiance 10"8 W/cmZHz. 131 C-3 31 and n2 with Respect to Spectral Irradiance Based on Equations (14) and (16), the ion population density is plotted against the Spectral irradiance of the dye laser, as shown in Figure 33. The ionization enhancement of DLI with reSpect to LEI is four orders of magnitude. Here the photoionization rate constant R of DLI was calculated assuming an N2 laser power density of 80 MW/cmz. The deviation of the calculated ionization enhancement from the experimental result of two orders of magnitude may be caused by several factors (131). For example, we have neglected collisional excitation to levels higher than the first excited level of the atom (113). That may increase the ion population in LEI. Also, the power densities of both lasers are not spatially homogeneous in‘ the experiment (148). These factors are apt to cause a high estimate for the enhancement factor. The ion population in DLI is determined mainly by the photoionization rate constant R. As shown in Figure 34, the ion population in DLI is linearly proportional to R, as long as R is at least one order of magnitude larger than the collisional ionization rate constant kZi’ If the N2 laser power is such that R is less than an order of magnitude greater than k21, the nonlinear dependence of the ion signal on the N2 laser power is expected (see Figure 34). Our previous 132 I- 'K- “ ' ' A .3 /".‘f3a 3 2w 10"" " fiir "T (62- ' .3_ - IO -4 .- |° " mo“ 6 / 8 >LEI K=IO o '5 1 J l '0 2.5 5.0 . 75 I0.0 (2.5 leo'~"’(wxcm2 Hz) Figure 33. Comparison of power dependen e of ionization for 8 DLI and LEI. A and c: K = 10 3'1; B and D: K e 10 s-l. 5 133 0 I05 (0’3 )07 R ( s' ') Figure 34. The N laser power dependence of ionization in DLI. he N laser power is linearly proportional to the pgogoionization rate constant R. As R drops below 10 8'1, ionization (fi./nT) as a function of R begins to deviate from fhe solid line of unity slope, as indicated by the dashed line. The arrow ('9) along the R axis denotes the value of the collisional ionization rate constant k21. 134 experimental results demonstrated that photoionization dominates the ionization pathway for sodium in DLI, following excitation to the 3P3/2 state by a dye laser. Also, the ion signal is proportional to the power density of the N2 laser ( in Chapter III ). That is in agreement with the calculations shown here. By contrast, the excited population density N2 in DLI is on the same order of magnitude as that of LEI, as shown in Figure 35. This calculation agrees with the experimental result; the fluorescence from the 3P3/2 to 351/2 level in the DLI case is not significantly different from that of the LEI case ( in Chapter III). Figure 33 and Figure 35 suggest that it would not be difficult to develope saturation DLI or saturation LEI spectroscopy in flames, comparable with saturated fluorescence spectroscopy, which has been popularly investigated because of the advantage of independence of power density (164-166). C-4 Temporal Profiles for Ionization and Fluorescence The predicted relationship between the temporal behavior of ionization and fluorescence for both DLI and LEI is given in Figures 36-37. Several characteristics of this relationship are as follows: (1) the decay of Figure 35. 135 Comparison of power dependence of fluorescence for DLI and LEI. A: K= 104 or 108 8-1; B: K =108 5.1; C: K = 104 5.1. The fluorescence signal is proportional to the excited state population den51ty nZ/nT. p._ _;30 Kiloe-l 4 A LEI fl: (3 _ / DLI )6" - K-nlo4 c - - f . P3. n1. (62 - (63 - - I04 - - '65 l 1 l 1 1 2.5 5.0 7.5 |0.0 2 .5 Ux Io9 (W/cmsz) A d B Z r C 2‘ '0" I D . (- 4 “52; . . . . . . Alcfz 2.5 5.0 75 (0.0 (2.5 (5.0 (75 ~~~ Tiuoplsec) Figure 36. The relationship of temporal profiles for ionization, expressed by ni/nT, and fluorescence, expressed by n /nT, in DLI. A and B are ionization profiles; C ang D are fluore cence profiles. A and c: K = 10 3'1, U = 10‘ W/cmZHZ; B and D: K = 108 s-l, U = 5 x 10'10 W/cmZHZ. 138 A_ -( -( IO . B -IO -2 '2 m (o :(0 n2 5 6 C .__ —_“—-~“‘fi D \ l l 2.5 5.0 7.5 l0.0 |2.5 I50 I75 - 9 TxlO (sec) .Figure 37. The relationship of temporal profiles for ionization, expressed by ni/nT, and fluorescence expressed by n2/nT, in LEI. A and B are ionization profiles;8C and D are fluoregcence profiles. A and C:8K = 10 5'1, U =18- W/cm Hz; B and D: K = 10 5’1, U = 5 x 10" W/cmZHz. 139 fluorescence is much faster than that of ionization; this is also well-known from experiments. The lifetime of fluorescence obtained here is on the order of nsec, in agreement with LIF observations 2) and coupling from the continuum to the ground state K(i -—> 1) is neglected. Here the reverse case is considered coupling to the intermediate state K(i -—> 2) is neglected. The ion population density based on coupling to the ground state is compared to that based on coupling to the excited state. Figures 40 and 41 Show the results for both DLI and LEI. The ion population density with K (i -—> 1) included can be obtained by solving a set of rate equations analogous to Equations (1-4). The result is similar to that based on the process K (i -—> 2), as given in the following: k2i A1‘2 , = -)\ t -A t where -l .- 11,2 - 2 [(K + Blng + Z) + f_i /(K+ 131ng + 2) - 4 [K(BlZgU + Z) + 3120 1:21] . (40) and [H and D2 are analogous to C1 and C2 in Equation (21). 146 I l 0.2 0| 5 l 1 l J ' 2.5 5.0 7.5 '00 I25 U )(|09(W/cr1'(2 Hz) Figure 40. The effect of different continuum relaxation processes on the power dependence of ionization in DLI. Dashed line ( --- ) denotes process K(i-*2); solid line denotes process K(i-r1). A: K = 10 sec-1; B: K = 10 sec‘l. 147 ) I> I 1 l J J 2.5 5.0 7.5 l0.0 u x (09(w /cm2 Hz) -Figure 41. The effect of different continuum relaxation processes on the power dependence of ionization in LEI. The ionization curves based on both processes6 K(i-+1) and K(i-+a) are identical. A: K = 10 sec"1 ; B: K = 10 sec“ . 148 As shown in Figure 41, with LEI identical results are obtained for the average ion population density vs. spectral irradiance for the continuum to ground state coupling and the continuum to excited state coupling. For DLI the deviation between the averaged ion population density for the two coupling schemes is very small, and decreases with increasing spectral irradiance, as shown in Figure 40. Consequently, for a given continuum relaxation rate constant K, whether the lower level is an excited state or the ground state has little influence on the average ion population density for DLI or LEI. C-7 Nonsteady State Versus Steady State for Different Laser Pulse Durations As Shown in Figures 42-43, the averaged ion pOpulation density for u sec laser pulses is identical under steady state or nonsteady state conditions. However, when nsec laser pulses are used, a difference is apparent, espeically at lower spectral irradiances. Consequently, the steady state formalism may be utilized for prolonged pulse durations; however, with a short pulsed laser, nonsteady state conditions must be considered in the analysis. 149 Figure 42. Comparison of the power dependence of ionization in DLI nonsteady state case and the steady state case for different laser pulse durations. A: laser pulse duration = 5 x 10.6 sec; B: laser pulse druation = 5 x 10"9 sec. K = 108 8-1. 150 LO ' F 1 T i 09 - 0.8 - / 0.7 ‘- 02 . 0.l l 1 I 1 5 5.0 75 (0.0 (2.5 u x (09 (W/cmsz) NL Figure 43. 151 Comparison of the power dependence of ionization in LEI for the nonsteady state case and the steady state case for different laser pulse durations. C: laser pulse duration = 5 x 10"6 sec; D: laser pulse duration = 5 x 10"9 sec. K = 108 s-l. —.. 152 '3 '0 ' I I l I )- H ,. .. 2:. n T 5.5. and non 5.5. C b 1) - -( 5.5. D L l J 1 l 2.5 5.0 75 (0.0 A ( Ux|09(W/cm2Hz) 2.5 153 D. Conclusion We have described the relationship between DLI and LEI under various conditions, using a rate equation approach; the applicability of this approach to the flame system has been shown. In this chapter, the numerical results are specific for sodium atoms excited to the 3P3/2 state by a dye laser tuned to resonance at 5890 A. In the DLI process excitation is followed by absorption of a photon from the N2 laser; in the LEI case excitation is followed by collisions with the combustion products in the flame. This special case was chosen because most parameters are available, and the relationship between DLI and LEI has been investigated experimentally. Essentially, the three-level system presented here for DLI and LEI is applicable to any atomic analyte with a Specific excited state as the second level provided the appropriate rate constants are used. We have investigated several aspects of DLI and LEI on the basis of the formulations derived in Section B; these include the temporal behavior of the excited state population (fluorescence) and of the ion population in both DLI and LEI, the validity of the steady state assumption, the effect of the relaxation rate constant K, the enhancement of ionization and fluorescence in DLI as compared to those in LEI, and the impact of the laser In (D 154 pulse duration. As a result, we have gained insight into the fundamental characteristics of DLI and LEI, and the relationship between the ionization and fluorescence yields in DLI and LEI. The DLI technique has been shown experimentally to enhance the ionization signal over that obtained with LEI (131). Herein, this enhancement was modeled on the basis of rate equation. Because of its independence of exciting laser spectral irradiance, saturation fluorescence spectroscopy has been widely developed in detecting trace elements. On the basis of the rate equation approach presented here, we expect it would not be difficult to perform a saturation DLI or a saturation LEI Spectroscopy with analogous advantages. ‘ A: 1.1:. £L .s \ 3U CHAPTER V FLAME TEMPERATURE DETERMINATION BY DUAL LASER IONIZATION A. Introduction Current interest in laser-enhanced ionization (LEI) (2-4, 10, 13-15,131) is attributable at least in part to the technique's selectivity and sensitivity to trace elements (10,131). In addition totrace element detection, recent studies have concentrated upon the effects of probe geometry (13) and electrical interference (14-15), and upon the use of dual lasers to enhance ionization (10,131). In this chapter, we report a new application of the dual laser ionization (or DLI) technique: the measurement of flame temperatures. Typically, measurements of flame temperatures are often carried out by spectroscopic techniques because these methods do not disturb the combustion processes. Especially in high temperature flames, the Spectroscopic methods can give accurate results when thermal equilibrium prevails in the flame gases. Among the various conventional spectrosc0pic methods, the line-reversal (167-170), and two line methods (170-172) have been widely 155 156 used. Both methods are based on estimates of the electronic excitation temperature of an atomic species introduced into a flame. The line-reversal method involves comparing the brightness of an emission line from the flame with that of a calibrated continuum background source at the same wavelength (170). The difficulties of this method lie in the background source stability and the reproducibility in flames above 2800 K (170,171). The two-line ratio method is based on the measurement of the relative pOpulations of two different energy levels of a particular atom introduced into the flame. This method is suitable for high temperature flames, plasma-jets and shock-heated gases (170).The two-line ratio method requires reliable transition probabilities or at least the ratio of the transition probabilities of the lines used. Therefore, it is necessary to select carefully those lines which may produce accurate results for the temperature range to be investigated. Other spectroscopic methods, such as emission-absorption (173), slope (174) and fluorescence (175) are also often used in measuring flame temperatures. In addition, the intensity distribution of the rotational or vibrational lines of a band Spectrum has been used to determine flame temperature. The principle of the rotational or vibrational temperature measurements is basically the same as that of the two-line ratio method. Recently, laser-induced fluorescence (LIF) has been 157 employed to determine electronic flame temperature, rotational flame temperature and vibrational flame temperature (176-178). Winefordner and coworkers reported several methods related to LIF; these are based on linearity between the fluorescence signal and the laser spectral irradiance, and saturation, respectively (178-179). The conventional Spectroscopic technique normally involves direct line viewing of radiation from a flame which results in the measurement of spatially averaged temperatures. LIF with spatially-resolved excitation and observation processes may provide a method to determine spatially resolved temperature profiles. On the other hand, the employment of the isolated droplet injection technique introduced by Hieftje and Malmstadt (14) can also achieve measurement of spatially resolved flame temperatures (180). Most Spectroscopic methods assume thermodynamic equilibrium, which does not necessarily prevail in flames. Daily reported a technique for recovering a true gas translational temperature by 22-+ analyzing the fluorescence spectrum from the (v' = 0) state of OH (181). In DLI, one of the two lasers employed is tuned to resonance with a transition of the analyte atom. The flame temperature measurement method presented here is independent of the nature of the resonant transition utilized. Our results, obtained with sodium and lithium as the ionized analytes, illustrate the use of single and ‘1); 0. (I) ' on). P by“: nt‘b}: ‘51 we Buy 158 double photon resonant transitions respectively in DLI temperature measurement. The degree of agreement obtained with the different analytes and different excitation schemes, and the agreement with the temperature measured by the line-reversal method in similar flames, provide evidence that the method is accurate. Another indication is the good agreement of our experimental ion mobility values with those determined by others. As reported previously (131), for some systems DLI offers a two-order of magnitude improvement in trace Na detection over single laser ionization enhancement techniques. An improved understanding of the ion behavior between probe electrodes should aid in optimizing the efficiency of ion collection in both DLI and single laser methods. In addition, the diffusion and mobility coefficients and ion lifetimes determined in the course of DLI flame temperature measurement should prove useful in characterizing ion behavior. ff ". 90%) (has 159 B. Experimental A detailed description of our experimental apparatus has been presented elsewhere (131). In our implementation of the DLI technique, a tunable dye laser, pumped by an N2 laser, and a fraction of the beam of the N2 laser were collinearly aligned and focused on the same, post-combustion region of the H2/02/Ar flame. Both lasers had a pulse duration of a 5 ns; the width of the Spectral profile of the dye laser was < 0.1 nm. Atomic sodium (or lithium) was obtained by nebulizing NaCl (or LiCl) solution into the flame with a pneumatic nebulizer. For sodium, the dye laser (Rhodamine 6G dye) was tuned to the 381/2 -> 3P3/2 transition (589.0 nm), while for lithium the dye laser (Rhodamine lOl dye) was tuned to the ZS -> 3D two-photon transition (639.2 nm). A pair of voltage-biased nichrome wires (0.7 mm diameter), separated by 5 mm, were suspended inside the flame 10 mm above the burner head. A three-dimensional micrometer-driven translation stage provided control of the bottom probe position with a precision better than :_ 0.01 mm. .The voltage between the biased probes was controlled by a commercial high-voltage power supply with digital readout. The probe current was passed through a load resistor and the resulting voltage drop was the input to a boxcar integrator. A strip-chart recorder and an oscilloscope 160 were used as output devices. Laser power was measured with a commercial power meter and maintained at constant levels throughout the eXperimentS. The probe configuration in the apparatus is depicted in Figure 44; the figure also defines the coordinates dt and db of the top and bottom probes relative to the laser beams for use in the following theoretical discussion. Because reversal of the bias voltage across the probes demonstrated the superior sensitivity of asymmetric probe configuration when the bottom probe was negative (Figure 45), Na+ and Li+ ions were collected at the variously positioned lower probe in all experiments reported here. The aspect of our DLI experiments that facilitates flame temperature measurement and also distinguishes the technique from CW laser methods is the ease with which ion lifetime (5. can be measured. The data in Figure 46 are representative of those obtainable with time-resolved DLI experiments. The plot was obtained by triggering the boxcar integrator with the firing of the N2 laser and temporally scanning the aperture delay, thus acquiring the time profile of the ion signal. x:0 I CL .g. n CL CT Displacement from beam 9 X Figure 44. 161 I W///////I///I E Schematic of probe configuration. The nichrome wire probes A and D were positioned horizontally and parallel to the collinear dye and N2 laser beams B and C. The laser beams' center was a 10 mm above the Meker-burner head E. The vertical, "displacement from beam center" distance x is defined such that dt>i 0 > db. Figure 45. Asymmetric sensitivity of DLI apparatus to ion Signal. Reversal of the probe bias voltage demonstrated the superior sensitivity of the system when cations were collected at the bottom probe. (Ionization Signal expressed in arbitrary units.) 163 Ionization -NOJ 999 III 43me C3000 I I \I O) O O I (mo .00. woo woo .mo 5 ..mo .30 .uno Lao .550 .80 .0mo .0350 (0.3% .CCCmVI cceh C0~CAM~ '6 CI 2’ U) C2 .9 +— CD .5 C2 2 I——-I — 5,15 Figure 46. 164 I--—-I -J 20;» Sample strip-chart recorder tracings for the Na+ ion Signal produced by the dual laser apparatus. In case "a" (case "b") the boxcar integrator aperture was 50 us (200 us), db = -0.6 mmIdb = -0.1 mm), and the probe voltage was 100 V(0.0 V). The liftime, E , determined in case "a" was 9.2 us and in case "b" was 40.9 ns. (Ionization signal expressed in arbitrary units.) I . 5». 1'6 Q)! 0 165 C. Theoretical In previous work (131), we concluded that the predominant trnaSport mechanism for ions produced in our DLI apparatus is drift due to the electric field of the probes. By determining ion lifetimes 5 first as a function of lower probe position db and second as a function of the probes' field, it is possible to determine independent values of the ion diffusion coefficient D and mobility coefficient p with the reSpective data sets. The flame temperature T can then be calculated with the Einstein relation (182, 183) T = qu-l u-1 (1) where q is the electron charge and k is Boltzmann's constant. For the single dimension defined by x in Figure 44, the equation of continuity (182) for the ion density n is 8n(x,t)/3t = Da 32n(x,t)/ax2 . (2) Substitution of n(x,t) = nx(x) nt(t) , (3) 166 into Equation (2) followed by equating both sides of the separated result to - 5-1 yields nt(t) = exp (-t/E) (4) and dznx(x)/dx2 + Da’lg'lnx(x) = o (5) Under the physically reasonable assumptions that the ions are completely absorbed at the lower probe, n (d ) = 0 x b (6) and that the maximum ion population exists in the ionizing laser beam, dnx (0)/dx = 0 (7) Equation (5) leads to the result -2DH1 (112) (3) 5:411 a for the lowest mode soulution. The value of Da must be distinguished from the ionic diffusion coefficient D sought for eventual use in Equation (1) because of the ion-accelerating and 167 electron-Slowing space charge effect. Such an effect is expected when the ion density exceeds 107 cm"3 (182); our previous work (131) suggests the existence of a substantially greater ion density in our experiments. Assuming therefore that our DLI flame environment represents the ambipolar diffusion (182) limit with equal electron and ion temperatures, we assert the familiar relation between the apparent and desired coefficients: DaI: 2D. (9) In the low, homogeneoous field arising from the bias voltage 0 between the probes separated by distance L, L = dt - db, f(10) The ionic mobility v can be defined as v = u¢L , (11) where the mobility coefficient 0 is to be determined. The ion lifetime §;may be interpreted as the time required for an ion formed in the beam (x = 0) to reach the negatively biased probe (x = d ), b Ide = V5 - (12) 168 Hence 6 and 0measurements determine uvia a = IdeL(("1<()'1 . (13) Following substitution of the mobility coefficient so obtained and the D value determined by Equation (8) and (9), Equation (1) yields the flame temperature. D. Results In this section we report diffusion coefficients and mobility coefficients for Na+ and Li+ in a stoichiometric HZ/Oz/Ar flame, together with the flame temperature calculated in each of the two cases. A comparison with the work of others and an analysis of the random error in this preliminary implementation of the DLI method are also presented. In Figure 47, a plot of ion lifetimeigversus db2 is given for Li; use of Equations (8) and (9) yields the Li+ 2 1 value D = 6.7 i 0.34 cm + s- A linear plot of Na lifetime versus db2 was also obtained, and similar 2 + analysis yielded DNa = 5.65:0.30 cm 5-1. Reported values for neutral Na are similar but somewhat higher. Ginsel (184,185) reported DNa= 3.2 cmzs-l for Na in a 2100 K flame and Snelleman (167,185) found DNa = 9.9 cmzs'1 in a 169 .HA mmz mumaocm ecu can ouon m03 momuao> moan meoum on» .mumo woman mom up mo oofluocom 0 mm L meduomwa :oH .hw ouomam n A ~52 can N3 0. .0 mod mod 00.0 No.0 H H H H H H H H H H H H ON 0m 00 3.3 00 170 C2H2/02/N2 flame at 2440 K. Ashton and Hayhurst (127,129) report DNa values between 5.5 and 13 cmzs.l for several Hz/Oz/N2 flame compositions. In the case of Li, Ashton and Hayhurst (186) reported DL1 = 6.8 cmzs-l at 1920 K and 8.5 cmzs-1 at 2100 K. With |db|= 0.9 mm, L = 6.7 mm, and 10 g_ 0 52400 V, Equation (13) and the linear plot of E versus 0-1 in Figure 48 combine to yield the Na+ mobility coefficient, Na+ 30.2 i 0.6 cmZV-ls-l The corresponding value, with'idb = 0.4 mm, L = 4.6 mm for Li+, was 11Li+ = 38.6 i 2.1 cmzvmls-l Substitution of these mobility coefficients and the diffusion coefficients discussed above into Equation (1) yields two independent estimates of the flame 2171 i 123 K from the Na DLI data and T = temperature: T 2014 i 150 K from the Li DLI data. AS shown in Table 4, these temperature values agree fairly well with each other and also with temperatures obtained by other workers (109,110) using different methods ttudy similar flames. The random error estimates reported above were calculated from the standard deviations in the diffusion coefficient, SD, and in the mobility coefficient, Su , using the eXpression -1 -1 2 2 -2 2 k (14) ST — qk u (SD + D u Sp) I which follows from 171 n . .mz mmB oumamcm 0:» wow 85 m.OI u 0 pump woman Hom .mmmuao> moan 090nm Hmoonmfloou Ho cofluocsm m no u msfluMHH coH p.53 .w. woo mod 3.0 08 HI .mv musmflm .06 loo 1 cm 33 .. 00. .ON_ .. CV. Table 4. 172 Acomparison of flame temperatures for Similar H2/02/Ar flames obtained by line reversal and dual laser ionization (DLI) techniques. Flame Composition (9. min-1) T Method Reference H2 02 Ar (°K) Employed Number 1.00 0.65 3.45 1990 line reversal 110 1.5 0.75 4.5 2000 line reversal 109 1.0 0.5 3.2 2014 Li+ DLI this work 1.00 0.50 3.45~ 2070 line reversal 110 2.0 1.0 4.0 2136 line reversal 109 1.0 0.5 3.2 2171 Na+ DLI this work 1.30 0.65 3.45 2210 line reversal 110 173 2 = (aT/aD)2sD s + (aT/aa)zsfi (15) 2 T and Equation (1). DLI values of (I and T permit the calculation of reduced mobility coefficients, u , as (182) (16) — (273.16K/T) (PAr/760 TOII))J . “0— For our 86.5% Ar post-combustion flame, PAr% 657 Torr. The reduced mobility coefficient for Na+ is thus found to beu0 = 3.29 cmZV-lS-l, which agrees well with Tyndall's drift-tube determination (187),)” = .3.02 cmZV-ls-l. The reduced mobility coefficient for Li+ is found to ber = 4.53 cmZV"ls-l which agrees well with the drift tube determinations (187,188) of Uoi= 4.68 cmZV-ls"1 by Tyndall and ”0 =4.56 cm2V"ls-l by Takebe et al. E. Discussion A fair assessment of the place of DLI among the many flame temperature measurement techniques (169-172) will require substantial additional investigation. It now appears that the DLI method possesses at least two advantageous features, and we are attempting to effect their development. First, the technique is dependent upon (1 174 the .identity of the ionized analyte element only to the extent that the dye laser is tuned to a resonant transition specific to the element used. Thus, special energy level restrictions encountered with the two-line ratio optical method (171,172) are avoided. Second, the wire probes can be suspended anywhere in the flame with very high Spatial resolution. Vertical profiles of flame temperature should thus be obtainable; it is possible that the droplet injection technique of Hieftje and Malmstadt (114) may further enhance possible Spatial resolution (180). Because the parallel laser beams and electrodes produce and detect ions in a horizontal, cylindrical corridor across the breadth of the flame, a determination of flame temperatures in successive flame annuli is desirable. However, recent evidence (180) of a large, virtually isothermal central zone in a similar flame suggests that the simpler, global estimate of temperature discussed above retains substantial worth. Several possible sources of error in and limitations of the DLI flame temperature determination require mention. The validity of Equation (9) is dependent upon the existence of ion-electron thermal equilibrium. This assumed equilibrium is similarly required in some optical methods (170,189). In Section C, the theoretical treatment neglects any vertical velocity of the cations attributable to gravity or convection. A more detailed theoretical approach could follow existing treatments include analogous terms. Figure 45 requires additional investigation and interpretation in the context of convective velocity. The quantitative impact of three experimental design factors must be noted as requiring additional investigation. The finite temporal aperture width of the boxcar integrator can introduce a small error in E values. In addition, there is small experimental uncertainty in the location of the collinear laser beams' center; this uncertainty will be reflected in the db values. Extension of the preliminary work reported here will require improved compositional definition and reproducibility of the H2/02/Ar flame. It is possible that slightly dissimilar flame-gas flow rates degraded the agreement between the Na and Li DLI temperatures. Recently, Mallard and Smyth (19) reported the use of a single laser in a laser-enhanced ionization ion-mobility study. Besides employing a dual laser apparatus that affords trace atom sensitivity advantages in some cases (131) and obtaining temperatures as well as mobility coefficients, the work reported here differs from that of Mallard and Smyth in that those authors measured the laser-pulse to ion-arrival time gap instead of determining 6. AS discussed above, measurements permit the easy estimation of both D and, 1) , but competitive ion-depletion processes may introduce additional signal decay time constants of the same magnitude as g, a problem now under investigation (192). It is interesting to note 176 the excellent agreement of our measured value Q‘Li+A‘NaI)= 1.28, with the eXperimental mobility ratios obtained by Mallard and Smyth (19) in C2H2/air and CO/O2 flames. In summary, it appears fair to characterize dual-laser ionization as a potentially attractive method for the determination of flame temperatures, diffusion coefficients, and mobility coefficients as well as ion lifetimes. Such capabilities strengthen the case for the continued application and development of DLI techniques. 177 CHAPTER VI ALTERNATIVE APPROXIMATIONS BASED ON THE EQUATION 0F CONTINU ITY A. Introduction The dual laser ionization (DLI) technique in flames has been discussed in previous chapters. The design of probe detectors used in DLI is simple, but the elucidation of ion behavior is not easy. The development of probe theories, since the 1920's, has provided the fundamental basis for charged particle behavior in a plasma or a plasma-like system (5). From the basic current-voltage curves of plasmas in which the probes are embedded, the fundamental characteristics of the plasmas, such as electron temperature, electron density and the potential distribution, can be determined. However, most theories assume collisionless conditions or permit only a few collisions; the valid domains of some of these theoretical models have been examined by Waymouth (193), and are described by the ratio of the probe dimensions and the 178 mean free path of charged particles to the Debye length (193). Schulz and Brown have attempted. to (extend such models to the case of collision-dominated systems (194). A review of the theoretical and experimental developments in electric probes has been given by Chen (195). A model is presented to describe the saturation ion current in this chapter. In addition, the ion density induced by DLI in the flame can be approximately estimated with this model. B. Theoretical Basis The sheath dimension usually serves as a useful parameter with which to characterize probe behavior. The determination of probe sheath thickness has been investigated. A theoretical formulation yielding the sheath-thickness under collisionless conditions was first presented by Langmuir (196). That is, _ g 6 age: 3/4 18- 3 (3:) (M) (F (1) under the assumption that the electric field E and potential V are equal to zero at the sheath edge (196). The symbols used in Equation (1) are 1 sheath thickness; SI , permittivity of free space; ji' current density; e, 179 electron charge; M, analyte mass;and 0 p' biasing voltage. The collisionless conditions of Equation (1) are inconsistent with those of our atmospheric flame system. From an approximation theory viewpoint, Biblarz et al. considered the sheath thickness in a. collision.— dominated MHD plasma (197). From Poisson's equation, a relation between Sheath thickness 15 and Debye length AD can be approximately estimated as follows(l97): 8 A 2 x (22) (2) S D kTe (Gone) is 1 = ' D no 632 , . (3) where 0p is the probe bias-voltage; k is the Boltzmann constant; Te is electron temperature; and no is the initial ion density. In relation to Equation (1), Equation (2) is more reliable for estimates of sheath thickness around the wire probe in a flame, because collision-dominated conditions for both MHD plasmas and flames are similar. In the flame, thermodynamic equilibrium, Te=Ti' is assumed. For Langmuir probe theory in collisionless environments it is assumed that no electric field can penetrate through the sheath edge, and both ions and electrons have a Maxwellian velocity distribution at the sheath edge (159). Therefore, the random ion current density Jr reaching the sheath edge is given as follows: 180 RT- _ _ 1 t J - en0(—27M) . (4) r The velocity factor ( gzfiik results from the ‘IT assumption of the Maxwellian velocity distribution. Bohm has improved this model by applying the physically reasonable condition that the Sheath cannot completely shield the electric probe. As a result, the electric field may ”leak" out from the sheath to some extent, and accelerate the charged particles arriving at the sheath edge (198). However, this model is only applicable to the collisionless, high density plasma (198,199). Waymouth assumed a diffusion-controlled gas discharge in the quasi-neutral region up to the sheath edge (193). He asserted the domain of his model to be A(3,/r < 10, P I-'p/1oo 1 > 1 and Ach > 10, where rp is the probe radius D and Ac is the particle mean free path. By contrast, the case of the sodium ion induced by DLI is collisionally dominated before reaching the probe. Several assumptions are made before deriving a simple model to describe the ion motion to the electrostatic probe. They are: (l) The Sheath along the probe is so thin that the ions may be collected completely by the bottom probe as they reach the sheath edge. The estimation of sheath thickness in the next section indicates the assumption is physically resonable. Thus we may avoid treating the 181 orbital motion of the ions under this assumption (195). (2) AS the probe is biased, the mobility-controlled motion of the sodium ion controls the ion velocity in the quasi-neutral region, instead of the thermal velocity or diffusion-controlled discharge presented by Langmuir and Waymouth, respectively, in a collisionless gas discharge (5,193). This assumption is based on the experimental evidence, as presented in Chapter V. In addition, Brown reached the same conclusion in his model under many-collision conditions, by using microwaves to measure independently the ion density in the gas discharge (194). (3) As the Langmuir probe is biased strongly negative, only ions reach this probe; i.e. for saturation ion current collection, the electrons can be repelled completely from the negative probe. This condition is required for elucidation of the steady-state current voltage characteristics (195). (4) The equation of continuity can be applied approximately to interpret the spatial and temporal behavior of ions in the collision-dominated atmospheric flame (182,200). In a simple model, the mobility-controlled motion of ions extends up to the sheath edge, as illustrated in Figure 49. The saturation ion current, I. is , reaching the sheath edge can be expressed as Iis = jisAs (5) 182 \ IONIZED PARTICLES _ \ \N\ (\ ‘ - \ I<-— V IIJ. E i I / G) / . / / >‘3 / 'p — QUASI «5(1an REGION —> HI. 0 Radial Distance from Center of Probe Figure 49. Model of ionized particles disturbed by a negative biased probe. The quasi-neutral region is extended up to the sheath edge. The ion velocity is controlled by mobility in this region. is the sheath thickness; r is the probe radius. 183 =l/2 eniViAS r (6) where the constant 1/2 arises from assuming that the sheath thickness is smaller than the probe dimensions, as discussed in detail by Chen (195); hi indicates the ion density reaching the Sheath edge; V. is the average ion 1 velocity dominated by ion mobility; AS is the surface area of the sheath (approximately equal to the probe area ) and jis is the saturation ion current density. Since only the ion current can be collected (given sufficient negative bias on the Langmuir probe), Equation (6) neglects any contribution from electron current. The mobility-controlled velocity is defined as v. = u.E . (7) where “i is the ionic mobility coefficient and E is the electric field. Under the quasi-neutral condition, that is, ne 5 ni, the electric field E can be considered as constant. The Poisson equation \7' <1) = -41re(n- - n) (8) II 0 implies V0 -E = const. (9) Applying the boundary conditions and integrating Equation 184 (9) yields where ()p is the probe bias-voltage, and L is the inter- probe distance. As in Chapter V, the equation of continuity is used to describe the ion density. Under the assumptions made previously, the diffusive motion of ions outside the sheath edge can be neglected. Therefore one obtains 2 n 3——i = D Vzn - V E at2 a i “i ni (11) azni ' ”uthn.E , 3t2 1 l (12) Substitution of ni(x,t)'= nx(x)nt(t) into Equation (12) leads to nt(t) = exp (-t/€ ) ,(13) and n x where g is the lifetime. Substitution of the lifetime obtained in Chapter V, _ IdblL g - ui¢p I15) into Equation (14) yields 185 nx (X) = no exp(-'Tx") b , (16) where n, is the initial ion density produced in the ionizing beam, and db is the distance from the ionizing beam to the bottom probe. Therefore, from Equations (13) and (16), the ion density can be eXpressed as ni(x,t) = n. exP(- 323-) exp(-t/g) b (17) Inserting Equations (7), (10) and (17) into Equations (6) leads to I. =-1-en exp(- -X—) exp(- Eh) A EB 15 2 ° db 5 i s L = —1-en exp(- __x_) exp(- E)u.A EB 13 2 0 db E l p L I ) where AS 3 Ap. Here n1 is defined as the ion density reaching the sheath edge; the ions need take t 2 g to arrive at the sheath, x flab: Thus the saturation ion current Iis can be simplified as I 3 1en exp( 2) A 32 is 0 ‘ “- 2 ~1 pL . (19) In contrast, while the Sheath is considered thick enough to allow numerous collisions in it, the ion density of Poisson's equation can be replaced by Equation (6). Electron density he is neglected in the sheath. Under the assumption that the electric field and potential equal 186 zero at the sheath edge (194,195), 2 -2 -2 : I. =2 .6014 Is “”1 (>er ‘ (20) where 2 1 _ x 1 1 r= [(3)2-1Ia5~(}-s-)1n —§+((—§)-1( rp P rp 1P (21‘) and ‘1 is the collecting length of the cylindrical probe, rp is the probe radius and As is the sheath dimension. C. Results and Discussion The steady state current-voltage curve can be divided into three regions: the positive ion saturation region, the transition (or partial collection of electrons region) and the electron saturation region (195). We have obtained analogous current-voltage curves previously (146). As the Langmuir probe is biased stongly negative, all the electrons are repelled and this probe collects only the positive ions. That is called ion saturation. As the biasing voltage is diminished, the negative probe begins to collect electrons due to thermal velocity; thus the ion current, compensated by partial electron current, decreases with decreasing negative biasing voltage applied to the Langmuir probe. 187 As shown in Figure 50, for ion current vs. negative voltage, the net ion current becomes smaller as the probe-beam distance db increases. The distance db changes from 3 mm to 1.5 mm; the ion current in the region of the transition changes by about 180%. Obviously, by considering the probe position the optimum DLI sensitivity in a flame is obtained by placing the negative biased probe as close to the ionizing earn as possible. This may reflect the increased probability of ion neutralization by collisions with foreign gases in the flame as the ion to probe path is increased. Most of the gases have a mean free path of the order of 10.8 m under atmospheric conditions (201). Consequently, even a 1 mm variation of beam to path distance may give rise to numerous collisions between ions and foreign gases. The applicable domain of Equation (19) is for the saturation ion current under strongly negative bias voltage on the Langmuir probe. We select values of 100 volts and 300 volts, respectively, which are located in the region of the plateau ( saturated ion current ), and we plot ion current against the reciprocal probe distance in Figure 51 and Figure 52. A straight line is obtained. Based on Equation (6), the ion density no can be 10 estimated to be 10 cm-3 from the slope of Figure 51, using the known values of the parameters, Ap W l cm2,¢p = 100 volt,ui==30 cmz/(volt sec) (146) and peak amplitude of ion signa1.= 40 mv on the oscilloscope ( for a load NEE m.H u o ”q .wnoum Eouuon ecu co momuao> mafia o>wummoc .m> Heaven :0“ Beacon no uon d .om onsmflm ooo=o> 385 95302 com on. 00. on H H 188 4| mmtscoIOe-rom ('ITD)|DU5!S u0| 189 O) I c» I A 0) Ion Sign) (a.u.) N 04 I I I l.5 2.0 2.5 _'_ -l L XIOImm) Figure 51. A plot of ion Signal vs. the reciprocal of interprobe distance. ‘Sodium ion is induced by DLI (BS + 3P ), Biasing voltage on the bottom profie 160 volt. The distance between top probe and ionizing beam is fixed at 4.25 mm. The arrow along Y axis indicates the amplitude of 40 mv observed on the oscillosc0pe. 190 O) N 0: 43 U‘ . I (on Signal (a.u.) l (.0 (.5 2.0 2.5 .I. x IO(mrri") L Figure 52. A plot of ionization vs. the reciprocal of interprobe distance. Sodium ion is produced by DLI(38 ->3P3/ 2). Biasing voltage = -300 volt. The distafice between the t0p probe and the ionizing beam is fixed at 4. 25 mm. 191 resistor, R1: 50 Kg , Iism8 x 10"7 amp). This estimate is reasonable in comparison with the previous value for the ion number generated during a laser pulse (131). Applying 10 the values of no: 10 cm-3,‘I>p = 100 volt and T11 Tex 2100 K (obtained previously) in Equations (2) and (3) leads to- ADj§12x10n2 1 mm and As 3 6 x 10— nun. The Sheath thickness has been assumed to be smaller than the probe diameter which is m 1 mm. This result is consistent with the assumption. By contrast, if bias voltages of 20 volts and 30 volts are selected from the transition region of the probe characteristic curve in Figure 50, a nonlinear plot of ion current against reciprocal probe distance is obtained, as shown in Figure 53 and 54, respectively. The ion current is partially balanced by absorption of electrons at the probe in the transition region, as follows: I = 1/2 As :anj (22) 3 1/2 Asvini - 1/2 ASVen e That is the reason why Equation (19) cannot be applied to the transition region. From the Equation (20), the saturation ion current is expected to be proportional to the square of biasing voltage; however, as shown in Figure 50, the ion current in the saturation region decreases to some extent as the biasing voltage becomes larger. The failure of Equation 192 ' I I I 9- .. 8- .. 7- - 6~ .. A. 5' ' 3. 34. _ 5%.35" - C: .0 2- . l- - I 1 L I I5 2.0 2.5 l - -—xlO(mm') I. Figure 53. A plot of ionization vs. reciprocal of interprobe distance. Sodium ion is produced by DLI(3535 + 3P 2). Biasing voltage = -20 volt. The digtance between the top probe and the ionizing beam is fixed at 4.25 mm. 193 Ion Signal (0.11) N 04 I A . I Figure 54. l I l.5 2.0 2.5 l-ExlO (mrn') A plot of ionization vs. reciprocal of interprobe distance. Sodium ion is produced by DLI (383 + 3P Biasing voltage = -30 volt. The distance gégween the t0p probe and the ionizing beam is fixed at 4.25 mm. 194 (20) to fit the experimental results is caused by the assumptions of this model. (1) The electric voltage is treated as zero at the sheath edge; actually, some electric field may penetrate the sheath (198). (2) The condition is for sheath thickness >> probe dimension, not like the thin sheath we have in the system. Chen pointed out that such a condition is unusual unless a magnetic field is applied (195). As the biased voltage of the bottom probe becomes less negative, more electrons are absorbed and the ion current becomes smaller. AS the bias voltage changes towards positive values, more electrons are collected to balance the ion current. The point where no net current can be detected is called the floating voltage. As shown in Figure 55, a relation between beam-probe distance db and applied positive voltage indicates the floating voltage decreases as db increases, due to the electron velocity being much larger than the ion velocity. Less positive voltage is needed to maintain the net current equal to zero. D. Conclusion Based on several physically resonable assumptions, a formalism has been used to characterize the behavior of 195 melon-05:55:55; I l I I I Positive Biasing Voltage Ul l I 0 fi?. Figure 55. 0.5 I.0 I.5 2.0 d (mm) Floating potential vs. distance from bottom probe to ionizing beam. The distance between the top probe and the ionizing beam is fixed at 5.0 mm. 196 the saturated ion current. In addition,the ion density may be estimated with this formalism. Ion signal sensitivity to biasing voltage and the reciprocal of the interprobe distance has been shown. In fact, we must recognize some limitations in the model described in Section B, such as : (1) the reference probe is too small to» fit the assumption ‘used in the Langmuir probe theory (195); (2) any emission of electrons by the probe in the flame, which may disturb the ion current, is neglected; (3) the effect of sheath thickness on the potential distribution is neglected; and (4) the boundary conditions cannot fit Equation (l6),which may reflect the neglect of difusion in treating the equation of continuity (131). Possible improvements, such as increasing the area of the reference probe, and insulating the portion of the probe outside the flame may eliminate some of the difficulties. CHAPTER VII THE EFFICACY 0F DLI IN AN Hz-Oz-Ar FLAME A.Introduction Recently, research in laser-induced ionization has become a very important area of Spectroscopy. This technique differs from a normal optical spectroscopic technique in at least two characteristics: (1) the former involves the ionization continuum of the analytes, whereas the latter deals with the discrete states; (2) an ion detector is employed in the former, whereas an optical detector is used in the latter. The advantages of an ion detector over an optical detector include freedom from light scattering, IND solid angle restrictions and higher efficiency. Basically, an atom can be converted into a positive ion and an electron with the aid of a laser; therefore the detection efficiency can be rearly unity, whereas the quantum efficiency of photomultiplier tubes is < 0.50 (22). Ion detectors employed in a laser-induced ionization technique include thermionic diodes, proportional counters, ionization chambers, electron multipliers, mass Spectrometers and electrostatic probes. Laser-induced 197 In (I) 198 ionization techniques can be classified according to the detection system used, the sample type, the atomization system and the ionization process. Thus, there are methods such as resonance ionization spectroscopy (R15) (22), multiphoton ionization spectroscopy (MPI) (86) and laser-enhanced ionization (LEI) (2). An application of the optogalvanic effect in flames, called LEI was introduced in 1976 (2,3). LEI is a technique to detect analytes introduced in a flame with a laser tuned to resonance with a particular energy level. Collisional ionization becomes more efficient for analytes starting from an excited state than from the ground states. The collisional ionization rate constant is enhanced by decreasing the energy defect between the ionization continuum and the discrete excited state, on the basis of the Boltzmann distribution (l47).Current research in LEI, primarily carried out by scientists at the National Bureau of Standards (NBS), includes trace metal analysis (6-8), electrical interference studies (14,15), and molecular LEI (16-18). In trace metal analysis, various methods related to laser design and detection systems have been attempted to improve the sensitivity and selectivity of ion detection; detection limits as low as 0.001 parts per billion (ppb) can be achieved for some elements (2). Dual laser ionization (DLI) is similar to LEI, but employs two lasers in producing the analyte ions in flames (FL 199 (131,146). In DLI, an N2 laser-pumped dye laser is tuned to a resonance transition of an analyte; ions are produced by the N2 pumping laser which has sufficient photon energy to cause photoionization (131,146). The energy level scheme used in DLI differs from that used in stepwise LEI with two dye lasers; in the latter each dye laser is resonant with a particular excited state, and the two lasers share a common intermediate state. This difference may result in a different ionization process following the dye laser excitation. Multiphoton ionization is predominant in DLI as the dye llaser is tuned to the transition of the 381/2 to 3P3/2 level of sodium (Chapter III), whereas the collisional ionization process is favored with decreasing the energy’ defect. between the continuum and the discrete state by stepwise excitation (6). If we consider the analyte in DLI to be a three-level atomic system, ion production can be related to the collisional ionization rate constant and the photoionization rate constant for the analyte in its pOpulating the .excited state, as treated by the rate equation approach in Chapter IV. Which of these processes dominates depends on the magnitude of these two factors. In this chapter, various ionization schemes of sodium and lithium are examined in order to extend the applicability of DLI. In addition, the competition between photoionization and collisional ionization is tested 200 experimentally and the results are_ compared with predictions based on the rate equation approach and other theoretical models. Finally, the detection sensitivity of DLI is compared with that of LEI. B. Experimental The two DLI beams are obtained by directing an N2 laser-pumped dye laser and a portion of the N2 pump laser into the same area of an H2-Oz-Ar flame. The beams are directed collinearly from opposite directions, with maximum temporal and spatial overlap over the burner head. The pulse durations of the two lasers are 5nsec. This is an inexpensive way to gain a dual-beam construction. An analogous design has also been used elsewhere (202). A premixed Hé-Oz-Ar flame was used, with a temperature about 2100 K as determined by the DLI method of Chapter V. Free atoms of the alkali selected element were obtained in the flame by driving the corresponding alkali chloride solution out of a pneumatic nebulizer with Ar gas. The dye laser was tuned to resonance with transitions to a higher energy level of the atom from either the ground or thermally excited states to produce the population in the upper states via one- or two-photon absorption; the ions produced were then collected by a 201 pair of voltage-biased nichrome wires suspended parallel to one another inside the flame. The resulting ion current passed through an electronic network where it was converted to the voltage domain; this voltage signal was the input to a boxcar integrator for signal processing. The readout system. was a strip chart recorder and an oscilloscope. Several organic dyes were employed in the eXperiment for selection of various excitation wavelength ranges. Rhodamine 66 was used for BS-BP one-photon and the BS44D two-photon transitions of sodium; Rhodamine B was used for the 35 #58 two-photon and the 3P-ISS one-photon transitions of sodium; DCM was used for the 28 + 2P one-photon transition of lithium, and Rhodamine 101 was used for the 28-3D two-photon transition of lithium. A photomultiplier tube in connection with a monochromator was employed to monitor the selected dye laser wavelength. The output power of the dye laser was varied by inserting neutral density filters between the flame and the front mirror of the laser cavity. The set of neutral density filters, recalibrated at 3371 A with a UV/VIS spectrophotometer (Cary 17), was also used to vary the output power of the N2 laser. Solutions containing 100 ug/ml (ppm) Na (NaCl) and 100 ug/ml Li (LiCl) were used throughout the experiments, except for the case of the 3P-+SS transition of Na and the 25 -93D two-photon transition of Li, where solutions containing 1000 ug/ml were used. 202 C. Results and Discussion In order to study the effect of the N2 laser on ionization enhancement in DLI and on the ionization pathways, the energy level schemes of Na and Li shown in Figure 56 were employed. In all cases except for the scheme shown in Figure 56d, the dye laser is tuned to a one- or two-photon transition of the analyte from the ground state and the N2 laser or collisions produce ionization. In the case of the scheme in figure 56d, the dye laser promotes the analyte to the 58 level from the thermally-produced excited 3P level. C-l Ion Background HThe ion signal induced by DLI is more complex than that in IE1. LEI signals can be observed by blocking the N2 laser beam. A significantly large ion background was observed in DLI with respect to LEI as exemplified by the Li (28-3D) two-photon resonance in Figure 57. Therefore, careful selection of the proper baseline under each set of experimental conditions is necessary for power dependence 203 Figure 56. Energy schemes for sodium and lithium DLI. A dye laser is tuned to a transition to an excited state via one- or two-photon absorption from the ground state or a thermally excited state; the wavelength in A is specified. The second (szx = 3371 A) laser provides energy sufficient to reach the ionization continuum. 204 I 33 L 53 53 1 ‘44 4D _wmw 3:) NNOm 514. 5.0b _hmn 4.0+ BIL. 6V thm 00mm L0r 33 (>33 Li 3D (AI Nmmw _hmn mOhw 23 SIP- 5.39 r 50” 40- ev 3.0 r 2.0 ~29 L0- .o-2s 205 .33 3. Jan .2 .3: mm 989E "3 mo coflumufloxm “mm + mm. couonmuosu map nmsounu 69:5 ma Hmmma who ms» :053 cmcwmuno mamcmflm coH .hm musmfim 505.263 505.903 . As 3 a $3 _ a mmmm loubgs uol 206 studies. Sources for the ion background in DLI include: (1) the dye laser; (2) the N2 laser; (3) the flame; (4) the broadband lasing of the organic dye. This latter probably occurs between one wall of the dye cuvette and the end mirror. Broadband lasing occurs over a range of wavelengths and depends on the dye employed. Thermal ionization from the flame is, however, constant with time and not detected by the gated integrator. For example, the laser output and the broadband lasing from Rhodamine B are shown in Figure 58. Because of the presence of two lasers and broadband lasing, there are several baselines induced by DLI, as shown in Figure 59. For convenience, the notation I (P1, P2, F, T) is used to indicate the ion background signal as a function of the N2 laser power P1, the dye laser power P2, the broadband lasing F and the flame temperature T. Therefore, signal 11(Pl, P2, F, T,) is obtained with irradiation by both the dye laser and the N2 laser; signal 12(P1, F, T) is obtained when the dye laser is blocked; 13(Pl, T) is obtained under N2 laser irradiation alone; 14(T) is obtained by blocking both lasers. Obviously, 12(Pl, F,T) is selected as the baseline for DLi and I1 - 12 is plotted against dye laser power for the measurement of dye laser power dependence. Similarly, 12 - 13 is selected for the measurement of power dependence of broadband lasing. When the signal 13(P1, T) - I4(T) is plotted against the N2 laser power, a slope of one is obtained. This demonstrates that this background 207 0 Figure 58. Lasing at 6154 A plus broadband 0 emission (over m 100 A rang) produced by a Rhodamine B tunable dye laser. 208 cm. 508.925 00.0 00$ 209 Iz'---- —_-———- I3--------- — -——- IONIZATION I 4 TIME Figure 59. Ion signals obtained for the energy scheme of . Figure 56 (c) [Na(3S + SS) two-photon excitation] under various experimental conditions. I (P1, P2, F, T) denotes ionization due to fhe N2 laser P , dye laser P , broadband lasing F and fl e temperature T; similar definitions apply to 12(P1,F,T)y I3(P1,T) and I4(T) . 210 contribution comes from the thermal population of sodium (3P level) followed by absorption of one photon from the N2 laser. This thermally-based ionization process is analogous to the resonance case of Figure 56a. The background contributed by I3 - I4 depends on the alkali concentration, and it seems to be negligible when less than 100 119/ml Na concentration is used. Based on the Boltzmann distribution, the thermal population ratio of the 45 level to the 3? level is 2.5 x 10‘3; thus ionization emanating from other thermally-populated excited states can be ignored. Multiphoton ionization by absorption of two photons from the N2 laser has not been observed for Na. Frank Curran (203) has, however, observed off-resonant multiphoton ionization for Cs, and K. The background 12 - 13 induced by broadband lasing is linearly proportional to the power of the N2 laser and to the power of the broadband emission. Figure 60 shows the dependence of the ion background 12 - I3 on the power of the broadband emission. Accordingly, the N2 laser in DLI can increase the backgound ionization by photoionization of excited levels produced thermally or by absorption of broadband radiation. 211 l I I I l 2 IO r - P d ’5 3. O V 5 'glob ' .2! C: 2 W ' I l L + l l l IO IO Power of Broad Band Losing Figure 60. Relative ionization from Na as a function of the power of broadband lasing from Rhodamine 6G, at constant N2 laser power. The log-log plot gives a straight line with slope = 1. 212 C-2 Sodium Ionization with 35 - 4D Two:photon Resonance Excitation Sodium DLI with 38 - 3P resonance excitation (Figure 56a) is discussed in Chapter III and Appendix A. The experimental ionization enhancement of DLI over LEI in that case is about two orders of magnitude, and photoionization is the pmedominant process following the (one-photon) dye laser excitation. As shown in Figure 61, sodium DLI and LEI, respectively, in the case of 3S - 4D two-photon absorption (Figure 56b), properly depends on the square of the dye laser power. Moreover, here the presence of the second (N2) laser in DLI provides no significant ionization enhancement. Clearly, this result demonstrates that collisional ionization must dominate both DLI and LEI, following the two-photon excitation by the dye laser. The predominance of collisional ionization over photoionization results in there being little effect of adding the N2 laser in DLI. Thus, ionization under the conditions shown in Figure 56b follows a different pathway and shows different sensitivity, compared to the case depicted in Figure 56a. In order to estimate the contribution of multiphoton ionization to DLI with 38 - 4D two-photon absorption, we assume both DLI and LEI undergo the process 213 (O IOP Ionization l IO I62— Dye Laser Power Figure 61. Dye laser power dependence of sodium ionization with two-photon resonance excitation (3S-t4D). The logarithmic coordinate scales are arbitrary; the straight line has slope = 2.<>indicates LEI; A indicates DLI. 214 of multiphoton ionization, as follows, Na(381/2) + 2hv(5787 Z.) + Na(4D3/2) + hv+Na+ + e Na(3Sl/2) + 2h\’(5787 A) +Na(4D3/2) + hv + hv'(337l i) + Na+ +e Ionization rates were calcualted from Equation (1), which is based on an analogous equation in ref(l24): 2 W=2 2 2 2 2 2 3 1lejl (31% Izkzl + Ezéulzml> (1) Here W denotes the overall ionization rate for DLI, and the first term of Equation (1) indicates the ionization rate for LEI;.§Lsz}2indicates the two-photon transition probability frg;1the 38 to the 4D state; E1 and E2 are the field amplitude of the dye laser and the N2 laser, respectively; Zk2 and Zk.2 are dipole matrix elements connecting the 4D3/2 level and the level of the continuum appropriate for the dye laser and the N2 laser, respectively. The ratio of the calculated multiphoton ionization rates for DLI over LEI is 1.1 when the power density is taken as 70 MW/cm2 for the dye laser and 80 MW/cm2 for the N2 laser. This calculation reveals that, unlike the case treated earlier (38 - 3P), under 38 - 4D resonance excitation there is no significant enhancement by adding an N2 laser photon over photoionization with 215 three dye laser photons. The calculated results differ for these two cases because two dye laser photons are required in LEI (figure 56a) for photoionization from the 3P level, whereas only a single dye laser photon is required in LEI, from the 40 level (Figure 56b). It is well-known that a two-photon ionization cross section for an excited state atom will be much smaller than that for single-photon ionization (77). According to the three-level rate equation treatment given in Chapter IV, the competition between photoionization and collisional ionization following dye laser excitation depends primarily on the values of the photoionization rate constant and the collisional ionization rate constant for the intermediate, excited state of the analyte. In order for photoionization to dominate,the photoionization rate constant must be larger than the collisional ionization rate constant by at least one order of magnitude (Chapter IV). Under this condition, the collisional ionization process is negligible. Based on the Boltzmann distribution, the collisional ionization rate can be enhanced nearly exponentially by decreasing the energy defect between the continuum and the excited state. The collisional ionization rate constant can be estimated from Equation (2) : (147) (BWkT )5 K=z.:[x j] °M* x exp(-E/kT) (2) J ' ' j ”M,xj ‘ 216 Here K is the ionization rate constant; [xj] is the concentration of component xj in the Hz-Oz-Ar flame (in our case the flame gases after combustion contain about 80% Ar as the major colliwion partner with alkali atoms, and about 20% 820). C’M',x. indicates the ionization cross section between an excited alkali atom M* and xj;uM'x. is the reduced mass of M and xj; E is the energy defect between the excited state and the continuum. In comparing collisional ionization rate constants for the cases shown -E/kt is the in Figures 56a and 56b, the exponential term e major factor. Based on Equation (2), the collisional ionization rate constant in the case of Figure 56b will be enhanced by a factor of 1.8 x 105 in comparison with that in the case of Figure 56a. The experimental result demonstrates the ionization enhancement of DLI over LEI is about 102 for the case of Figure 56a. Based on the rate equation approach, the ionization enhancement of DLI over LEI is mainly determined by the ratio of the photoionization rate constant to the collisional ionization rate constant following the dye laser excitation (in Chapter IV). Because the collisional ionization rate constant for the case of Figure 56b is a factor of 1.8 x 105 larger than that for the case of Figure 56a, and the photoionization cross sections are on the same orders for these two cases (145), we would expect Coljisional ionization to dominate as is found 217 experimentally. C-3 One- or Two-Photon Resonance Excitation Similar results were obtained for the Li 28 - 3D two-photon transition (see iFigure 56f), the jpower dependence of the dye laser gave a slope of 2 and the ratio of DLI/LEI was'L1.This indicates that the ionization pathway is dominated by collisions as discussed in Section C-2. For the 28 » 2P one-photon transition of Figure 56e, the observed ionization enhancement of DLI to LEI was, surprisingly, more than three orders of magnitude. Also, power dependence measurements indicated that the ionization pathway was mainly due to a multiphoton process involving one photon from the dye laser and the other photon from the N2 laser. The ionization mechanism is thus similar to that of Figure 56a. As noted previously the ionization enhancement of DLI over LEI is approximately determined by the ratio, from the excited intermediate State, of the photoionization rate constant to the COllisional ionization rate constant. Based on Equation (2), the relative value of the collisional ionization rate Constant for the cases of Figure 56a Na and 56e Li can be 218 estimated. The concentration xj in Equation (2) is the same for these two cases, becuase the same composition flame was used. The collision cross sectional”, x. (where M* is the alkali atom in its first excited sgate) is approximately equal too M,x. (where M is in the ground state ). Kelly and Padley‘ in flame experiments (161) and Johnston and Kornegay in shock tube experiments (204) have suggested that the collisional ionization process M+x. + M+e +x. 3 (a) may be interpreted on the basis of three subreactions M+x. 3" M +x. (b) J J * *1: M +x. '* M +xj (c) ** + - M +xj + M +e +xj (d) where M and x. are as defined previously; M* is the analyte in its first excited state and M" is the analyte in a higher excited state. The optical cross section for initial electronic excitation (step (b)) is about thousand-fold smaller than the ionization cross section for ionization steps (c) and (d) (161,203). Hence it is resonable to assume OM*'xj EoM'xj. Kelly and Padley have . _ 02 __ 02 determinedoNa' Ar - 2700 A and °Li,Ar - 1200 A , as well - 2 __ 02 as ONa,HZO - 11000 A andoLi' 320 - 5500 A (161). The energy defect E is 3.04 ev for Na and 3.54 ev for Li; kTg 219 0.18 ev for a 2100 K flame. Based on these data and Equation (2), the ratio estimation gives KNa = 20 (3) KLi . where K and K indicate the collisional ionization rate Na Li -constant for Na and Li, respectively. The photoionization rate constant R is equal to the product of the photoionization cross section a and the photon flux phot. (photons/sec.cm2) of the N2 laser (153); i.e. pho.“’ - (4) The value ofcz for Na from the 3P state to the phot. ionization threshold is 7.38 x 10.18 cm2 andOphot for Li from the 2P state to the ionization threshold is 15.20 x 10.18 cm2 (145). Thus, the ratio of photoionization rates gives Ru- TIN—‘2 , ‘5’ a if identical N2 laser powers are assumed. therefore, comparison of DLI/LEI ionization enhancement between the cases of Figure 56a and 56e can be estimated as RLl _ (6) K . L1 40 RNa KNa . I8 220 Experimentally this ratio is > 10. Thus this extimation gives an enhancement ratio of the same order of magnitude as that obtained experimentally. When the formalism outline in Section C-2 for Na (38-4D) two-photon excitation is applied to Li, the collisional ionization rate constant from the 30 state (Figure 56f) is calculated to be 8 x 104 times larger than that from the 2P state 3 for the (Figure 56e). This value is much larger than 10 measurement of the DLI to LEI ratio (in Figure 56e). Therefore, it is again expected that collisional ionization following the dye laser exctation dominates the case of Figure 56f. This is in agreement with the experimental results. C-4 Na 38 - SS Two-photon Absorption and 3P - 58 One-photon Absorption In order to obtain a measurable LEI or DLI signal upon 38 - 58 two-photon resonance excitation, the position of the electrode probes were adjusted to be as close to the laser-beams(s) as possible; otherwise no significant signal could be obtained. The DLI signal in this case (Figure 56c) is smaller and harder to obtain than that of the case in Figure 56b under similar experimental 221 conditions. The 58 level is lower by 0.18 ev than the 4D level which decreases the collisional ionization rate constant in case of Figure 56c by about a factor of three. This may contribute somewhat to the experimental difficulty. The dye laser power dependence plot shows the required slope of 2, and the DLI/LEI ratio is ml for 38-* 58 case (Figure 56c. These results are analogous to the cases of Figure 56b and 56f. Based on Equation (2) the collisional ionization rate constant in the case of Figure 56c is estimated to be about 7 x 104 times larger than that calculated for Figure 56a. Again, collisional ionization is expected to predominate after 38 -* 58 resoonance excitation (Figure 56c). The experimental result is consistent with this mechanism. An interesting case is shown in Figure 56d, where the 3P level is thermally populated, and resonance excitation is provided by absorption of one dye laser photon to the 58 state. The DLI signal obtained under these conditions is shown in Figure 62; LEI (no N2 laser irradiation of the flame) produces essentially identically results. In both cases the eXpected slope of one is obtained from the plot of dye laser power dependence, as shown in Figure 63. Once again DLI/LEI: 1, demonstrates that collisional processes dominate the ionization step. The laser excitation involves only one photon, as in Figure 56a, and 56e; however, now the energy defect is sufficiently small that the effect of the N2 laser in case x322“: 8. m3 3 a SS Eoflufimcmuu mmm +xm m on» an @0265 xmom cm.“ on» mouMOflocw A «m3 .mm .8302. mo .3 ammo .coflumufloxo couonmuoco mm 1......” an?» HAD Scan «:30QO now oz .No 925E s... _ n so 223 l0: 1 L T I I A." - 3. or- . V 5.. - “3 0N c 2" - Power of Dye Laser figure 63- Dye laser power dependence of sodium ionization with one-photon absorption (3P3 + 58) . The 3P3/., level is thermally populated. A indicates ELI; " 0 indicates LEI. The slpe of each line is one. 224 of Figure 56d is insignificant. 0. Conclusion As discussed above, it is clear that the energy defect between continuum and the resonantly excited state of the analyte has substantial influence on the ionization enhancement of DLI over LEI. When the resonant excited state is sufficiently close to the ionization threshold, the collisional ionization dominates photoionization following the dye laser excitation. As a result, neither the additional N2 laser nor additional photons from the tuned dye laser make significant contribution to ion production under this condition, except for inducing more ion background, as discussed in Section C-l. The competition of collisional ionization and photoionization can be approximately’ gauged by the comparison of the collisional ionization rate constant and the photoionization rate constant from the resonantly excited state, based on the rate equation approach described in Chapter IV. Satisfactory agreement between calculated prediction and experimental observations is achieved. Influence of the energy defect on. the ionization Process has also been observed by Smyth and coworkers, who noted that oxide molecules in a CZHZ/air flame can be 225 either ionized collisionally or ionized by two photons resonant irradiation of a dye laser, depending on the energy defect between the ionization threshold and the resonantly excited state (16-18). The collisional ionization rate constant increases exponentially with decreasing energy defect. And when the energy gap is small, the multphoton ionization rate is not changed significantly upon the addition of N2 laser radiation (see, for example, the case of Figure 56b, calculated in Section C-2) Moreover, it has been pointed out that the photoionization cross sections for some elements decrease as the photon energy over the ionization threshold increases (145,205). These factors result in the domination of collisional ionization over photoionization when a higher energy level is selected for excitation. In summary, it appears that if the resonantly excited state of the analyte in the flame is more than about 2.5 ev below the ionization threshold, then photoionization predominates over collisional ionization. Under such conditions, DLI offers distinct advantages over LEI in sensitivity for trace element analysis. The excited analyte absorbs a single photon from the N2 laser (3371 A = 3.6 ev) which raises it energy above the ionization threshold. Similar excitation into the continuum by the tunable dye laser above (LEI) would require multiphoton absorption of at least two (more likely three) dye laser photon, and thus would demand significantly higher dye 226 laser power than is required for DLI. An example of the sensitivity of DLI is given in Figure 64. A strong Li ion chloride solution with trace Li conta mination; however, no significant Li ion signal is detectable with LEI from the same NaCl solution. 227 Figure 64. Spectra of (a) lithium DLI and (b) lithium LEI (x 200) with ZS-+2P excitation. The reagent is 100 ng/ml Nacl solution with trace Li contamination. 228 A.| £89962, .3 1...... 595.902, CHAPTER VIII SUGGESTIONS FOR FUTURE DEVELOPMENT OF DLI A.Summary Two main subjects have been investigated in the previous chapters: (1) flame and ion properties probed by DLI and (2) the relative merits of DLI and LEI techniques. The first subject included flame temperature determination by DLI, the measurement of ion mobility and diffusion coefficients, and the measurement of ion life time with respect to the biasing voltage on the probes and the position of the ionizing sources (Chapter V). A current and voltage-dependent formulation has been derived to characterize the ion production by the lasers and to estimate the ion density in the flame (Chapter VI). In the second subject, two theoretical models based on quantum mechanical methods (Chapter III) and rate equations (Chapter IV) have been studied to gain insight into the ionization processes, ion spectral and temporal profiles, the relationship between ionization and fluorescence, and the ionization enhancement of DLI over LEI. Finally, optimal use of DLI, based on the analyte's energy levels, has been suggested (Chapter VII). 229 230 B. Proposal for DLI Development B-l DLI-diagnosis of Spectral and Temporal Information Regarding Excited States Most current research into OGE (the optogalvanic effect) in flames is related to ion production characteristics. However, the possibility of DLI or LEI providing information about excited state populations is worthy of exploration. The use of DLI to study excited state structure entails two steps, described below. 1. Spectral Characterization of Excited State Population Molecular LEI developed at NBS has clearly revealed that the LEI spectra of oxide molecules were identical to the one photon absorption spectra from the ground state to the resonant intermediate state, and that the intensity and the resolution of LEI spectra were better than those from laser-induced fluorescence (17,18). Zare et al. reported OGE spectra of 12 in a discharge tube resembled the laser-induced fluorescence in both spectroscopic features and relative absorption probability (46). The .resemblance of the LEI spectra in a discharge tube to the 231 corresponding emission spectra was also reported (35). It appears possible to employ OGE as an alternative to optical spectroscopies (e.g. fluorescence) to identify discrete excited energy states of atoms and molecules in flames, and to investigate the oscillator strength for each resonance state. It is possible to imagine the tunable dye laser as a probe of the excited state location, and the N2 laser as an efficient means of converting the excited state species into ions. The ion spectra thus provide information about discrete states, which is conventionally gained by absorption or emission of light. The current development of OGE in flames still concentrates on the low-lying levels of atoms and molecules, but the scope of OGE in gas discharges has been extended to the high-lying levels (Rydberg states). Five detection methods of Rydberg states usually employed are fluorescence, field ionization, collisional ionization, photoionization and OGE (Chapter I). The last four methods are related to ionization spectroscopies and show superiority to the fluorescence method. Dalsart et al. have employed the OGE method to obtain new data on Kr Rydberg states, which did not appear with the field ionization method (57,58). Therefore, discovery and classification of Rydberg states of atoms in flames with high resolution via OGE spectroscopy is possible, and worthy of to development. As discussed in chapter VII, DLI 232 may lose its sensitivity and act as normal LEI (i.e. single laser in radiation) when the dye laser is tuned to resonance with transition to higher energy levels. Therefore, double resonance OGE ("stepwise excitation") with two high resolution tunable lasers (the second laser being used as a probe) may provide a better tool to investigate atomic Rydberg states. 2. Temporal Studies of Excited State Population (Lifetime Measurement by DLI) From the Na energy scheme shown in Figure 65a, one obtains the ionization rate equation as %=(R¢+rw+k)nf-Kniy m where ni and nf are the ion density and the excited state population density, respectively; R and r are photoionization cross sections for one photon (N2 laser) and two photons (dye laser), respectively, starting from the excited state, and ¢ and w indicate the photon flux of the N2 laser and the dye laser, respectively. K is the relaxation rate constant of the ion and k is the collisional ionization rate constant. The one-photon (NZ-laser) photoionization process from the excited state was found to dominate the ionization pathway (Chapter III, IV and VII), if the alkali element was excited to its first excited state. Therefore,r¢ and k may be considered Figure 65. 233 Partial energy level diagram of sodium. The dye is tuned to resonance with the 38 + 3P transition. Na+ may be induced by one-photon absorption of the N2 laser, absorption of two additional photons from the dye laser, and collisional energy exchange. K indicates the relaxation rate constant from the continuum, including all types of relaxation. LElock diagram of an experimental set-up for temporal profile measurement by DLI..1%is the N2 laser;;E is a dye cuvette in which the second laser beam is produced; C is the flame system; D are flat mirrors; E is two pairs of flat mirrors used to variably delay the light path of the N laser. 2 234 235 negligible in comparison with R¢. under these conditions. If the two additional conditions, R¢ nf >> Kni and the N2 laser profile is ad function are assumed, Equation (1) can be integrated as D II fRCb(t)nf(t)dt f6(t)n (t)dt f nf(0) . (2) By using flat mirrors to optically delay the N2 laser, the temporal profile of the beam may be lag adjusted by T nsec with respect to that of dye laser. Substitution of lag-time T into Equation (2) gives n. = f5(t-T)nf(t)dt n T) f( , (3) where nf(T) indicates the population of the excited state at time T. By varying the lag-time T successively, one may obtain a set of data nf(Tj) against Tj' and the lifetime of fluorescence can be determined from the temporal profile. DLI measurement of the lifetime of the excited Population possesses all the advantages of the DLI technique. In addition, two special advantages are Provided here: (1) the temporal profile of the excited Population is obtained by an ionization method, instead of conventional photon spectroscopy; (2) a slow ion detector 236 is used, instead of a fast photon detector. The possiblity of DLI-provision of spectral and temporal information about excited states may result in the superiority of DLI to other optical spectroscopies related to discrete states, not only in showing an extreme sensitivity to trace elements but also in providing more information about the dynamics of processes involving continuum and discrete levels. B-2 Re-examination of Sensitivity and Selectivity of DLI As discussed in chapter VII, in comparison with normal LEI,under certain circumstances DLI shows much higher sensitivity to ion detection, because the photoionization process prevails from the resonantly excited state DLI does not show better sensitivity in separating two elements with almost identical energies of their resonantly excited states or with low ionization potentials, because the N2 laser may ionize both elements simultaneously by one photon absorption. Some possible ways to improve DLI selectivity are: (1) by choosing different energy levels as intermediate excited states, but then DLI may lose its prevailing sensitivity as higher excited states are chosen. 237 (2) by using time-delay (i.e. the N2 laser pulse is lag adjusted with respect to the dye laser pulse) to decrease the excited population of the interference matrix before irradiation with the N2 laser; this method is restricted to long liftime excited states of analytes. (3) by using a double resonance OGE spectroscopy with two tunable dye lasers; this may allow both high sensitivity and high selectivity to ion detection through the choice of various double-resonance laser combinations. B-3 Saturation Dual Laser Ionization Based on the rate equation approach described in Chapter IV, "saturation DLI" may be achieved with power densities of the dye laser of similar order of magnitude to those which provide saturation laser-induced fluorescence. Saturation ionization spectroscopies have been widely developed in non-flame systems; their advantage is independence of laser power (206). 238 B—4 DLI in Vappr Cells Versus DLI in Flames DLI may also be applied in a vapor cell. experimental set-up of DLI in a vapor cell is illustrated in Figure 66. A schematic preliminary experiments were carried out, and it was possible to obtain an ion signal, as shown in Figure 67. Several advantages of DLI in a vapor cell exist such as: (1) it is easy to control and simplify the matrix in a vapor cell. (2) it is possible to separate multiphoton ionization from collisional ionization by controlling the pressure in the cell. Several disadvantages (in relation to the alkali elements), such as dimerization, oxide and hydroxide conta minations, and light scattering by the quartz windows, also exist. The investigation of DLI in vapor cells may complement the studies of DLI in flames, and provide additional important fundamental phenomena. 239 Figure 66.. Block diagram of the experimental set-up for DLI in a vapor cell. The cell and windows are quartz, and the electrodes are nichrome plates. The ion current from the center electrode is input to a boxcar averager.The entire cell is placed in a furnace (indicated by the dashed line), which is maintained at a controlled temperature in the 350-400 °C range. meson 509E: e mmm<5~z 29E ”62332. -muoofie + «.98 - mmmdj m>o 5L * m meJOm—kzoo NEH—Hamming. 52.. «z 241 .mcofiuflpcoo oaumnmmOEuo Hops: oosflouno coon m>on woe Hmsmwm Goa on» mono: .poxomH o>mn ou 0:50m mm3 dawn on» moans“ musmmoum Hofluflsfi one .sofluwmcouu mm + mm 9.» 398.... owns» 8.53 96 2.» 5? So an @0035“ .Hamo Noumnqm ca oz mo Hmamflm sea was .bmmusmfl V 0689 - V 9689 ‘- REFERENCES 242 REFERENCES la. P.D. Foote and F.L. Mohler, Phys. Rev. 88, 195 (1925). b. F.L. 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Alkemade, Quant. Spectrosc. Radiat. Transfer 88,11 (1979). H.A. Wilson, Rev. Mod. Phys. 8, 156 (1931). N.A. Krall and A.W. Trivelpiece, "Principles of Plasma Physics” (McGraw-Hill, New York, 1973) p. 71. M.J. Seaton, Mon. Not. R. Astr. Soc. 118, 504 (1958). APPENDICES 254 APPENDIX A TWO-STEP LASER-ASSISTED IONIZATION OF SODIUM IN A HYDROGEN-OXYGEN-ARGON FLAME* A. Introduction Laser enhanced ionization (LEI) in flames and plasmas has been observed with various experimental designs (4,20,51-53,64,207,208). In the usual LEI experiment, ionization results from the absorption of a resonant laser photon followed presumably by collisions of the excited atom with flame gas combustion products (4,20). Absorption of a resonant laser photon with an energy E reduces the effective ionization energy and increases the ionization rate (4,20) by a factor of exp (E/kT), where T is the flame temperature; this factor can easily be on the order of 104. In this paper we report a relatively simple and inexpensive method for producing laser-assisted ionization in a flame. The method utilizes a two-step process, as suggested by various authors (22:23). The first step is the absorption of a resonant 255 laser photon by an atom in the ground state, followed by the absorption of an off-resonant photon by the atom in the excited state. The sum of the energies of the two photons is such that it exceeds the ionization energy of the atom. The fact that two laser photons are being used to ionize the atom does not necessarily mean that the ionization proceeds through a straight-forward two-step process . It has recently been proposed that photoionization might be collision assisted (209). Since collisions are frequent in a flame at atmoSpheric pressure, this latter possibility was investigated, and some experiments are presented to elucidate the predominant ionization mechanism. 8. Experimental The experimental setup is shown in Figure 68. A relatively cool ( 1800 K) Hz-OZ-Ar flame is burned from a circular Méker burner and shielded by a mantle flame of the same composition to prevent the entrainment of air. Sodium is introduced into the inner flame by nebulizing a sodium salt solution with a pneumatic nebulizer driven by the argon stream. A homemade tunable dye laser of the Hansch design (103), using Rhodamine 6G as a dye, is . Figure 68.. Experimental arrangement for simultaneous observation of laser-assisted ionization and laser induced fluorescence. (a) (b) Overall view..IL boxcar; DL, dye laser; F; flame; L, lens; M, mirror; 0, oscilloscope; PL, pump laser; PM, photomultiplier; R, x-t recorder; 8, signal; T, uv rejecting filter; TL, trigger line. Detailed view of probes and laser beams. IF; inner flame; OF; outer flame; P, probe; R , Load Resistor; 8, signal. Dimensions are not to scale. The waist diameter of the laser beams is of the order of 0.1 mm; the distance between the probes is a few mm; the diameter of the inner flame is approximately 15 mm. 257 Ome wax 3185 258 pumped by a N2 laser (Model 0.5 - 150, NRG, Inc., Madison, WI). The pulse duration is 5 ns for both lassers. The dye laser beam is focused in the center of the flame, approximated 2 cm above the burner head, well away from the combustion region. The width of the spectral profile of the dye laser at a wavelength of 5890 8 was measured by using the fluorescence excitation profile as discussed by Omenetto et al. (137) and fround to be 0.7;); 0.1 1:. The wavelength of the N2 laser is 337 nm. Output powers were measured with pyroelectric power meter (Model J3 - 05, Molectron Corp., Sunnyvale, CA). Part of the N2 laser beam was split off from the pumping beam and also directed into the flame, where it was focused with a quartz lens. Positioning devices carrying mirrors and lenses facilitate in maximizing the spatial overlap of the two laser beams. The degree of temporal overlap between the two laser pulses can be varied by changing the optical path lengths of one or both lasers. The path lengths were adjusted in these experiments for maximum temporal overlap of the two lasers at the burner. The ionization signal was detected with a pair of biased nichrome wires, which had a diameter of 0.7 mm. These probes were mounted on micrometer-driven translation stages and located in the immediate neighborhood of the irradiated region but were not irradiated themselves. Ionization signals were measured across an interchangeable load resistor in the probe circuit. The signals from the (1 FA "N U) .J (M) U: LA): 259 probes were usually processed by a boxcar averager with gated integrator (Model 162 - 164, Princeton Applied Research, Princeton, NJ) and read out by an x-t recorder. A photomultiplier (RCA 1P28), wired for last pulse processing, monitored the fluorescence from the 3P + 38 transitions of sodium. Both the ionization and the fluorescence signal can be observed on a storage oscilloscope (Model 564 Tektronix, Inc., Beaverton, OR). Appropriate shielding prevents stray light due to the dye laser from entering the photomultiplier. A UV rejecting filter in front of the photomultiplier was used to cut out stray light due to the N2 laser. Two rf chokes, consisting of several wire turns around a ferrite core, were soldered into the high-voltage power line of the N2 laser; both the laser and the chokes were put inside a grounded Faraday cage, consisting of 0.5 mm copper plating. These measures substantially decreased the rf noise from the NZ-laser discharge. C. Results and Discussion Experiments were performed to measure the enhancement of the ionization signal with both the dye laser and the N2 laser irradiating the flame over the Signal obtained with the dye laser alone. For these (‘5 rr b—l () '11 r? ’(J 260 experiments, the dye laser was tuned to the Na(381/2 + 3P3/2) transition and a Na concentration of 12 g/mL was nebulized into the flame. The laser peak powers were of the order of 40 and 100 kW for the dye laser and the split off part of the N2 laser beam, respectively. The ionization and signal was integrated over time. With the dye laser only, ‘an ionization signal of 9.0 mV was obtained; with both lasers the ionization signal increased to 1.3 V. No signal was obtained with the N2 laser alone. The enhancement factor was thus 144 for these experiments. The exact enhancement factor depends on the configuration of the beams and the probes, the intensities of the beams, and of the composition of the flame. We observe that this factor can be improved by moving the probes closer to the irradiated region. The latter manipulation, however, tends to affect the reproducibility of the experiment because of the more critical alignment. Moreover, when the lasers irradiate probe surfaces, nonspecific occurs, which is possibly due to electrons being liberated from the probe material by laser photons or due to off-resonant multiphoton ionization of atoms and molecules in particle sheaths which might envelop the probes. To investigate the analytical utility of the two-step ionization technique, we measured the ionization signal and the degree of ionization as a function of the sodium solution concentration. The reaults are given in Figure 69. The dye laser was tuned to the Na(3Sl/2 + Figure 69. 261 Ionization siganl (O) and ratio of ionization signal to sodium solution concentration ((3 ) vs. sodium solution conentration; both lasers are irradiating the probed volume. The dye laser was tuned to the BSk-t3P3/2 (589.0 nm) transition. 262 3 l0.0 Normalized Signal (o.u.) ES 0'6.) (.0 I0.0 _ IOOO No Concentration (pg/mL) 263 3P3/2) transition, the N2 laser irradiated the same flame volume, and the time-integrated ionization signal was measured. The analytical curve shows a nearly constant slope of 1 over more than 2 decades of solution concentration, and the lowest concentration detected was 0.1 ug/mL. From the fact that a slope of 1 occurs it can be concluded that associative ionization is not present to any significant extent, since two sodium atoms are required (2Na* + hv ? Na2+ + e -) (210,211) and a slope of 2 would result. The nonlinearity of the curve in Figure 69 may be due to a decrease in the ion collection efficiency caused by the formation of charge sheaths (8) or by ion-electron recombination. A plot of the ratio of the ionization signal to the sodium. solution concentraiton vs. the sodium solution concentration has been previously related to the degree of ionization (4). Such a plot, shown in Figure 69, also exhibits nonlinearity. This phenomenon has been observed with a different ionization scheme but in virtually the same flame (4). That the deviation from linearity in Figure 69 was not due to nebulizer characteristics was checked by plotting the thermal emission from the Na(3P 4 38) transitions against sodium solution concentration. The latter plot showed deviations from linearity in a concentration range well above that of Figure 69, due to the combined effect of self-absorption and decreasing atomization efficiency with increasing concentration. 264 Profiles of the ionization and fluorescence signal were obtained by tuning the dye laser across the Na(381/2 + 3P3/2) transition and are shown in Figure 70. The sodium solution concentration nebulized into the flame was 12 ug/mL. The difference in the full widths at half-maximum (fwhm) which is evident from the profiles of Figure 70, has been observed in a related experiment by van Dijk et a1. (4) where a flashlamp laser was used. The fluorescence excitation profile in Figure 70 essentially represents the spectral laser profile because the width of the Na(3P + 38) transitions is known to be approximately 70 mA in our flame (212), which is small compared to the observed width. Saturation of the Na(381/2 + 3P3/2) transition hardly affects the latter conclusion, since the broadening of the excitation profile depends on the square root of the natural logarithm of the dye laser power (137) and is therefore a weak function of this power. The measured fwhm of 0.7 A of the fluorescence excitation profile is consistent with the value which we obtained when using a monochromator to resolve the spectral laser profile. Broadening of the ionization profile might be related to saturation of the laser-excited level, space charge effects (8), and possibly recombination (4). On a microsecond time scale the onset of the recombination might occur and this might partially account for the difference in widths observed in the profiles of 265 Figure 70- Profile of ionization signal ((3) and fluorescence ( O ) obtained by scanning dye laser across the 35.5 to 3P3/2 (589.0 nm) Na transition. max = 0.7 3'. for fluorescence profile and 1.5 34 for ionization profile. Sodium solution concentration = 12ug/ml, probe voltage = 400 V. 26' 6 .82»..on .228 Ea... 4 52055.80 ON ON 0.. 0.. no 0 0.0- T m..- ON: mm- _ . . . . . _ . . _ _ . . . O . . . . . . . . o . . no. . . . . . (Om . . . 10m . . 10v . . . . 1 Om ‘ .. Om . i ON . . 1 0m . . 40m. . J 00— (‘no) (cums peznoquN 267 Figure 70 (4). As noted by Muller et al. (213), appreciable charge densities are needed to give rise to noticeable recombination on a microsecond time scale. We offer the following hypothesis to account for recombination under our experimental conditions: the possible existence of charge sheaths around the probes might partially nullify the electric field between the probes and lead to an increase in the contribution of difussion to the motion of the charges in the "field-free” region. Therefore, a significant numbers of ions might be able to overcome the repulsive field at the positive probe. These ions have a higher probability of being neutralized because of the electron sheath enveloping the latter probe. An analogous reasoning applies to the electrons. As the charge densities in the sheath are higher than in the surrounding plasma, the recombination rate will also be higher near the sheaths. The fact that space charges diminish the field might also decrease the collection efficiency of the probes and give rise to broadening of the ionization profile. We investigated the dependence of the ionization and fluorescence signals on small variations in flame gas composition. The influence of changing the oxygen content on the signals is quite noticeable but different for the excited-state population and the ionization. However, the ratio of the ionization signal to the fluorescence signal shows only a weak dependence on the 02 concentration. The 268 ratio of the ionization signal to the fluorescence signal is proportional to the degree of ionization B , provided 8 is small and the 381/2 - 3P3/2 tranSltlon lS saturated s a [Nah/(mm + [Nan = [Nah/[Nah «i/F (1) where Naflr is the density of the excited sodium atoms, i=ionization signal, and F=fluorescence signal. In an analogous experiment, where we varied the argon content of the flame, a similar weak dependence was observed, as is evident from the curves in Figure 71. From these experiments one can conclude that if the degree of ionization is low, the discrete to continuuhl step is predominately photon absorption and thus affected only slightly by collisions with 02 or Ar. On the other hand, if the degree of ionization is high, this conclusion does not necessarily hold because a variation in the ionization rate will have little influence on for close to unity. Rough calculations indicate that the degree of ionization within the laser irradiated volume may indeed be quite high. When the discrete to continuum step is brought about solely by collisions, the dependence of i/F on the O 2 concentration in the flame is much more pronounced (4,214). Changing the voltage across the probes results in a change in the ionization signal, as is shown in Figure 72. For this experiment we used various sodium solution 269 Figure 71. Dependence of ionization and fluorescence signals on Ar content of flame. The dye laser was tuned to Na(BSp + 3P3/2) transition; the sodium concentration was 12 ng/ml. - Fluorescence signal plotted vs.;1r flow — Ionization signal plotted vs. Ar flow - Ratio of ionization-to-fluorescence signal plotted vs. Ar flow. .270 $5553. 32... 894 0... 0.0. 0.0 0.0 0N 0.0 . _ . . q a . HO 1 0m H .i o... 1 00 . n 00 . .. Os . 1 00 M q . s“ .. om . .\ . i3 oi 1 OO (nu) loufigs pazuoquN 271 Figure 12. Dependence of ionization signal on probe voltage for various sodium solution concentrations. The dye laser was tuned to the 383 + 3P3/2 transition. 'ldc component in the signal, probably due to thermal (non-laser) ionization, was eliminated with a capacitor in the signal line. 0 - Sodium concentration 10 ppm £5 - Sodium concentration 1 ppm C3 - Sodium concentration = 100 ppb l0,000 Ionization Signal (on) 272 l 5 IO 50 lOO Probe Voltage SOOIOOO 273 concentrations, and the dye laser was tuned to the 381/2 to 3P3/2 transition. With increasing voltage the curves are seen to level off, especially those. of the higher concentrations. The decreasing slopes indicate that the current drawn from the plasma approaches saturation, which means that with high voltages eventually all the available charge carriers in the probed region are being collected. A check as to the transport mechanism can be obtained by' plotting the measured decay time of the ionization signal vs. the reciprocal of the applied probe voltage 2¢p' According to Equation A13 of the Appendix, such a plot is expected to yield a straight line: indeed we found this to be the case. From the slope of this plot we calculate, using Equation A13 with 2L = 2.8 m, that 2 l -1 the ionic mobility “ii is on the order of 20 cm V- s . When we assume that the additional decay time ‘re, introduced by the circuitry, especially the load resistor (= 100 k0 ),is simply added to the characteristic decay time 71, we find from the intercept of the plot of decay time vs. inverse probe voltage that ¢e = 20 3. Hence the stray capacitance of the circuitry is 200 pF, in resonable agreement with estimates based on cable length and input capacitance of the apparatus. Using the relation ‘ui == qD/(kT), where q = elementary charge, 0 = diffusion coefficient, k = Boltzmann's constant, and T = flame temperature, we calculated the order of magnitude of Hi from measurements 274 of the diffusion coefficient in flames by Ashton amd Hayhurst (185) and found our result to be within the range of the latter authors. Electronic mobilities are expected to be much larger because of the difference in mass between the ions and the electrons (215). When we calculate the decay time under the assumption that diffusion is the predominant transport mode, we find, using rdiff = (2L/1r)2/D (182), and D = uikT/q,r diff is of the order of several milliseconds and is therefore much larger than our observed values. Two conclusions pertaining to the particular conditions of our experiment can be drawn from these experiments: (1) The predominant transport mechanism is drift due to the electric field of the probes. (2) The current is limited by the ions. It follows from our measurements and from Equation A13 that the actual decay time of the charge cloud is several microseconds. In order to eliminate the contribution of the circuitry to the decay time constant, we plotted this constant vs. the value of the load resistor. These latter measurements support our observation that Ti is of the order of a few microseconds, since for low values of R1 the observed time constant becomes independent of R1. The temporal dependence of the ionization signal was measured with a load resistor R1 of 5 k0 . The peak amplitude V0 of this signal was 12 mV and the decay was 275 close to exponential with a time constant T of 7.9 i 0.2 us.An estimate of the total number of ions collected in this pulse follows from V0 Joe-UT dt = Nqu (2) where q is the elementary charge. From these results N is found to be approximately 108 Note that the exponential decay is consistent with Equation A4 of the Appendix. By tuning the dye laser across the 38 + 40 two-photon transition of sodium and using a 100 ug/mL sodium solution concentration, the profile shown in Figure 73 was obtained. The signal from this transition is weaker than the signal of a 3P - 3S transition when referred to the same solution concentration. The peak observed with the dye laser only is probably due to collisional ionization proceeding from the 40 level (4,10). The fact that very little enhancement of the latter peak occurs when the N2 laser is present might mean that the ionization induced by the dye laser and the collicions is nearly complete, or alternatively, that the cross-section for photoionization from the 4D level to the continuum is small. The continuunt signal observed with both lasers irradiating the flame disappears when the dye laser is blocked or when the N2 laser is blocked. This indicates that the continuum signal is due to off-resonant two-photon ionization by both lasers. 276 Figure 73. Ionization profiles obtained by scanning the dye laser across the Na(38-+4D) two-photon transition; center wavelength = 5787 in R2 = 50 k0, 249 = 100 V; sodium solution concentration = 100 ug/ml. (a) Upper trace: N2 laser beam interrupted Lower trace: both the N2 laser beam and the dye laser beam operative. (b) Detailed profile. 277 3% 05:28 3.... . 05:28 memo??? on w ONLY..- . r1140 . . 3 3 l _ 278 0. Conclusions We have shown that ionization of seed atoms in a flame can be achieved relatively simply by irradiating the atoms simultaneously with one resonant and one off-resonant laser pulse, both of which have a duration of a few nanoseconds. From the experiments conducted we conclude that the predominant mechanism. for ionization proceeding from the Na(3P) level is two-step photoionization; in the case of population of the Na(4D) level, collisions cause the excited atom to ionize. The described method to measure ion mobilities has been tested and been found to yield a value consistent with previous results. Although the detection limits by the two-step method are not as low as those obtained by normal LEI (8), it is expected that perfection of this method will improve these limit. Feasible improvements are: using a slot burner and extended probes runing parallel to the laser beam for several inches to increase the collection efficiency of the probes; using an ultrasonic nebulizer instead of our pneumatic nebulizer to increase nebulization efficiency; narrowing the bandwidth of the dye laser to increase its spectral irradiance. 279 ELM In this appendix we develop eXpressions for the mobility controlled ion density in a flame. As an approximation to our experimental conditions, we consider two parallel plane probes at a distance 2L from each other, with a voltage difference 2¢p applied to them by an external source. The probes are located inside the flame and the charge density is assumed to be uniform throughout the space between the probes when the applied voltage is zero. We are interested in the case in which the distribution of the ions is primarily determined by the electric field; consequently, we neglect here diffusion, the overall movement of the flame gases, recombination, and ion production. The continuity equation for the ion density then reads ani/at = -uiV(niE) (A1) '1; where ”i denotes the ionic mobility and E denotes the electric field. If the contribution of the laser-induced 04 charges to the field E is small, the E is nearly constant during a laser pulse. The latter assumption allows us to 280 separate variables as follows ni(x,y,z,t) = Ni(x,y,z)fi(t) (A2) Sustituting Equation A2 into Equation A1 gives 1 3fi “i Since the left-hand side of Equation A3 depends on t only and the right-hand side on the spatial variables only, we set both sides equal to a constant —l/%: The solution for fi(t) is found to be fi(t) = e-t/Ti (A4) The equation for the steady state can be written as V(NiE) - Ni/(uit i) = 0 (A5) Using the identity V(aA) = OVA + AVa (A6) where a and A represent differentiable but otherwise arbitrary scalar (a) and vector (A) functions of the Spatial coordinates, Equation A5 becomes 281 NiVE + E Ni - Ni/(uiri) = 0 (A7) If we assume that the field E is nearly uniform throughout the probed region, then E = - ¢p/L (A8) If our attention is restricted. to the one-dimensional case, then substitution of Equaiton A8 in A7 gives BNi/BX = -NiL/(pui'ri) . (A9) Hence Ni = n exp[-xL/(4Puirifl I (A10) where n is a constant of integration. Thus, the ion density is highest near the negative probe and decreases in the direction of the positive probe (located at x = +L). Identifying Ti with the characteristic time it takes for an ion to drift from x = 0 to x = -L L = _V,. (All) where vi is the average drift velocity. In the limit of a low, uniform field 282 ' i 1 (A12) Combining Equation A8, A11, and A12 _ 2 Ti - L /(ui®p) (A13) establishes a relation between the characteristic decay time and the ionic mobility in terms of the distance between the probes and the applied potential. Using Equation A10 and A13 Ni = n exp (-x/L) -L < x < L (A14) which agrees with the solution found for the so-called plasma-capacitor in the limit of low charge density (216). Due to the absence of the diffusion term in Equation AS, the charge density does not obey the boundary conditions Ni(:L) = o. * o o Obtained jointly with C.A. van Dijk and F. M. Curran. 283 APPENDIX B PHOTOIONIZATION CROSS SECTION BY QUANTUM DEFECT METHOD The quantum defect method has been used in the calculation of photoionization cross sections. This method uses interpolated or extrapolated quantum defects to determine the asymptotic forms of atomic wave functions ( 100,205,217 ). In this appendix, some related parameters are calculated by simple numerical methods and compared with the original work by Peak (100). These parameters can oe substituted into a general formula to calculate atomic photoionization cross sections. The equations used in reference (100) are summarized below. The notation is identical to that of the original work. The initial bound radial function P i for the nlSL \) electron is _ 8 -p/v t. -t Pv2(r) — z K(v,2,) (2p/v) e é=obt(v'“p , (1) where p =izr and v is called the effective quantum number 284 and defined by evz = 22 ( s is the energy, measured in Rydbergs, required to remove the n1 electron, and z is the residual charge and equal unity for neutral atoms ). The continuum function Gk,£.(r) is defined by Gk,2,(r) r» iv“;i sin [k'r- 1/2 2'1: + 131-1n (2k'r) + iz argr (1' + 1 - ET ) + flu'] , (2) where k'2 = 223 ' denotes the energy in Rydbergs of the ejected electron, and u (s') is the extrapolated quantum defect for the n'l'S'L' series. The quantum defect u' for the n'l'S'L' series is defined by u' = n' - v'.( n' is the principal quantum number and v' is the effective quantum number for the n'l'S'L' series. ) Consequently, matrix element 9 (v,l; e'l') is written in the form: Q 2 dr g(vI£;€"£')--z-z-fpv£(r) erIzl(r) ‘ O = “”76'1')cosvu'+h(v2;e'2') sinnli,‘ (3) or B(v2;s'l') g (”'z76'1') = 5%(v,2) cos n Do+ n'(€9) + x(v2;e'£')1 h (4) w ere (5 B(vl?.;e'2.') = g” ( 132+hz)15 ) and 1: (v+x) = arctan(-h/f) (6) The photoionization cross section can be derived as 285 2 ' - 47Taa02( z + 2 ' ' av (E ,V) — .3 3'2 2 E: )liulcg' X If?” (r) r Gk.,~,.(r) drl (7) or 3 a (e',v)= 5.449O9x10‘19-- 1 + ' 2 '3 " 2250.2) ( e v )X 2 C [G(v2;e'£' cos + ' ' ”1+1 2. ) “(v u (e )+ x (v£;e'2') )]1 (8) where . U _ TI' 15 l ‘ G (V118 8') - ( 2: ) ( li-s v2) B( vz;e'2') (9) and the coefficient C1. is defined in reference (205). Table 5 shows a comparison of G( v1; e'z') and. x( v2;”e'£') values calculated here with Peach's results. The difference of numerical methods employed here from those in reference(100) lies in the DVERK( from DMSL routine library), which is used in calculating the continuum function G, and the DCADRE used for the matrix element 9. With the obtained G and ‘x values and Equation (9), the photoionization cross sections can be estimated.The Fortran program is listed below. 286 Table 5. Comparison of Parameters for Photoionization Cross Section Calculation v ; e' 2 = 1 G(v,£;e',£') x(v'2;e',£') a'(cm2) (Rydberg)a?d this work Peach this work Peach this work v = 3; £'= 2 3.141 3.154 0.301 0.299 1 759 x 10'19 v = 0.4 2'= 0 1.252 1.297 -O.312 -0.314 ' v = 2; 2'= 2 2.731 2.730 0.226 0.225 -18 , 1.176 x 10 v = 0.1 2 = 0 0.995 0.996 -0.304 -0.300 287 \a \l 9 \l 1 2 4 0 ( o 3 I 2 F Y 1 9 H E u H 9 : t 9 n R ) \a z E o 0 H I 0 2 D I \I \l \l l\ 1‘ u 9 .1 1.. 1 T )I 9 X o o o C TV. 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