Laser Induced Breakdown Spectroscopy on Suspended Particulate Matter in an Electrodynamic Balance

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Title:
Laser Induced Breakdown Spectroscopy on Suspended Particulate Matter in an Electrodynamic Balance Interaction Processes and Analytical Considerations
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1 online resource (172 p.)
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english
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Warren, Richard A, Jr
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University of Florida
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Gainesville, Fla.
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Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Chemistry
Committee Chair:
Omenetto, Nicolo
Committee Members:
Angerhofer, Alexander
Brucat, Philip J
Smith, Ben W
Hahn, David Worthington

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Subjects / Keywords:
aerosol -- libs
Chemistry -- Dissertations, Academic -- UF
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Chemistry thesis, Ph.D.
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theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
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Abstract:
Laser induced breakdown spectroscopy (LIBS) has becomeincreasingly popular as a sampling technique since its inception following theinvention of the laser. In what is typically an atomic emission method, asingle laser pulse performs the sample ablation, vaporization, and excitationin a single step allowing any phase of matter to be rapidly, qualitativelystudied for the presence of numerous elements. Minimal sample preparation andthe relative simplicity of the typical LIBS instrument make it appealing asboth an analytical tool for the laboratory and for commercial-industrial applications.1,2,3  LIBS has a tremendous potential in the areaof aerosol analysis as it provides a method for in situ analysis of the density and composition of environmentalaerosols which few methods can accomplish as rapidly and remotely.Quantification of sample compositions is possible with LIBS, but requirescareful consideration of the complex mechanisms controlling the sample ablationand excitation mechanisms. Though the physical arrangement for a LIBS aerosolmeasurement can be quite simple the processes involved are all but.4,5 Aerosols are composedof small discrete particles which, when sampled in the lab or in the field, aredifficult to control.6 Variations in themeasurements on these particles can be caused by laser-particle scattering,particle to particle matrix defects and effects, spectral interferences andparticle-photon resonances which are not seen in continuous samples.2,3 This research focuses on the two problems listed above:sample control issues and sources of signal variation, which limit analytequantification. The electrodynamic balance, which has been used by previousresearchers for optical characterization of aerosols7 is used here for LIBSmeasurements. This technique provides complete control of confined, chargedaerosol particles. With this precise handling capability, consistentlaser-particle and plasma-particle interactions are observed with bothspectrally integrated / time resolved and time integrated / spectrally resolveddetectors to provide details on the processes involved for micrometer sizedcharged aerosol particles.
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Statement of Responsibility:
by Richard A Warren.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Omenetto, Nicolo.
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RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2014-05-31

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1 LASER INDUCED BREAKDOWN SPECTROSC OPY ON SUSPENDED PARTICULATE MATTER IN AN ELECTRODYNAMIC BALANCE : INTERACTION PROCESSES AND ANALYTICAL CONSIDERATIONS By RICHARD ANDERSON WARREN JR A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013

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2 2013 Richard Anderson Warren Jr.

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3 All that is gold does n ot glitter, Not all those who wander are lost; The old that is strong does not wither, Deep roots are not reached by the frost. J.R.R. Tolkien

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4 ACKNOWLEDGMENTS I thank my advisor and mentor, Doc (Nico) Omenetto, for his infinite patience, extensive e xperimental guidance, and unending knowledge in the field of spectroscopy and others of which I hope a small amount has rubbed off. His guidance and tutelage was invaluable both in my lab experience and life outside the lab. I want to thank him for enterta ining my endless distractions, whims, and arguments. I truly enjoyed the science arguments, Doc. I also want to thank Ben Smith for his pats on the back and the words of encouragement both in the fun times and those others. It takes more than one person to met my new lab mates. I thank Jonathan Merten, who got me started with the project discussed here, for his help and technical assistance with my particle production and sh owing me a prototype EDB. I would like to apologize to Dan Shelby for walking in his lab and scaring him senseless almost on a daily basis. I now fully appreciate what that can do! Also, I greatly appreciate all the scientific debate and conversation, Dan. extend my appreciation to my family members who have supported me in many ways. My deepest thanks go to my mother for pushing me and not letting me back up (o r fall countless were undoubtedly used.

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5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 LIST OF ABBREVIATIONS ................................ ................................ ........................... 11 ABSTRACT ................................ ................................ ................................ ................... 16 CHAPTER 1 LASER INDUCED BREAKDOWN SPECTROSCOPY FOR AEROSOL ANALYSIS ................................ ................................ ................................ .............. 18 Introduction ................................ ................................ ................................ ............. 18 The LIBS Technique ................................ ................................ ............................... 18 LIBS Sampling Concerns ................................ ................................ ................. 20 Matrix Effects ................................ ................................ ................................ .... 20 Aerosols ................................ ................................ ................................ .................. 21 Aerosol Descriptors ................................ ................................ .......................... 22 Reynolds numbers ................................ ................................ ..................... 23 Optical Particle Analysis ................................ ................................ ................... 24 Aerosol Charges ................................ ................................ ............................... 24 The Electrodynamic Balance for Single Particle Trapping ................................ ...... 25 The Quadrupolar Field for Trapping ................................ ................................ 26 Paul Trap Variants ................................ ................................ ............................ 27 Trap Constants ................................ ................................ ................................ 29 Modes of LIBS Particle Experiments ................................ ................................ ...... 30 Laser Particle Interactions ................................ ................................ ................ 31 Diagnostics for the Laser Particle Interaction ................................ ................... 32 Simultaneous Multi element Analysis: Signal Persistence ................................ ...... 33 Conclusions ................................ ................................ ................................ ............ 34 2 PARTICLE GENERAT ION AND CONFINEMENT ................................ .................. 41 Introduction ................................ ................................ ................................ ............. 41 Vibrating Orifice Aerosol Generator ................................ ................................ ........ 41 Particle Charging ................................ ................................ ................................ .... 42 The Electrodynamic Balance and Particle Trapping ................................ ............... 43 Trap Parameter Determination ................................ ................................ ......... 44 Spring point ................................ ................................ ................................ ...... 45 Experimental Results and discussion ................................ ................................ ..... 45 Injection ................................ ................................ ................................ ............ 45

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6 Trapping ................................ ................................ ................................ ........... 46 Trap Parameters ................................ ................................ .............................. 47 V AC Variations ................................ ................................ ............................ 47 V DC variations ................................ ................................ ............................. 48 Evaporation ................................ ................................ ................................ ...... 48 Stable Particle Diameters ................................ ................................ ................. 49 Trap with Cylindrical Confinement Fields ................................ ................... 50 Conclusions ................................ ................................ ................................ ............ 51 3 DIMENSIONAL ANALYSIS OF THE AEROSOL PARTIC LES ............................... 62 Introduction ................................ ................................ ................................ ............. 62 Time of Flight Measurements ................................ ................................ ................. 63 TSI Aerodynam ic Particle Sizer (APS) ................................ ............................. 64 Light Scattering ................................ ................................ ................................ ....... 64 Fresnel Theory ................................ ................................ ................................ 65 Ba ................................ ................................ ..................... 66 Lorentz Mie Theory ................................ ................................ .......................... 67 Size Descriptions ................................ ................................ .............................. 67 Exp erimental Results and discussion ................................ ................................ ..... 68 Spring point Measurements ................................ ................................ ............. 69 Illumination ................................ ................................ ................................ 70 Conclusions ................................ ................................ ................................ ............ 71 4 THE LASER INDUCED PLASMA AND SINGLE PARTICLE LIBS ......................... 80 Introduction ................................ ................................ ................................ ............. 80 Laser Plasmas ................................ ................................ ................................ .. 80 Particle LIBS ................................ ................................ ................................ ..... 82 Experimental Details and Discussion ................................ ................................ ...... 85 Optical Arrangement ................................ ................................ ........................ 85 Breakdown Threshold measurements ................................ .............................. 86 Laser Pulse Shapes ................................ ................................ ......................... 87 Time Integrated Measurements ................................ ................................ ........ 88 Particle Plasma Measurements ................................ ................................ 89 Laser Particl e Measurements ................................ ................................ .... 89 Results and Conclusions ................................ ................................ ........................ 90 Effects of the EMF in the Balance ................................ ................................ .... 90 ABT v. BBT ................................ ................................ ................................ ....... 91 Particle Size Limits ................................ ................................ ........................... 92 Partial Particle Ablation ................................ ................................ .................... 97 Micro particle Generation ................................ ................................ ................. 98 5 STATISTICAL CONSIDERATIONS FOR LASER PARTICLE AND PLASMA PARTICLE INTERACTIONS ................................ ................................ ................. 112 I ntroduction ................................ ................................ ................................ ........... 112

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7 Theory ................................ ................................ ................................ ................... 115 Correlation ................................ ................................ ................................ ...... 115 Methods ................................ ................................ ................................ ................ 116 Results and Discussion ................................ ................................ ......................... 117 Conclusions ................................ ................................ ................................ .......... 120 6 SIMULTANEOUS MULTI ELEMENT ANALYSY S ................................ ................ 130 Introduction ................................ ................................ ................................ ........... 130 Experimental Considerations ................................ ................................ ................ 133 Results and Discussion ................................ ................................ ......................... 135 Conclusions ................................ ................................ ................................ .......... 137 APPENDIX A MATHIEU EQUATIONS ................................ ................................ ........................ 148 B S AMPLE PARTICLE SIZE CALCULATIONS FOR THE VOAG ........................... 149 C SEMANTIC CONSIDERATIONS FOR LASER SAMPLE COUPLING IN LASER INDUCED BREAKDOWN SPECTROSCOPY ................................ ...................... 150 LIST OF REFERENCES ................................ ................................ ............................. 162 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 172

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8 LIST OF TABLES Table page 2 1 Calcium chloride solutions used for particle generation.. ................................ .... 53 2 2 Magnesium Chloride solutions used for particle generation.. ............................. 53 3 1 Relationships between different mean reportable values for particle distributions. ................................ ................................ ................................ ....... 73 3 2 Parameters for monodisperse particles generated from the TSI 3050 VOAG and the associated er ror from the calculated diameters. ................................ .... 73 3 3 The measured particle diameters were trapped and the spring point was measured. ................................ ................................ ................................ ........... 73 4 1 D escription of optics used for alignment, ablation, and signal collection to be used in conjunction with F igure 4 1. ................................ ................................ ... 99 6 1 Resonant atomic emission lines detected by the Leco Paschen Runge poly chromator.. ................................ ................................ ................................ 139 6 2 Transition probabilities and energy levels for corresponding transitions of the six elements monitored with the polychromator ................................ ................ 140 6 3 Sodium chloride pellet composition.. ................................ ................................ 140 6 4 Graphite pallet composition ................................ ................................ .............. 141 6 5 Neutral resonant lines mo nitored with six channels of the Paschen Runge polychromator. ................................ ................................ ................................ .. 141

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9 LIST OF FIGURES Figure page 1 1 Amorphic particle characterization. ................................ ................................ ..... 35 1 2 The LIBS event processes. ................................ ................................ ................. 36 1 3 The LIBS signal ................................ ................................ ................................ .. 37 1 4 3 D Quadrupolar b ihyperbolic t rap. ................................ ................................ ..... 38 1 5 The EDB.. ................................ ................................ ................................ ........... 39 1 6 Vector Field in the Quadrupole ................................ ................................ ........... 40 2 1 VOAG Schematic Representation. ................................ ................................ ..... 54 2 2 EDB Electrical Schematic.. ................................ ................................ ................. 55 2 3 Frequency, V AC and V DC dependence for partic le balancing. ............................ 56 2 4 Bimodal distributions of particles. ................................ ................................ ....... 57 2 5 Control Window.. ................................ ................................ ................................ 58 2 6 Calibration curves for trap electrode voltages. ................................ .................... 59 2 7 General effects of field parameters on a two particle array within the EDB. ....... 60 2 8 Anomolous trapping ................................ ................................ ............................ 61 3 1 Aerosizer ................................ ................................ ................................ ........... 74 3 2 Scattering regimes ................................ ................................ .............................. 75 3 3 Light Scattering ................................ ................................ ................................ ... 76 3 4 ................................ ................................ .......... 77 3 5 Particle size distributions ................................ ................................ ................... 78 3 6 Size distribution analysis ................................ ................................ .................... 79 4 1 Optical setup for LIBS signal collection. ................................ ........................... 100 4 2 Measurement of the breakdown threshold in laboratory. ................................ .. 101 4 3 Laser Pulse Shapes. ................................ ................................ ........................ 102

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10 4 4 Anomalous plasma see ding ................................ ................................ ............. 103 4 5 The HeNe signal used for targeting ................................ ................................ .. 104 4 6 BBT Plasma formation and signal ................................ ................................ ... 105 4 7 Representative spectra for BBT (a) and ABT (b) LIBS measurements ............. 106 4 8 ABT and BBT RSD measurements ................................ ................................ 1 07 4 9 Ensemble averaged spectra ................................ ................................ ............ 108 4 10 Particle diameter versus mass ................................ ................................ ......... 109 4 11 Qabs versus particle size parameter ................................ ............................... 110 4 12 Critical time for breakdown ................................ ................................ .............. 111 5 1 The first method for calculation of the correlation providing ................. 122 5 2 The second method for calculation of the correlation providing ............ 123 5 3 ABT and BBT noise comparison ................................ ................................ ...... 124 5 4 Nitrogen noise correlation ................................ ................................ ................. 125 5 5 H( ) noise correlation ................................ ................................ ...................... 126 5 6 Calcium noise corre lation ................................ ................................ ................ 127 5 7 Signal to background plots for two major calcium neutral and ion lines. ........... 128 5 8 Calcium Ion to neutral trends for ABT and BBT measurements. ...................... 129 6 1 Optical setup for simultaneous multi element analysis.. ................................ ... 142 6 2 Emission traces generated from 6 samples ................................ ...................... 143 6 3 Demonstration of the tuning ability for the Paschen Runge spectrometer. ....... 144 6 4 Calibration curves using various integration times.. ................................ .......... 145 6 5 R 2 and sensativity versus delay time ................................ ................................ 146 6 6 Determinatin of optimal focal depth ................................ ................................ 147

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11 LIST OF ABBREVIATIONS Abbreviations ABT Above the air breakdown threshold AC Alternating current AES Atomic emission spectroscopy BBT Below the air breakdown threshold CC Correlation Coefficient CCD Charge coupled device DC Direct curren t iCCD Intensified charge coupled device ICP Inductively coupled plasma LIBS Laser induced breakdown spectroscopy LIP Laser induced plasma LTE Local thermodynamic equilibrium MPI Multiphoton ionization m/z Mass to charge ratio pLTE Partial local thermodyna mic equilibrium RSD Relative standard deviation S/N Signal to noise ratio Stk Stokes Number

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12 Constants c Speed of light in vacuum 8 m s 1 [LT 1 ] e Elementary charge 19 C, [Q] eV E lectron volt 19 J, [ML 2 T 2 ] g Gravitational field strength: 9.81 m s 2 [LT 2 ] h Plank constant 34 2 T 1 ] 34 J S, [M L 2 T 1 ] k B Boltzmann constant 23 JK 1 [ML 2 T 2 K 1 ] m e Electron rest mass 31 kg, [M] m p Proton rest mass 27 kg, [M] N A Avo gadro constant 23 mol 1 0 Electric permitti vity 12 1 [M 1 L 3 T 2 Q 2 ] 0 Magnetic permeability 7 1 [MLQ 2 ]

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13 Symbols A ki Spontaneous emission transition probability [T 1 ] a Radius of a particle, [L] B Magnetic flux density, [ MT 1 Q 1 ] BPP Beam parameter p roduct C Stark effect coefficient C a Vapor concentration in equilibrium with a particle surface [ML 3 ] C i Vapor concentration of i [ML 3 ] C 0 Dimensional trap constant C s Slip correction factor [null] C Vapor concentration far from the particle [ML 3 ] D 0 Beam diameter [L] d a Aerodynamic particle diameter [L] d d Droplet diameter [L] d min Minimum particle diameter [L] d p Dried particle diameter [L] D ij Diffusivity for vapor i in gas j [L 2 T 1 ] D[1,0] Length moment mean [L] D[2,0] Number surface mean [L 2 ] D[3,0] Number volume mean [L 3 ] D[3,2] Surface area moment mean [L] D[4,3] Volume moment mean [L] E Electric field strength [MLT 2 Q 1 ] E i Atomic energy levels [ML 2 T 2 ] E Ionization energy [ML 2 T 2 ]

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14 g Statistical weight [Null] H ( ) line (656.3 nm) Im Imaginary component of a complex number l Length [L] m Mass [M] M 2 Ratio of BPP to an ideal Gaussian beam [Null] M i Molecular weight of I, [M] N e Electron n umber density [L 3 ] N i Number density of ith state or type [L 3 ] N T Total particle number density [L 3 ] p Electric dipole moment [LQ] P Electric polarization, [M 2 Q] p i Vapor pressure of I, [ML 1 T 2 ] q Charge, [Q] [M 1/2 L 3/2 T 2 ] Q abs Absorption efficien cy [Null] Q ex Extinction efficiency [Null] Q scat Scatter efficiency [Null] r o Radial dimension parameter [L] Re Reynolds number / Real component of complex number [ N ull] / [ ] t Time [T] T Temperature K = [ML 2 T 2 B 1 U g Nozzle gas flow [LT 1 ] V AC Voltage of alternating current [ML 2 T 2 Q 1 ] V DC Voltage of direct current, [ML 2 T 2 Q 1 ] V p Particle velocity [LT 1 ]

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15 V 0 Direct current offset voltage required for a given m /z, [ML 2 T 2 Q 1 ] z o Vertical dimension parameter [L] Z r distance required for be am to increase by 2 1/2 [L] Scattering angle / P olarizability, [ R adian] / [M 1 T 2 Q 2 ] Electric permittivity, [M 1 L 3 T 2 Q 2 ] Refractive index / Viscosity, [Null] / [MT 1 L 1 ] Correlation coefficient [ N ull] dw Divergence [R adian] Drag parameter [Null] Measured wavelength [L ] Magnetic permeability, [MLQ 2 ] Frequency [T 1 ] Charge density / I mpact parameter / P article density [QL n ] / [L] / [ML n ] Cross section [L 2 ] Dimensionless time variable [ N ull] e Electric susceptibility, [M 1 T 2 Q 2 ] Angular frequency [T 1 ] s Stark width [T 1 ] d Doppler Width [T 1 ] 0 Unperturbed frequency / Minimum beam radius [T 1 ] / [L] n Order of dimensionality Variable dimensionality Denotes fundamental unit

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16 Abstract of Dissertation Presented to the Graduate School of the Un iversity of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy LASER INDUCED BREAKDOWN SPECTROSCOPY ON SUSPENDED PARTICULATE MATTER IN AN ELECTRODYNAMIC BALANCE: INTERACTION PROCESSES AND ANALYTICAL C ONSIDERATIONS By Richard Anderson Warren Jr. May 2013 Chair: Nicol Omenetto Major: Chemistry Laser induced breakdown spectroscopy (LIBS) has become increasingly popular as a sampling technique since its inception following the invention of the laser In what is typically an atomic emission method, a single laser pulse performs the sample ablation, vaporization, and excitation in a single step allowing any phase of matter to be rapidly, qualitatively studied for the presence of numerous elements. Mini mal sample preparation and the relative simplicity of the typical LIBS instrument make it appealing as both an analytical tool for the laboratory and for commercial industrial a pplications. 1 2 3 LIBS has a tremendous potential in the area of aerosol analysis as it provides a method for in situ analysis of the density and composition of environmental aerosols which few methods can accomplish as rapidly and remotel y Quantification of sample compositions is possible with LIBS, but requires careful consideration of the complex mechanisms controlling the sample ablation and excitation mechanisms Though the physical arrangement for a LIBS aerosol measurement can be qu ite simple the processes involved are all but. 4 5 Aerosols are composed of small discrete particles which, when sampled in the lab or in the field, are difficult to control. 6 Variat ions in the

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17 measurements on these particles can be caused by laser particle scattering, particle to particle matrix defects and effects, spectral interferences and particle photon resonances which are not seen in continuous samples. 2 3 This research focuses on the two problems listed above: sample control issues and sources of signal variation which limit analyte quantific ation. The e lectrodynamic balance which has been used by previous researchers for optical characterization of aerosols 7 is used here for LIBS measurements. This technique provides complete control of confined, charged aerosol particles. With this precise handling capability, consistent laser particle and plasma particle interactions are observed with both spectrally integrated / time resolved and time integrated / spectrally resolved detectors to provide details on the processes involved for micrometer sized charged aerosol particles.

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18 CHAPTER 1 LASER INDUCED BREAKDOWN SPECTROSCOPY FOR AE ROSOL ANALYSIS Introduction This research involves careful handling of charged, micro aerosol particles for highly controllable application of laser radiation in the vicinity of the sample. Several previous studies in this area have focused on interactions of robust laser gas plasmas interacting with particulate matter. 8 9 It is felt that the direct understanding of the effects of the local plasma conditions and sample composition would be better obtained through techniques offering more control over the conditions leading up to the plasma event as well as the resulting pla sma laser particle interactions To accomplish the level of control required between the particle laser and particle plasma interaction, an electrodynamic balance (EDB) will be used to spatially confine these charged micro particles produced from aerosoli zed solutions as described in several previous Raman and fluorescence studies. 10 11 In this way, laser radiation at pulse energies which would otherwise not form a plasma in air at laboratory conditions can be used to initiate plasmas from a direct laser particle interaction s The resulting plasma environment can be studied for effects of species frac tionation and the persistence of different species within. Three detector systems are incorporated in order to provide temporal, spatial, and light scattering data. The work performed here will focus on charged aerosolized matter generated from salt contai ning liquids. The LIBS Technique Laser Induced breakdown spectroscopy, an atomic emission technique that is capable of identifying and quantifying the composition of a substance regardless of its physical state as a solid, liquid, or gas was made possible by the creation of the laser

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19 source. Laser Induced Breakdown Spectroscopy instruments can contain as few as 3 elements: a focused laser beam, a sample, and a n optical detector capable of providing wavelength v. intensity data. This can prove to be relative ly inexpensive when compared to other instruments which provide the same service. The LIBS technique rapidly followed the invention of the laser, but for some 20 years was limited primarily to studies on the physics of plasma formation. 12 By 1980 there was a growing interest in the analytic al possibilities and the field of LIBS as we know it began. It was quickly recognized that while this rising superstar in atomic emission spectroscopy had a plethora of advantag es over its sister methods with ease of sampling, lack of preparation, standoff measurement capability, and using a single laser source to accomplish heating, vaporization, atomization and excitation. 13 A typical LIBS measurement involves focusing a pulsed laser into a sample with sufficient irradiance to cause the vaporization, atomization and subsequent excitation of the sample. (FIGURE 1 2) This is convenient as all of the sampling steps are performed by a single laser source. The LIBS signal is transient by nature; it changes over time an d only persists for a finite time depending on many variables including the sample composition, a mbient pressure, and laser power and frequency. This transient emission signal, either whole or by parts, is collected and analyzed to provide information on t he nature of the sample. (FIGURE 1 3) Spectroscopic measurements are typically performed during the early cooling stages when both neutral and ionized species are present in the plasma but after the continuum has decayed. Several factors lend to rall utility as an analytic al technique. One of the most enticing of these is the sample preparation or lack thereof. Sample homogenization is often t he only step

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20 inconsistencies e ven this step is unnecessary. Some consider this to be a non destructive technique 14 since the laser pulse typically removes pico nanogram quantities of material. This is a completely subjective argument since the cases of particulate analysis and in combustion studies, there is clearly an irreversible sampl e the mass removed and chemical processes can completely change the sample. 15 LIBS Sampling Concerns Aside from its potentially destructive nature, there were also some other inherent issues that arose with the LIBS methods. First, each laser pulse and emission collection is necessarily an independent experiment, essentially collecting information about a new sample with each laser pulse, providing measurement to measurement variations on any analysis. This type of variance is often attributed to changing the sample site / laser interactions or to inhomogeneities within a sample. 2 Secondly, there are variations in sample to sample measurements. Among these are what are k nown as matrix effects as well as the problems associated with thermodynamic considerations for plasma diagnostics. Matrix Effects Matrix effects are one source for spurious signals when attempting to quantify concentrations of species in samples with diff ering matrices. 16 17 Consider the hypothetical scenario where a researcher is attempting to identify a copper concentration in both an iron sample and a n aluminum sample, both containing the same mole fraction of copper. It is likely that while both samples clearly contain the same amount of copper, the integrated intensity collected for copper emission for each

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21 are likely vastly different. This results f rom differences in the materials, or matrices, in which the copper is included. This is actually a rather simplistic view of the matrix effect. In fact, these effects are not only due to factors such as absorption cross section, material density, lattice b inding affinities, differing heats of fusion, vaporization, ionization, which are solely dictated by the sample but also on factors such as laser pulse width, wavelength and sampling rates which are source dependent. 5 2 The source dependencies are discussed at length in the appendix. In general all of the se cross sample studies and would seem to require that for quantization of sample contents a need for a set of matrix matched standards to derive calibration data. These ma trix matched standards do not exist for many samples. Matrix effects in LIBS and the impossibility of having matrix matched standards for all imaginable samples is currently the Achilles heel to the technique when it comes to absolute quantization. 3 Fortunately, rigorous plasma diagnostics may offer a better understanding of the intricate interplay of all of these factors and allow for the correction or even negation of the effects. Aerosols Specifically, aerosols are a suspension of solid or liquid particles which exists long enough to be measured. 18 The aerosol is the gaseous analogue to the hydrosol aerosols by many common names: smoke, fog, smog, dust, mist, cloud, and fumes among others. While these are colloquial terms they still give information about the specific types of particles suspensions we are referring to. We know cl ouds are typically liquid suspensions while dust is a solid. The rigorous classification of these aerosols takes place at several levels of observation and have been formally described by

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22 several authors by their size, phase, macroscopic composition, chemi cal composition and origin. 19 Dust for example originates from the mechanical degradation of a solid, is representative compositionally and chemic ally of the bulk material and may range in size from .1 micrometer to .1 millimeter in diameter. 20 Aerosol Descri ptors A typical discussion about an aerosol will quickly come to a description of size in gives information relevant to describing how the bulk aerosol may disperse as w ell as how this aerosol may react with its environment. The particle size is not a trivial or simplistic value. As particles can take on many geometries such as spheres, rods, ellipsoids, cubic, and heterogeneous agglomerations and aggregations of these sh apes, measuring an implicit mass or diameter becomes more difficult. (FIGURE 1 1) One dimensional parameter completely describes the size of a sphere or cube while it takes two for a cylinder and three or more for higher order geometrical shapes. 21 Because of this, equivalent diameters, e quivalent volumes and equivalent masses are often used. The equivalent parameter given for a particle is the comparison to a spherical droplet which has some identical property to the particle in question. 22 The analogy to spheres is used because analytical solutions to the theoretical equations representing responses to external fields exist and can be calculated in situ. Since the response to an external field can be well described we can generate techniques which can be used to describe a generic aerosol. The interaction with gravitational fields and electromagnetic fields are employed for these analyses. Gravity is an ever present, locally m easured vector field that has the effect of pulling particles contained in an aerosol toward the earth or any other massive body.

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23 The rate at which particles fall to the earth over time outside a vacuum is dictated primarily by the force applied by the fie ld, g, the particle size parameter, d p and density the particles in the media being traversed, N p velocity as it applies to falling skydivers. If in a vacuum, the skydiver would constantly accelerate to the gro und even after opening his or her parachute as there would be no resistive force to counteract the force applied by gravity. Fortunately for our skydivers the density of air is such that it provides a drag force which rapidly equilibrates upon the exiting of the plane. The average skydiver falls at a rate of 60 m/s which would not make for a comfortable landing. The parachute when opened provides additional aerodynamic drag which slows the diver to a comfortable landing speed. These principles are d irectly applicable to aerosol gravimetric analysis and behaviors in the EDB.The parameters which describe the interaction of our particles and our skydiver Reynolds numbers The Reynolds number is a unit less term which re lates the effects inertial forces and viscous forces have on flow. Three regimes exist: laminar flow, turbulent, and intermediate or slip flow. The Reynolds number is calculated from equation (1 1) shown in its simplified form when dealing with normal labo ratory conditions. Flows with numbers <10 fall into the laminar flow regime while numbers greater than 2000 are turbulent. The drag force which decelerates falling particles in the micrometer range, Re(10^ 4) in a gas is laminar and caused by momentum tran sfer processes between collisions of the particle and the gas molecules. The effect particles experience is a direct de s cent following the gravitational force. 1

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24 (1 1) Stokes law Particles fall at different rates through the atmosphere. This rate is dependent on p, a, size parameter, d p an d the diameter, d a which equates any measured value to the diameter of a spherical droplet of water which settles at the same rate and can be calculated using Stokes Law, (1 2), which provides a general description for bodies interacting with a continuous fluid medium. 1 (1 2) Optical Particle Analysis Optical techniques are some of the most theoret ically complex measurements due to the dependence on temperature, refractive indices, angles of detection, wavelength of light used and even the polarization and intensity distribution of the source. Yet because of the detection efficiency and rapid rates of parameter determination these are often employed in laboratory settings as cost effective tools for particle characterization. 21 Most useful for this work are scattering measurements to determine d p Aerosol Charges Most aerosols carry a net charge w hether naturally produced or artificially induced. The principles of electro neutrality apply to particles and in either case this charge tends to diminish over time due to exposure to UV radiation, collisions with particles of gas and other aerosolized pa rticles when dealing with non radioactive

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25 aerosols. 23 There are some detrimental effects of the charge on these particles as the rates of sedimentation are enhanced due to coulombic and imag e forces. In these studies only particles of common electrical charge are used for analysis. As they have a tendency to disperse from each other, the effe cts of agglomeration and aggregation are reduced. Generically, The attractive and repulsive forces for charged particles in the Stokes regime can be described by eq 1 3 and the terminal velocity of a particle in a field are given by eq 1 4 when these part icles are introduced into an electric field. 7 The terminal velocity of a charged particle is highly important in the electric field of the EDB. (1 3) (1 4) The Electrodynamic Balance for Single Particle Trapping Aerosols have been collected through mechanical confinement methods using filters and solutions for a well over a hundred years. Impactors, impingers, and konometers with windows coat ed with petroleum jelly, submerged in exotic solutions and consisting of convoluted series of plates and springs, reminiscent of the finest Rube Goldberg machines were the state of the art in aerosol analysis up until the late 21 Over time newer and more refined devices have been developed to sample aerosols. One such device forms the cen terpiece for this research. charge on the electron which used levitation, several techniques have been developed to confine charged particles against the force of gravity and flows. As a matter of semantics and for our purposes, levitation refers to the application of a force which

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26 counteracts the force of gravity. The levitated body is free to move in the X Y plane. Confinement refers to the application of a force such that motion i n all three dimensions in an ion cyclotron resonance cell to thousands of tons of mag lev trains racing down electro magnetic rails at hundreds of miles per hour. The se methods use the magnetic field component to do the work of counteracting gravity. Another set of devices works off of the electric field component and include devices like 3 d hyperbolic, (Figure 1 4), linear quadrupolar, planar traps, and the relativel y new orbitrap. 24 These devices are electrodynamic. design of the quadrupole trap for ionic research. 25 Subsequently Straubel and Wuerker created electrodynamic balances for microparticles. Simpler designs such as the Paul S traubel trap can both confine micro and macro charged particles in and out of vacuum (Figure 1 5). Originally these EDBs were used for aerosol array analysis, but over time they were used for single particle analysis. 20 Here we combine these two paralleled research areas into one: LIBS on confined aerosols. The Quadrupolar Field for Trapping As mentioned, there is a distinct difference between the electrostatic particle levitator used by Milliken and the particle traps used today which are electrodynamic. droplets, while levitated were free to move about in the axial directions as there is no horizontal stabilization force. Recent work by Dutouquet employs such a method of levitation for analysis of nanoparticles in vacuum conditions. 26 Confinement is preferred to levitation for these studies.

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27 Quadrupole fields were first proposed for use and developed by Nobel laureate Wolfgang Paul and his group in 1953 while working at the University of Bonn. Such fields are generated by many mechanisms but are all uniquely defined by having four poles of alternate phase. Three dimensional bih yp rperboloidal and linear quadrupole traps are typical for mass analyzers in modern electric sector mass spectrometric analyzers and ion trapping systems. The advantage of using the bihyperboloidal quadrupole over the linear variety is the ability to have vertical stabilization forces as well restorative forces in the radial directions. In both devices there exists a set of electric field parameters that provide either stable or unstable trajectories for a given m/z. To see how the field stability parameters give rise to selective stability regimes, a DC and AC potential are applied to the quadrupole in F igure 1 4, and the equations of motion for a particle in the field are solved. The solutions for stable trajectories give rise to the familiar Mathieu stability diagram. Note that stability regimes are defined solely by the parameters a z and q z which are proportional to the AC field frequency and magnitude and DC field magnitude. The shaded areas are regions of stability while the unshaded area represents unstable regimes with respect to mass to charge ratios. Paul Trap Variants Since its invention, many variations of field s and geometries have been developed. The Paul Straubel traps are what are known as planar traps, i.e. their confinement fields are generated by planar structures. 27 The electrodes in this variety of trap are supplied both alternating current and direct current in order to provide a radial stabilization and a balancing force to confine charged matter within. The double ring

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28 electrodynamic balan ce it a hybrid design with components of both Paul and Straubel and is essentially a stack of planar traps capable of 3 d confinement. The general theory of operation of the EDB is described by the solutions to the equations of motion for a charged mass i n a quadrupolar field and in the limit of the center of the trap, the solutions are identical to those of the homogenous Mathieu equations. 28 Another consideration for the EDB is that the radial and vertical components of the field are 90 degrees out of phase and that the EMF in the vertical direction will always be twice that of the horizontal. For particles and clusters confined in these fields, any destabilization of the trajectories will occur along Z and thus, only the conditions which form stable trajectories along Z need be considered. The vector field in torative forces ( Figure 1 6). (1 5) geometric center of the Paul trap, stable trajectories are also possible which involve clusters and arrays outside t hat center. Davis et. al. studied numerical solutions to these scenarios through imposing boundary conditions to the general equation, eq 1 6, predicting accurately the formation of coulombic crystals and particle arrays within the traps. 7 Here the unit less parameters describe the drag, AC field and gravitational imbalance. (1 6)

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29 These clusters and arrays can be manipulated within the balance by careful adjustment of the DC and AC fields of the balance electrodes having the effect of exte nding, compressing, rotating, and even selectively destabilizing particles in the cluster due to the stability parameters, a and q, found in eq. 1 7 and 1 8. Mapping the boundary for values of a z and q z which yield convergent solutions to the equations of motion produces the Mathieu stability diagram. V AC provides no time averaged force within the trap and thus it is necessary to equate F z using V DC (1 7) (1 8) This selective stability allows for the collection of many charged ae rosol particles and subsequent selection of one individual particle with known parameters for LIBS analysis. (Figure 1 7) The trap used in all of the experiments described in this text is the bi tauroidal 3 d Paul trap and was selected for its optical acce ss, ease of construction and cost effectiveness. With the level of control given by the Paul trap, individual charged particles from a single electron to fifty micrometers or more can be trapped for study, theoretically. Once confined, a single particle ca n be analyzed to determine the mass, charge and diameter using a laminar gas flow and measurement of the V DC required to stabilize the particle. 29 This relationship is shown in equation 1 9 (1 9) Trap Constants The DC field within the trap is n ot uniform and requires that a trap constant or geometrical constant, C 0 be used to determine the actual field strength. Davis et al. have tabulated these values for several trap geometries including the double ring EDB.

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30 These trap constants are dependent on the radius, a and vertical separation, 2z 0, of the trap rings. In the center of the trap volume equation 1 10 can be used to calculate the balancing voltage. (1 10) Modes of LIBS Particle Experiments There are at least two distinct types of interaction that can be had when performing aerosol LIBS measurements in the electrodynam ic balance. One possible scenario is to use a high energy, pulsed laser to produce a robust laser plasma in the medium containing trapped aerosolized particles. The second scenario involves using a lower power pulse so that dielectric breakdown of the carr ier gasses containing the aerosol particles does not occur in the pure gas. In this first case there is always going to be a laser plasma formed, but there will not always be a particle enveloped by the plasma. This type of measurement can produce direct particle hits, laser particle interactions, or can produce a plasma which subsequently engulfs the particle. This is the scenario most often described experimentally by Windom, Carranza, and Hahn. 8 30 31 Gornushkin and coworkers have worked on theoretical modeling these plasma analyte interactions as well. 32 33 Noll and his group describe size resolved analysis using 20 800 nm CaCl 2 aerosols and note the relationship between signal inten sity and particle diameter. 34 Hahn and his group report an effective upper particle limit on the order of 2.11 m and note that current reports are <10 m 35 for linear analyte response. The requirements for complete particle study. 15

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31 In the second scenario where insufficient irradiance for clean gas breakdown is provided, the re is only one possibility to produce a LIBS signal: the direct laser particle interaction. The methodologies described here provide means to identify the energy transfer mechanisms between the plasma and the particle versus the laser and the particle and identify differences in the resulting plasma involving the diss ociated particle matter. Laser Particle Interactions Energy must be transferred into the sample via mechanisms which are dependent on the timescale of the laser pulse used. An accepted mechanism of transfer between laser and bulk samples using nanosecond infra red pulses on solid, bulk samples is that of Multi photon absorption leading to initial ionization. Upon the formation of free electrons, a transfer of energy deposition mechanisms occurs from those of laser sample to laser plasma processes. Inverse Bremsstr ahlung processes cause cascade collision ionization processes, forming a robust plasma. 1 4 P hase explosion s due to rapid heating of a material past the boiling point can occur in samples 34 An overheated zone is confined to its given phase by elev ated pressures generated by the rapid vaporization of surrounding material. When the pressure drops the superheated material rapidly changes phase via phase explosion. This explosion produces a high pressure, rapidly expanding plume of hot dense material w hich inhibits the further removal of material from the surface. 36 Laser heating and conductive heat dissi pation through a sample does not proceed to a large extent as the heat dispersion processes are much slower than the timescale of the laser pulse. The general pro cess shown in F igure 1 2 can be applied to particles as well.

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32 In aerosols, the laser energy i s scattered by the particle and explosive plumes erupt from the particle while heating and vaporization ensue. It has been shown that the dielectric breakdown threshold decreases with the seeding of a sampling cavity and that this threshold is also lowere d as the size of the particles used to seed the cavity increases. 37 Laser particle interactions can be assured through the collection of spectra created when ou r laser is fired below the breakdown threshold, BBT. If the laser is operated above the breakdown threshold, ABT, we must ensure that the particle lies within the focal volume of the laser. Rayleigh length The Rayleigh length is the characteristic length along the axis of propagation that is required for the doubling of the beam waist diameter. 38 It is the focal volume produced by the product of the beam waist and the Rayleigh length that will be taken into consideration for laser particle versus plasma particle discussions. When sufficient power is available to produce a plasma, If the particle lies within the focal volume it is considered a laser hit while if the particle is outside the focal volume, it will be considered a plasma hit. Diagnostics for the Laser Particle Interaction Plasma diagnostic techniques which rely heavily on th e thermodynamic properties of plasmas offer direct insight into the mechanisms which produce and define the life of the LIBS plasma. Researchers have used these types of analysis to attempt to determine the causes of matrix effects and subsequently correct for them. The the excitation temperature governing the velocity distribution of particles within the plasma, T ex the electron temperature, T e and the electron number density, N e A set of

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33 relationships exist from which these values can be experimentally determined, most of which are derived from an assumption of equilibrium which one should take into consideration when attempting to apply them to the laser induced plas ma. 2, 39 Most commonly used are the Saha Bo ltzmann rel ationships in association with S tark broadening parameters to determine electron number densities and excitation temperatures. 3 Simultaneous Multi element Analysis: Signal Persistence Since the introduction of the intensified charge coupled det ector, iCCD, many research groups have adopted them as the detector of choice. With high speed gating on the order of nanoseconds in current systems and the ability for both high signal gains and infinitely variable gates, ever finer slices of the transien t plasmas may be captured while providing highly resolved spectral windows when coupled to an appropriate spectrometer. Using a series of images collected, the average life of a representative laser sample interaction can be assembled. The disadvantages to this method are: 1) Each LIBS plasma is a different experiment and convolving spectra does not give direct insight into the sho t to shot variations. 2) Using large gate width s provided by iCCD camera systems causes a significant loss of temporal resolutio n. In order to get a better representative sample for the aerosol measurements, a broadband and continuous in time detector will be used. A Paschen Runge polychromator capable of monitoring up to 32 individual elements simultaneously will be used for so spectrally integrated waveforms representative of the persistence of an emitting species within the laser plasma. This method of collection has been recently reported by Noll for rapi d compositional analysis of recyclable alloys and for very fast, 1kHz, acquisition of

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34 LIBS data. 40 41 Simultaneous observation of and recording from a single plasma event provides shot to shot discrimination of varying plasma parameters throughout the plasma lifetime at the cost of spectral resolution. Conclusions Plasma particle interactions have been described by several research groups in the LIBS field. Currently there is no method for consistently observ ing laser particle interactions with aerosolized matter. The incorporation of LIBS with the electrodynamic balance provides the level of sample control required for diagnostic measurements to be made on the laser particle and plasma particle interaction in order to determine the degree of material incorporation, diffusion, and the plasma parameters which differ between the two events. By spatially confining a charged particle in 3 dimensions interactions of plasma and particle as well as laser particle can be studied with a consistency unattainable by other means. A clear advantage to using the EDB for these studies is that the stability characteristics of the balance allow for arrays of particles to be confined and possibly selectively ejected. Using the parameters pioneered and defined by Davis and his group 7 we can use the EDB to size particles and monitor the consistency of m/z for the aerosols under study eliminating the need for separate instrumentation for these verifications.

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35 Figure 1 1 Amorphic particle characterization can take on many descriptors. Maximum and minimum diameters, equivalent weights, diameter and volumes are all used to describe the size. Chemical characterization is also possible.

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36 Figure 1 2 The LIBS event processes through several phases starting with the laser pulse and ending with deposition of the ablated material.

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37 Figure 1 3 The LIBS signal is integrated either in its e ntirety or in time resolved slices using an initial delay, T d to avoid continuum emission and a gate with a width of T g

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38 Figure 1 4. 3 D Quadrupolar Bihyperbolic Trap. This type of trap consists of a ring electrode and two end caps, all electronically isolated. I n mass spectrometric applications the DC bias voltage is often left at ground potential leaving stability solely dependent on the AC frequency, often in the MHz range.

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39 Figure 1 5. The EDB. Here two ring electrodes are energize d with a DC voltage superimposed on an AC field. These traps stability regimes can be approximated by the Mathieu equations when close to the center of the trap.

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40 Figure 1 6. Vector Fiel d in the Quadrupole at t=0, top bottom This demonstrates that the EMF applied to the center is null. Plots are generated using Mathcad software.

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41 CHAPTER 2 PARTICLE GENERATION AND CONFINEMENT Introduction The instrument for single particle analysis consists of elements fac ilitating three primary functions: particle generation and charging, particle trapping and selection, and data acquisition. These three custom elements combined make the single particle LIBS system. The parameters of liquid aerosols are more easily control led than those solid aerosols due to the tendency for liquid droplets to form spherical structures. A vibrating orifice aerosol generator is employed for the particle production which can produce monodisperse aerosol flows of liquid droplets. The aerosol f low produced by the VOAG is charged in order to interact with our EDB fields. The charging of aerosol particles and the subsequent interactions with the EDB must be characterized for the sake of consistency in LIBS measurements. Vibrating Orifice Aerosol Generator Charged particle generation is accomplished with a TSI 3050 vibrating orifice aerosol generator (VOAG) unit which has been custom modified for our application by removing the unit from its factory enclosure, building a custom desolvation chamber and adding a conductive exit plate for inductive aerosol charging. The VOAG F igure 2 1, uses a piezoelectric ceramic crystal to perturb a liquid jet, ideally producing a monodisperse flow of particles. The liquid jet is formed by creating sufficient head pressure behind interchangeable pinholes which can range in diameter from 10 50 um. Changing pinholes produces liquid jets, and subsequently particles, of varying diameter. The dependence on the diameter of the liquid jet, the flow rate, and the drive fre quency applied to the piezoceramic crystal can be seen in equation 2 1. The theoretical

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42 diameters, D d and dried particles, D p can be calculated using both equations 2 1 and 2 2, assuming spherical droplets and dried particles. Masses of the droplets and subsequent desolvated particles are calculated from the \ volumetric concentrations of the solutions and salts. Here D d is the droplet diameter, Q is liquid flow rate, f is the drive frequency for the piezo, and C is volumetric concentration of the solute. 42 (2 1) (2 2) Thus the particle size can be manipulated by changing the drive frequency or the initial solution con centration. While the particles which dry from the solutions may not be spherical, they will always have a known mass determined from the original droplet size and the concentration of the solutions. Particles ranging from 4 25 microns have been generated trapped, and studied. Dispersion gas es are used to prevent droplet aggregation while a flow of dry nitrogen is used to desolvate and dilute the droplet stream, producing dried particles. While particles produced from different solutes may dry to differe nt final geometries as in the case of sodium chloride particles, the masses of the different particles can be directly calculated from solute concentration and initial droplet diameters. Particle Charging Uniform charging of the particles is achieved indu ctively. The resulting charge on the particle produced from conductive liquids can be calculated using equation 2 3 (2 3)

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43 where q 0 is the initial charge, is the permeability of free space, L B is the breakup length of the liquid jet and d p is the droplet diameter whi ch can be calculated from equation 2 4. V C is the charging voltage, and e is the fundamental charge. H is the (2 4) headspace gap from the generator to the charging electrode and is a correction factor for the nonuniformity of the electric field. This value has been determined to be 0.8 by Reischl et al. for our geometry. 43 The VOAG has been retrofitted with a stainless steel inductive charging pl ate, electronically isolated from the piezo body, which enables the application of potentials up to 200 V DC Particles, once charged, are introduced into the trap through a sealable orifice above the trap assembly for confinement and study. The particles u sed for study are produced from the chloride salts of sodium, calcium, and magnesium dissolved in 50/50 V/V isopropanol and water solution. The VOAG and this charging method are describe d at length in TSI documentation and by Reischl and Davis. 43 44 45 The Electrodynamic Balance and Particle Trapping In the double ring electrodynamic balance, EDB, manipulation of the d rive frequency and the amplitude of both the drive and DC ring voltages is critical to stabilizing or ejecting particles and arrays confined in the trap volume. The AC source is a HP arbitrary function generator whose signal output is amplified using a Rea listic 100 W audio amplifier. The amplified signal is sent to a step up transformer producin g AC amplitudes of up to 2200V b p. This signal is divided into two channels for the upper and lower ring electrodes. A schematic is presented in Figure 2 2.

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44 Each el ectrode DC potential can be controlled both simultaneously (bias) and independently (offset) to manipulate particles into the path of a HeNe targeting laser awaiting ablation. These two types of DC manipulation have different effects of the particles in th e trap. Offset voltages are used to counteract the downward forces on the particle. Bias is applied to squeeze or compress arrays and to change the levitation height within the trap. This is represented in Figure 2 3. Trap Parameter Determination Determini ng the diameters of particles in the balance at any given time is essential. Imaging of particles in the trap can provide information which is used to determine the exact properties of the balance through characterization of the fields. A HeNe laser co pro pagates with the ablation laser for alignment purposes and to of balancing voltages on a per particle basis. With a centered particle and known AC and DC voltages the calculation of the trap constant, C 0, and the inductive charging efficiency for the system can be performed. This calculation requires particles whose diameters are already known. Plotting the square of the radius, a 2 offset DC voltage divided by the radius, V DC /a, results in a line ar trend according to E quation 2 5 and can be used for the determination of C 0 29 The i mages of arrays and (2 5) clusters also provide information about the mass to charge distribution of the species being generated as can be seen in Figure 2 4.

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45 Spring point When the offset V DC voltage does not exactly balance the m/z, as described by equation 1 9, for particles in the trap violent vertical oscillations of can be observed. 46 This lower threshold value is known as the springpoint and provides direct measurement of the mass t o charge ratios for the aerosol particles. Using 1 9, 1 10, 2 5 and particles of known mass allows for complete characterization of the balance. Experimental Results and discussion The chloride salt of calcium and the nitrate salts of potassium and magne sium were used to make solutions of varying concentrations in 50/50 V/V solutions of HPLC grade water and filtered, reagent grade isopropanol. Selection of the salts stems from both convenience and that several studies have been performed using aerosols fr om these salts. 47 48 Solution concentrations were calculated and made to yield various dried particles diameters in order to determine the minimum and maximum particle diameters capable of being stably confined in the balance. Table 2 1 and 2 2 give concentrations and operational parameters for the system. The impurity of the solids and solvents were neglected in the calculations of the particle diameters because of the reagent purity used for preparation. There was no measurable effect of this a ssumption. Injection These solutions were loaded into standard plastic 25 cc syringes and injected particle on the size order of the orifice used in the VOAG results in device failur e or, at best, intermittent operation. The effects of inefficient filtration and filter failures were observed as multiple jets emitted from the VOAG instead of a single, homogenous flow.

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46 A syringe pump provided a constant flow and backpressure through th e VOAG. Pressures were monitored using an attached pressure gauge for diagnostics as well as to maintain normal startup and operational conditions, NOC. High pressures are often required to initiate the liquid jet, but are undesired for normal operation. T his higher pressure is developed by temporarily increasing the desired flow rate by a factor of 10. Once the liquid jet was observed the flow rate was decreased to NOC. After system equilibration, charging voltages were applied and particles introduced int o the trap. Charging voltages were varied from 0 100 V DC as was required by the solution being used. It was found that for all calcium solutions the charging voltage required was 20 25% that required for magnesium solutions. Insufficient charging volta ge created particles with very high mass to charge ratios and subsequently required high DC offset values and AC field values to stabilize the particles. Using the maximum voltage, 100 V DC did not produce particles with sufficient charge to cause the dryi ng particles to disintegrate from coulombic forces. The phenomena is known as coulombic explosion and unfortunately was not observed. 23 Trapping Trapping of a single particle began with the introduction of a cascade of particles into the chamber with the trap energized. Initially arrays of particles find stable trajectories in the trapping f ields. To isolate a single particle, the magnitude of the AC trapping field is lowered while simultaneously adjusting the offset voltage which destabilizes the array and causes particles to be ejected. Coulombic repulsions work favorably for this process. Squeezing particles into an ever smaller space increases the inter particle repulsions and causes destabilizations. Once only one particle remains,

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47 the AC field magnitude is increased and the offset and bias voltages adjusted to maximize the HeNe back scat ter signal detected at the spectrometer. Trap Parameters The EDB is an air tight, optically accessible chamber. Both the trap and charging 5. This interface is coupled via RS232 to a SR 245 computer inte rface. The DC voltage for charging and the electrodes is sent through a fast 10X voltage amplifier prior to signal mixing with the AC voltage applied to the ring electrodes and the charging plate on the VOAG. The 10x amplifier was designed and built by Ste ve Miles of the UF Dept. of Chemistry Electronics Shop This amplifier allows all dc voltages the range of 100 to +100 V DC stainless steel round rods delicately curved around a exact curvature and in the surface morphology of the individual ring electrodes which made an observable effect on the performance of the b alance with respect to the geometric field center. Acid polishing, fine sand blasting and extensive sonicating were used to diminish these effects to an appreciable degree, though there were mixed results. V AC Variations The AC frequency v. primary and s econdary voltage response was recorded with a high frequency, high voltage probe at the ring electrodes and is presented in Figure 2 6. As expected when the drive frequency increases the efficiency of the transformer increases and produces higher gain on the secondary over the frequency range

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48 monitored Also, as the primary voltage amplitude is increased the secondary voltage amplitude increased. Higher AC field strengths exacerbate the violent oscillations observed on unbalanced particles. T he force on t he particle is proportional to the magnitude of the AC field and the charge on the particle T his result is not abnormal and was seen by Davis and others. 7 Within the range of particles observed 4 20 micrometer, and in the frequency range used, 60 400 Hz, higher frequencies tend to increase the radial displacement of the particle in the trap from center. These trends are shown in F igure 2 7 for a two particle array. V DC variations V DC offsets are introduced after power amplification of the AC field. Each of the two offset V AC channels is coupled to the balance electrodes. Individual particles for these experiments were trapped using a drive frequency ranging from 60 hz to 400 hz and an amplitude of 1310 1550 V AC DC offsets are controlled with custom LabV and a Stanford Research Systems SR 245 computer interface. This allows for the rapid manipulation of the parameters to accommodate particles of varying m/z. Increasing the V DC in the balance controls the vertical position of the particle. With a voltage required to balance the mass in the trap equal to V 0 a voltage below this causes the particles to reside below the mid plane, oscillating normal to the AC field lines while voltages greater than V 0 put them above. When the V DC equals V 0 particles or arrays of monodisperse particles hover, virtually stationary in the mid plane. Evaporation As the particles are generated from solvated salts, there is a finite amount of time required to evaporate the solvent from the particles. This is seen in the tra p volume as a

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49 change in V 0 over time. This phenomenon has been reported and observed by Lin, Campillo, Davis, Liu and others and can be described in the continuum regime by isothermal diffusion controlled quasi steady state evaporation of a sphere whose re lationships were originally derived by Maxwell. 20 49 Assuming ideal vap or gas relationships, the concentrations may be expressed as vapor pressures and integrated. (2 6) (2 7) This relationship demonstrate s that over time the radius of the particle will reduce with the square root of time. The total charge on the particle is left unperturbed resulting in a change in mass to charge, m/z. This is observed in the balance as dV 0 /dt and must be taken into account before assuming that particles are desolvated. (2 8) Upon initial confinement, wet particles require rapid changes in V 0 to remain balanced. This is likely caused from local heating from the HeNe used for observation and alignment. Once evaporation was complete, V 0 stabilized. Stable Particle Diameters Particles from 2 20 micrometers were produced from solutions using the VOAG, charged and introduced into the balance. As a general rule, the larger the particle, up to about 50 micrometers, the broader the stability regime in the a z and q z plane on the Mathieu diagram. Hence, there is a much greater tolerance for V AC and V DC parameters to keep any given charged particle in the trap. Since mass grows with the cube of the radius and the charge can grow with the square, there is an upper limit

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50 of liquid particle diameter whose desolvated counterpart will possess sufficient charge to be trapped within the limits of our V DC range. As well, particles with sufficient charge can disintegrate due to Coulombic repulsion upon desolvation. The bounds theoretical limits are presented by Aardahl et al 45 On the opposite end of the range spectrum, with small particles, particle gas interactions become dominant. Local flows and eddies cause destabilization, and subsequently, the particles cannot be confined. Field imperfections have ever increasing effects on small diameter parti cles as well. As our instrument was not precision machined these local field anomalies are real and caused observable issues on particles below four micrometers. Trap with Cylindrical Confinement Fields The EDB was originally designed to be operated with symmetric AC fields on both electrodes. At some point during the operation of the balance it was observed that no particles were being trapped in the volume between the rings regardless of V AC or V DC amplitudes and frequencies. Particle production and cha rging were confirmed to be normal as well as the AC and DC outputs from the signal mixer. Video acquisition was verified as being real time Analysis of the acquired images (Figure 2 8) showed that arrays of particles were confined radially atop the upper by both the magnitudes of the V AC and the V DC In an analogous manner to the particles which could be confined within the trap, increasing the V AC amplitude accentuates the displacement and increasi ng V DC affects the mean distance from the ring electrode. The difference between the two trapping situation s lies in the symmetry of the motions.

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51 It was discovered that a fault in the RG 6 cable supplying the V AC to the upper electrode had created a situa tion where the upper electrode was being inductively charged by the lower electrode. This faulty line and inductive charging created a new type of trap with cylindrical symmetry. When the observation camera and illumin ation was adjusted to monitor th e even t, arrays of particles were observed to accumulate in a ring formation with even spacing between one another. When some minimum inter particle separation was achieved, confinement of additional particles displaced ones already in the field. Sufficient V D C was not available to balance the particle from the lower ring and attempts were not made to apply V DC to the upper ring and V AC to the lower ring, though this methodology should provide sufficient V DC to reach the spring point. This trapping method requi res at least two independent rings. When one ring is used the symmetry becomes planar and follows the principles Paul Straubel planar trap. Conclusions An electrodynam ic balance consisting of two to roidal rings and operating at atmospheric pressure is an effective tool to confine and study aerosol particles on the order of four to twenty micrometers in diameter as either arrays or as individual particles. We successfully trapped particles as small as 2 m and as large as 20 m, though the smallest particl es are rather difficult to consistently confine due to the conditions of atmospheric pressure and field inhomogeneity. While operating in reduced pressure or a vacuum would lower the minimum size limit it would also greatly increase the complexity of the device. Sample introduction, gas routing and temperature regulation would be all but impossible using the current system. The system is highly sensitive to any gas flow in the chamber. Another side

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52 effect of pressure adjustments it the associated change in dielectric breakdown threshold. After all, in a pure vacuum one cannot form a plasma as there is no material to be ionized. As our aerosol particles are generated from solution it is important to allow adequate time for evaporative processes to occur to ensure that no liquid solvent remains. The effects of the desolvation process can be observered and the rate quantified through the relationship of dV 0 /dt. These desolvated particles generated from the VOAG demonstrate a small SD in V 0 once allowed to dry in the trap, indicating consistent m/z. While the m/z is determined from the balance, the diameter of the particles produced should be verified by other means. The double ring cylindrical balance provides several notable results. First, the observation of uniform inter particle spacing provides evidence of the consistency of the inductive charging arrangement used. Secondly, the uniformity of the vertical displacement while V DC is below the springpoint shows the consistence of the mass to charge ratio of t he particles. As a logical deduction, with uniform charging and uniform mass to charge, the particles are necessarily of uniform mass. This is a new and novel approach to simultaneously verify charge, mass to charge, and mass of an aerosol flow. Finally, t his type of trap offers, through a slight modification, the development of a compact accelerator with no upper ring or turning electrodes. The implications of this new electrode configuration deserves further consideration. Solving the EOM for this device could provide a new method of charged particle analysis and reaction mechanisms.

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53 Table 2 1. Calcium chloride solutions used for particle generation. Calculated using a frequency of 60 kHz and a flow of .140 ml/min. D d Mass (g) /250 ml 50/50 ISO/Wate r Orifice diameter D d 5 4.890 10 23 9 4.890 20 42 12 12.71 20 42 15 24.826 20 42 Table 2 2. Magnesium Chloride solutions used for particle generation. Interchangeable orifices allow for one solution to produce two particle diameters. Dia meter (D p ) Mass (g) /500 ml 50/50 ISO/Water Orifice diameter D d 6 17.026 10 23 13.5 17.026 20 42

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54 Figure 2 1 VOAG Schematic Representation.

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55 Figure 2 2 EDB Electrical Schematic T1 is a step up transformer. Vdc 1 and Vdc 2 are termin al connections for independent V DC offset voltages. L1 and L2 are inductors acting as choke s preventing V AC feedback into the V DC source s C1 and C2 are 47 nF capacitors providing infinite resistance to DC current. J1 and J2 connect to the upper and lower balance electrode.

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56 Figure 2 3. Frequency, V AC and V DC dependence for particle balancing and graphical demonstration of the spring point (bottom two tiles). The off axis motion is due to field asymmetries caused by small defects in the balance.

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57 Figure 2 4. Bimodal distributions of particles can be seen in (a). M anipulation of the array lead eventually to a single, confined particle illuminated by the HeNe laser.

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58 Figure 2 5. Control Window. This is a custom I/O for the electrodynamic balance which al lows simultaneous Laser and spectrometer control, visualization of the trap interior and control of all trap parameters including V bias V offset V charging and polarity of the electrodes.

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59 Figure 2 6 Calibration curves for trap electrode voltages. Trap electrode voltages are sensitive to both input frequency and primary amplitude. The vertical deviations are lines of constant voltage from .1 to 2.1 volts on the primary in .1 V increments.

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60 Figure 2 7 General effects of field parameters on a two parti cle array within the EDB. Higher frequencies tend to accentuate the motion of the particle and pull it close to the ring electrode. Raising and lowering the DC voltage changes the vertical position in the trap with V DC = V 0 creating the condition of balanc e.

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61 Figure 2 8 The particles confined above the upper ring of the EDB provide insight into the charge distribution and the mass to charge distributions.

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62 CHAPTER 3 DIMENSIONAL ANALYSIS OF THE AEROSOL PARTICLES Introduction Particle size analysis is an active area of research in chemistry, chemical engineering and environmental sciences. The size and structure of particles in aerosols control how the environment and biological organisms will react to exposure. Miners were among the first populations to recognize long term health risks associated exposure to aerosols as a side effect of hard rock mining, though the true causes were not understood until the mid 19 th century. 19 With an understanding of the problem come solutions. Dust particles created by mining process were analyzed for size and morphology using konometers and microscopes. It was discovered that dust with certain aerodynamic diamete rs would become trapped in the lungs causing silicosis. Particles with a diameter of roughly one micrometer are the most hazardous to human health as they are most easily deposited in the tissues within the lung. Environmental impacts of industrial and com bustion exhaust are of great concern to environmental scientists and ecologists. Nucleation and accretion of industrial and automotive exhaust, salt aerosols from sea spray, and the chemistry that follows their entry into the atmosphere are under observati on for clues to local and global environmental impacts. In all of these cases the absolute size of the particles, as much as the composition, affect the outcomes of the chemical and physical processes. 19 There exist numerous methodologies to determine size and compositional aspects of various aerosols and are discussed at length in the first three chapters of a book by Spurny 21 and in a recent review of single particle measurements by Miles et. al 50 Few techniques are practically accomplished in the field due to the size and

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63 elaborate nature of most measurements. Here the theory behind the techniques directly applicable to the particle LIBS experiments conducted in an EDB are presented and i nclude scattering measurements, time of flight techniques, and electronic metering. With the increasing uses of portable LIBS systems, in situ measurements for particle analysis may well be accomplished with a field portable aerosol analyzer / LIBS analyze r as well in the near future. Time of Flight Measurements Time of flight measurements quantify the time required for an object to traverse a given distance. If the kinetic energy of the object is known, the mass can then be measured from the velocity, dx /dt, where x is the distance traversed. This i s the basic operational principle of the TSI aerosizer which is used to calibrate the EDB and the VOAG. The aero dynamic particle sizer, F igure 3 1, uses two gas flows to introduce particles into an observatio n area. One flow contains the particulate samples while the other contains clean, dry carrier gas identical to that containing the sample. Particles are accelerated through a nozzle and subsequently pass through two detectors spaced a known distance apart. As the particle occludes the laser beams, the decrease in signal at the detector marks the time to traverse the distance, providing the time of flight used to calculate the size. 6 Particles are accelerated at different rates in flows according to their Stokes number, stk The velocity of the particle is calculated from the gas flow within the nozzle, U g the transit time, and the tra nsit time of a small particle in the free molecular regime. The Bernoulli equation for compressible flow can be used to calculate the gas flow within the nozzle. Using U g v p, and S tk the aerodynamic velocity can be calculated from equation 3 1.

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64 (3 1) TSI Aerodynamic Particle Sizer (APS) The TSI 3603 APS works on the principle of aerodynamic time of flight. A differential pressure is driven against the opening of the noz zle in these instruments which acts as a critical orifice. This critical orifice creates a sonic flow and supersonic expansion on the detector side. Dahneke and Chen showed that the particle in this supersonic expansion reaches terminal velocity rapidly. 51 Detection is accomplished as described previously. The terminal velocity is a function the particle size and density. The system is intended to be calibrated using polystyrene spheres or other solid micrometer sized particles of well defined size. Monodisperse aerosols such as those generated by the TSI 3450 may also be used to calibrate the instrument per TSI 44 though issues were reported by Che n et al. that involve the irregular acceleration of droplets which can lead to incorrect calibration. 52 The acceleration of liquid droplets causes them to deform into ellipsoid s, broadening the response signal and also leading to aerodynamic diameters smaller than the stationary particle. As our particles begin as liquid droplets, the effects of particle elongation on the reported diameter values should be taken into considerati on. Also noteworthy is that while there is single particle detection, it takes some thirty seconds to generate the distribution report on an aerosol flow. No individual particle may be sized with this instrument. Light Scattering Another useful technique t o determine particle properties is light scattering. Strictly speaking light has but a few interaction processes with matter, though the interactions can become quite complex. According to the accepted solutions to

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65 ction of light with a sphere developed by Gustav Mie and Lorentz, the solutions lead to two matrices which completely describe extinction and scattering. Beautifully simple solutions they may be, incredibly complex they can become. Thus arise the immediate pitfalls of scattering measurements: assumptions and complexity. One can base analysis on many theories which include many levels of assumption. The real advantages to light scattering methods are the speed of measurement and simplicity of most analytical methodologies used to acquire data. The utility of the se methods stem from the fact that particles of varying size scatter light with differing angular intensities Rayleigh correctly described the scattering of light for particles with diameters much sma ller than the wavelength of the incident light. Here the electric field is assumed to be homogenous around the scattering particle. This creates an oscillating dipole, scattering the light both forwards and backwards with respect to the incident light. Ray leigh scattering 6 Hence photons in the blue are scattered more efficiently than photons in the red. This is observable when we go outside on a clear day. Other theories exist for particles which are of the same order to larger than wavelength of incident light. These theories can describe particles with diameters of micrometers to hundreds of meters in diameter. 53 See F igure 3 2. The decision to refer to matter as a particle, bulk, or even a wave, after all, is simply a matter of seman tics and/or perspective. To describe the effects of objects on light we begin with the approach: the basis for classical light scattering and Fresnel. Fresnel Theory For particles much larger than the wavelength of light, a theory must be applied which is different than that of the oscillating dipole of Lord Rayleigh. Let us consider

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66 diffraction which is described as a small deviation from rectilinear propagation. This phenomenon occurs when light passes a sharp edge or when waves on the ocean encounter an obstacle such as a jetty or a pier. Lines of minimum and maximum intensity can be seen on a projection plane placed downfield from the source and interfering body. Huygen proposed that this effect was due to plane waves being composed of spherical radiator s. This theory was put into a formalized mathematical location of the minima and maxima observed when considering angles not far from that of propagation. This theory ca n describe scattering of light by a planar object such as a knife edge or the orifices used by the VOAG. (3 2) When coherent light passes a knife edge or a pattern in a screen a diffraction pattern can be seen on a downfield screen. Babinet proposed that for any arbitrary pattern in the screen, the diffraction pattern of the original pattern and the complimentary pattern should necessarily be identi cal yet of differing phase. In F igure 3 equations for the two situations yield the same diffraction pattern. In this case the two fields generated are indeed out of phase such that adding the two field yields the original incident field. Hence, the size of the object with respect to the wavelen gth of light being scattered defines the appropriate theory to consider when performing an analysis. Just information about the incident radiation on the determination of th e scattered field and

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67 not of the obstruction itself. It can only describe these fields within small angles of propagation, as well. Larger aerosol particles have a more complex interaction with the radiation. The field is not uniform about the particle and responds differently. The particle may reflect, absorb, or refract the incident light and as such a different theory must be applied which considers the boundary and curl conditions described by olved by Lorentz and Mie. 53 Lorentz Mie Theory Another more rigorous theory which involves both the characteristics of the incident electromagnetic wave and the medium impinging the field must be considered ctromagnetic propagation can in theory be solved for any shape in an electromagnetic field. In this case, there is no restriction on angle, or on dimensions of the interfering body. Lorentz and Mie solved spherical homogenous particle. The solutions to this problem describe the fields both inside and outside of the sphere. The functions indicate that spherical waves propagate which are angularly and polarization dependent. Several programs have been writte n most notably by Bohren, Huffman, and Laven. These programs provide the ability to rapidly calculate the efficiency matrices Q ex Q Scat and Q abs for arbitrary particles as well as angular distribution functions. 54 Size Descriptions Distribution analysis can be described in several ways. Take for example a given series of particles of 1, 2, 3, 4, and 5 length units in diameter. The size of these particles can be dis cussed as a simple diameter average, a cross sectional average, a surface area average, or as the volumetric average. To define S tokes parameters and Reynolds numbers, the D[1,0], or number weighted mean is ideal. For chemical kinetics or

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68 evaporation which are rates related to the surface area, the surface area moment mean is a better descriptor. In the case of mass, which is proportional to volume, the volume moment mean is used. The m ost common means are expressed T able 3 1 with numerical examples. Exper imental Results and discussion The agreement of calculated diameters to the VOAG generated particle diameters were studied using several sizing techniques. The vibrating orifice aerosol generator is designed to produce monodisperse aerosols but will only d o so under certain conditions. 42 The system requires a stable liquid jet, dependent on a constant back pressure of liquid. VOAGs also only produce monodisperse aerosols when operated in certain frequ ency regimes. Particle diameters were initially calculated using frequencies, flow rates, jet diameters, and solution concentrations in accordance with equations 2 1 and 2 2. As a primary verification of the produced diameters, the aerosols produced from t hese solutions were measured with a TSI 3603 PSA, which also allowed for the frequency dependence to be determined and also the regimes which provided either monodisperse, bimodal or continuous diameter distributions. It is notable, also, that only uncharg ed aerosols were analyzed due to dramatics losses in transfer efficiency of charged particles through the instrument. When charged were used no instrument response was observed. r backpressure and to control the particle number density introduced into the instrument. Dispersion gas, house nitrogen, is set to 2.0 LPM. Carrier gas, also house ni trogen, is set to 8 LPM using KFR suspended float system rotameters. The nitrogen generated no

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69 signal response from the instrument without active operation of the VOAG, indicating that the particulate concentration in the filtered was negligible. Solutions were introduced into the VOAG using a Harvard model digital syringe pump at a flow rate of .239 mL/min using a 25mL disposable plastic syringe. The piezo drive amplitude was 19 V AC at initial f requency of 60 kHz driven by a Tekt ronix arbitrary function ge nera tor. The sine function was used. This arrangement has a calculated the Aerosizer exhibited large losses when measuring highly charged aerosols. Solutions containing 1.5 6, 4.89, and 12.42 g/ 250mL of calcium chloride dissolved in 50/50 V/V isopropanol and HPLC grade water solutions were prepared in volumetric glassware and then used to create the aerosols. The calculated d p from the spectively. After optimizing the frequency for monodispersion and diameter, the measured volume weighted mean values were 7.2, attributed to a change in piezo frequency from 60 kHz to 55 Khz which caused d d the initial estimate for this demonstrates a perfect agreement with measurement. The Aerosizer was disconnected and the VOAG co nnected to the EDB for particle confinement. There was no further use for the PSA. Spring point Measurements With the VOAG calibrated for particle diameter production and connected to the EDB chamber, the stainless steel charging cap was reinstalled and a constant charging voltage of 46.355 V was applied. The trap was energized with 1310 V AC at 60 Hz. No bias voltage was applied. Particles were introduced into the chamber in approximately

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70 500 ms bursts and the chamber resealed to eliminate external flows. A fter entered a steady state. The particles in the balance were selectively ejected until one remained. The remaining particle was balanced using the minimum DC voltage required to eliminate the violent vertical/diagonal oscillations to measure the spring point. Using identical parameter s for particle production from calcium and m agnesium solutions repeatedly showed decreased charging efficiency for the magnesium and is the reas on the triple channel 10x amplipfier was introduced into the system. Operating within the output range of + 10 V DC from the SR 245 would not provide a sufficient balance. W Improvement was seen in trapping efficiency of the Mg containing particles when higher potentials were used but was still poor compared to Ca. It was decided that Ca would be the eleme nt of choice for the measurements. Illumination Small particles are inherently hard to see with the human eye under normal conditions. In order to view the particles entering balance chamber volume and confined Physics mo del 117G argon ion laser was beam expanded and directed into the balance chamber. The laser was operated between 55 and 280 mW cw output based on the requirements to visualize the particles. The scatter image was recorded with a Supercircuits PC 23 Black a nd white CCTV camera and imaged using Labview. Particles in the a>5 micrometer size have large scatter cross sections and are easily visualized in this fashion. Particles below four microns were not capable of being imaged using this system.

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71 With particles centered and balanced, a 10 mW HeNe laser was focused through an F/1 S1 fused silica lens and made to illuminate the particles in the absence of the argon ion area illumination. The beam is used to identify the precise alignment of the excitation laser fo r subsequent LIBS experiments. The interference of electromagnetic radiation can be used to determine many parameters of a sample including diameter and refractive index. The HeNe which co propagates with 1064nm Nd:YAG ablation laser provides a source of c oherent radiation for interference measurements. Davis used light scattering measurements as early as scattering profiles. 28 parameters. Conclusions The TSI aerosizer demonstrated that the precise diameter of dried particles created from solu tions could be calculated using equations 1 2 and 1 3 with minimal error. Also, since it has been reported that liquid droplets cause negative systematic errors in the terminal velocity measurement process, it can be inferred that either desolvation was co mpleted during the transit time from the VOAG to the Aerosizer which is on the order of 10 seconds. A secondary demonstration of this is given by consistent measurement of the aerodynamic size. It was shown that the desolvation process is roughly linear wi th respect to a 2 and any deviations in measured size should be attributable to this trend as the transit time for the different size particles is very similar in the laminar flow, 8 10 s. For future particle diameters calculations the calculated value will be taken as the calibration value since there was no measurable discrepancy between the two.

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72 The very small RSD in the spring point measurements allows a secondary verification of the results of the Aerosizer. The VOAG was run using parameters known to gi ve a bimodal distribution as shown from the Aerosizer. The particles were trapped and thei r spring point measured. These calcium c hloride particles, measuring 13.5 and 5.2 and 8.9 indicating that the operation of the VOAG can be evaluated rapidly and in situ for normal operation. Furthermore, assuming consistent charging of the particles, which has been shown to be the case by Reischl et al. we can consistently collect particles of precisely the same mass and rej ect any that deviate from the expectation voltage. 41 Thus the trap parameters define the diameters. The difference in voltage required to effectively trap calcium chloride and magnesium nitrate particles demonstrate that the charging efficiency of the sol utions of different materials may be substantially different. Both jets were inductive ly charged using the same 46.3 V DC ; yet the magnesium particles required an order of magnitude higher V DC offset voltage to reach the spring point. A higher V DC indicates that the mass to charge is an order of magnitude higher on the magnesium particles. High mass to charge ratios will provide higher inertial force to field force ratio and thus require elevated V AC to be applied to the ring electrodes to be confined. These were abandoned as an element for study because of the difficulty associated with trapping them.

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73 Table 3 1. Relationships between different mean reportable values for particle distributions. Values provided are for the set of particles Descriptor Repre sentation Equation Value Numeric mean D[1,0] 3 Number volume mean D[2,0] 3.1 Surface area moment mean D[3,2] 3.2 Volume moment mean D[4,3] 4.1 Table 3 2. Parameters for monodisperse particles generated from the TSI 3050 VOAG and the associated error from the calculated diameters. The VOAG is in excellent agreement with the calculated particle diameters. these are repor ted, yet not significant. Concentration d d ( d p ( Flow Rate (cc/ min) Piezo (kHz) D[4,3] d d ( d p ( 1.56 g/250ml 41.8 7.17 .238 60.0 7.2 .03* 4.89 g/250ml 41.8 9.55 .238 55.0 9.8 .25 12.42 g/250ml 41.8 14.33 .238 60.0 14.3 .03* Table 3 3 The measured particle diameters were trapped and the spring point was measured. Concentration Trap Frequency V AC trap (V) V charge (V) V offset (V) d p ( 1.56 g/250ml 60 Hz 1310 46.335 .039 7.2 4.89 g/250ml 60 Hz 1310 46.335 .400 9.8 12.42 g/250ml 60 Hz 1310 46.335 .703 14.3

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74 Figure 3 1. A sheath flow of carrier gas accelerates particles from the sensor flow. In standard PSA the particles acceleration is dependent on the flow within the nozzle. In Aerosizers the terminal velocity is measure d and is acceleration independent. The total flow is equal to the sum of sensor and sheath flows.

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75 Figure 3 2. Particles much smaller than the wavelength of incident light are described primarily by Rayleigh scattering where particles greater than about .1 micron are best described by Lorentz Mie scattering. The intensity grows roughly as a 2

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76 Figure 3 3 Light with wavelengths smaller than the radius of the particle have more complex interactions and cannot be fully described by Fres nel diffraction theory. Apart from Fresnel theory only being applicable in the small angles regime there are no considerations for internal reflection and absorption.

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77 Figure 3 4 s produces the original electric field. E 0 =E a +E b. This principle is applied to measurements of the orifices used for the VOAG to ensure the consistency of the jet diameters after installation of new pinholes as well as spectrometer slit calibrations.

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78 Figure 3 5 Tuning the frequency on the VOAG while maintaining a constant flow and solution concentration can fine tune the diameter of the particles produced. Changing the liquid flow rate can have similar effects.

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79 Figure 3 6 Size distribu tion a nalysis for calcium c hloride p articles. Diameters were calculated using the above equations incorporating frequency and concentr ation. The parameters were fine tuned using the TSI Aerosizer. Certain frequency ranges produce highly irregular distribut ion of diameters as can be seen in the upper right.

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80 CHAPTER 4 THE LASER INDUCED PLASMA AND SINGLE PARTICLE LIBS Introduction The quadrupole electrodynamic balance is presented here as a tool for the analysis of direct laser particle and plasma particle in teractions in the area of Laser Induced Breakdown Spectroscopy (LIBS). This method provides a means to manipulate charged aerosols, measure particle diameters, and characterize constituent particles on an individual basis. An electrodynamic balance is asse mbled and characterized. The dielectric breakdown threshold is measured, providing the pulse energies for measurements below and above the threshold. Particle sizes are measured by aerodynamic sizing and monitoring the spring point within the balance. Limi tations of particle size for quantification by the LIBS method are discussed. Laser Plasmas The plasma condition as is typically described requires that free electrons be formed from neutral species, and these free electrons and neutrals should exist in a quasi static state and exhibit some collective behavior. 36 Plasmas are readily formed from high temperat ures, when k B T is of the order of the ionization potential. They are also formed in the presence of high magnitude electric fields which cause a dielectric for ioniz ation. Lasers can create all of these conditions through a variety of energy transfer processes. The nature of the energy transfer process is dependent on the timescale and frequency of the laser excitation and the electrical properties of the media intera cting with the pulse. 55 Nanosecond timescale infrared radiation produced by the flashlamp pumped pulsed laser such as the Nd:YAG has become a popular choice for

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81 LIBS due to cost and simplicity. 12 Extremely high electric field magnitudes can be produced by these lasers and used for triggering a dielectric breakdown in gasses and other non absorbing media. The dielectric breakdown of purified, filtered air and subseque nt plasma formation using a focused laser beam occurs in stages. The first stage of plasma formation after focusing a several nanosecond long laser pulse into a medium involves single and multiphoton absorption processes which lead to the initial ionizatio n or overcoming the dielectric breakdown threshold of the medium, both of which can produce free electrons. These initial processes are as much frequency dependent as they are timescale dependent. Following the creation of free electrons, inverse bremsstr alung processes become the dominant energy transfer mechanism and lead to cascade collision ionization from highly energetic electrons. This causes a rapid growth in the free electron number density. This volume of free rapidly increases and can effectively absorb the remainder of a laser pulse. This absorption of photons and intense electron heating causes the rapid expansion into the surrounding environment. What follows is the propagation of a shockwave and sonic expan sion of the plasma volume creating a large pressure gradient inside and outside the shock front. This leads to a rarefication of the volume inside the shock front, helping to drive the expansion of the plasma volume. The plasma expands rapidly at first the n assumes an almost constant volume, cools and rarifies, eventually recombining to form neutrals species. The recombination and cooling is later followed by aggregation and condensation. This is the life of a laser plasma created by typical nano second pul ses.

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82 Thus the laser plasma formation is not simply a result of dielectric breakdown but is a cascade of events leading to a dense, hot plasma with typical temperatures on the order of 10 4 K and electron number densities, N e of 10 17 10 18 per cm 3 which even tually withers away. These processes require a higher fluence in pure gasses than the same laser focused into a volume of gas containing micro particles. 37 The effects of wavelength and laser fluence required to consistently form a plasma in a particle containing atmosphere were studied by Pinnick et al 54 described with respect to J/cm 2 required for initiating the plasma event. This wavelength dependence was attributed to local field enhancements. 55 The primary reasons parti cles lower the threshold energy is the exhibition of higher extinction coefficients due to scattering phenomena which can be nonlinear or single photon processes. Simply put: the presence of particles makes it easier to deposit energy. This leads to heatin g of both the particle and the gas surrounding the particle. Energy transfer processes are enhanced and thus lower irradiance is required for plasma formation. These processes are discussed in greater detail in Appendix C. Resonances can occur with certain particle sizes when compared to the excitation wavelength further increasing the electric field magnitude and Q ext 56 The presence of particles can lower the threshold at a given wavelength by up four orders of magnitude, from 10 10 W/cm 2 to 10 6 W/cm 2 depending on diameter and laser wavelength. 57 As particle sizes grow past a certain size it is reasonable to assume they might act as a bulk, con tinuous samples which are in fact nothing but very large particles. Particle LIBS Laser Induced Breakdown Spectroscopy, LIBS, has been used for compositional

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83 by Radzie menski et al. 58 Today the laser plasma is used to both produce aerosols and to evalu ate their physical properties. 4 In the case of the hyphenated LIBS technique, laser ablation LIBS, the production and subsequent LIBS analysis of an aerosol from a matrix is used to decrease matrix effects found when directly sampling a solid. 59 The analysis of aerosols presents with a unique set of challenges for the LIBS community. Hahn and Omenetto describe these at length in a recent review of LIBS in a section ded icated to aerosols and bioaerosols. 2 3 Among the list of concerns are the intricacies of the related sampling statistics 31 stemming from the discrete nature of the LIBS aerosol measurement and the effects of maximum mass loading 15 of a laser plasma by the aerosol. Amodeo et al report a method for the analysis of aerosols composed of nano picometer diameter sodium chloride and metal particles and indic ate that at low mass loadings measurement times become a concern. 60 Diwakar et al. describe both diffusion 61 and the appropriate sampling statisti cs for the analysis of aerosols at length. 9 In each of these studies the effects of particle plasma interactions were in vestigated. It is noteworthy that previous reports on the limitations of size for quantitative analysis refer to particle size identification and not specifically for quantified compositional analysis of the aerosol. As alluded to earlier, all bulk samples are particles, though they may be quite large. A topic receiving much less consideration recently has been the effects of the direct laser particle interactions in the LIBS aerosol system. A review of the laser matter interactions in which the energetic pathways are described was produced by Lushnikov and Negin. 5 Theoretical modeling of field strengths and temperature gradients leading

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84 to phase explosions within microspheres was considered by Belov before Radziemenski an work on the topic. 62 The effects of resonance and refractive index were later calculated as well. 63 64 Pinnick et al. showed experimentally the dependence on wavelength and particle diameter on the dielectric breakdown threshold. 55 56 The LIBS l aser particle interaction is an event that requires a focused, pulsed laser to be coincident with a particle whose cross sectional area is on the order of 10 12 m 2 an event which, statistically, can occur in all LIBS aerosol measurements. One approach in the literature for this measurement which has gained traction is the falling droplet method. One produces a droplet at a known time and height and delays the firing of a laser to produce a coincidence. This method suffers from several drawbacks including t he lower size limit for particle production and deviations from an ideal trajectory caused by Stokesian dynamics. Another consideration is the irradiance used for the aerosol measurements. The effects of seeding a plasma with particulate matter are well kn own and discussed at length by Radziemenski, Lushnikov and Pinnick and reported as early as 1982. 3,12,17 With these effects in mind, laser particle interactions should only be observed when operating at laser irradiances below that required for dielectric breakdown of the gaseous matrix. This type of measurement will be referred to as below the breakdown threshold BBT, in this work with ABT representing irradiances above the dielectric breakdown threshold The schematic and operational parameters of the q uadrupole electrodynamic balance for application in LIBS aerosol analysis along with initial results were first presented in 2010 at the Winter Conference for Plasma Spectrochemistry. 65 Recent LIBS aerosol work by Dutouquet et al. use a balance operated in vacuum and at radio frequencies, both requirements for

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85 confinement of charged aerosols and microparticles with large S toksian drag parameters and low m/z. 26 It is the purpose of this work to provide and characterize a method of analysis to consistently study the laser particle interact ion and the events leading to a robust laser plasma using a quadrupole, double ring electrodynamic balance. Experimental Details and Discussion With the particles and parameters of the VOAG characterized and the function of the trap demonstrated, an ablat ion laser and optical collection system was incorporated. It was necessary to fit the Balance chamber on an X Y Z stage to allow for fine way hub to which a deceleration chamber and cap are attached in the top axial position. Three equatorial positions are fitted with S1 grade fused silica windows and the lower axial position has been fitted with a regulated gas inlet for trap flushing and gas replacement. The remaining equatorial positi on mounts the balance electrodes using a vacuum flange fitted with 2 BNC connectors for electrical connection. Optical Arrangement Three laser systems are used for the LIBS experiments. Two systems are used for illumination and positioning, and one for abl ation. The ablation laser is a Q switched Big Sky Ultra Nd:YAG operating at the fundamental and fired by remote trigger. The Nd:YAG is reflected off a dielectric mirror, which is transparent at 632 nm, prior to focusing into the chamber. The 1064 YAG pulse energy is measured using a S cientech model 200LA pyroelectric power meter and the beam waist by measuring the minimum hole diameter produced in a paper sample in the focal plane within the trap. This is also

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86 calculated from from the equations describing a diffraction limited beam. The calculation (4 1) (4 2) (4 3) (4 4) A HeNe is made to co propagate with the Nd:Y AG by transmission through the dielectric mirror. The collimated HeNe scatter from the target particle is back collected through the focal lens using a pierced mirror and its intensity observed with an Ocean Optics spectrometer. This allows the particle po sition to be optimized within the beam prior to ablation for each particle. The Spectra Physics model 117G argon ion laser was used for illumination through an Ocean Optics fiber optic with a divergence of 25.4 degrees and core of 400 micrometers. This pro vided total chamber illumination. The setup is schematized in Figure 4 1 with individual optical elements described in Table 4 1. Breakdown Threshold measurements The dielectric breakdown threshold in the trap was measured by observing the pulse energy bot h before and after the trap. The front window remained and the electrode pack was removed for these measurements. The results are seen in Figure 4 2. At a setting of 5.5 which corresponds to 35 mJ, intermittent breakdown was observed which is regarded by Chen et al. to be the breakdown threshold for the gas. 66 At a setting of 6.5 which corresponds to 40 mJ, an optically thic k plasma was

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87 consistently formed, absorbing a significant fraction of the incident radiation for all subsequent energy settings. Laser pulse energies below 35 mJ/pulse are used for studies below air breakdown threshold (ABT) and pulse energies above 65 mJ/ pulse are used for above breakdown threshold measurements (ABT). It is a convenient fact that the air breakdown threshold occurs at the midrange or the laser output energy. An analogous measurement was performed in pure argon displacing laboratory air thr ough the regulated gas inlet. Plasma images were taken while flushing the trap to demonstrate the effects of lasing in a seeded cavity when operating above the breakdown threshold for the pure gas. It can be seen that the plasmas formed are highly erratic spatially. If the laser fluence is great enough, ultimately these plasmas will expand, engulf each other and become one large elliptical pla sma. The micro plamas shown in F igure were generated with 85 m/J per pulse and are seeded in such a way that the fus ion never occurs. Using this arrangement, t he breakdown threshold for argon occurs at 80 mJ / pulse at the laser head this value being greater than that measured in clean lab air. Figure 4 3 shows that as the trap is flushed the irregularities of plasma s eeding disappear. Laser Pulse Shapes The laser profile was measured as we ll using a fast rise time photo diode whose rise time is <200 ps and a TDS 520D 500MHz 1Gs/s Oscilloscope externally triggered by the Q switch sync output from the Big Sky Ultra. This trigger scheme is preferable to that of triggering by the pulse in that the pulse width and decay with respect to Q switch trigger in can be observed. Figure 4 4 shows the results of these measurements. The detector was tested for linearity using Thor Lab s .3 ND filter. The pulse energies were adjust ed (increased) by changing the Q switch delay time via the factory recommended

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88 front panel control with arbitrary units ranging from 0 10 in increments of 0 .5. Lasing output was not observed below a setting of 3.5. Maximum output is obtained with a flash lamp to Q switch delay of 163 s. As the Q switch delay is increased, a decrease in laser output is observed along with pulse stretching. A minimum FWHM pulse width of 7.8 ns is obtained when the maximum energy and minimum Q switch delay is used. A maximum FWHM pulse width of 55 ns is obtained at the maximum Q switch delay. Time Integrated Measurements Measurements of spectral emission are typically collected as time integrated, spectrally resolved or as spectral ly integra ted temporally resolved signals It has been shown by Carranza et. al. that while iCCD cameras provide significantly more gain on the signal, CCD detectors provided a greater signal to noise ratio. 67 A system which us es a photomultiplier or any other continuous detector will be locked spectrally for each measurement, its spectral integration determined by the instrumental bandpass. These measurements were carried out with an Ocean Optics LIBS 2000 spectrometer. The in strument incorporates seven broadband, high resolution spectrometers which provide a spectral resolution of .1 nm and a spectral range of 200 900 nm. All channels are triggered by the same clock and provide a spectrometer to spectrometer jitter of less tha n 20 ns. The system has a fixed integration time, t g of 1 ms and a variable delay time, t d This ensures that regardless of the t d value, the entirety of the emission signal will be integrated. The plasma emission signal is back collected using a pierced mirror. The plasma emission is collimated by the same lens used to focus the excitation laser and the pierced mirror projects it onto a heptafurcated fiberoptic cable coupled to the spectrometer module. The pierced mirror collects the emission from the dir ection of

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89 beam propagation in order to collect consistent signals with small particle spacial fluctuations. Real time images and snapshots are acquired using a Supercircuits PC 243C CCD color video camera. Particle Plasma Measurements Measurements for par ticle plasma interaction were conducted using a laser energy of 65mJ/pulse at the sample which corresponds to the maximum output of the Big Sky Ultra output. This provided 300 GW/cm 2 to the beam waist. Particles were suspended in the balance and aligned wi th the HeNe beam. Once the particle scatter signal was maximized by monitoring the output of the LIBS 2000 spectrometer, the Nd:YAG was triggered, creating a large luminous plasma in the vicinity of the particle. (Figure 4 5) A LIBS spectra was recorded fo r each laser shot. Every laser shot removed completely the particle in the balance. The process of particle capture, scatter signal maximization and signal acquisition was repeated for 50 particles per set. The V DC offset voltage was monitored for each par ticle ensuring similar m/z The calcium chloride particles described and characterized in T able 3 2 were used for these measurements. Laser Particle Measurements Measurements for the laser particle interaction were conducted using a laser pulse energy of 3 0 mJ/pulse. The procedure is the same as for the above breakdown threshold measurements with the exception of laser energy. While this energy is below the breakdown threshold of purified, filtered air, this energy provided sufficient fluence to initiate th e LIP on the particle. Without a particle in the beam waste of the Nd:YAG there is no emission signal as there is no plasmas formed. The laser was free run to ensure this condition prior to sampli ng. This effect can be seen in F igure 4 6. The calcium

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90 chlor ide particles described and characterized in T able 3 2 were used for these measurements. Results and Conclusions In order to verify that the operational conditions provide a laser particle interaction between the particle and the excitation pulse, the cham ber was flushed and moved 0 .5 mm from the HeNe beam and the excitation laser fired. No luminous plasma was observed and no signal recorded on the spectrometer. The same particle was moved back into the HeNe and its scatter signal optimized. The particle was completely ablated upon triggering of the excitation beam. As seen in Figure 4 6, an intense LIBS emission signal representative of calcium chloride was recorded. Ense mbles of 25 spectra were recorded and averaged for each particle diameter. Effects of the EMF in the Balance Particles and plasmas confined by a quadrupole experience many forces from external fields and from collisional interactions. The equations of mot ion described by Davis 28 consider gravitational and electrical fields as well as Stoksian drag, which can be a restorative force in s. Drag effects are reduced in reduced pressure In the quadrupole field within the EDB or any quadrupole, there is no potential with respect to ground only at the centroid of the field. For all other space there exists a field gradient. A one needs for each field present two state variables to describe the state of the system. Thus a plasma state may not be defined for a plasma in such a field using only pressure and temperature. (4 5)

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91 In the case of the EDB we may need the external electric and magnetic field magnitude T he associated torque on the plasma has been shown to significantly alter the emissions of some eleme nts 68 The effects of the electric field were studied using a triggering mechanism which can consistently trigger the laser at any phase angle of the high voltage AC carrier designed through collaboration with electrical engineer, Steve Miles of the UF department of chemistry Electronics Shop Signal to background ratios are taxen and the argon ion line at 488 nm is observed for any change in intensity. There are no visible effects from this other external field on laser plasmas in the canter of the trap at any phase angle, though other positions were not tested. ABT v. BBT Representative spectra are pres ented in Figure 4 7 from the LIBS analysis of 9.8 2 particles with the laser operated at 35mJ/pulse for set (a) and 85mJ for set (b). The spectra are presented sequentially in the order of ablation. Using the EDB we have a 100% direct particle hit r ate, eliminating the need for complex sampling statistics or processing to discriminate hits and misses. ABT spectra are marked by a higher continuum contribution compared to BBT spectra as well as a higher variance in the emission signal from particle to particle. The higher continuum contribution is not unexpected at higher fluences as more radiation can be absorbed by the plasma after formation. On initial observation of the data in Figure 4 7showing the LIBS emission signal and a significantly larger variance in the emission signals across the set of ABT measureme nts. The most dramatic noise is at the calcium emission lines. Causes of this variance cannot be completely attributable to the indiscriminate formation of a

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92 plasma in the trap. As with BBT measurements, small variations in the position of the particle wit h respect to the plasma provide large fluctuations in the interaction of the particle and the LIP, but this position is highly controlled. Apart from the high RSD in the calcium lines, another feature stands out. The hydrogen beta emission is consistent ly visable across all of the ABT measurements and yet it stands out as a 36% RSD above the background in the BBT measurements. Our sample, CaCl 2 is used as a desicca nt due to its hygroscopic nature. Desolvation of the CaCl 2 containing droplets will thermody namically first produce CaCl 2 2 O. Particle Size Limits Analysis of the RSD per pixel for 14.3, 9.8 and7.2 emissive volume. The RSD plots show that the noise in the signal is equivalent to the noise in the continuum. This indicates that there are no significant fluctuations in the calcium emission compared to that of the continuum. This trend results from complete incorporation by laser ablation and subsequent plasma formation. The same 7.2 micron particle ablated by a 35 mJ/pulse excitation show an increased RSD at calcium emission lines and hydrogen 656 showing the variation of signal associated with incomplete ablation processes. These effects only become more pronounced as particle diameters increase. A classic calibration demonstrating this e ffect could not be constructed using the becomes all but impossible due to field imperfections from the hand wrought electrodes. Aerodynamic drag forces begin to dominate the

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93 at low masses. A maximum frequency of 400 Hz and atmospheric pressure conditions are the limiting parameters. Limits of Laser Particle Interactions For plasma particle interactions, Asgill showed that the particle size limits are diffusion and heat transfer processes limited. 15 The plasma contains the energy absorbed from the pump source and transfers this into the particulate. Ther e is no energy directly transferred into the particle from the laser source with the exception of the occasional particle being in the beam waist which is a statistical occurrence. The laser particle hits are attributed as a noise source by Hahn and Niema x. 61 In the EDB we have direct laser absorption in the particle which we hoped would allow for complete ablation of larger masses, which would extend the dynamic range for quantification above those reported by Hahn and Omenetto. 3 Having been previously reported that an upper size limit for quantification exists from 2 The enthalpy of vaporization of is calculated from enthalpies of formation values tabulat ed in the Journal of Physical Chemistry Reference Data and found to be 1216 atomize. 69 Our excitation pulse is 85mJ for the ABT measurements and 35 mJ for BBT, both a full three orders of magnitude greater tha t the required energy for complete vaporization and atomization. As the mass of a spherical particle increases with the cube of the radius, a linear relationship should be observed when plotting signal intensity versus particle radius cubed. Non normalize d ensemble averages for sets of 20 particles of each diameter,

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94 7.2, 9.8, and 14.3 m, are presented in Figure 4 9 for laser energies BBT. It is readily observable that the expected cubic relationship in signal intensity and diameter does not exist for any calcium emission, indicating that a linear relationship between mass and signal intensity does not exist when operating below the breakdown threshold and supplying three orders of magnitude more energy than that required to potentially generate such a tren d. Closer examination of the nature of the laser particle interaction and its fundamental differences to that of the plasma particle interaction with respect to relationship between a large micro particle and the bulk material offers a rationale behind t his effect. The apparent energetic dilemma can be explained by following the energetic pathways as described by Lushnikov and Negin 5 The calculation for the enthalpy of vaporization does not incorporate the energy requir ed for ionization or any energy losses to the surrounding in the form of convection, radiative losses, ionization of the surrounding gasses or transmission of the excitation pulse prior to dense plasma formation, nor does it consider the proportion of the beam which can interact with the particle. Consider that in these experiments, the beam diameter is up to 10 times that of directly deposited on the particle increases p roportionally to the square of the particle radius, but the particle mass increases cubically, respectively. It follows that the photon to atom ratio, PAR, available for excitation decreases as particle diameters increase for any given pulse shape.(Figure 4 10) The photon atom ratio is a concept introduced by Stipe et al. 70

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95 A second equally i mportant consideration is that of the transition from absorption of laser energy from the particle to the inverse Bremsstrahlung processes after the formation of optically thick plasma at the excitation wavelength. It is this decoupling process that termin ates the laser material interaction in a traditional bulk sample, and it is this mechanism that limits the laser particle interaction time to the same timescale The processes for plasma formation and propagation via a nanosecond pulse are absorption, heat ing, and cascade ionization rapidly followed a decoupling of the laser. These events can take place long before the pulse could 3 the energy required for full plasma incorporation, it simply cannot reach t he sample to accomplish these processes. Thus all events wh ich involve plasma formation fro m laser particle interactions inherently undergo plasma particle processes as well when the particle mass is not completely laser ablated by the laser Third, we co nsider the scatter cross section for a representative spherical particle and the air using Mie Theory and a n algorithm developed by Laven 54 in order to determine th e proportion of light which can be absorbed by varying diameter particles, Q abs (a). Using published values from CaF 2 as a surrogate for CaCl 2 ,which has limited information regarding the complex refractive index, the average absorption is found to be appr consistent from one particle to another since in the Mie regime the scatter cross section increases with the square of the radius. Figure 4 11 offers an optimistic maximum val ue of 7% by Q abs The same calculation was done for a sphere of superheated air at 5000K

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96 and plotted along side Q abs for the particle. It is concluded that absorption by air offers an insignificant contribution to the heat transferred to the particle for p lasma formation. The fourth and likely the most critical consideration regarding the laser particle interaction and its differences from the plasma particle interaction involves the breakdown threshold and the irradiance (W/cm 2 ) required We consider a pu lse with a 4 ns FWHM as shown in Figure 14 with an irradiance just below the dielect ric breakdown in air Knowing the square dependence of the extinction coefficient with radius, the results presented by Weyl 57 and the threshold measurements by Pinnick 55 and the absorption trends shown by Chen et a l. 71 can be combined into Figure 4 12. For this pulse, the amount of time during which the laser can interact directly with the particle is limited by the characteristic time it takes to achieve the critical irradiance, form an optically dense plasma, and change the scattering scenario from that of particle dominated scattering to that of plasma dominated scattering mechan isms. After this time only photons not scattered by the plasma can reach the particle. It is this decoupling of the laser from the particle surface which limits the laser interaction and the mass ablated via the interaction. After the absorption processes are dominated by inverse Bremsstrahlung processes. T he rapid, the fluid dynamic expansion of the vaporized mass decays to an equilibrium state and further mass removal should be considered by diffusion models as per Asgill and Hahn. 61 A direct result of this characteristic time is that in ord er to extend the linear dynamic range of aerosol analysis into larger particle sizes, it is not necessarily more energy we require, but more time for deposition of the energy from the laser pulse. Long er pulses with lower peak power will provide greater ma ss action.

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97 A second consequence of this critical time is that every laser particle interaction which forms a plasma must then be a plasma particle interaction, creating two clear regimes for the processes which dominate. We are lead to revisit and clarify the terms ABT and BBT and the conditions that follow from each. Clearly, if a plasma is to be formed, the dielectric breakdown threshold must be breached. Energies ABT will form a plasma with or without the presence of a particle while BBT will not. In bo th cases the energies are above the dielectric breakdown threshold for the particle/air system. In both ABT and BBT measurements we always have a direct particle hit, i.e a laser interaction followed by plasma interaction. Thus, the primary difference is the ratio of energy absorbed by the particle to energy absorbed by the plasma and the energetics can then be defined by plasma dominated events or by particle dominated events. Long pulses offer a greater amount of time for the laser to interact with the particle directly. The last consideration on the limits of particle size involves the excitation wavelength. Infrared excitation at 1064 nm has, as a consequence of its frequency, some of the least desirable effects when applied to LIBS laser particle ana lysis. The frequency has a poor absorption cross section for the analyte and a very high absorption cross section for the plasma. In fact, examination of collider resonance conditions shows that the higher is the excitation frequency the lower the plasma absorption cross section will be. Partial Particle Ablation When performing BBT measurements well as other diameters it was necessary to position the particle exactly in the center of the 1064 nm beam. In one study the particles we re placed on the beam edge to investigate the resulting effects. When this was done, the particle could be partially ablated in a way

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98 that gave a LIBS signal and left part of the particle remaining in the trap. Since a luminous plasma would form indicating particle contact and the LIBS signal showed the interaction and that mass was removed in order to provide the calcium signal. What was unexpected was the resulting behavior of the particle. It remained vertically centered in the balance indicating that the mass to charge ratio remains constant after partial ablation with 1064 radiation. As a rule: the volume of a sphere is reduced cubically with respect to the radius a The c harge on these particles was assumed to reside entirely on the surface which would decrease quadratically with respect to a which is not expected One explanation is that of a uniform charge distribution throughout the particles. Conductive spheres produc ed from the conductive solution should have a uniformly distributed electrical charge. Even dielectric spheres of CaCl 2 should provide relatively smooth distributions. Another possible explanation is that the 1064 radiation induces a local dipole in the ch arge sphere causing the local charge on the particle to be lower in the vicinity of the ablated material. This measurement was repeated several times and recorded in live video. Micro particle Generation Following ablation of all particles a flow of part icles is observ ed traversing the z direction on either side of the balance rings after approximately 420 ms and rapidly moving. The motion of these particles is unperturbed by the electric field on the rings indicating that they are electrically neutral. T hese observations were made using the CC TV camera originally intended for alignment purposes.

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99 Table 4 1. Description of optics used for alignment, ablation, and signal collection to be used in conjunction with Figure 4 1. Optical Element Description Dia meter Focal Length (F#) Material L1 BCV Lens 50 50 (1 .0 ) S1 Fused Silica L2 PCV Lens 50 120 (2.4) S1 Fused Silica L3 PCV Lens 25 80 (3.2) UV/AR Quartz L4 PCV Lens 25 120 (4.8) UV/AR Quartz L5 BCV Lens 25 110 (4.4) S1 Fused Silica M1 / M4 Mirr or 50 N/A Coated Aluminum M2 Dielectric Mirror 25 N/A Coated BK7 M3 Pierced Mirror 300 x 300 N/A Coated Aluminum P1 Dove Prism 30 N/A BK7 F1 Fiber Optic 1.00 ( 0 .22) UV Vis XSR F2 Fiber Optic 0 .400 ( 0 .22) UV Vis highOH

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100 Figure 4 1. Opti cal setup for LIBS signal collection Laser paths are shown with red arrows. Signal paths are shown with blue. 632 and 1064 nm laser beam s are made to co propagate on the primary optical axis and focused on the sample volume. Collimated plasma emission is back collected with the pierced mirror and F matched to an optical fiber and spectrometer.

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101 Figure 4 2. Measurement of the breakdown threshold in laboratory air is shown. Unfiltered Lab air was measured to ensure that chamber s eeding would not cause spurious plasmas to be formed when performing BBT measurements.

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102 Figure 4 3 Laser Pulse Shapes. Changing the pulse energy by controlling the flash lamp to Q switch delay causes both pulse stretching and increased the tim e from Q switch trigger to pulse output. FWHM values range from 7.8 55 ns. The observed undershoot is due to operation of the detector in photovoltaic mode v. operation with a forward bias.

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103 Figure 4 4 As argon flushed the cell the effects of chamber seeding diminish, eventually allowing the formation of a single plasma. The 488 nm emission line on argon is shown here centered as a spectral image. The scale is approximately two centimeters from top to bottom.

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104 Figure 4 5 The HeNe sign al used for targeting is shown here. In the bottom trace, the only signal recorded is from the Fresnel reflection from the front window on the balance chamber. Upon illumination of an incident particle centered in the balance the signal reaches a maximum. This condition is repeated for each partice.

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105 Figure 4 6. Signals here result from below breakdown threshold measurements using a broadband spectrometer. In the absence of a particle, no plasma is formed and no signal is generated. Using i dentical conditions with the introduction of a particle in the laser focus yields a luminous plasma formed from the interaction of the laser with the particle.

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106 Figure 4 7. Representative spectra for BBT (a) and ABT (b) LIBS measurements on 9.8 icles. The two general trends observed from ABT and BBT measurements for all particle diameters are that pixel by pixel RSD increases as laser energy decreases and as particle size decreases.

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107 Figure 4 8. Demonstrating the significa nt differences in %RSD and noise trends in measurements made ABT and BBT. ABT spectra generally show a greater variation in the calcium emission signal with respect to the background. There appears to be a significant vari ation in the hydrogen emission in BBT interactions. The exception to the rule is 6 ABT.

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108 Figure 4 9. Here the ensemble averaged spectra for nominal 7.4 (a), 9.8 (b), and 14.3 emission of calcium, there is no visib le trend suggesting a relationship between mass and signal intensity.

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109 Figure 4 10. As the particle diameter increases the mass increases cubically (dash) while the cross section in the excitation beam increases quadratically (solid). Volume and cross se

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110 Figure 4 11. Plotting Q abs v. particle size parameter shows that the extinction coefficient for differing particles of identical composition can be substantially different. Ablation processes decrease the particle diameter making the interaction uniquely dynamic.

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111 Figure 4 12. Comparing the irradiance of a pulse to the threshold for plasma formation crit which defines the termination of the direct laser particle interac tion.

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112 CHAPTER 5 STATISTICAL CONSIDERATIONS FOR LASER PARTICLE AND PLASMA PARTICLE INTERACTIONS Introduction Each LIBS spectrum collected from a sample is taken from a unique experiment conducted with one unique sample interface configuration and one las er pulse. The inherent noise in the spectral data and the way in which that noise propagates into the uncertainties for absolute sample quantification is one of the primary reasons LIBS is not yet widely accepted as a quantitative analytical technique. Sam ples are most often collected by averaging an ensemble of spectra collected through repeated experiments. 72 The ability to accurately represent information about sample compositions is limited by an analysis of the noise composition of different signal components either by the variance in normall y distributed data, comparison of relative standard deviations or by inferences from a calibration graph. 73 Work by Michel and Chave show explicitly that the assumptions of normality are not always applicable. 74 Attempts to correct for shot to shot fluctuations in signal and background intensity have been made by considering the signal to background ratios, multivariate analysis, and even acoustics considerations. 75 76 77 Each of these methods is a normalization process. Poussel and Mermet note that for low concentrations, using a peak to background ration appears to lower the LOD. 78 The P/B method as well as S/N and averaging were compared for gaseous and particulate systems by Alvarez et al 79 Ingle and Crouch offer an ex ten sive treatment of statistical considerations for spectrosc opic analyses. 80 LIBS nowadays vary from the analys is of soils, complex organics, recyclable materials and other materials which are highly amorphous and/or do not have matrix

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113 matched standards available 81 82 LIBS is even being applied to molecular systems such as explosives and bio weapons. 83 84 R esearchers are depend ing on more rigorous chemom etric methods which combine multivariate normalization and techniques such as principal component analysis or singular value decomposition to pull important information out of the seemingly noisy mess that the ensembles of spectra can produce. 85 86 These methods are often effective because, while not immediately obvious in the spectral data to the casual observer, each spectral component has an intrinsic interdependence on an another. Ju st as the spectral features are intertwined, so must be the processes that govern both plasma particle and laser particle interactions. When laser plasmas are formed in air we should expect to see emission from nitrogen and oxygen, the primary components o f our atmosphere. In Florida and other damp environments it is common to see a significant contribution from water vapor as well. Trace elements can also appear such as carbon from CO 2 87 When laser plasmas are for med on or adjacent to bulk samples we expect to see emission from the representative constituents in that particular sample as well as the surrounding environment. The net signal will contain some combination of sample and environment. This emission intens ity interdependence is highly correlated to where and how one focuses the laser on the sample. It is common practice to have a bulk sample positioned such that it lies on a plane some few millimeters before the actual focal length of the lens used for the excitation pulse. It has been noted that the sound of the shockwave from the LIBS event can be directly related to the emission. 88 76 LIBS operators are likely familiar with the dramatic audible changes which occur from slight changes in sample depth. If a laser is

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114 operated at pulse energies that breakdown air at the focus, it makes sense by our last conclusions that one should have the sample in a location which the plasma is formed only by interaction with the sample and not the atmosphere. Due to the transition of energy deposition mechanism at the onset of an optically dense plasma and the orders of magnitude differences in the critical irradiance required to initiate dielectric breakdown on differing media, the total energy of the plasma analyte system can be greatly affected by very small fluctuations in space or peak pulse power With particles the sample depth as well as the radial positions within the beam can create signal variances. An e xtreme case of position sensitivity is the hit no hit comparison in exemplified in work by Carranza et al. for on online particle monitoring. 31 No particle returns no signal. In the present work, this issue has been all but eliminated by the sampling methods, bu t large signal variances are still present despite the careful positional control. In plasma systems we have at least two processes occurring either simultaneously or sequentially A plasma must be formed, clearly, but whether the plasma is formed in air s imultaneously with the plasma formation from the particulate matter is an interesting consideration. For both ABT and BBT the processes were originally considered as being coincident. In order to determine the interdependence of the events we use several s tatistical approaches originally presented in an unpublished work by Omenetto and in the theses presented by Heh Young Moon. 89 The considerations compare how the noise in the signal and the noise in the background are related in order to make inferences about the spectral information and vice versa.

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115 Theory Noise in any measured value is comprised of se parate components or types having definite origins. An instrument has a certain level of signal fluctuation even in the absence of any signal input. This type of fluctuation is specifically referred to as dark noise. Adding an input signal may or may not a ffect the dark noise. If the signal does not affect the dark noise we say that the two types of noise are uncorrelated. A signal itself may have a component such that there is a system response in the absence of an actual signal. This type of response is k nown as the background. Each type of response can have its own associated noise and may be correlated or uncorrelated. The effects of this can be seen from the definition of error and the rules for propagation of error. The error in an arbitrary response f unction composed of only signal noise and background noise is found by differentiation and application of the chain rule and given by Eqns. 5 (1 3): (5 1) (5 2) (5 3) Correlation Theta is defined here as the correlation coefficient and has a range of 1 to 1. When is zero we say that the errors are uncorrelated and the errors can be calculated simply as the RMS noise and will be considered from here out as SD. RSD are calculated by the wavelength to wavelength (pixel to pixel) ratio of the SD to the mean.

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116 Without some assumptions or a priori knowledge, the correlati on coefficient shown in Eq. 5 3 is unsolvable as we cannot directly measure the noise in the background under a peak. For LIBS measurements it is accepted to take the off peak continuum intensity as the background intensity for the line and the associated noise. When considering two or more events occurring either simultaneously or independently we can consider the dependence of one event on the other by calculating the correlation coefficient between the two events, in particular the Pearson Product Momen t Mean, since the definitions are equivalent. (5 4) Methods The correlation coefficient, is calculated using two approaches in order to determi ne the relationships between signal and background and represented in Figures 5 1 and 5 intervals which include both S and B. The maximum is determined by careful observation of the L is determined to be 16 pixels. A signal array, X i is defined at pixel one and a background reference array, Y i at X i + i = X i+16 was then plotted with respect to wavelength. In the second ap proach four lines corresponding X and calculated with respect to each Y i between the emission of each signal datas et ABT(6,9,12) BBT(6,9,12). The average spectral intensity, SD, and RSD of each set is also calculated in a similar fashion.

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117 Lines Used: Ca(I) 633.9 nm Ca(II) 373.7 nm N(I) 744.2 nm N(II) 500.0 nm H( ) 656.3 nm Results and Discussion The lines that were chosen for correlation analysis are of interest as they represent species that all show strong emission from the plasma and which must have different origins. In filtered laboratory air it was observed that nitrogen is present but not calcium. Any calcium emission observed is representative of the particulate loading and nitrogen emission is representative of the air plasma. The following trends are observed. Ca(I) :Y i Sample : sample / plasma Ca(II):Y i Sample : sample / Plasma N( I) :Y i Plasma : sample N(II) :Y i Plasma : sample H( ) :Y i Moisture : sample/plasma Several themes are observed from the statistical analysis which produce SD and RSD plots. First, the RSD plots for BBT show smaller variance in emission lines than those RSD plots for ABT.(Figure 5 3) In ABT RSD measurements are typically higher than that of the continuum while BBT shows positive and negative deviations with respect to the background. Second, the standard deviation of pixels corresponding to e mission lines is always greater than that of those containing only continuum. Plots of show excellent correlation between background noises from the blue up to 630 nm though a different trend is observed in the red to NIR. This proved to be a good proof of concept for the correlation algorithm used. These data also indicate

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118 an incr easing correlation of (S+B):B as the photon to atom ratio increases. That is to say that as the pulse energy increases there is an increasing relationship between the emission of calcium from the particles, the nitrogen from the plasma and the hydrogen w hich can originate from both vapor laden air and the particles. 4. The spectral oxygen. Looking at 656.3 H( ) in the ABT cases (black) the increase in correlation in from N(I): Th e increase of correlation in the H( ) noise is clearly visible as particle size decreases. In the case of BBT measurement the Noise correlation remains relatively constant and exhibits a high 0 .9 in the vicinity of H( ). T he range of 642 nm to 650 nm contains several e mission lines of calcium. T he FWHM of the noise bandwidth associated with the calcium lines decreases and the correlation of those emission lines to the nitrogen emission and the continuum increases as particles get smaller. In Figure 5 5 the noise in the hydrogen emission signal is compared to the spectral window containing N(II), Ca(I), and plasma continuum. The data indicate that ABT, the larger the photon to atom ratio, PAR the higher the correlation between H( ) emission noise and N(II) emission noise at 500 nm. I n the ABT measurements, there is also a monotonic increase in the correlation between H( ) and the continuum emission. BBT measurements show a consistently high correlation between all emissions. Two c onsiderations can explain the processes at hand. First, in the plasmas that are formed the free electrons which contribute to the continuum can come from either the ionization of the surrounding gas or from the ionization of the target particle. Secondly, the hydrogen can come either from the hydrated calcium chloride crystal or from the vapor

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119 laden surroundings. In the BBT case we know that the peak laser power is insufficient to cause a dielectric breakdown only in the surrounding gas; this is an experi mental requirement. It follows that the free electron contribution as well as the hydrogen should come from the CaCl 2 This produces a high correlation between both the noises in the H( ) and the continuum regardless of the extent of ablation of the partic le. For the ABT, application of the same logic tells us that a plasma can be formed in the absence of the particle. A large robust plasma is formed from a laser pulse whose beam waist is an order of magnitude larger than the particle. The proportion of en ergy which is deposited in the particle to that deposited into the air plasma by the pulse is very small The plasma is dominated by laser plasma and plasma particle interactions and incorporates a significantly higher fraction of the free electron contrib ution from the surrounding gas es. This is clearly seen in the ABT 9 and 12 data. If the water comes from the particle but the electron density comes from the surroundings a low correlation between the noises in the two would be expected. Variations in pa rticle water content will cause uncorrelated noise compared to the independently varying gas plasma. The calcium neutral correlation to the continuum background, N(II) and other Ca(I) lines is shown in Figure 5 6 for 14.3, 9.8 and 7.2 m particles using 35 and 80 mJ per pulse of excitation energy. We see a monotonic increase in the correlation to the signal and background noise for ABT conditions. The correlation plots indicate that when ablating 7.2 m that signal (S+B) fluctuations in the signal are dependent on plasma processes (B) That is to say: when the continuum increases, the signal increases. The noise in the calcium lines is consistent with respect to the background

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120 and a S/B plot would improve the S/N compared to the average alone. In cases of larger particles this would not hold true. Comparison of the noise in the Ca(I) to N(II) for ABT shows anti correlation. An increase in c al cium neutral emission is accompanied by a decrease in the emission intensity of the nitrogen ion. This is explicable by considering the signal sources as we did for hydrogen. Both hydrogen and calcium come from the ablation and incorporation of the particle in the laser plasma. Conservation rules dictate that in increase in energy deposition to the p article necessitate s a decrease in energy to the plasma. Conclusions Noise correlation plots provide a means to interpret the interrelated processes involved in both laser particle and plasma particle interactions. Plasma particle noises a ppear to be unc orrelated while l aser particle noises appear highly correlated or anti correlated. When working with aerosols whose mass is too great to be fully ablated, the continuum noise (plasma background) and the noise from particle emission is enhanced by operating the laser BBT. This is the same situation observed when dealing with solid samples. You focus the laser into the sample at a depth before the focal plane. The spot size on the sample increases compared to being exactly at the focus The Irradiance drops, and the plasma formed has the highest laser sample interaction possible prior to laser sample separation and laser plasma dominated energy transfer mechanisms. As is the case for 7.2 m particles, when the particle is completely ablated by the energy depos ition, correlation is improved by increasing the amount of total ener gy in the system. Along with noise correlation, it is also important to consider the signal to noise. Figure 5 7 shows signal to background ratios for calcium neutral and ion lines and t he

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121 corresponding noise. Better precision is observed for BBT as particle size decreases while the reverse is observed for ABT. The calcium ion to neutral ration is shown in Figure 5 8 and indicates decreasing temperatures as particle size increases. These results are a topic for further consideration.

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122 Figure 5 1. The first method for calculation of the correlation providing

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123 Figure 5 2 The second method for calculation of the correlation providing

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124 Figure 5 3. Demonstrating the significant differences in %RSD and noise trends in measurements made ABT and BBT. ABT spectra generally s how a greater variation in the calcium emission signal with respect to the background.

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125 Figure 5 4. From top to bottom the plots show the correlation of N(I) emission at 744.2nm for 7.2, 9.8 and 14.3 m particles. ABT are shown in black and BBT in blue.

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126 Figure 5 5. From top to bottom the plots show the correlation of H( ) at 656.3nm for 7.2, 9.8 and 14.3 m particles. ABT are shown in black and BBT in blue.

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127 Figure 5 6. From top to bottom the plots show the correlation of Ca( I ) at 633.9nm for 7.2, 9.8 and 14.3 m particles. ABT are shown in black and BBT in blue.

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128 Figure 5 7. Signal to background plots for two major calcium neutral and ion lines.

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129 Figure 5 8 Calcium Ion to neutral trends for ABT and BBT measurements.

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130 CHAPTER 6 SIMULTANEOUS MULTI ELEMENT ANALYSYS Introduction The introduction of the gated CC D and iCCD camera systems as an effective and efficient optical transducer has allowed the LIBS community and other optical spectroscopies to perform many types of measurement with an ease and speed previously unattainable with earlier detector types. The CCD and iCCD cam era systems signal to noise was considered by Mueller et al. 90 and Carranza et al. 67 for steels with differing results. Mueller reports that the S/N is the same or bette r for a CCD while Carranza et al. show improvement for the iCCD. Granted, Mueller et al. worked on large bulk materials and Carranza et al. with aerosol laden air. Consideratio n s for the m easurements include an optimization of delay and integration times for signal collection of a calcium line. These optimizations would not be possible without time resolution. C ommonly reported in the LIBS literature by individuals using iCCD systems, the d etectors are triggered at time, t d after laser pulse initiation and the charge collected and integrated from the iCCD over a gate width, t g When used with a suitable spectrometer current iCCD array systems can provide either imaging or rapid broadband de tection at a particular time referenced to plasma initiation, t 0 Whether operating for imaging or spectral measurement, all space or time dimensions are recorded simultaneously. These qualities can be analytically advantageous and simultaneously quantitat ively an Achilles heel to any application which measures a dynamic process like the laser induc ed plasma as iCCD and CCD systems record the

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131 same interval for each spectral line that may or may not produce the optimal S/N for that particular species. Each LIBS experiment is an entity unto itself. Each laser pulse is unique; each laser pulse perturbs the sample causing the interaction to be unique. 91 The community has approached this issue statistically, relying primarily on S/N enhancement through signal averaging through enumeration of data from many excitation pulses or by single shot normalization methods While this is an effective approach for homogenous samples for which there are sufficient material and time required for acquisition there exist many applicati ons which this is not the case. Inhomogeneity in the form of inclusions or as layers can also c ause significant signal variance when sampling across them, causing misidentification. 92 93 94 In certain cases, most notably LIBS for aerosols, the sample is simply not massive enou gh for averaging multiple shots A CCD system simply cannot provide a complete representation of any event for any given plasma for two reasons. Firstly, time is treated as a scalar and secondly the measurement is only defined for predetermined gate. LIBS signals are also transient by nature and present limitations to the inferences which can be made about any single measurement from time integrated detectors. Also, situations exist in which this traditional sampling method is impractical or simply impossi ble. In the cases of LIBS methods for single particles, in aerosol analysis, or for industrial production lines, the sample exists in a different state immediately after measurement rendering ensemble averaging impossible. Carranza and Hahn 95 Gornushkin et al. 75 and Radziemski et al. 58 report in separate accounts that for diagnostic purposes it is often beneficial to record information about the plasma by

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132 sampling using time resolved measurements and in the case of single shot measurements time resolution is imperative for the improvement of sampling statistics. The physics of the laser plasma and experimental evidence both tell us that the average temperature and d ensity of the plasma decrease over time. 96 While the conditions in the very earliest times of plasma formation are often assumed 33 extensive work has been done to identify t he populations and densities of ions and neutrals within and around the plasma. In doing so, it has been observed through several studies that delay times can be optimized for different species in order to optimize S/N and sensitivity. 15 97 30 Fisher analyzed the emission signal decay of hazardous metals in order to optimize the signal to noise of their emission signals. Their results indicate the time delay selec ted for signal integration is species dependent. 97 Hohreiter and Hahn 98 describe a technique which uses time resolved measurements to investigate the relationship between single and double pulse LIBS measuremen ts as a tool to of ICP MS Groh et. al 99 s how using dual monochromators coupled to time resolved detectors that the transient response signal of aerosolized matter entering the ICP plasma could be monitored. Individual processes such as vaporization and ionization were charachterized from the part icle injection into an ICP flame by Neimax, et. al. The experimental requirements of multiple monochromators and multiple iCCD imaging systems, while effective, greatly increase the overhead of the measurement in both time and cost. This work demonstrates that analogus measurements can be simultaneously observe many species throughout the persistence of the plasma event

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133 and optimize each analysis for each species within a single shot event. Other methods simultaneous measurement of multiple emission lines. Variants such as these have been reported recently for alloy discrimination. 41 100 A Paschen Runge po lychromator fitted with 32 PMT detectors is used to simultaneously collect the persistence profiles of six elemental species in a laser induced plasma on pelletized samples and considered for use in the analysis of aerosols Calibration plots are generated and statistically analyze d to determine the optimal delay times and integration times for collection. Fitness and instrumental sensitivity are compared at varying delay times to demonstrate the independence of in the plasma emiss ion It is shown that by carefully selecting delay times and integration gates when collecting time resolved measurements that one can limit nonlinear effects on calibration curves such as self absorption and self reversal when dealing with frequency dep endent optically opaque plasmas. Experimental Considerations Two laser systems are used for the LIBS experiments. One system is used for illumination and positioning, and one for ablation. The ablation laser is a Q switched Big Sky Ultra Nd:YAG operating a t the fundamental frequency and fired by remote trigger. The Nd:YAG is reflected off a dielectric mirror, which is transparent at 632 nm, prior to focusing into the sample with an F/1 suprasil lens. The plasma emission is back collected and collimated usin g the F/1 focusing lens, reflected on a front surface U/V enhanced pierced aluminum mirror and condensed onto an Ocean Optics p 1000 2 UV VIS optical fiber with a 50ax120mm suprasil lens. A two lens system is used at the fiber output to create a region of collimation and create an f matched input for a

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134 polychromator. When needed, filters are always installed in the collimated region. This collection method reduces effects signal variance due to spatial variances by effectively collecting emission from the e ntire plasma. The general arrangement is shown in Figure 6 1. In order to perform the simultaneous time resolved analyses a Leco, Paschen Runge polychromator fitted with 32 photomultiplier tubes (PMT), originally from a Leco glow discharge SA 2000, was con verted from continuous to pulsed operation and retrofitted for use with NIM HV power supplies. The 32 PMT correspond to 32 wavelengths for elemental detection. Wavelength assignmen ts can be found in Table 6 1 A selection of 6 common elements was chosen. T he elemental and pertinent spec troscopic data is presented in T able 6 2 and found to be 12.5 um. The grating was reported by the manufacturer as 2400 groove/mm and the spectral bandpass of .025 .040 nm through fixed exit slits. The bandpass variance is a product of dispersion and uniform width exit slits. Six individual HV power supplies are used to control each channel separately for gain control. The spectrometer uses R300 tube s below 300 nm and R 306 tubes above. Both Hamamatsu R 300 and R306 m PMT TDS 520 D 2 channel and a HP54542 C 4 channel, 500 MHz oscilloscopes. Signal disambiguation and tuning was performed using both multi element and single element hollow cathode lamps coupled through the same fiber optic used for plasma sampling. The Q switch synchronization output from the Big Sky is used to trigger both oscilloscopes for acquisition.

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1 35 Individual samples of the pure elements corresponding to the PMT response desired were used to tune and verif y the response of the spectrometer. The signals from all 6 pure substances are compared in F igure 6 2. The Paschen R unge has an entrance slit mounted on an adjustable translation stage to traverse tangent to the Rowland circle. Moving the entrance slit acr oss the Rowland circle simultaneously tunes or detunes all spectral lines on the exit arc within the spectrometer. It was demonstrated that tuning one line simultaneously tunes all lines as shown in Figure 6 3 raphite and sodium chloride matrix containing increasing mass fractions of six elements whos e compositions can be found in T ables 6 3 and 6 4 A method blank was prepared from each using pure graphite and pure sodium chloride, respectively. Reagent grade p owered samples from Alpha Aesar and Fisher Scientific were massed on an analytical balance, combined and homogenized by milling. The pellets were easily made by compression of the homogenized powders for forty Resu lts and Discussion g and t d values and plotted to generate compositional calibration curves for each element from each sample. (Figure 6 4) Both pellet sets, the graphite and sodium chlorid e, display ed significant self absorption at higher concentrations with the emission of zinc I and silicon I showing self absorption as concentrations of 1% by mass. In the case of zinc emission from NaCl matrices th e resonant transition at 213.9 nm the s ignal has completely diminished within the first few microseconds. The general trend observed with respect to the calibration curves generated from the two sample sets is that of significantly higher non linear effects from the sodium

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136 chloride matrix when compared to the graphite at the same concentration. Assuming LTE and a Bol tzmann distribution of populations across a density of states which is similar for the neutral emitters, there should not be a significantly higher population of one state when comp aring two plasmas with similar parameters. In the case of the sodium chloride matrix a condition must exist whi ch selectively increases these populations compared with the graphite plasma. This is, in fact, a matrix effect. It is expected that at earlier times in the plasma the population of ions will be at a maximum and the neutrals at a minimum since the temperatures are highest at these early times. However, the slopes of the c alibration curves decrease mono t on ically over time indicating a continuous re duction of emitters. With regard to instrument sensitivity and accuracy, early times in the plasma emission provide the steepest calibration curves and instrumental sensitivity, but the optimum time to collect data for calibration varies from 1.5 to 5.25 m icroseconds and is element dependent This trend is shown explicitly in F igure 6 5 A novel depth profile optimization was used to determine the optimal focal plane in the sample. Ranges of 2 mm were scanned while the emission signals were collected. The ratios of two time resolved emission signal were taken. As the signals are transient and decaying, at late times when the signals become background noise limited the ratio will fluctuate rapidly on the order of the noise frequency. This is an indication of the relative t otal plasma emissivity. Figure 6 6 illustrates that a depth of .2 mm (focal flane within the sample) provides the longest lived signal persistence and the best laser sample energy coupling.

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137 Conclusions The Paschen Runge polychromator coll ects many wavelengths, representing many possible sample constituents. By simultaneously collecting the time resolved signals from multiple elements within the laser plasma on e can discern plasma to plasma fluctuations as well as element to element trends. This allows for the integration optimization of each elemental emission signal from a single laser sample interaction which is not possible with iCCD or CCD camera systems coupled to e chelle or other grating spectrometers. This particular polychromator s uffers from two major design issues. Leco designed this particular instrument to be used for DC signal collection. The PMT bases were determined by Hamamatsu to be capable of pulsed operation, but significant noise exists in the signal outputs. Also, the e xit slits in the instrument are fixed. The selection of only resonant lines by Leco means that self absorption will be a persistent problem from plasma emission collection. In order to improve the S/N on the PMT outputs many spectra were averaged. Ten sets of 32 spectra after several cleaning shots were required to get presentable results. Repetitive sets were taken lieu of one, 320 shot sequence due the variance in the signal observed after a few decades of ablation. Finding a new sample spot on the pellet is not an issue, but this is unacceptable for individual aerosol. Different PMT bases may fix this problem. Even if the S/N for the device is improved the issue of line selection still exists In the case of studying particle interactions th e Paschen R unge could be an invaluable tool for analysis since not only is each shot a ne w experiment because of the nature of the generic LIBS experiment, but there is an entirely new sample as well.

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138 Incorporating this type of detector as the collection device for p article interactions could provide volumes of information unattainable from an iCCD system

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139 Table 6 1 Resonant atomic emission lines detected by the Leco Paschen Runge polychromator. Aluminum, copper, iron, magnesium, silicon and zinc were selected for i solated, non interfered lines. Element Channel # Wavelength Interferances Nitrogen (N) 1 149.262 Carbon (C) 2 165.701 Ar Nitrogen (N) 3 174.272 Fe Phosphorus (P) 4 177.499 Cu Sulfur (S) 5 180.731 Mo Ti Arsenic (As) 6 189.042 Boron (B 2) 7 2 08.959 W, Mo Zinc (Zn) 8 213.856 Co Copper (Cu) 9 219.226 Lead (Pb) 10 220.353 Co Nickel (Ni) Refract 11 225.386 Oxygen refract 12 260.572 Chromium (Cr) 13 267.716 W Silicon (Si) 14 288.158 Mo, Zr, W Niobium (Nb) 15 316.34 Ce,W Tin (Sn 2) 16 317.505 Copper (Cu 2) 17 327.396 Ar Zinc (Zn) 18 330.294 Ce Zirconium (Zr) 19 339.198 Mo, Ar Cobalt (Co) 20 345.351 Cr, Ni Nickel (Ni 2) 21 349.296 Titanium 22 365.35 Mo Iron (Fe) 23 371.994 Cu, Ar Magnesium (Mg) 24 383.829 Molybd enum (Mo) 25 386.411 Zr Aluminum (Al) 26 396.152 Ni,Nb,Zr,Ar Manganese (Mn) 27 403.449 Nb, Cr, Ni Vanadium (V) 28 411.179 Ar,Cr,Mo,W Cerium (Ce) 29 413.765 Chromium (Cr 2) 30 425.433 Nb Tungsten 31 429.461

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140 Table 6 2 Transition probabilities an d energy levels for corresponding transitions of the six elements monitored with the polychromator Element Wavelength (nm) A ki (hz) E i (cm 1 ) E k (cm 1 ) Zn I 213.856 7.09e+08 0 46745 Si I 288.157 2.17e+08 6 299 40 992 Cu I 327.396 1.37e+08 0 30535 Fe I 371.993 1.62e+07 0 26 874 Mg I 383.829 1.61e+08 21 911 47 957 Al I 396.152 9.8e+07 112.061 25 347 Table 6 3 Sodium chloride pellet composition. Pellets 1 through 5 were initially made and tested. Pellets 1b through 4b were made to supplem ent the linear portions of the response region. Blank Pellet 1 2 3 4 5 1b 2b 3b 4b element Mass % Al 0.000 1.034 0.640 0.379 0.159 1.656 0.768 0.456 0.296 0.141 Cu 0.000 3.870 2.440 1.432 0.602 6.243 0.602 5.927 0.305 0.483 Fe 0.000 4.024 2.8 90 1.201 0.640 6.259 0.656 0.383 0.280 0.218 Mg 0.000 0.778 0.458 0.242 0.122 1.264 0.605 0.412 0.289 0.149 Zn 0.000 3.110 1.720 0.928 0.503 5.029 0.735 0.426 0.317 0.167 Si 0.000 1.791 1.041 0.561 0.288 2.940 0.692 0.429 0.464 0.197

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141 Table 6 4 Graph ite pallet composition Blank Pellet 1 2 3 4 5 6 7 element Mass % Al 0.00 0.8867 1.1197 0.6921 0.5672 0.4467 0.2586 1.9219 Cu 0.00 1.7902 2.2605 1.3972 1.1451 0.9018 0.5222 3.8800 Fe 0.00 0.7773 0.9815 0.6066 0.4972 0.3915 0.2267 1.6846 Mg 0.0 0 0.1515 0.1913 0.1183 0.0969 0.0763 0.0442 0.3284 Zn 0.00 0.8493 1.0724 0.6629 0.5433 0.4278 0.2477 1.8407 Si 0.00 0.8900 1.1238 0.6946 0.5693 0.4483 0.2596 1.9290 Table 6 5 Neutral resonant lines monitored with six channels of the Paschen Runge po lychromator. Aluminum, Iron and copper all have similar upper energy levels as do zinc, silicon, and magnesium. Element Wavelength (nm) A ki ( H z) E i (cm 1 ) E k (cm 1 ) Zn I 213.856 7.09e+08 0 46745 Si I 288.157 2.17e+08 6 299 40 992 Cu I 327.396 1.3 7e+08 0 30535 Fe I 371.993 1.62e+07 0 26 874 Mg I 383.829 1.61e+08 21 911 47 957 Al I 396.152 9.8e+07 112.061 25 347

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142 Figure 6 1. Optical setup for simultaneous multi element analysis. The Rowland circle recording up to 30 elements. 6 channels are used. Collection of back collected signal eliminates spatial fluctuations by optical integration.

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143 Figure 6 2. Emission traces generated from 6 sampl es of pure substances corresponding to the detectors response. Different species exhibit different behavior. From the trace, it is possible that the iron detector is on the line wing. Mg and Fe persistence follows markedly different trend than Al and Cu. Line wing?

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144 Figure 6 3 Demonstration of the tuning ability for the Paschen R u nge spectrometer. Moving the entrance slit across the Rowland circle simultaneously tunes or detunes all spectral lines on the exit arc within the spectrometer. Tuning one line simultaneously tunes all lines.

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145 Figure 6 4. Calibration curves using various integration times. The curves are generated from sodium chloride pellets containing various concentrations of the elements of interest. Trends are shown as simple connected points.

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146 Figure 6 5 Early times in the plasma emission provide the steepe st calibration curves and instrumental sensitivity, but the optimum time to collect data for calibration varies from 1.5 to 5.25 microseconds.

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147 Figure 6 6 Ratios of emission signals were used to determine the optimal focal depth in the sample. If one signal tends to zero, the ratio goes to infinity or zero causing large fluctuations. A variation of only four millimeters causes significant chage in the persistence of the emission. 20 20 20 20 20

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148 APPENDIX A MATHIE U EQUATIONS Stability is solely dependent on a and q

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149 APPENDIX B SAMPLE PARTICLE SI ZE CALCULATIONS FOR THE VOAG

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150 APPENDIX C SEMANTIC CONSIDERATIONS FOR LASER SAMPLE COUPLING IN LASER INDUCED BREAKDOWN SPECTROSCOPY Introduction As science expands our understanding of processes and phenomena occurring naturally around us, we deve lop new theories and techniques, and as a consequence, we have created and adopted new terminologies to describe the newly illuminated physical processes and methodologies. This natural neology has occurred in the field of laser induced breakdown beginning with the simplest convention, the name. Laser Induced Plasma Spectroscopy was considered, though the acronym makes a humorous reference. LIBS, or Laser induced breakdown spectroscopy, came out as a popular favorite for the field. Throughout the LIBS liter ature, scientists work to explain extremely complex and interconnected events that are involved with the inception, evolution and termination of the plasma state, which can be quite complex. Energy transfer processes in the laser plasma and laser matter in teractions have been discussed at length by several authors in the field 2,3 and are incorporated into several recent reviews. 59,102 Among the language used to describe the processes involved in laser sample interactions throughout the literature is a term which has become popularized through use, but has not been given a clear and concise definition. In fact, I would argue that the potentially clear reports with the haze of uncertain denotation. To couple systems has an intuitive meaning for this author of joining intertwining or combining Merriam 102 This particular set of definitions does not seem directly applicable to photon

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151 matter interactions and certainly does not cover the interactions with a depth of understanding necessary at the level of peer review. So, we begin with the question: couple A perusal of some recent literature hints at several colloquial definitions. Windom et al. refer to laser sample coupling mechanisms between a laser and a solid and differentiates laser sample coupling and effects of hydrodynamics. 59 Michel and Chave indicate there is a difference in laser material coupling and laser pulse plasma interactions 74 Gunther and Hattendorf imply t hat coupling is affected by absorption only in certain samples 103 In other articles, lasers are coupled to fibers implying transmission. Lasers are coupled to samples, lasers to plasmas, plumes and samples, plasmas to samples. LIBS seems very coupled and the literature does not immediately offer much in the way of explicitly describing the coupling processes. Within the literature, attempts have already been made to clarify this in tables, plots and graphs but fall short of a unified explanation. A review by Winefordner et al. of matter interaction and samples first by phases and then the solid phase by bandg ap. 13 Each of the five sub categories has its plasma formation characterized by description of free electron formation pathways. While this description improves the view of what may be meant by laser sample coupling by introducing the idea of a bandgap, th e processes are unclear and the categories which are described are overlapping. A better metric for categorization of the interactions is needed, and to rediscover this metric we only need to consider the fundamentals of the interaction pathways.

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152 Present ed here is a synopsis of the events occurring in the laser bulk and laser plasma interactions from the perspective of fundamental mass and force carrier interactions. Three systematic approaches are used to determine, perhaps, a better choice of diction wh ich can clarify our intent and enhance our communication regarding these laser and plasma processes. Laser Material Interactions In LIBS we have two distinct types of interaction which derive from one fundamental relation. They are the laser analyte and t he plasma analyte processes. One could say they are coupled We have a mass (the analyte) and a force carrier (the ons to those equations. These considerations along with basic thermodynamic heat transfer considerations can describe all the events leading up to plasma initiation and the energetic consequences of that plasma formation. The Network Analogy Considering t he highly interconnected nature of the laser material processes we first look at the system as a two port network representing input and output transmission and reflection in order to identify the nature of coupling Four matrices can be generated to descr ibe all possible interactions in the 2 port system. The physical analogy of the multi port network for designing impedance matched electrical circuits is not new and is applicable to our question of laser sample coupling. In the schematic of the two port n etwork shown, P 1 and P 2 are the input and output. S 12 and S 11 represent input transmission and reflection, and S 21 and S 22 represent output reflection and

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153 transmission. In theory, one could define a higher order multi port scenario which combines all possi bilities of the energetic pathways discussed by Lushnikov and Negin 1 for all time dependent frequencies and impedances for each of the processes. Defining the complex impedance functions of a material has been the subj ect of solid state physics and plasmonics for decades. Resonators (antennas) have been developed which are said to enhance certain techniques such as SERS. These antenna tricks are used across the physics, chemistry and medical communities, and the applica tions can others. Each technique relies on absorption or scattering from the equivalent of an embedded antenna. The system response provides information about resonant conditions and is translated into physical descriptions of interactions. All matter can be described by its frequency and power dependent impedance. Consider the following depiction of dipoles. A material with a frequency dependent permittivity is embedded in a medi a with a different dielectric function. This case presents the option to select frequencies which resonate with either material or possibly both, depending on the nature of the dielectric functions. The dipoles can represent either an EM transverse wave in a vacuum or the dipoles of a media like a fiber optic cable. This schematic depicts a sample as an embedded antenna and is immediately recognized as describing a particle embedded in a plasma as well. This analogy can also represent a plasma in air or any two boundary model, and is mathematically

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154 equivalent to the network diagram. Impedance matching of the local oscillator and antenna allows for the greatest amount of power throughput, with the least loss in the system. Maxwell The interactions of the e lectric field with matter have been extensively studied and generally described by J.C. Maxwell through a set of classical equations known 36 104 The state of a transverse wave across two media with different electrical for the system. Of great importance when calculating these fields are the electrical properties of the domain the transverse wave occupies and the electrical properties of the wave itself. Rigorous mat hematics aside, there are a finite set of outcomes for a wave interacting with a boundary of two materials as a consequence of the continuity and curl requirements for the field. The accepted interpretations of these outcomes are as follows. The wave can b e unchanged across the boundary via undisturbed transmission. The wave can be sent back to the source through reflection. The wave can be elastically or inelastically scattered by an interface. The wave can be absorbed through interference and inelastic co llisions. Strictly speaking these are all scattering events. 53

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155 Following conservation laws, the sum of all of the associated energies for each interactions and since these p rocesses are understood, coupling as referred to in the LIBS literature must be described by one or all of these terms. 11 The two distinct interactions in LIBS aforementioned are simultaneous ly described as follows: (i) The pulsed laser produces intense, coherent electromagnetic transverse waves which oscillate at a given frequency within a given media. All components of the field can be quantified; (ii) Matter is composed of atoms and ions which are themselves composed of positively and negatively charged particles. As a result of (ii), all matter can be polarized to some extent through interactions with external forces. While most matter does not exist with permanent electric dipoles, an external e lectric field can induce such a dipole. The ability for an EMF to induce a dipole or polarize a material is parameterized requires energy. The energy deposited is stored as a charge separation as in a capacitor. This extent of this is charge separation is the polarization density, P and describes the average dipole. For any material we can use the relationships between polarizability and susceptibility along with the dri ve and receiver oscillator frequencies to evaluate the dynamics of the electric field at any point. The relations are presented without derivation below. From these relationships we determine frequency dependent

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156 dispersion properties for a given material. These dispersion relationships define how EM waves propagate in and around the material, e.g. a laser and a particle or bulk. 104 It follows th at a review of the general dielectric properties of solids liquids and gasses provides a better categorization than previously offered by Winefordner et al. because the electric susceptibility, polarizability and permittivity are fundamental observables wh ich define the dielectric function for a material regardless of phase. The ranges are shown in a power scale below and demonstrates why there is overlap in the descriptions provided by the aforementioned table; there is overlap in susceptibility. Calculat ing the electric field magnitude at any point in space around an object as a function of time will provide the portions of energy transmitted, scattered, absorbed and reflected from the impinging field. In the case of laser plasma initiation, the contribut ions to energy deposition from reflection and general elastic scattering are null by definition. This leaves inelastic scattering and absorption processes as the sources for depositing the remaining energy. Mie A comprehensive theory describing all of th ese energetic pathways for spherical objects with diameters greater than those of the Rayleigh Gans regime was developed

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157 by Gustav Mie and Lorentz and is known generally as Lorentz Mie theory or simply Mie theory. The derivations and descriptions are beyon d the scope of this work but 53 Mie scattering theory can be used to determine the magnitudes of each effect through the determination of three matrices: Q ex Q abs and Q sca Q abs is simply the difference in Q ex and Q sca These solutions are well known and similar solutions exist for cylinders, sheets, and other geometric entities. Thus we can completely describe the interaction of a laser beam with a given sample. Coupling was not discussed by Maxwell or Mie, though other physical processes were. Several computer algorithms have been written to solve these equations and can be found free of charge and in open source format. An alter consider attenuation by k losses from a plane wave which may be applicable to large particles or bulks. In this approach we take a complex plane wave and consider losses due to a co mplex component of the refractive index as follows.

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158 describing the absorption of light by a mat erial with a complex refractive index. Both of these approaches imply that the phenomena of laser coupling as described by many authors is perhaps a more familiar relationship when dealing with the interactions of a laser and a sample. One more approach w ill be considered to directly compare the relations shown for absorption by solids, liquids and gasses to that of the remaining 99.9% of the known universe which exists in the plasma state. Laser Plasma Interactions The two most important parameters for t he laser plasma are arguably the electron number density and the temperature. 2 In the absence of external fields, these two state variables can define the plasma state. Hence, these are the two plasma parameters listed most often in the literature for lase r plasma diagnostics and are often calculated from the Saha Boltzmann or from scattering techniques. Both are optical methods relying on UV Vis range signals and require careful spectrometric calibration and highly sensitive and elaborate optical setups wh ich negate two of the most appealing aspects of laser plasma spectroscopy: its low cost and experimental simplicity. The typical laser plasma is a temporal event resultant from the dielectric breakdown of vaporized samples or from a gaseous medium. These p lasmas exist on the timescale of microseconds to milliseconds. Determining the plasma state at any given time for these transient plasmas has often relied on the application of pLTE statistical mechanics after having the condition verified or simply assume d to exist in some cases. Previous works show that laser plasmas range in temperature from 10000

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159 18000 K and have variations in electron number density at least spanning 10 14 10 18 per cc. 4 These temperature and density ranges often occur in a single plasma event as a function of time. High temperatur es and pressures exist at early times in the plasma and both decrease as plasma expansion and cooling occurs. Once dielectric breakdown occurs and free electrons are formed the dependence on sample electric permittivity becomes less important and the pred ominant consideration is that of highest frequency collider frequencies. 56 In neutral plasmas this will be that of the electron collision frequency which is also known as the fundamental plasma frequency, 0 Generally speaking when the drive frequency is much lower than the plasma frequency the wave is reflected. When the frequencies are resonant the wave is absorbed. When the drive frequency is much greater than the plasma frequency the wave is transmitted unchanged. This can be seen by consideration of the dispersion relationships in the laser induced plasma. For an ideal, collisional plasma the polarization density is determined by the electron number density, electron mass, and the deviation from resonance of the oscillator as follows. Rearrangement a nd simple substitution gives the frequency dependent relative permittivity of the plasma. 105 Using this information we know the frequency dependent extinction coefficient. When the frequencies match, the plasma ab sorbs energy. When the frequencies mismatch the plasma energy absorption suffers.

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160 The case of the ideal plasma discussed here is qualitatively little different than a conductor with free electrons in the conduction band. The electrons on the surface have a given frequency and will reflect, transmit or absorb in the same manner as our plasma. After all, a mirror reflects light for a reason. This provides the final nail in the electrodynamics and terminology. Summary In order to effectively discuss LIBS processes we, as a community, should be as c lear and consistent in our communication as possible. There are enough ambiguities in these complex processes that we should not exacerbate the situation with a poor choice pro cesses referred to. Absorption, either single or two photon, always play a role, both in plasma formation and plasma excitation. The absorption process can be optimized by selection of an appropriate excitation frequency. Energy not absorbed by the system cannot be used for development of a plasma or excitation of the sample. These processes can be optimized by matching the excitation frequency to the given sample. When choosing a sample laser combination we need to consider the complex permittivity of the material and the frequency of the laser. These cases are described as follows: (i) Band gap = 0. Free electrons are present, the susceptibility is unity, and the plasmon frequency determines absorption and energetic losses as described by the dispersion rela tionships.

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161 (ii) Band gap > 0. The absorption spectrum, dictated by ( ) will provide all relevant energy transfer information up to the point ionization occurs. (iii) Plasma state. At the time of free electron formation in the gas phase, the absorption coefficients for both the plasma and the sample need to be considered. If the excitation source is not completely absorbed, energy can be simultaneously deposited into both the sample and the plasma. Excitation of electrons from the valence band to the conduction ban d in case (ii) creates case (i). Ionization of (i) or (ii) creates case (iii). Each of these interactions and the procession form one to the other are predictable based on the susceptibility and ionization potential of the material. The interactions of la ser radiation with the plasma which is formed can be described by Maxwell and if a spherical plasma is created, by Mie. Instead of using coupled to describe these processes we can consider: (i) Sample/plasma absorption a. Energy available to the system (ii) Sample/pl asma transmission a. Energy not available to the system (iii) Sample/plasma reflection/scattering a. Energy not available to the system

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162 LIST OF REFERENCES 1. Miziolek, A. W.; Palleschi, V.; Schechter, I., Laser induced breakdown spectroscopy (LIB S) : fundamentals and applications Cambridge University Press: Cambridge, UK ; New York, 2006; p xvii, 620 p. 2. Hahn, D. W.; Omenetto, N., Laser Induced Breakdown Spectroscopy (LIBS), Part I: Review of Basic Diagnostics and Plasma Particle Interactions: Still Challenging Issues Within the Analytical Plasma Community. Applied Spectroscopy 2010, 64 (12). 3. Hahn, D. W.; Omenetto, N., Laser Induced Breakdown Spectroscopy (LIBS), Part II: Review of Instrumental and Methodological Approaches to Material Analys is and Applications to Different Fields. Applied Spectroscopy 2012, 66 (4). 4. Hahn, D. W., Laser Induced Breakdown Spectroscopy for Analysis of Aerosol Particles: The Path Toward Quantitative Analysis. Spectroscopy 2009, 24 (9), 26 33. 5. Lushnikov, A. A. ; Negin, A. E., AEROSOLS IN STRONG LASER BEAMS. Journal of Aerosol Science 1993, 24 (6), 707 &. 6. Baron, P. A.; Kulkarni, P.; Willeke, K., Aerosol measurement : principles, techniques, and applications 3rd ed.; Wiley: Hoboken, N.J., 2011; p xiv, 883 p. 7. Davis, E. J.; Buehler, M. F.; Ward, T. L., THE DOUBLE RING ELECTRODYNAMIC BALANCE FOR MICROPARTICLE CHARACTERIZATION. Review of Scientific Instruments 1990, 61 (4), 1281 1288. 8. Hahn, D. W., Laser induced breakdown spectroscopy for sizing and elemen tal analysis of discrete aerosol particles. Applied Physics Letters 1998, 72 (23). 9. Diwakar, P. K.; Loper, K. H.; Matiaske, A. M.; Hahn, D. W., Laser induced breakdown spectroscopy for analysis of micro and nanoparticles. Journal of Analytical Atomic Spe ctrometry 2012, 27 (7). 10. Laucks, M. L.; Roll, G.; Schweiger, G.; Davis, E. J., Physical and chemical (Raman) characterization of bioaerosols Pollen. Journal of Aerosol Science 2000, 31 (3), 307 319. 11. Vehring, R.; Aardahl, C. L.; Davis, E. J.; Schwe iger, G.; Covert, D. S., Electrodynamic trapping and manipulation of particle clouds. Review of Scientific Instruments 1997, 68 (1), 70 78. 12. Thakur, S. N.; Singh, J. P., Laser induced breakdown spectroscopy 1st ed.; Elsevier: Amsterdam ; Boston, 2007; p xxiv, 429 p.

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163 13. Winefordner, J. D.; Gornushkin, I. B.; Correll, T.; Gibb, E.; Smith, B. W.; Omenetto, N., Comparing several atomic spectrometric methods to the super stars: special emphasis on laser induced breakdown spectrometry, LIBS, a future super star. Journal of Analytical Atomic Spectrometry 2004, 19 (9), 1061 1083. 14. Krzemnicki, M. S.; Hanni, H. A.; Walters, R. A., A new method for detecting be diffusion treated sapphires: Laser induced breakdown spectroscopy (LIBS). Gems & Gemology 2004, 40 ( 4), 314 322. 15. Asgill, M. E.; Hahn, D. W., Particle size limits for quantitative aerosol analysis using laser induced breakdown spectroscopy: Temporal considerations. Spectrochimica Acta Part B Atomic Spectroscopy 2009, 64 (10), 1153 1158. 16. Diaz, D.; Hahn, D. W.; Molinat, A., Evaluation of Laser Induced Breakdown Spectroscopy (LIBS) as a Measurement Technique for Evaluation of Total Elemental Concentration in Soils. Applied Spectroscopy 2012, 66 (1). 17. Diwakar, P. K.; Jackson, P. B.; Hahn, D. W., The effect of multi component aerosol particles on quantitative laser induced breakdown spectroscopy: Consideration of localized matrix effects. Spectrochimica Acta Part B Atomic Spectroscopy 2007, 62 (12), 1466 1474. 18. Hinds, W. C., Aerosol technology : pr operties, behavior, and measurement of airborne particles 2nd ed.; Wiley: New York, 1999; p xx, 483 p. 19. Friedlander, S. K., Smoke, dust, and haze : fundamentals of aerosol dynamics 2nd ed.; Oxford University Press: New York, 2000; p xx, 407 p. 20. Bar on, P. A.; Knovel; Willeke, K., Aerosol measurement [electronic resource] : principles, techniques, and applications / edited by Paul A. Baron, Klaus Willeke 2nd ed. ed.; Wiley: New York, 2001. 21. Analytical chemistry of aerosols Lewis: Boca Raton, 1999; p 486 p. 22. Jennings, B. R.; Parslow, K., PARTICLE SIZE MEASUREMENT THE EQUIVALENT SPHERICAL DIAMETER. Proceedings of the Royal Society of London Series a Mathematical Physical and Engineering Sciences 1988, 419 (1856), 137 149. 23. Da vis, E. J.; Bridges, M. A., THE RAYLEIGH LIMIT OF CHARGE REVISITED LIGHT SCATTERING FROM EXPLODING DROPLETS. Journal of Aerosol Science 1994, 25 (6), 1179 1199. 24. Watson, J. T.; Sparkman, O. D., Introduction to mass spectrometry : instrumentation, appl ications and strategies for data interpretation 4th ed.; John Wiley & Sons: Chichester, England ; Hoboken, NJ, 2007; p xxiv, 818 p.

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164 25. Dawson, P. H., Quadrupole mass spectrometry and its applications American Institute of Physics: New York, 1995. 26. Du touquet, C.; Wattieaux, G.; Meyer, L.; Frejafon, E.; Boufendi, L., Determination of the elemental composition of micrometric and submicrometric particles levitating in a low pressure RF (Radio Frequency) plasma discharge using LIBS (Laser Induced Breakdown Spectroscopy). Spectrochimica Acta Part B: Atomic Spectroscopy (0). 27. Yu, N.; Nagourney, W., ANALYSIS OF PAUL STRAUBEL TRAP AND ITS VARIATIONS. Journal of Applied Physics 1995, 77 (8), 3623 3630. 28. Davis, E. J., ELECTRODYNAMIC BALANCE STABILITY CHARA CTERISTICS AND APPLICATIONS TO THE STUDY OF AEROCOLLOIDAL PARTICLES. Langmuir 1985, 1 (3), 379 387. 29. Zheng, F.; Laucks, M. L.; Davis, E. J., Aerodynamic particle size measurement by electrodynamic oscillation techniques. Journal of Aerosol Science 2000, 31 (10), 1173 1185. 30. Windom, B. C.; Diwakar, P. K.; Hahn, D. W., Dual pulse laser induced breakdown spectroscopy for analysis of gaseous and aerosol systems: Plasma analyte interactions. Spectrochimica Acta Part B Atomic Spectroscopy 2006, 61 (7), 788 796. 31. Carranza, J. E.; Fisher, B. T.; Yoder, G. D.; Hahn, D. W., On line analysis of ambient air aerosols using laser induced breakdown spectroscopy. Spectrochimica Acta Part B Atomic Spectroscopy 2001, 56 (6). 32. Kazakov, A. Y.; Gornushkin, I. B.; Ome netto, N.; Smith, B. W.; Winefordner, J. D., Radiative model of post breakdown laser induced plasma expanding into ambient gas. Applied Optics 2006, 45 (12). 33. Dalyander, P. S.; Gornushkin, I. B.; Hahn, D. W., Numerical simulation of laser induced breakd own spectroscopy: Modeling of aerosol analysis with finite diffusion and vaporization effects. Spectrochimica Acta Part B Atomic Spectroscopy 2008, 63 (2), 293 304. 34. Strauss, N.; Fricke Begemann, C.; Noll, R., Size resolved analysis of fine and ultrafin e particulate matter by laser induced breakdown spectroscopy. Journal of Analytical Atomic Spectrometry 2010, 25 (6), 867 874. 35. Ottesen, D. K.; Wang, J. C. F.; Radziemski, L. J., REAL TIME LASER SPARK SPECTROSCOPY OF PARTICULATES IN COMBUSTION ENVIRONME NTS. Applied Spectroscopy 1989, 43 (6), 967 976. 36. Griem, H. R.; Lovberg, R. H., Plasma physics Academic Press: New York,, 1970.

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165 37. Radziemski, L. J.; Cremers, D. A., Laser induced plasmas and applications M. Dekker: New York, 1989; p xiv, 445 p. 38. Fowles, G. R., Introduction to modern optics 2nd ed.; Dover Publications: New York, 1989; p viii, 328 p. 39. Cristoforetti, G.; De Giacomo, A.; Dell'Aglio, M.; Legnaioli, S.; Tognoni, E.; Palleschi, V.; Omenetto, N., Local Thermodynamic Equilibrium in Las er Induced Breakdown Spectroscopy: Beyond the McWhirter criterion. Spectrochimica Acta Part B Atomic Spectroscopy 2010, 65 (1), 86 95. 40. Bette, H.; Noll, R.; Muller, G.; Jansen, H. W.; Nazikkol, C.; Mittelstadt, H., High speed scanning laser induced brea kdown spectroscopy at 1000 Hz with single pulse evaluation for the detection of inclusions in steel. Journal of Laser Applications 2005, 17 (3), 183 190. 41. Werheit, P.; Fricke Begemann, C.; Gesing, M.; Noll, R., Fast single piece identification with a 3D scanning LIBS for aluminium cast and wrought alloys recycling. Journal of Analytical Atomic Spectrometry 2011, 26 (11), 2166 2174. 42. Remiarz, R.; Agarwal, J., Improved Polystyrene Latex and Vibrating Orifice Monodisperse Aerosol Generators. TSI: TSI Qua rterly, 1982; Vol. VIII(3), pp 3 12 43. Reischl, G.; John, W.; Devor, W., Uniform electrical charging of monodisperse aerosols. Journal of Aerosol Scielce (1997), 8 (55). 44. Keady, P.; Nelson, P., Monodisperse Particle Generators for Calibrating Aerosol Instrumentation. Proceedings ed.; TSI: Institute of Environmental Sciences, 1984; Vol. A34, pp 94 100 45. Aardahl, C. L.; Vehring, R.; Weber, R.; Schweiger, G.; Davis, E. J.; Wiedensohler, A., Electrodynamic trapping of aerocolloidal particles: Experiment al and theoretical trapping limits. Journal of Colloid and Interface Science 1997, 192 (1), 228 237. 46. Aardahl, C. L.; Vehring, R.; Davis, E. J.; Schweiger, G.; Swanson, B. D., Trapping two particle arrays in a double ring electrodynamic balance. Journal of Aerosol Science 1997, 28 (8), 1491 1505. 47. Dixon, P. B.; Hahn, D. W., Feasibility of detection and identification of individual bioaerosols using laser induced breakdown spectroscopy. Analytical Chemistry 2005, 77 (2), 631 638. 48. Hohreiter, V.; Hah n, D. W., Plasma particle interactions in a laser induced. Analytical Chemistry 2006, 78 (5).

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167 60. Amodeo, T.; Dutouquet, C.; Le Bihan, O.; Attoui, M.; Frejafon, E., On line determination of nanometric and sub micrometric particle physicochemical characte ristics using spectral imaging aided Laser Induced Breakdown Spectroscopy coupled with a Scanning Mobility Particle Sizer. Spectrochimica Acta Part B Atomic Spectroscopy 2009, 64 (10), 1141 1152. 61. Diwakar, P. K.; Groh, S.; Niemax, K.; Hahn, D. W., Study of analyte dissociation and diffusion in laser induced plasmas: implications for laser induced breakdown spectroscopy. Journal of Analytical Atomic Spectrometry 2010, 25 (12). 62. Belov, N. N., Distribution of optical field within a spherical particle. 19 82 63. Belov, N. N., SIMILARITY OF OPTICAL FIELDS IN LOW ABSORBING PARTICLES. Optika I Spektroskopiya 1988, 64 (6). 64. Belov, N. N.; Suslov, S. O., CALCULATION OF MULTILAYER PARTICLE OPTICAL CHARACTERISTICS BY THE METHOD OF PHASE FUNCTIONS. Optika I Spek troskopiya 1992, 72 (1). 65. Warren, R. A., Jr.; Shelby, D.; Merten, J.; Smith, B.; Winefordner, J. D.; Omenetto, N., LIBS Studies of Single Suspended Particles for the Investigation of Laser Particle and Plasma particle Interactions In Winter Conference on Plasma Spectrochemistry Fort Meyers FL, 2010. 66. Chen, Y. L.; Lewis, J. W. L.; Parigger, C., Spatial and temporal profiles of pulsed laser induced air plasma emissions. Journal of Quantitative Spectroscopy & Radiative Transfer 2000, 67 (2), 91 103. 67 Carranza, J. E.; Gibb, E.; Smith, B. W.; Hahn, D. W.; Winefordner, J. D., Comparison of nonintensified and intensified CCD detectors for laser induced breakdown spectroscopy. Applied Optics 2003, 42 (30), 6016 6021. 68. Rai, V. N.; Zhang, H. S.; Yueh, F. Y.; Singh, J. P.; Kumar, A., Effect of steady magnetic field on laser induced breakdown spectroscopy. Applied Optics 2003, 42 (18), 3662 3669. 69. Chase, M. W. J., et. al., Journal of Chemical and Physical Reference Data 1985; Vol. Part 1 Al Co. 70. Stip e, C. B.; Choi, J. H.; Lucas, D.; Koshland, C. P.; Sawyer, R. F., Nanoparticle production by UV irradiation of combustion generated soot particles. Journal of Nanoparticle Research 2004, 6 (5), 467 477. 71. Chen, Y. L.; Lewis, J. W. L.; Parigger, C., Spati al and temporal profiles of pulsed laser inducedair plasma emissions. Journal of Quantitative Spectroscopy & Radiative Transfer 2000, (67), 91 103.

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168 72. Tognoni, E.; et al., Laser Induced Breakdown Spectroscopy (LIBS) Cambridge University Press: 2006. 73. Mermet, J. M., Limit of quantitation in atomic spectrometry: An unambiguous concept? Spectrochimica Acta Part B Atomic Spectroscopy 2008, 63 (2), 166 182. 74. Michel, A. P. M.; Chave, A. D., Analysis of laser induced breakdown spectroscopy spectra: The ca se for extreme value statistics. Spectrochimica Acta Part B Atomic Spectroscopy 2007, 62 (12), 1370 1378. 75. Gornushkin, I. B.; Smith, B. W.; Potts, G. E.; Omenetto, N.; Winefordner, J. D., Some considerations on the correlation between signal and backgro und in laser induced breakdown spectroscopy using single shot analysis. Analytical Chemistry 1999, 71 (23). 76. Anabitarte, F.; Rodriguez Cobo, L.; Lopez Higuera, J. M.; Cobo, A., Normalization of laser induced breakdown spectroscopy spectra using a plasti c optical fiber light collector and acoustic sensor device. Applied Optics 2012, 51 (34), 8306 8314. 77. Zorov, N. B.; Gorbatenko, A. A.; Labutin, T. A.; Popov, A. M., A review of normalization techniques in analytical atomic spectrometry with laser sampli ng: From single to multivariate correction. Spectrochimica Acta Part B Atomic Spectroscopy 2010, 65 (8), 642 657. 78. Poussel, E.; Mermet, J. M., Simultaneous measurements of signal and background in inductively coupled plasma atomic emission spectrometry: Effects on precision, limit of detection and limit of quantitation. Spectrochimica Acta Part B Atomic Spectroscopy 1996, 51 (1), 75 85. 79. Alvarez Trujillo, L. A.; Ferrero, A.; Laserna, J. J.; Hahn, D. W., Alternative Statistical Methods for Spectral Dat a Processing: Applications to Laser Induced Breakdown Spectroscopy of Gaseous and Aerosol Systems. Applied Spectroscopy 2008, 62 (10). 80. Ingle, J. D.; Crouch, S. R., Spectrochemical analysis Prentice Hall: Englewood Cliffs, N.J., 1988; p xv, 590 p. 81. Harmon, R. S.; Remus, J.; McMillan, N. J.; McManus, C.; Collins, L.; Gottfried, J. L., Jr.; DeLucia, F. C.; Miziolek, A. W., LIBS analysis of geomaterials: geochemical fingerprinting for the rapid analysis and discrimination of minerals. Applied Geochemist ry 2009, 24 (6), 1125 1141.

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169 82. Gondal, M. A.; Nasr, M. M.; Zulfiqar, A.; Yamani, Z. H., Determination of trace elements in volcanic rock samples collected from cenozoic lava eruption sites using LIBS. Journal of Environmental Science and Health. Part A, Toxic/Hazardous Substances & Environmental Engineering 2009, 44 (5), 528 535. 83. Hybl, J. D.; Tysk, S. M.; Berry, S. R.; Jordan, M. P., Laser induced fluorescence cued, laser induced breakdown spectroscopy biological agent detection. Applied Optics 2 006, 45 (34), 8806 8814. 84. Gottfried, J. L.; De Lucia, F. C.; Munson, C. A.; Miziolek, A. W., Laser induced breakdown spectroscopy for detection of explosives residues: a review of recent advances, challenges, and future prospects. Analytical and Bioanal ytical Chemistry 2009, 395 (2), 283 300. 85. Sirven, J. B.; Bousquet, B.; Canioni, L.; Sarger, L., Laser induced breakdown spectroscopy of composite samples: Comparison of advanced chemometrics methods. Analytical Chemistry 2006, 78 (5), 1462 1469. 86. Cha rlton, B.; Fisher, A. S.; Goodall, P. S.; Hinds, M. W.; Lancaster, S.; Shore, S., Atomic spectrometry update. Industrial analysis: metals, chemicals and advanced materials. Journal of Analytical Atomic Spectrometry 2008, 23 (12), 1636 1692. 87. Dikshit, V. ; Yueh, F. Y.; Singh, J. P.; McIntyre, D. L.; Jain, J. C.; Melikechi, N., Laser induced breakdown spectroscopy: A potential tool for atmospheric carbon dioxide measurement. Spectrochimica Acta Part B Atomic Spectroscopy 2012, 68 65 70. 88. Cao, H.; Gao, L M., Research on sound fields generated by laser induced liquid breakdown. Optica Applicata 2010, 40 (4), 897 907. 89. Moon, H. Y. Diagnostic and analytical studies of laser induced plasmas University of Florida, Gainesville, FL, 2010. 90. Mueller, M.; G ornushkin, I. B.; Florek, S.; Mory, D.; Panne, U., Approach to detection in laser induced breakdown spectroscopy. Analytical Chemistry 2007, 79 (12), 4419 4426. 91. Castle, B. C.; Talabardon, K.; Smith, B. W.; Winefordner, J. D., Variables influencing the precision of laser induced breakdown spectroscopy measurements. Applied Spectroscopy 1998, 52 (5), 649 657. 92. Aragon, C.; Bengoechea, J.; Aguilera, J. A., Influence of the optical depth on spectral line emission from laser induced plasmas. Spectrochimica Acta Part B Atomic Spectroscopy 2001, 56 (6), 619 628.

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170 93. Vadillo, J. M.; Garcia, C. C.; Palanco, S.; Laserna, J. J., Nanometric range depth resolved analysis of coated steels using laser induced breakdown spectrometry with a 308 nm collimated beam. Jou rnal of Analytical Atomic Spectrometry 1998, 13 (8), 793 797. 94. St Onge, L.; Sabsabi, M., Towards quantitative depth profile analysis using laser induced plasma spectroscopy: investigation of galvannealed coatings on steel. Spectrochimica Acta Part B Ato mic Spectroscopy 2000, 55 (3), 299 308. 95. Carranza, J. E.; Hahn, D. W., Sampling statistics and considerations for single shot analysis using laser induced breakdown spectroscopy. Spectrochimica Acta Part B Atomic Spectroscopy 2002, 57 (4). 96. Griem, H. R., Spectral line broadening by plasmas Academic Press: New York,, 1974; p xiv, 408 p. 97. Fisher, B. T.; Johnsen, H. A.; Buckley, S. G.; Hahn, D. W., Temporal gating for the optimization of laser induced breakdown spectroscopy detection and analysis of toxic metals. Applied Spectroscopy 2001, 55 (10). 98. Hohreiter, V.; Hahn, D. W., Dual pulse laser induced breakdown spectroscopy: Time resolved transmission and spectral measurements. Spectrochimica Acta Part B Atomic Spectroscopy 2005, 60 (7 8). 99. Groh S.; Garcia, C. C.; Murtazin, A.; Horvatic, V.; Niemax, K., Local effects of atomizing analyte droplets on the plasma parameters of the inductively coupled plasma. Spectrochimica Acta Part B Atomic Spectroscopy 2009, 64 (3), 247 254. 100. Noll, R.; Sturm, V.; Aydin, U.; Eilers, D.; Gehlen, C.; Hohne, M.; Lamott, A.; Makowe, J.; Vrenegor, J., Laser induced breakdown spectroscopy From research to industry, new frontiers for process control. Spectrochimica Acta Part B Atomic Spectroscopy 2008, 63 (10), 1159 1 166. 101. Wen, S. B.; Mao, X. L.; Greif, R.; Russo, R. E., Analysis of laser ablation: Contribution of ionization energy to the plasma and shock wave properties. Journal of Applied Physics 2007, 102 (4), 10. 102. Merriam Webster Inc., The Merriam Webster d ictionary Merriam Webster: Springfield, Mass., 2004; p xvii, 939 p. 103. Gunther, D.; Hattendorf, B., Solid sample analysis using laser ablation inductively coupled plasma mass spectrometry. Trac Trends in Analytical Chemistry 2005, 24 (3), 255 265. 10 4 Schwartz, M., Principles of electrodynamics Dover Publications: New York, 1987; p viii, 344 p.

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172 BIOGRAPHICAL SKETCH Andy Warren received his Bachelor of Science degree in Chemistry from Georgia Coll ege & State University in 2007 where he was named the Top Graduating Senior for the Department of Chemistry and Physics A s an undergraduate, Andy maintained GC/MS and FTIR instrumentation for the department of chemistry He w orked as an electrical and HVAC/R contractor, welder and consultant for his company, Designed Mechanics, throughout his undergraduate tenure. After graduating, h e joined the doctoral program at The University o f Florida where Andy has been the recipient of numerous honors and awards, including the University of Florida graduate teaching award and a Grinter Fellowship While at UF, A ndy became a member of the research group of Nicol Omenetto and began his research in laser induced plasma spectroscopy His research was centered on single particle LIBS for which he designed novel instrumentation. H is research has been presented at several international conference meetings Andy is now pursuing a commercial industrial role in in st rument design and development