1 T HE ROLE OF PLASMA PARTICLE INTERACTIONS IN QUANTITATIVE LIBS ANALYSIS OF AEROSOLS By MICHAEL L.E. ASGILL A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIRE MENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2012
2 2012 Michael L.E. Asgill
3 To my late mother, who instilled in me a life long love of learning
4 A CKNOWLEDGEMENTS I thank my advisor, Dr. David W. Hahn, for his patienc e and guidance throughout my academic career at the University of Florida. I would not be where I am today without his support. I acknowledge Professor Nicolo Omenetto for his many detailed discussions on the subject matter. I also thank my siblings Sylve ster Harding, Nicola Asgill, and Violet Asgill Peters for their continuing moral support. I thank my friends and colleagues (Gabriel Espinosa, Prasoon Diwakar, Phillip Jackson, Bret Windom, Michael Bobek, Richard Stehle, Sara Smith, Julia Setlak, Julien Br issonneau, Chris Loper, and Nathan Rhodes) who have walked this path with me and provided much assistance along the way. I also acknowledge my girlfriend, Kimberly Simmons, for assistance in proofreading this document.
5 T ABLE OF CONTENTS p age ACKNOWLEDGEMENTS ................................ ................................ ............................... 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 Laser Induced Breakdown: The Beginning of LIBS ................................ ................ 13 Breakdown in Gases ................................ ................................ ........................ 14 Breakdown of Solids ................................ ................................ ......................... 15 Impurities, Surface Defects and Aerosols ................................ ........................ 16 Attachment, Recombination, and Diffusion Losses ................................ .......... 16 Attachment & Recombination ................................ ................................ ..... 17 Diffusion ................................ ................................ ................................ ..... 17 Laser Induced Breakdown Spectroscopy (LIBS) ................................ .................... 18 Instrumentation ................................ ................................ ................................ 19 Challenges ................................ ................................ ................................ ....... 20 Detection ................................ ................................ ................................ .... 22 Interaction ................................ ................................ ................................ .. 23 Excitation ................................ ................................ ................................ ... 23 Equilibrium ................................ ................................ ................................ ........ 24 Aerosol LIBS ................................ ................................ ................................ ........... 26 Con ditional Analysis ................................ ................................ ......................... 27 Upper Size Limits ................................ ................................ ............................. 28 Plasma Particle Interactions ................................ ................................ ................... 29 Dissociation and Mass Diffusion Timescale ................................ ..................... 30 Heat Diffusion Timescales ................................ ................................ ................ 31 Plasma Expansion ................................ ................................ ............................ 33 Plasma Diagnostics ................................ ................................ ................................ 34 Boltzmann Temperature ................................ ................................ ................... 34 Saha Boltzmann Temperature ................................ ................................ ......... 36 Electron Density ................................ ................................ ............................... 36 Thomson Scattering ................................ ................................ ......................... 37 Summary ................................ ................................ ................................ ................ 39 2 TEMPORAL ANALYSIS OF AEROSOL UPPER SIZE LIMITS ............................... 40 Experimental Methods ................................ ................................ ............................ 40 Experimental Setup ................................ ................................ .......................... 40 Conditional Analysis Algorithm ................................ ................................ ......... 43
6 Peak Profile Matching ................................ ................................ ................ 44 Statistica l Matching ................................ ................................ .................... 45 Results and Discussion ................................ ................................ ........................... 47 Conclusions ................................ ................................ ................................ ............ 54 3 DISTINGUIS HING BETWEEN GASEOUS AND AEROSOL PHASE ANALYTES 56 Experimental Methods ................................ ................................ ............................ 56 Results and Discussion ................................ ................................ ........................... 60 Conclusions ................................ ................................ ................................ ............ 69 4 INVESTIGATION OF THE POLARIZATION EFFECTS OF LIBS ........................... 70 Experimental Methods ................................ ................................ ............................ 71 Results and Discussion ................................ ................................ ........................... 74 Spectral Data ................................ ................................ ................................ .... 75 Temporal Data ................................ ................................ ................................ .. 80 Conclusions ................................ ................................ ................................ ............ 84 5 OBSERVATION OF THOMSON SCATTERING IN GASEOUS PLASMAS ............ 86 Exp erimental Methods ................................ ................................ ............................ 86 Results and Discussion ................................ ................................ ........................... 92 Conclusions ................................ ................................ ................................ ............ 96 6 MUL TI COMPONENT AEROSOL STUDY ................................ ............................. 97 Experimental Methods ................................ ................................ ............................ 97 Intensity Normalizaton ................................ ................................ .................... 100 Plasma Diagnostics ................................ ................................ ........................ 103 Results and Discussion ................................ ................................ ......................... 106 Conclusions ................................ ................................ ................................ .......... 115 7 SUMMARY AND FUTURE WORK ................................ ................................ ....... 116 LIST OF REFERENCES ................................ ................................ ............................. 120 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 128
7 L IST O F TABLES Table page 2 1 Number of spectra remaining after each filtering algorithm ................................ 47 3 1 Parameters for the double pulse system ................................ ............................ 58 6 1 Range of delays used in each spectral window ................................ ................ 100 6 2 Elemental lines used for temperature and electron density calculations, alon g with their respective spe ctral windows and the property each line determined 106
8 L IST OF FIGURES Figure page 2 1 Experimental apparatus for upper size limit stud y. ................................ ............. 41 2 2 Spectra corresponding to the 15/5 s delay/gate of the 2.47 m silicon spheres. The peak shown corresponds to the 288.16 nm Si I line. .................... 45 2 3 Spectra, corresponding to the 15/5 s window of the 2.47 m silica particles, showing the results of the s tatistical matching algorithm. ................................ ... 46 2 4 Probability plot of the 288 .16 nm silicon emission line (P/B) for the 15/5 s detector gate corresponding to the 2.47 and 4.09 m diameter microspheres. .. 48 2 5 Ensemble averaged spectra corresponding to two different det ector gates (as noted) for the 2.47 and 4.09 m sized silica microspheres. ......................... 49 2 6 P/B ratios of the silicon emission line as a function of temporal gating for the 2.47 and 4.09 m microspheres and for the silicon rich nanoparticles. .............. 51 2 7 Ratio of the silicon analyte response of 4.09 m to the 2.47 m silica microspheres as a function of plasma evolution time. ................................ ........ 53 2 8 Ensemble averaged spectra corresponding to the full data set and the top 10% for the 2.47 m sized silica microspheres and the 35/5 s gate. ............... 54 3 1 Experimental apparatus for the double pulse and single pulse LIBS configuration. ................................ ................................ ................................ ...... 58 3 2 Timing schematic for the double pulse and single pulse experiments employing the double laser platform ................................ ................................ .. 61 3 3 1000 shot average LIBS spectra for 90% gas phase carbon (left) and 10% gas phase carbon (right) for both single pulse and double pulse ....................... 62 3 4 LIBS calibration curves for 90% gas phase carbon (left) and 10% gas phase carbon (right) for both single pulse and double pulse configurations. ................ 64 3 5 Signal to noise ratio as a function of the percentage of gaseous carbon for a fixed total carbon concentration of 5.8 g/L. ................................ ....................... 66 3 6 Slopes of the calibration curves as a function of percent gas phase carbon for the single pulse and double pulse LIBS configurations. ................................ 67 3 7 Ratio of double pulse to single pulse LIBS calibration curve slopes as a function of the percentage of gas phase carbon. ................................ ................ 68
9 4 1 Experimental apparatus for spectral LIBS measurements. ................................ 73 4 2 The earliest ICCD gate (0/100 ns) for the spectral data along with the reference laser pulse. ................................ ................................ ......................... 74 4 3 Spectral data recorded for breakdown of pure nitrogen gas, as recorded at a delay of zero (left) and 1 s (right) with respect to the incident laser pulse. ....... 76 4 4 Spectral data recorded in side scatter for breakdown of the steel target at a delay of zero (left) and 1 s (right) with respect to the incident laser pulse. ....... 77 4 5 The Fresnel reflectivity values for horizontal and vertical polari zation states for pure copper and iron surfaces as a function of the angle of incidence. ......... 79 4 6 Temporal data recorded for breakdown of pure nitrogen gas corresponding to collection in backscat ter and side scatter. ................................ .......................... 82 4 7 Temporal data for breakdown of steel target, as recorded in side scatter (left) and back scatter (right), with resp ect to the incident laser pulse. ....................... 83 5 1 Experimental apparatus for Thomson scattering temporal measurements. ........ 88 5 2 Sample spectra showing the extraction of the green probe signal The laser waveform is given as a reference. ................................ ................................ ...... 91 5 3 Differential scattering coefficients versus delay at all distances from the ................................ ................................ ................................ 93 5 4 Times at which the local maxima occur. The shaded data points refer to the absolute maxima at each spa t ial position. ................................ .......................... 94 5 5 Differential scattering coefficient for both l ocal maxima at each spatial position. The shaded data points refer to absolute maxima. .............................. 94 5 6 Thomson scattering spectra showing the signals for the plasma with the green probe laser, plasma on ly, and the subtracted green laser only. ............... 95 6 1 Sample TEM images of aerosol particles formed in aerosol stream during particulate analysis. Particles ranged in size from 50 500 nm. ........................ 99 6 2 Sample EDS spectrum for the sodium matrix experiment.. ................................ 99 6 3 Calibrated lamp source irradiance as a function of wavelength. ....................... 103 6 4 Sample spectra. These plots correspond to Lu II at various times. .................. 104 6 5 Sample spectra for the H alpha line at various times (l eft) and linear fits used to determine Stark broadening of the H alpha line (right). ................................ 105
10 6 6 All spectral windows used after all irradiance corrections have been applied. Shown here are the spe ctral windows at a delay of 1.5 s. .............................. 107 6 7 Boltzmann plot of Ar II. ................................ ................................ ..................... 108 6 8 Bulk plasma temperature calculated from Ar II (left) and N II (right). ................ 109 6 9 Local plasma temperature as determined by Lu II (left) and Mn II (right). ........ 110 6 10 Local plasma temperat ure as determined by Lu II (left) and Mn II (right) with representative error bars ( 1 ................................ ................................ ....... 111 6 11 Temperatures derived from all species. The full temporal range is shown on the left and a close up view of the first 15 s on the right. ................................ 112 6 12 Temperatures derived from all species on a log log scale. The slope shift point at 15 25 s is clearly evident in this presentation. ................................ ... 113 6 13 Bulk plasma electron d ensity, as measured by the H and Ar II 484.78 nm lines, on a semi log scale. Full error bars denote one standard deviation. ....... 114 6 14 Comparison of the local plasma temperature using Lu II in normal matrix versus the heav y sodium matrix. ................................ ................................ ...... 115
11 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy THE ROLE OF PL ASMA PARTICLE INTERACTIONS IN QUANTITATIVE LIBS ANALYSIS OF AEROSOLS By Michael L.E. Asgill A ugust 2012 Chair: David W. Hahn Major: Mechanical Engineering Laser I nduced Breakdown Spectroscopy (LIBS) is an analytical technique that uses atomic emission t o identify and quantify the chemical composition o f a sample. LIBS q uantitative analysis is idealized by instantaneous and complete dissociation, vaporization, and ionization of the sample within the focal volume with the atoms and ions quickly diffusing throughout the ensuing plasma. This ideally results in a homogenous distribution of exited atoms and ions whose atomic emission is proportional to the concentration of the elements present. However, r ecent work has shown this i dealization to not be the cas e. The current study seeks to provi de additional insight into the plasma particle interactions that cause the LIBS response to deviate from this idealization Measurement s with silica particles near the previously reported upper size limit range showed tha t increased residence time within the plasma does not affect the upper size limit despite the presence of sufficient energy within the plasma to completely dissociate the particles. Experiments with solid carbon particles and carbon dioxide gas showed not only that the LIBS analyte response was dependent on the source of the sample, but also that the two different sources of carbon could be distinguished after the fact.
12 Data was gathered in an attempt to quantify a possible polarization matrix in LIBS measu rements, but such data showed no significa nt polarization short of time dependent Fresnel reflectivity effects due to plasma light being reflected off the sample surface. Experiments done at very early times, less than 1 s, confirmed the presence of pl asma condition s sufficient to induce Thomson s cattering in a LIBS plasma but the satellite peaks could not be observed. Plasma temperature measurements with multi element aerosols revealed a distinctive change in the slope of the temperature cur ve; this re flects the effects of local plasma cooling on plasma properties. A change in the matrix of the aerosols resulted in measurable shifts in the temporal temperature profile. Overall, the current set of experiments shows the strong dependence of the LIBS signa l on plasma particle interactions and highlights the need for a complete understanding of this phenomenon. Finally, additional experiments are proposed to further facilitate this understanding.
13 CHAPTER 1 I NTRODUCTION This research d issertation covers studies on the fundamental processes governing the use of laser i nduced breakdown spectroscopy for analysis of aerosol particles. The first step of this process is a review of the laser induced breakdown event and the major factors that affect the analytical signal ; then follows a summary of the basics of laser induced breakdown spectroscopy including the instrumentation and major challenges. Next, the focus shifts to aerosol analysis by this technique with special emphasis on the interactions of the plasma with individual aerosol partic les. Following a summary of relevant plasma diagnostic techniques i s a detailed explanation of works completed and p roposed by the author for the advancement of current knowledge in the field of laser induced breakdown spectroscopy of aerosol particles. Laser Induced Breakdown : The Beginning of LIBS Laser induced breakdown can be defined as the generation, by the end of the laser pulse, of a highly ionized gas, i.e a plasma. [ 1 ] Once the plasma is formed, it emits light over a very wide spectral range producing its characteristic bright white light. It will also absorb ver y strongly along many wavelengths, especially early in its lifetime, thereby greatly reducing the percentage of its parent laser beam that is transmitted. Therefore, plasma formation can be qualitatively verified in an experiment as a glow or flash or qua ntitatively by measuring the ionization and the laser beam attenuation at the focal point. Laser induced breakdown is accomplished by focusing a laser beam to a small enough focal volume to produce an irradiance, I (W/m 2 ), that is greater than or equa l to the threshold irradiance, I th for breakdown. There are many factors that influence which
14 mechanism will be dominant in the breakdown process, and thus the threshold irradiance. The more important of these factors include the state (solid, liquid, or gas) and type of material, the presence, or absence, of impurities and surface defects, and the wavelength of the laser. The following description of plasma inception foll ows the treatment by Weyl [ 1 ] Breakd own in Gases There are two main processes that govern plasma inception in a gaseous medium. The first is impact ionization, also called inverse Bremsstralung or cascade ionization. It i nvolves the absorption of photon s from the laser beam by free electrons When the electrons gain sufficient energy they are capable of transferring enough energy to a bound electron within a neutral atom to strip the electron from the atom, thereby ionizing it. [ 1 ] The process foll ows the formula e below where e represents the electron h the energy of a photon and M the medium. ( 1 1 ) ( 1 2 ) The two free electrons in re action ( 1 2 ) will continue to absorb laser radiation until they undergo impact and ionize two more neutrals, thereby creating four electrons, and so on, causi ng a catastrophic increase in ion concentration within the focal volume. The two necessary conditions for this reaction are that there needs to be at least one seed electron, and the electrons have to absorb enough energy to exceed the ionization energy of the gas. This mechanism requires relatively high laser irradiance and is more prevalent at shorter laser wavelengths.
15 As mentioned above, impact ionization requires a seed electron to occur. [ 2 ] At high laser irradiances and shorter wavelengths, a mechanis m known as multi photon ionization, MPI, can create such seed electrons. MPI occurs when a neutral atom simultaneously absorbs multiple photons, whose combined energy exceeds the ionization energy of the atom. [ 1 ] The process follows the following formula, where m represents the total number of photons needed for MPI. ( 1 3 ) It is important to note that there are other ways of creating a seed electron. For example, very high laser irradiances may create an electric field strong enough to strip a valence electron from its outer shell by the tunneling effect. [ 1 ] [ 3 ] Also, there are natural ions present in the atmosphere, as well as those created by cosmic rays and radio activity. Breakdown of Solids Similarly to gases, breakdown of pure non absorbing, or transpare nt, solids will be controlled by MPI and impact ionization, with the band gap replacing the ionization energy, resulting in rather high breakdown thresholds. However, if the solid absorbs at the laser wavelength, a third ionization mechanism is observed called the t hermal run a way It occurs when absorption of radiation on the solid surface causes rapid vaporization and the formation of a vapor layer on the solid. The vapor layer insulates the rest of the solid and absorbs the energy from the laser beam. The vapor can reach a high enough temperature as to become partially ionized, at which point absorption by sufficiently high temperature, its formation can drive a shock into the surroundi ng air. If
16 the shock is strong enough, it heats the air causing thermal generation of more electrons, which can lead to breakdown through impact ionization at sufficient laser irradiance s [ 4 ] [ 5 ] Impurities, Surface Defects, and Aerosols Even the purest of materials are expected to have impurities and surface defects (cracks, grooves, spherical spores) and these play an important role in the plasma breakdown process. [ 6 ] Materials that are not of optical quality are found to have much lower breakdown thresho lds. For example, impurities it solids can have energy levels that lie close to the conduction band of the bulk material, thereby requiring a much lower threshold irradiance to produce seed electrons. They can also cause local field enhancements or localiz ed heating that would lead to a thermal runaway It has been shown that in metals, breakdown occurs on thermally insulated defects. [ 7 ] Microscopic suspended particles also have a similar effect on the breakdown of liquids. [ 8 ] Soluble impurities, however, do not noticeably reduce the breakdown threshold. In general, focal volumes will have a distribution of particle sizes. The larger the focal volume, the greater the probability of it having a large inclusion that will greatly reduce the breakdown threshold [ 9 ] For experiments in unfiltered gaseous mediums, the actual breakdown threshold will be determined by the size of the largest aerosol within the focal volume. [ 1 ] This can cause sporadic breakdown events a t low irradiances. Attachment, Recombination, and Diffusion Losses Just as impact ionization, MPI, and thermal runaway s increase the number of mechanisms work to reduce t he electron density. A more complete picture of electron density, n e growth is given by the following equation [ 1 ]
17 ( 1 4 ) where m is the minimum number of photons required for MPI, W m is the MPI rate coefficient, D is the electron diffusion coefficient and i a r are the impact ionization, attachm ent, and recombination rates, respectively. Attachment & Recombination Attachment is especially important in the presence of molecular gases. It occurs according to two main mechanism s : three body attachment ( 1 5 ) and two body dissociative attachment ( 1 6 ) Three body attachment becomes decreasingly likely as electron energy increases. Conversely, two body dissociative attachment has an energy threshold equal to the difference between the ener gy needed to split AB and the energy gained by the attachment of the electron. [ 10 ] It therefore becomes more likely as the electron energy increases. Similar to attachment, electron ion recombination has three body and two body diss ociative mechanisms shown below: ( 1 7 ) ( 1 8 ) Diffusion Diffusion of electrons out of the focal volume has two regimes. When the Debye D the distance over which significant charge separation occurs, is larger than the radius of the laser beam, the electrons can diffuse freely as a single species.
18 Howe ver, when the Debye length is smaller than the beam radius, the electrons cannot with them in order to diffuse out. The diffusion then becomes ambipolar and the diffu sion coefficient is reduced by the square root of t he electron to ion mass ratio, about two orders of magnitude. [ 1 ] It is important to note that the processes in equation ( 1 4 ) do not always work independently o f each other. For example, electron impacts that do not have enough energy to ionize, but that can bring a neutral to within 1 or 2 h of ionization can make that neutral very easy to ionize by MPI. Also, electron ion recombination can create a population of excited state neutrals that can be easily ionized by MPI or impact ionization. [ 11 ] Laser Induced Breakdown Spectroscopy (LIBS) Laser I nduced Breakdown Spectroscopy (LIBS) is an analytical tech nique that uses atomic emission to identify and quantify the chemical composition of a sample. Early after their development, lasers were used primarily as an ablation source with their first use in spectro chemical analysis reported in the mid 1960s [ 12 ] However, LIBS could not compare with other similar techniques such as inductively coupled plasma mass spectrometry (ICP MS) and ICP atomic emission spectroscopy (ICP AES), in terms of accuracy and precision. With the development of better instrumentation, the accuracy of LIBS began to increase, which, coupled with its unique advantages, led to a renewed interest in the community in the 1980s. LIBS enjoys several advantages including the ability to make in situ measurements, little or no nee d for sample preparation, applicability to solid, liquid, gaseous and aeroso l samples, simultaneous measurement of multiple elements, and
19 very short processing times. The simplicity of a LIBS setup along with operation without sample preparation allows for the instrumentation to be taken directly to the source of the sample. Also, since only an optical port is required for measurement LIBS measurements can be taken without noticeable impediment to normal operations. This makes LIBS the measurement system of choice in many applications, such as process monitoring [ 13 ] remote sensing [ 14 ] biomedical applications [ 15 ] and detection in hostile environments. [ 16 ] However, quantitative measurement with LIBS is not a trivial pursuit. As discussed above, LIBS uses a focused laser beam to vaporize and ionize the sample, creating a highly energet ic plasma. At the termination of the laser beam, the radiation has a blackbody profile i.e. continuum, as the free electrons, which have a broad Maxwellian energy distri bution, begin to lose energy via Bremsstralung radiation, ion recombination, and attachment mechanisms. As the plasma cools even more, the emission becomes dominated by the relaxation of excited electrons within the energy levels of ions and neutrals, crea ting distinct peaks in the emission spectrum whose wavelengths directly correspond to the change in energy levels of the electrons. These atomic emission peaks can then be compared against known, tabulated emission wavelengths to identify the emitting spec ies within the plasma. Also, since the intensity of the peaks is proportional to the mass concentration of the species in the plasma, it is possible to make quantitative analyses. Instrumentation The basic LIBS setup consists primarily of a laser, a spect rometer and a detector. The laser produces a collimated beam of photons at a specified wavelength. Any number of mirrors, selected for maximum reflection at the selected wavelength, may be
20 used to direct the laser towards the sample of interest, where a le ns is used to focus the beam onto the focal volume, forming the plasma. Once the plasma is created, more mirrors, effective in a broad or narrow wavelength range, may be used to direct the plasma light towards a se cond lens which focuses it either into a f iber optic cable or directly onto the entrance slit of a spectrometer. If used, a fiber optic cable simply transmits the light along its length to a spectrometer; however, it can be placed closer to the emitting plasma than the spectrometer itself, resulti ng in less loss of plasma light and limiting the introduction of stray light in some cases The spectrometer disperses the light acc ording to wavelength and direct s it onto the detector. The detector is usually either a charge coupled device (CCD), intens ified CCD (iCCD), or a photo multiplier tube (PMT); it converts the light into an electrical signal using the photoelectric effect. The electrical signal then travels to a data acquisition (DAQ) device which changes it from an analog to a digital signal fo r recording and/or display on a computer. Unlike other plasma sources, such as inductively coupled plasmas (ICP), LIBS plasmas are highly transient, cycling from ambient temperatures to plasma temperatures between 30,000 and 60,000 K and back to ambient c onditions many times a second. As a result, setting a proper delay between the laser pulse and the start of plasma collection and a proper integration time of the signal is critical to ensuring that the light captured by the detector corresponds t o times w hen atomic emission from the plasma is prevalent. [ 17 ] Challenges As stated by Corsi et al., [ 16 ] many of the complications that arise during quantification in LIBS stem from the nature of a laser induced breakdo wn. Focusing the
21 laser beam, for example, results in a very small sampling volume. This in turn causes the LIBS signal to highly dependent on the homogeneity of the sample. Not only does the sample need to be homogeneous but the fraction of the sample that is ablated, vaporized, and analyzed must be representative of the relative concentrations in the bulk sample. Also, any surface contaminants or defects affect not only the reproducibility of the plasma itself, but also the species measured in the results. In addition, the intensity of the measured peaks is dependent on not just the species concentration but the properties of the plasma itself, i.e. temperature and electron density. These properties are in turn dependent on the energy and wavelength of the emission source as well as the type of sample and the ambient gas into which the plasma propagates. Corsi and colleagues [ 16 ] go on to categorize the different elements that can affect the measured intensity o f any emitting species within laser induced plasmas into four main categories described by the following equation, where S refers to the measured intensity and A ij is the Einstein transition probability for spontaneous emission of the selected emission lin e: ( 1 9 ) Here, int represents the interaction of the source laser with the sample and incorpor ates any heating, ablation, ejection and vaporization of the particles to be included in the plasma. Similarly, exc represents the excitation, that is, the actual breakdown process and factors affecting the growth of the plasma, and the electronic, ionic, and neutral relaxations within the cooling plasma that lead to emissions from the plasma. Lastly, det governs the detection of plasma light, i.e. the processes between
22 the emission of the light by the plasma, to its collection, and the eventual determina tion of the signal intensity. Detection Detection of plasma light can be subdivided into two categories: collection of the light, and its transmission through the instrumentation, i.e. the probability that a photon of a particular wavelength makes it thro ugh all the instrument pathways and is accurately reflected in the intensity measurement. An accurate total transmission measurement must take into account all possible losses including reflectivity of collecting mirrors, transmittance of focusing optics, transmission efficiency of the fiber optic, dispersion by the spectrometer, detection efficiency of the detector, electrical losses along cables, and analog to digital conversion efficiency, many of which are wavelength dependent. It is possible to calcul ate this wavelength dependent transmission function based on manufacturer provided data for each component of the system. More commonly, the transmission function can be measured using a calibrated emission source with a known absolute emission intensity a t each wavelength. The transmission through the instrumentation can be obtained by comparing the measured spectral emission with the actual emitted intensity. While transmission through instrumentation can be measured and accounted for, little can be done to improve it short of costly equipment upgrades. Light collection offers more room for possible improvement in the overall det ection function. It involves maximizing the amount of plasma light collected while minimizing the quantity of stray light that co ntaminates the measurements. Maximizing plasma light is a simple matter of increasing the solid angle of the collected light, usually by moving the capturing optics as close as possible to the plasma without interfering with its
23 formation or damaging the o ptics. When doing so, it is possible to saturate the detector, making the use of filters (neutral density, high/low/band pass) necessary to attenuate the signal without sacrificing solid angle. Interaction As mentioned before, because of the high irradianc es needed to initiate breakdown, the focal volumes involved in LIBS are very small, sometimes orders of magnitudes smaller than that of the bulk sample. Therefore, in order for the measurements to be useful, it must be assumed that the concentration of ato ms in the focal volume is the same as that in the entire sample and that the signal measured is representative of the concentration in the focal volume. [ 16 ] Many factors can affect whether this objective is ach ieved, such as laser fluence, wavelength and pulse width, [ 18 ] [ 19 ] crater depth in solids, [ 20 ] particle size in aerosols, [ 21 ] [ 22 ] and the presence, or absence, of other elements within the sample. [ 23 ] A ctual values for some of these parameters vary depending o n experimental conditions and so the assumption must be verified for each setup. The effect of additional elements in the sample on the intensity of the measured element, that is, the lack of independence of the LIBS signal on the analyte source, is refer red to as matrix effects and will be discussed in detail later. In general, matrix effects may be reduced by increasing laser power, using matrix matched standards, that is, a sample of similar composition as that of the sample of interest with known conce ntrations of elements, to calibrate the system response, and separating the ablation and measurement process. [ 24 ] Excitation The excitation factor covers the formation, growth, and cooling of the LIBS plasma. The formation of laser induced plasmas has been covered earlier in this chapter. After
24 the plasma is formed, it simultaneously cools and expands behind the shockwave generated by its formation. [ 25 ] During cooling there are three distinct periods that characterize the plasma. The first is right at the end of the laser pulse, at which time the plasma emits the most photons but this emission is dominated by broadband blackbody radiation. Any atomic emissions that occur during this period come from singly and, rarely, doubly ionized species, e.g. N II and N III. The second period contains emissions from singly ionized and neutral species, e.g. N II and N I. As this period progresses, the percentage of photons emitted from atomic emission rises noticeably. The third period is dominated by neutral and some mole cular emissions, e.g. N I and N 2 + with the backg round blackbody radiation becoming negligible. As much as possible, LIBS data should be confined to the second and third emission periods, due to complications from the equilibrium condition. Equilibrium The excitation, ionic, and radiation temperatures. These temperatures are defined by the Maxwell, Boltzmann, Saha, and Planck functions, respectively. [ 16 ] The kinetic temperature is determined by the collisional rate and energies of the species present. There is a kinetic temperature for electrons, neutrals, and each ionized state within a LIBS plasma. However, the timescale required to reach c ollisional equilibrium within the kinetic temperatures are assumed to be equal and are collectively referred to as the electron temperature, T e The excitation temperature, T exc is related t o the distribution of electrons within atoms. In a low energy environment, almost all of the atoms in a species have their valence electrons in the ground state. As the energy of the species increases, the
25 percentage of atoms with electrons in excited ener gy levels increases, until the populations of these energy levels becomes non trivial. The distribution of these electrons in excited energy levels thus correlates to the excitation temperature. As the energy of the species continues to rise, the electron s will begin to escape their orbitals altogether, creating singly ionized, and then doubly, triply, etc. ionized species. The distribution of the ionizations states of atoms of a specific element can be used to determine the ionic temperature, T ion of the system. All systems emit radiation, however, as a system becomes more energetic, the wave number and frequency of its emission increases. This in turn can be used to sin gle value, then the temperature of the system becomes defined and the system is said to be in thermodynamic equilibrium. However, within LIBS plasmas, the timescale required for the radiative temperature to converge on the others is longer than that for at omic emission. Therefore, it becomes necessary to discuss local thermodynamic equilibrium (LTE). Local thermodynamic equilibrium is the state within the plasma when the electron, excitation, and ioni c temperatures have converged to the same value but the r adiative temperature has not. This creates a situation where at any time, the temperature in any given differential control volume within the plasma is defined but the temperature of the entire plasma is not. For this localized temperature to exist, the en ergy lost by radiation from the control volume has to be easily replaced by collisional energies in order to render the non equilibrium negligible. [ 16 ] [ 26 ] As such, the collisional rate should be at
26 least ten times that of the radiative losses, which requires a minimum electron density given by the McWhirter criterion (cm 3 ): [ 16 ] ( 1 10 ) for which the criterion holds. It is possible for the criterion to hold for some energ y transitions but not for others, in which case the plasma is considered to be in partial LTE. [ 27 ] It is important to note that the criterion is a necessary but insufficient condition for LTE. [ 28 ] Experimentally, LTE can be verified by measuring the excitati on temperature and comparing it to the ionization and electron kinetic temperatures. Aerosol LIBS An aerosol is a solid or liquid particle suspended in a gas medium. LIBS can be used to measure aerosol particles in a variety of processes such as combustion [ 29 ] waste management, [ 30 ] ambient air analysis, [ 31 ] bio aerosol identification [ 32 ] and continuous emissions monitoring, [ 33 ] [ 34 ] with interest in fine particulate matter (e.g. PM2.5 and PM10) peaking in recent years in the face of increased emission and poll ution standards. [ 35 ] Aerosols can be measured at either ambient conditions or within a flow of some gaseous medium, the more notable being air, nitrogen and argon. As such, the detection of the particulate form of elements present in the suspending medium ( e.g. oxygen and nitrogen in air flow) becomes moot, and quantification impossible. Therefore, some caution must be exercised in the use of carrier gases so as to minimize interference with the aerosol. Aerosol analysis differs from others mainly in that an aerosol particle is a very discrete unit. With solids, liquids, and gases, as long as the plasma forms within the
27 sample volume, each laser spark will provide useful information about the sample. However, for aerosol analysis, even though the plasma forms within the flow volume, there is no guarantee that each laser spark will encompass an aerosol particle. complicated by partial hits, in which only a portion of a part icle lies within the plasma, and multiple hits. At high particle loadings (particles per unit volume), in which the probabilities for single and multiple hits dominate and the miss probability becomes negligible, the aerosol stream is a continuum of partic les similar to a (porous) solid, enabling the ensemble averaging of data to produce accurate results. [ 36 ] This is not the case for very low particle loadings. In low particle loadings, in which the probability of a miss dominates, ensemble averaging no long er becomes viable. For instance, at a hit rate of one percent, averaging one hit with 99 misses may bring the measured peak within the noise level of the averaged spectrum, lowering the signal to noise ratio (SNR) and raising the detection limits. However, the very discrete nature of the aerosol particles provides a solution, in the form of conditional analysis. Conditional Analysis Conditional analysis refers to the method of discriminating between hits and misses during the processing of a LIBS spectrum, [ 37 ] [ 38 ] and has been used for low loading situations such as toxic metals in waste streams [ 34 ] and ambient air measurements. [ 31 ] [ 39 ] For other media, a low concentra tion manifests itself as a consistently low signal present in most plasma shots, providing little or no actual signal for analysis. For aerosols, a low concentration manifests itself as the occasional high
28 possible to separate hits from misses, by setting some threshold value. The hits then provide measurable signals, from which quantitative analyses can be done. Any measured concentrations must then be multiplied by the pa rticle sampling rate (PSR) to obtain the true concentration. This method greatly enhances the SNR and sensitivity, and lowers detection limits of LIBS during aerosol analysis. Work by Hahn and colleagues [ 37 ] h ighlight the need for a large enough number of hits to accurately reflect the particle size distribution and particle loading. In particular, they noted that about 19 hits are required to accurately reflect the volume m ean diameter of a typical size distri bution. They also note the importance of terminating data collection based on a pre determined number of shots, rather than a desired number of hits, as the latter can skew the determination of the PSR. Carranza et al. [ 40 ] found that using SNR value s to set the hit threshold was more robust than using the peak to base ratio (P/B). Upper Size Limits Many studies involving aerosol particles delve into quantitative analysis and as such make the fundamental assumption, stated or not, that all species in the aero sol particles sampled are completely broken down and vaporized. However, many studies have shown that there is a distinct upper size li mit, past which aerosol particles do not completely dissociate. [ 41 ] The exact value of that limit is unclear and may depen d on the thermo physical properties of the particles themselves, such as melting points and volatility, and on the laser parameters [ 42 ] Essien et al. [ 43 ] reported an upper size limit of beryllium aerosols at 10 m in diameter whereas Carranza and Hahn [ 22 ] reported 2.1 m in silica micro spheres, Vors and Salmon [ 44 ] reported a limit of 5 m using carbon
29 rich particles (glucose and hydrogenocarbonate paticles) and Gallou et al [ 45 ] reported a 7 m limit with cupper s ulfate particles Carranza and Hahn [ 22 ] suggested that the incomplete vaporization can be due to insufficient particle residence time in the plasma. Though many papers have cited a 10 m upper size limit for co mplete particle vaporization, [ 46 ] [ 47 ] it is important to determine the actual limit for each sample and experimental setup to ensure accuracy of quantitative results. This may be determined by observing a deviation from a linear mass response for progressiv ely increasing aerosol diameters. [ 22 ] Plasma Particle Interactions The presence of a measurable upper particle size limit calls into question some of the fundamental assumptions used in LIBS to explain analyte response, namely that the sample is instantaneously and completely dissociated and diffused within the highly energetic plasma, resulting in emission at the bulk plasma temperature and a linear signal with increased mass concentration. As explained by Hah n, [ 42 ] the validity of those assumptions is dependent on process rates. If the vaporization and dissociation timescales are much less than the analytical timescale, then the processes can be modeled as instanta neous and the signal response would scale linearly with analyte mass. Likewise, if the timescales for diffusion of heat and analyte mass through the plasma are much less than the analytical time scale, then the plasma can be modeled as homogeneous and the atomic emission observed would correspond to bulk plasma conditions. Considerable research has been conducted to determine which case is appropriate.
30 Dissociation and Mass Diffusion T imescale To that end, Hohreiter and Hahn [ 48 ] used quantitative plasma imag ing of calcium to measure the diffusion timescales. Their results show that the diffusion timescale is quite finite, that is, it is on the same order of magnitude as plasma emission, ~15 s for the vaporization of 2 m glass particles Most of the early ti me calcium emission originate s in an area surrounding the location of the original particle and slowly diffuse s out during the analysis. This result is in agreement with Lithgow and Buckley, [ 49 ] who found spatially inhomogeneous atomic emission in magnesium containing aerosols and Hieftje et al. [ 50 ] who proposed a similar diffusion process in analytical flames and plasmas. Based on the spatial positioning of the calcium particles within the plasma relative to the location of the incident laser pulse, Hohrei ter and Hahn [ 48 ] also concluded that the dissociation process is dependent on the particle plasma interactions as opposed to particle laser interactions. This is in agreement with Carranza and Hahn [ 22 ] who used the Poisson probability distribution to calculate particle sampling rates using both the laser beam sample volume and the plasma sampling volume. They found experimental sampling rates to correlate with the pl asma sampling volume, indicating that particle plasma interactions drive the breakdown process. These results suggest that the heat transfer rate from the plasma to the particle (dissociation), the mass transfer rate of the atomic species (mass diffusion) and the radiative decay rate of the plasma (plasma cooling ) are all on the same timescale as atomic emission ; as such, instantaneous behavior, as described earlier cannot be assumed in a LIBS plasma. Indeed, Dalyandar et al. [ 51 ] calculated the dimensionl ess
31 Lewis number, relating thermal diffusivity, to the mass diffusivity, D, during a numerical simulation and found it to be on the order of 1. In light of these findings, Hohreiter and Hahn [ 48 ] propose a temporal analogue to the upper size limit, in which a particle within a plasma dissociates at early times, when the plasma is very energetic, until the plasma cools to such a point that vaporization is no longer possible. At that point, dissociation ceases and the measured mass of the particle plateaus, if it is no t completely dissociated by that critical time Heat Diffusion Timescales Along these lines, Diwakar et al. [ 23 ] used magnesium cadmium particles to c alculate the emission temperature of atoms versus delay time and found the temperature to increase with time over a certain early time regime Given the localized nature of aerosol particle emissions as stated above and the fact that bulk plasma temperatur es decrease rapidly with time, it was concluded that the temperatures measured were local plasma temperatures around the particle. The authors theorize that in order to dissociate, the particle draws a large amount of energy from the immediately surroundin g plasma. Since the rate of heat transfer within the plasma is on the same timescale as the particle dissociation, the heat lost by the plasma to the particle is not rapidly replaced, creating a localized cooled plasma around the dissociated atoms, causing them to emit at a lower temperature. As the atoms diffuse to the hotter parts of the plasma and energy is transferred to the localized cooled plasma from the bulk, the emitting temperature of the atoms begins to rise until the particles reach an equilibri um temperature with the plasma. These results are consistent with measurements done by Diwakar et al. [ 52 ] who found inflections in the slopes of the
32 temperature curve of Lu and the ion to neutral ratio of Mg at around the 15 20 s point. Miclea et al. [ 53 ] a nd Groh et al. [ 54 ] found similar results in an inductively coupled plasma. Diwakar and companions [ 23 ] went on to perform temporal measurements with sodium and magnesium with concomitant masses of copper, zinc o r tungsten and found up to a 50% increase in the neutral emissions, with enhancements decaying wi th time. They again attribute this finding to the suppression of local plasma temperature s about the particle due to the added masses, which results in a highe r neutral to ion ratio. The time decay of these emission enhancements corresponds to the heating of the atomic species as the plasma approaches equilibrium, lowering the neutral to ion ratio. This provides evidence of significant matrix effects with aeroso l LIBS related to local plasma cooling. Their work contrasts with work by Essien et al. [ 43 ] which shows agreement of lead atomic emission from lead acetate, lead chlori de and lead nitrate within 10% in the 20 to 40 s delay range but only a 27% agreement between cadmium nitrate and cadmium chloride. More importantly, in that same study, the researchers found enhancement of lead emission in the presence of sodium. This enhancement decreased between 20 and 30 s with a suppression of background emission of 30% for all delays examined This trend of decreasing enhancement is similar to that observed by Diwakar et al. [ 23 ] The suppressed background is consistent with d ecreased bulk plasma temperatures due to the cooling effect of the additional sodium mass on the local plasma conditions, which in turn requires additional heat to be diffused from the bulk plasma for equilibrium. The takeaway theme from these studies is that the non ideal state of LIBS plasmas diminishes with time. Whereas previous assumptions placed heat and mass
33 tran sfer rates in the nanosecond regime or faster, these recent studies show them to be mor e on the order of tens of micro seconds, well within the analytical timescale. However, the longer the delay between plasma formation and signal collection, the closer the plasma will be to a uniform heat and mass distribution and the lesser the effects of the matrix on the signal. Such findings serve as a p artial motivation for the current research. Plasma Expansion In addition to these diffusion problems, experiments have been done on the effects of the analyte phase on the signal response of LIBS, with the results also challenging the assumption of signal independence on analyte source. Hohreiter and Hahn reported a different analyte response for gas phase and particle phase carbon samples, finding a stronger response, that is, increased calibration slope for the particulate aerosol. [ 55 ] This is attributed t o plasma shock expansion which can carry the lighter gas phase species out of the emitting volume i.e. rarefaction while the heavier solid species have enough inertia to resist the shockwave. Just as important as the spread between the phases is the sp read within; gas phase species showed a variation in calibration slope of about 10% whereas solid phase aerosol species show ed a variation on the order of 100%. This order of magnitude difference highlights the effects of plasma particle interactions on th e LIBS signal. The rarefaction phenomenon is corroborated by Windom et al. who experimented with double pulse LIBS (D P LIBS) at atmospheric pressures and found that the P/B for gaseous species during D P LIBS varies little compared to that for single pul se LIBS (S P LIBS) whereas the P/B for particulate aerosol species increased significantly. [ 56 ] The
34 rarefaction reduces the percentage of gaseous species within th e plasma volume, which increases coupling of the plasma with the solid aerosol particles, the reby increasing the signal to noise and the peak to continuum ratios D P LIBS refers to the use of two lasers, or a single laser with split pulses, with a delay between the two pulses, in which the second plasma forms wholly within the expanded volume of the first. [ 57 ] It has been shown to increase the analyte signal for solids. [ 58 ] [ 59 ] [ 60 ] [ 61 ] Plasma Diagnostics Plasma diagnostic tools enable the determination of plasma properties that help to characterize plasma behavior Chief among these properties are p lasma temperature and electron density. Included below are methods for calculating the Boltzmann and Saha Boltzmann temperatures, as explained in the above subsection on equilibrium, as well as two methods for determining the electron density within plasma s. Also included is an analysis of Thomson scattering, which aids in determining temperature at very earl y times, before atomic emission become s dominant. Boltzmann Temperature The most popular method of calculating the plasma temperature is the Boltzmann plot method, which actually calculates the excitation temperature, T exc During LTE, the population of the excited levels for each species follows a Boltzmann distribution given by: [ 16 ] ( 1 11 ) where is the population density of excited level i of species s n s is the total number density of species s g i is the statistical weight and E i the excitation energy of the level, k
35 is the Boltzmann constant, and U s (T) is the internal partition function of the species at temperature T given by: [ 16 ] ( 1 12 ) Assuming the level populations follow the Boltzmann distribution, and that the plasma is optically thi n at that wavelength, the intensity of the emission line corresponding to the transition from upper level i to lower level j can be given by: [ 16 ] ( 1 13 ) The excitation temperature can be determined from the intensity ratio of a pair of spectral lines corresponding to different energy levels of the same element in the same ionization state. However, the precision of such a calculation is usually low due to errors in not only the measured intensities but also in the reported values of transmission probabilities, A ij and statistical weights. Linearization of equation ( 1 13 ) helps to reduce sensitivity to those errors, producing: [ 16 ] ( 1 14 ) Given the line intensities and upper energy levels, ( 1 14 ) enables us to plot the left side of the equation versus the upper energy level, E i producing a linear plot with a slope of The more transitions used, the less sensitive the temperature becomes to errors in any single value. Generally, a wide s pread in the upper energy levels of the chosen transitions improves the accuracy of the measured temperature.
36 Saha Boltzmann Temperature The plasma temperature can also be calculated by using a combination of the Saha ionization and Boltzmann excitation di stributions. It is important to note that the temperature obtained from this method is both the ionization and excitation temperatures (T ion =T exc ), thereby making the implicit assumption of LTE. The Saha Boltzmann equation in terms of neutral and singly i onized species is given by : [ 16 ] ( 1 15 ) where I a nd II denote the atomic and singly ionized species, respectively, E ion the first ionization potential and ion th e lowering correction parameter Similarly to the Boltzmann equation, the Saha Boltzman equation can be linearized to yield: [ 16 ] ( 1 16 ) Plotting the left side of the equation versus the energy differences yields a linear plot with a slope of Also, since geometric factors cancel out, the elect ron density, ne, can be obtained from the intercept without absolute intensity calibrations. [ 62 ] Electron Density Other than the Saha Boltzmann method mentioned above, the electron density can also be obtained from Stark broadening. Stark broadening is caus ed by the electric field generated by free electrons perturbing the energy levels of the atoms, thus broadening the emission wavelength of these levels. Since the main broadening mechanism in LIBS is Stark broadening [ 63 ] the electron density can be derived from the
37 Stark broadening equation. This equation, given as full width at half maximum (FWHM) in nanometers is: [ 16 ] ( 1 17 ) The first term in the sum is from the electron interaction and the second is from the ion interaction. Under the assumption of negligible ion broadening, typical in LIBS, equati on ( 1 17 ) simplifies to: [ 16 ] ( 1 18 ) The temperature dependent electron impact half width, w is given in the literature. [ 64 ] Thus, by measuring the FWHM of an emission line, the electron density can be obtained independen t of any LTE assumptions. Thomson Scattering Thomson scattering is an analytical technique in which incident radiation interacts with charged particles in the plasma, causing the frequency of the incident radiation to shift. It can be used to measure both electron temperature and number density without the assumption of LTE. Also, because Thomson scattering requires high electron densities, it can be used to probe for pl asma properties at very e arly times when atomic emission is not present and continuum em ission dominates The description presented here follows the definitive work by Evans and Katzenstein. [ 65 ] For Thomson scattering to be possible, the probe frequency must be much higher than the plasma frequency [ 65 ] : ( 1 19 )
38 where n e is the plasma electron density, e the charge of an electron and m e t he electron mass. The driving force in Thomson scattering is the Thomson scattering parameter, given by [ 65 ] ( 1 20 ) Here, k is the wave nu mber of plasma fluctuations and D is the Debye length given by [ 65 ] ( 1 21 ) where k B is the Boltzmann constant and T e the electron temperature with the other variables defined above. The Thomson scattering parameter effectively separates he plasma fluctuations are probed on such a small scale that only individual electron scattering is measured, the plasma fluctuations are probed on a scale larger th an the Debye length and is referred to as coherent scattering. In this regime, the scattering frequency is simultaneously and equally red and blue shifted, creating two satellite peaks on either side of the original peak. The distance between these satelli te peaks and the original peak is given by [ 65 ] ( 1 22 ) where k is the wave vector given by [ 65 ]
39 ( 1 23 ) where is the scattering angle between the directions of the initial and the scattered wave. The third regime refers to 0.5< electron satellite peak s are unresolved from the central ionic peak. These above regimes are based on the assumption that LTE holds, or that deviations from LTE are limited. If the electron temperature in the plasma becomes much greater than the ion temperature then this assumption no l onger holds. In that scenario a different effect occu rs, referred to as ion acoustic resonance, in which the central peak corresponding to the initial laser wavelength disappears altogether, leaving two resonance peaks at [ 65 ] ( 1 24 ) where m i is the mass of the ion. Summary The above studies and corresponding comments are intended to show that there are significant matrix effects in aerosol LIBS. Specifically heat and mass diffusion limits, upper size limits and rarefaction events all affect the signal response of a LIBS analyte. Only by probing the plasma particle interactions can these effects be unders tood and compensated for, leading to a more robust quantitative analytical technique. Therefore, understanding and quantifying the plasma particle interactions in laser induced plasmas becomes the focus of this research.
40 CHAPTER 2 T EMPORAL ANALYSIS OF AEROSOL UPPER SIZE LIMITS As mentioned in the previous chapter, aerosol particles in the microme ter size range and above have been shown to go through incomplete dissociation resulting in an effective upper size limit for aerosol analysis, with the actual limiting size varying according to the composition of the particle. This can be attributed to th e also aforementioned finite time scales for heat diffusion within the plasma. The aerosol particle can be seen as consuming energy in its immediate surroundings to drive its dissociation. Since the diffusion of energy from the bulk plasma is not immediate a large particle may run out of energy in its locality before the dissociation process is complete. It has also been shown, however, that after some time, about 20 s, that the local temperature about the particle begins to increase, consistent with the arrival of energy from the bulk plasma to the localized area about the particle. The question this study attempts to answer is whether the heat diffusing into the localized area is sufficient to restart or otherwise compensate for incomplet e dissociation. That is to say, it attempts to discover if increased residence time in the plasma results in an increase in the perceived upper particle size limit for complete dissociation. Experimental Methods Experimental Setup This section follows the presentation in the published work of Asgill and Hahn. [ 66 ] Briefly, a 1064 nm Q switched Nd:YAG laser operating with 300 mJ pulse energy, 10 ns pulse width, and 5 Hz pulse repetition rate was used as the plasma source. The laser pulse energy corresponds to the saturation region with respect to laser pulse energy
41 absorption by the plasma, as reported in an earlier study using the same optical system. [ 67 ] For plasma generation, an expanded, 12 mm diameter beam was focused inside the aerosol sample chamber usi ng a 75 mm UV grade plano convex lens. The plasma emission was collected along the incident beam in a backward direction and separated using a 50 mm elliptically pierced mirror. The collected plasma emission was launched into an optical fiber bundle, cou pled to a spectrometer (2400 grove/mm grating, 0.12 nm optical resolution), and recorded with an intensified charge coupled device (iCCD) array. The setup is pictured below in Figure 2 1 Specific detector gates (delay and integr ation widths) are discussed below. Figure 2 1 Experimental apparatus for upper size limit study. The aerosol generation system has been reported on previously by Hahn a nd coworkers. [ 68 ] Aerosols were generated (1) by the nebulization of aqueous solutions of silicon (SPEX ICP grade silicon standards), and (2) by nebulization of monodisperse silica particle suspensions in deionized water (spherical SiO 2 particles with Beam Dump Plasma V olume Pierced Mirror Laser Nd:YAG CCD S pectro meter Fiber Optic
42 monod isperse diameters of either 2.47 or 4.07 m). The silica particles were purchased as dry powders (Bangs Labs), and subsequently diluted with ultra purified deionized water to yield the desired particle concentrations. The particle suspensions were nebuli zed at a rate of about 0.15 ml/min; the nebulizer output was subsequently mixed with a gaseous co flow stream of 42 lpm of purified, dry air. For the case of the monodisperse silica particle suspensions, the particle concentrations in solution were dilute d to produce aerosol particle number densities in the range of 50 cm 3 in the LIBS sample chamber. All particle suspensions were subjected to sonication before and periodically throughout all experiments to reduce potential particle agglomeration in suspe nsion For the case of the nebulized aqueous silicon solutions, well dispersed nano particles were produced in the LIBS aerosol sample chamber following droplet desolvation, with a resulting particle size in the range of about 50 to 100 nm and correspondi ng particle number density in the range of 10 6 cm 3 [ 68 ] LIBS based analysis for all experiments used the neutral silicon atomic emission line at 288.16 nm. For all analysis, the LIBS analyte signal was the r atio of the integrated atomic emission line peak area (full width) to the adjacent continuum base emission intensity, referred to as the peak to base (P/B) ratio. The continuum intensity was interpolated using the adjacent, featureless continuum emission intensity on both sides of the silicon emission line. For temporal signal investigation, single shot spectra w ere recorded using a series of i CCD gates, including a 15 s delay and 5 s integration width with respect to the incident laser pulse (denoted 15/5), and additional gates of 35/5, 50/10 and 70/20 s for the analysis of the silica microspheres. Additional
43 gates were explored with the nebulized aqueous silicon so lutions to further map the silicon temporal analyte response. For the aqueous silicon solutions, ensemble averaging (minimum of 3000 individual spectra at each known aqueous silicon concentration) was used to quantify the 288.16 nm silicon P/B signal as a function of the temporal gating. These measurements were made at a fixed silicon concentration of 2000 g/ml in solution, which yielded a silicon mass concentration of 5.6 g/l in the LIBS sample chamber. These conditions correspond to a well dispersed aerosol flow of silicon rich nanoparticles such that each plasma event samples on the order of 10 3 partic les per plasma volume. Such a sampling condition is well suited for ensemble averaging. Conditional Analysis Algorithm For the monodisperse silica particle experiments, single shot conditional analysis was used to identify and analyze individual spectra corresponding to individual silica particles. The conditional data analysis approach was reported previously [ 31 ] [ 39 ] [ 40 ] and entails the identification o f individual LIBS spectra corresponding to the presence of a single, discrete particle based on the targeted analyte atomic emission signal, the silicon peak, exceeding a predetermined threshold value. For the current study, the threshold value for the 2 88.16 nm silicon emission peak was set to obtain an average of about 5 false hits (i.e. hits recorded for the nebulization of ultra purified water only) for every 1000 laser shots. After all single shot spectra that exceeded the threshold were collected, additional spectral filtering algorithms were then used to screen out false hits and any other anomalous spectra that exceeded the threshold. As noted above, the conditional analysis threshold value was set to allow the
44 detection of a small number of fals e hits, namely spectra that contain no actual silicon emission, along with very weak or noisy spectra that may correspond to noise events or actual silica particles hits with atypical spectral response. The presence of a small number of false hits or very weak hits ensures that the single shot detection threshold is sufficiently low to enable identification of actual analyte hits at signal levels approaching the single shot noise limit realized for a given spectral location. Peak Profile Matching The col lected spectra were subsequently filter ed using the following approach. The filtering algorithm is based on the similarity of the silicon emission line profile for a given single correspond ing to the ensemble average of thousands of individual spectra recorded for the aqueous silicon standard solutions, as described above. Specifically, the silicon line profile of a given single shot spectrum was compared to the standard line profile using a width of 5 pixels centered about the peak of the actual silicon emission line. First, the P/B as calculated from the left two pixels was compared to that from the right two pixels, to ensure some measure of symmetry in the peak. Only spectra that deviate d by no more than 50 percent over the left and right two pixels were accepted. Secondly, the P/B over all five pixels was compared to a square peak with a width of 5 pixels whose value was equal to that of the center pixel. In an ideal emission peak, the c enter pixel is the brightest, thus the area under the square peak should always be greater than that under the five pixels. Consequently, the ratio of the P/B of the square peak to that of the original peak should always be greater than unity. Only spectra whose ratio of square P/B to original P/B was greater than 0.9 were accepted.
45 Figure 2 2 below shows two spectra corresponding to the 15/5 s gate of the 2.47 m silicon spheres and demonstrates the effects of the peak matching algorithm. While spectrum is simply high intensity noise whereas the passed spectrum has a clearly identifiable peak. Both spectra were close to the pass/fail peak matchin g threshold. Figure 2 2 Spectra corresponding to the 15/5 s delay/gate of the 2.47 m silicon spheres. The peak shown corresponds to the 288.16 nm Si I line. It is seen that unlike the one that passed, the spectrum that failed the peak matching algorithm had no discernible peak and was well below the detection t hreshold of the system. Statistical Matching Finally, the lowest 20% of the resulting accepted spectra, as based on the full P/B ratio, were rejected for each detector gate. It was observed that the lower 20% of the
46 P/B ratios yielded an identical probabi lity distribution for both the 2.47 and 4.09 m silica particles, as described below; hence a single threshold was set for each detector gate to remove the bottom 20% using the aggregate cumulative probability distribution of both particle size data sets. Individual inspection of a great number of t he rejected 20% of the spectra revealed very noisy spectral data with no clearly discernable silicon emission lines, as shown in Figu re 2 3 below for the 15/5 s delay of the 2.47 m silica particles. Figu re 2 3 Spectra, corresponding to the 15/5 s window of the 2.47 m silica particles, showing the results of the statistical matching algorithm. The peak in the failed spectrum is seen to b e about the same magnitude as the spectral noise whereas the peak that passed but was near the threshold is about 40 50% larger than the largest noise spike in its vicinity.
47 Overall, this filtering algorithm resulted in the rejection of approximately 40 to 75% of all identified spectra that exceeded the initial conditional analysis threshold. Most importantly, the spectral rejection rate was consistent for both particle sizes at each respective temporal detection gate. Table 2 1 Number of spectra remaining after each filtering algorithm Delay/g ate ( s) Particle s ize ( m) Original number of s pectra After peak m atching After statistical m atching 15/5 2.47 4.09 210 186 184 175 138 144 35/5 2. 47 4.09 307 282 163 171 122 140 50/10 2.47 4.09 427 352 194 159 150 130 70/20 2.47 4.09 578 536 134 151 105 122 Results and Discussion This section follows the published work of Asgill and Hahn. [ 66 ] The probability plot of the P/B ratio for the 288.16 nm silicon atomic emission line is shown below in Figure 2 4 for the 15/5 s gate for both the 2.47 and 4.09 m silica particles. The data represents spectra that passed the first two filtering algorithm s resulting in 184 and 175 individual spectra for the 2.47 and 4.09 m sizes, respectively. The lower 20% of these were then o mitted because of their statistical similarity, yielding a final count of 138 and 144 spectra for the 2.47 and 4.09 m diameters, respectively. Since the 20% cut off was based on the population of both particle sizes, the exact cut off percentage varied, r anging from 18 to 25% over all eight data sets: 15/5, 35/5, 50/10 and 70/20 s for both sizes. This resulted in 105 to 150 final spectra for each detector gate and particle size, with the number of spectra agreeing to within 15 % for a given gate. The rejec ted 20%
48 contained spectra well below the single shot detection limit and a non Gaussian ensemble averaged spectral profile, unlike the ensemble average of the upper 80% or the silicon rich nanoparticles. The rest of the discussion will refer to the ensembl e average of the silica spectral data that passed all three steps of the filtering algorithm for each detector gate and particle size. Figure 2 4 Probability plo t of the 288.16 nm silicon emission line (P/B) for the 15/5 s detector gate corresponding to the 2.47 and 4.09 m diameter silica microspheres. The vertical line shows the cut off point (20%) for the final step of the spectral filtering algorithm. Figure 2 5 below shows the ensemble averaged spectra for the 35/5 and 70/20 s gates for both the 2.47 and 4.09 m silica particles. For a given gate, the spectra are presented with indentical intensity scale. The first feature of note i s the practically
49 identical continuum emission at each gate, which demonstrates that the overall bulk plasma emission, integrated over the entire emitting plasma, is not affected by the size of the particle present. This is consistent with imaging studies that show that the effects of included particles are localized within the plasma, leaving bulk plasma properties largely unaffected. [ 48 ] The second feature of note is that the 4.09 m silicon atomic emission peak is larger than that of the 2.47 m particle, with the ratio of the two peak areas seemingly consistent. This ratio is quantified below. Figure 2 5 Ensemble averaged spectra corresponding to two different detector gates (as noted) for the 2.47 and 4.09 m sized silica microspheres. For each detector gate, the two spectra have the identical intensity scale, with the lower silico n peak corresponding to the 2.47 m size.
50 The P/B ratios of the 288.16 silicon line as a function of detector gate is shown in Figure 2 6 for the 2.47 and 4.09 m silica spheres as well as the nebulized silica nanopaticles. As men tioned in the previous section, the aqueous solution of silicon nanoparticles results in a high number density of aerosol within the sample chamber; as such, the nanoparticle data is ensemble averaged over 3000 laser shots with no filtering algorithm appli ed. All P/B data sets show the same temporal behavior, revealing a maximum in the P/B ratio around 30 35 s delay relative to plasma initiation. The transition energy (6,299 40,992 cm 1 ) of the 288.16 nm Si I line is consistent with this temporal behavior [ 17 ] and is in agreement with previous studies. [ 22 ] The overall consistency of the data for the different sized particles is surprising, and quantified below. Given (1) that the microspheres may not completely dissociate due to upper size limits, [ 22 ] (2) the differences in the effective sampling volume for the nanoparticles, [ 69 ] and (3) the unknown effects of size on analyte response, it becomes very difficult to effectively compare the silicon rich nanoparticles to that of the microspheres. Nonethele ss, the experimental ratio of the nanoparticle signal to the 2.47 m microsphere signal at a delay of 30 s, based on interpolation of the Figure 2 6 data, is in reasonable agreement with the predicted ratio (7 experimental vs. 3. 5 predicted) based on the nanoparticle silicon mass concentration (5.9 g/l), the estimated representative plasma volume (~5 mm 3 per references [ 48 ] and [ 69 ] ), and the silicon content of an averag e 2.47 m silica particle. [ 66 ] Incomplete vaporization of the microspheres, uncertainty in the representative plasma volume, variability in silica particle analyte response ( Figure 2 4 ) and potentially reduced signal after ensemble
51 averaging with single shot analysis of discrete hit events [ 40 ] [ 70 ] may all have contributed to t he greater experimental ratio. Figure 2 6 P/B ratios of the silicon emission line as a function of temporal gating for the 2.47 and 4.09 m microspheres and for the silicon rich nanoparticles. The P/B ratios of the silicon rich nanoparticles have been divi ded by a factor of 10. The error bars correspond to the detector gate width, with the symbol corresponding to the center of detector gate Figure 2 7 presents the ratio of the average analyte response of the 4.09 m particles compared to that of the 2.47 m particles as a function of detector gate. The data reveal that the 4.09 to 2.47 m analyte response ratio is essentially constant with time and significantly less than the ideal ratio of 4.5, the cube of 4.09/2.47, expected for complete vaporization and subsequent linear silicon mass response. This behavior
52 suggests that these silica particles are not completel y vaporized in the laser induced plasmas, thereby confirming earlier studies. More importantly, providing additional residence time, even out to 70 s following breakdown, does not result in additional vaporization and analyte response beyond what is observed through the first 20 s of plasma evolution. These results suggest that the plasma particle vaporization process is not controlled by simple e nergy conservation within the plasma, as ample energy exists within the plasma to dissociate a 2.5 m silica particle, as noted previously. [ 22 ] We must then look to process rates, including the diffusion of he at to the dissociating microsphere and the diffusion of analyte mass throughout the analytical plasma to understand the dissociation process. Previous work has shown that plasma particle interactions control the dissociation of aerosol particles, [ 22 ] [ 69 ] however, it is possible that some particles were sampled in part directly by the laser beam, that is, the laser beam strikes the particle. This laser partic le interaction may alter the overall plasma dynamics, and thus the resulting analyte response. It may somewhat expand the range of linearity of response by providing additional laser induced dissociation and may partially explain the large distribution of analyte response, P/B, seen in Figure 2 4 Though the current study provides no means of distinguishing between plasma particle and laser particle interactions, it is possible to analyze the largest analyte respons es in the above data set. Specifically, for a given particle size and detector gate, the top 10%, by P/B ratio, of the fully processed data were ensemble averaged.
53 Figure 2 7 Ratio of the silicon analyte response of 4.09 m to the 2.47 m silica microspheres as a function of plasma evolution time. The x error bars correspond to the detector gate width, with the symbol corresponding t o the center of detector gate. The y error bars represent the standard deviations of the m easurements. Figure 2 8 below shows the results for the 35/5 s gate corresponding to the 2.47 m silica microspheres. The smaller peak corresponds to all previously analyzed hits, N =122, while the larger corresponds to the top 10 %, N =12. Though the top 10% shows an enhanced peak, as expected, the continuum emission is essentially identical, which is indicative of similar bulk plasma conditions. The top 10% of all the data sets were processed in a manner similar to Figure 2 7 The ratio of 4.09 to 2.47 m particle response was again constant but slightly higher at 2.0. This larger analyte response might be the result of direct laser particle interactions or
54 simply represent particles closer to the plasma center and thus subjected to higher plasma tempera tures and electron densities. It is noted that the probability of laser particle sampling is much less than that of plasma particle sampling based on Poisson statistics. [ 71 ] Though the range of dissociation may be slightly extended, the conclusion of non li nearity still holds for these particle sizes. Figure 2 8 Ensemble averaged spectra corresponding to the full data set and the top 10% for the 2.47 m sized silica microspheres and the 35/5 s gate. The lower silicon peak corresponds to full data set. Both spectra have the same intensity scale. Conclusions In summary, as per Asgill and Hahn, [ 66 ] the proces ses that drive aerosol particle vaporization and dissociation are important in controlling the resulting analyte response. Based on fundamental studies to date, it is clear that these processes are important
55 within the first tens of microseconds following laser induced breakdown. Furthermore, the kinetics of heat transfer to the sample particle and diffusion of analyte mass away from the particle occur on timescales that are both finite and comparable. Given these rate controlled processes in combination with an overall dynamic plasma evolution that is also of a finite time scale, it is expected that upper size limits will exist for a linear analyte mass response as derived from individual aerosol particles. While the laser induced plasma as an analytica l plasma is a particularly complex and dynamic system, these considerations can also a pply to other analytical plasma techniques including ICP MS and LA ICP MS. Clearly increased understanding of the overall plasma analyte interactions will lead to impro vements in LIBS as a quantitative analytical technique and may benefit the larger analytical community.
56 CHAPTER 3 D ISTINGUISHING BETWEE N GASEOUS AND AEROSO L PHASE ANALYTES As mentioned earlier, many matrix effects have been found in LIBS related to the expansion shockwave of a laser induced plasma and plasma particle interactions in general Ho hreiter and Hahn showed a stronger response, in the form of a steeper slope, for particulate analytes as compared to gaseous ones. [ 55 ] Similarly, using double pulse LIBS, Windom et al. [ 56 ] f ound that the P/B for gaseous phase analytes departs very little from that in S P LIBS whereas for aerosol particles the D P P/B was notably enhanced, by a factor of four, when compared to that of S P LIBS. Given these two results, this study explores whe ther the combined effects of the above findings can be used as a means to discriminate between solid and gaseous analyte signals. Carbon was chosen as the analyte in this study because of its ubiquitous nature. For instance, carbon plays a key role in char acterizing combustion systems; carbon dioxide is a sign of complete combustion while carbon rich soot is an indicator of fuel rich combustion. In addition, LIBS has been evaluated as an analysis tool for hydrocarbons and combustion gases. [ 72 ] [ 73 ] These two carbon sources are also emission controlled as carbon dioxide is a greenhouse gas and soot is a carcinogen and pollutant. The goal of this study is to determine if LIBS is capable of differentiating between solid phase and gaseous phase carbon based analyt es. Experimental Methods This section follows the presentation by Asgill et al. [ 74 ] A double laser platform was used in this study and is described below. The platform employed two Q switched Nd:YAG lasers (8 10 ns pulse widths) both operating at a frequen cy of 5 Hz. Both beams were expanded and collimated to allow for a tighter focus. A schematic of the
57 system is given in Figu re 3 1 and details of the lasers are provided in Table 3 1 The first laser (Big Sky CFR 400), denoted Laser 1, was used for all of the single pulse measurements. The second laser (Continuum PRII 8000), denoted Laser 2, was added for the double pulse measurements, always firing prior to Laser 1. Both lasers were spatially oriented su ch that their focal points coincided within a standard six way vacuum cross sample chamber (15.2 cm across, 3.5 cm ID). The flash lamp of Laser 2 was used to trigger a digital delay generator ( SRS DG535), which then triggered the flash lamp of Laser 1. Bot h Q switches were internally triggered. The delay between the firing of Laser 2 and Laser 1 was kept constant at 1 s. A delay of 1 s was selected in an effort to maximize the P/B difference with the double pulse configuration for a solid phase analyte, and minimize the double pulse response for a gaseous analyte, based on previous work. [ 56 ] Specifically, in the previous study it was found that the enhancement with a double pulse configuration was maximized for the particulate phase of an aerosol in this temporal delay regime, while such enhancements were minimal for the gaseous fraction. A digital oscilloscope (2.5 Gsample/s) and fast response phototube (Hamamatsu R1193U 51, 200 ps rise tim e) were used to continuously measure the actual pulse to pulse delay throughout the experiment and maintain the value at 1 s. Carbon was the analyte species of interest for all experiments, and was introduced as either a gaseous phase, particulate phase (solid phase), or mixture of the two phases. For the gas phase analyte, CO 2 (Praxair 4.0 Instrument Grade) was the source o f carbon, it having been well established in the literature that for gas phase species, the analyte signal is independent of the molecular source. [ 55 ] [ 75 ] [ 76 ] To generate the
58 solid phase analyte, a dilute solution of carbo n (as oxalic acid in water) was nebulized, which produces a high number density aerosol of carbon rich particulates following droplet desolvation, with a mean size of about 100 nm. [ 68 ] The carbon solutions were prepared by diluting ICP CertiPrep) to the desired concentration using ultra purified deionized water. A pure nitrogen (Praxair 99.7% N 2 <32 ppm H 2 O) co flow was used as the balance for all experiments. Figu re 3 1 Experimental apparatus for the dou ble pulse and single pulse LIBS configuration. Table 3 1 Parameters for the double pulse system Laser 1 wa velength 1064 nm Laser 2 wavelength 1064 nm Laser 1 energy 300 mJ/pulse Laser 2 energy 300 mJ/pulse Orientation of lasers Perpendicular Pre pulse delay 1 s Gate delay 8 s Gate width 5 s Plasma Volume Pierced Mirror Beam Dump Laser 1 Nd:YAG CC D Laser 2 Nd:YAG Spectro meter Fiber Optic
59 All gaseous flows were passed through HEPA filters and were metered with digital mass flow controllers (Alicat Scientific MC 20SLPM D, MC 10SLPM D, & MC 50SLPM D and Matheson Gas Products 8272 0434) appropriately size d to the relevant flow rates for high accuracy. The diluted carbon solutions were nebulized at a rate of about 0.15 ml/min using a flow of 5 lpm of nitrogen through a pneumatic type nebulizer (Hudson model #1724) and mixed with a nitrogen co flow of 43.7 lpm. The exact nebulization rates were measured by gravimetric analysis using the initial and final mass of solution in the nebulizer. The combination of analyte concentration in solution, the exact nebulization rate, and total gas flow rates was used to determine the true concentration ( g/L) of analyte in the test chamber. T he total carbon concentrations (gaseous and solid phase) were adjusted to provide a range of about 3 to 20 g C/liter of gas. For each total carbon concentration, the gaseous to sol id carbon ratio was increased by increasing the flow rate of the carbon dioxide stream while proportionately decreasing the concentration of carbon in the nebulized solution. This allowed the total carbon concentration in the sample stream to remain consta nt while investigating the effects of analyte phase. The conditions were adjusted to vary the percentage of solid carbon and gaseous carbon from about 10% gas phase carbon and 90% solid phase carbon as elemental carbon mass (designated 10/90), to about 90 % gas phase carbon and 10% solid phase carbon (designated 90/10). For all five total carbon concentrations investigated, the exact gas/solid mass concentration ratios tested were 9.6/90.4, 24.2/75.8, 47.4/52.6, 73.2/26.8, and 89.3/10.7 with relative stand ard deviations of 0.60%, 0.82%, 1.82%, 1.17% and 0.62%, respectively.
60 T he plasma was created in the center of the sample chamber using a 50 mm diameter, 75 mm focal length plano convex lens (1064 nm AR coating). Spectral emission from the plasma was collec ted by backscatter on axis with Laser 1, through a pierced mirror and coupled through a fiber optic cable into the spectrometer. The light was dispersed by a 0.275 m spectrometer (Acton Research Corp. Spectra Pro 275, 2400 grooves/mm and 0.15 nm resolution ), and recorded by an intensified CCD array (Princeton Instruments 1024MLDS). The ICCD was triggered by the Q switch sync from respect to Laser 1 for both single and double pulse configurations, as shown in Figure 3 2 For the single pulse experiments, Laser 2 was shuttered. For each carbon concentration and gas/solid percentage, data were recorded using six individual 1000 shot averages spread over multiple days for both single pulse and double pulse configura tions. All data were processed using the 247.9 nm Carbon I atomic emission line (21,648 61,982 cm 1 ) integrated over the full width and normalized to the adjacent continuum plasma emission (Bremsstrahlung and recombination emission) to attain the final peak to base ratio (P/B) as the analyte signal. In addition, the signal to noise ratio (SNR) was calculated as the ratio of the full width peak area to the RMS noise of the adjacent featu reless continuum intensity, as evaluated over the same number of pix els. Results and Discussion This section follows the published work of Asgill et al. [ 74 ] Figure 3 3 below shows representative S P and D P LIBS spectra corresponding to 89.3% gas phase carbon and 1 0.7% solid phase carbon (referred to as 90/10), and for the 9.6% gas phase carbon and 90.4% solid phase carbon (referred to as 10/90), at a fixed total carbon
61 concentration of 5.8 g/L. There are two features of note in these spectra, each consistent for a ll data examined. Figure 3 2 Timing schematic for the double pulse and single pulse experim ents employing the double laser platform. Firstly, both the carbon emission peak and the cont inuum intensity of the S P spectrum are greater than those of the D P spectrum. These values will be quantified below in terms of both the P/B and SNR values. This observation is consistent with earlier work [ 56 ] and is attr ibuted to a rarefied condition created by the first laser induced plasma (Laser 2) into which the second laser (Laser 1) is fired. Since the overall species density is diminished by the expansion of the first plasma, the continuum emission is also subseque ntly reduced in the D P configuration. Secondly, as the percentage of particulate carbon increases (from 10% to 90% particulate carbon in Figure 3 3 ), the overall emission intensity of the C I line increases
62 for both S P and D P c onfigurations. This is consistent with work by Hohreiter and Hahn [ 55 ] which found increased analyte response for particulate phase species compared to gaseous phase species. The S P and D P fs ns studies showed similar qual itative behavior, as discussed below. Several processes likely contribute to these finding, though the exact mechanisms are not fully understood. Due to their low density, gas phase species undergo rarefaction in expanding plasmas; this causes the number d ensity of emitting species, measured some microseconds following breakdown, is reduced from the original ambient values. On the other hand, due to their considerable mass and the times required for particle vaporization, [ 42 ] particulate phase species are more resistant to rarefaction, causing an enrichment of particulate phase species in the emitting plasma. Figure 3 3 1000 shot average LIBS spectra for 90 % gas phase carbon (left) and 10% gas phase carbon (right) for both single pulse and double pulse All data were recorded at a fixed total carbon concentration of 5.8 g/L. The spectra have been offset and do not have the same intensity scales.
63 The effects of gas and particulate phase in combination with the single and double pulse configurations are quantified below in terms of P/B values. Specifically, the P/B ratios were calculated for all carbon concentrations, gas/solid ratios, and S P and D P configu rations. By holding the gas/solid mixture fraction constant and varying the overall carbon concentration, calibration curves were created for each gas/solid mixture fraction for both S P and D P configurations. Figure 3 4 shows the calibration curves for the 90/10 and 10/90 gas/solid carbon mixtures. The curves display good linearity, with all correlation coefficients greater than 0.982, and with the typical value greater than 0.99; however, the variability was observed to increa se with increasing gas phase carbon content. The calibration curves are consistent with the previous work [ 56 ] in that the D P calibration curves have greater P/B values and slope s than the ir respective S P curve s for a gi ven gas /solid percentage, reflecting the with greater carbon emission peaks compared to the continuum emission with the D P configuration. For example, the slope values are 0.15 0.02 (standard deviation) and 0.28 0.04 for the single and double pulse co nfigurations, respectively, for the 90% gas phase ( Figure 3 4 data). Similarly, the slope of the 10% gas phase calibration curve is 0.36 0.0 2 for the single pulse data and 0.62 0.0 4 for the double pulse data. This trend held f or all gas phase carbon mixtures, but as the percentage of gaseous carbon increased, the difference between the two signals decreased. The increased slope also reflects greater sensitivity of the D P configuration compared to S P, although the signal to no ise values are actually reduced, as discussed below.
64 Another important characteristic of the calibration curve data is an increased overall analyte response, as measured by calibration curve slope, when shifting from 90% gas phase (primarily gaseous phase carbon) to 10% gas phase for either pulse configuration. This is consistent with the spectral data (see Figure 3 3 ) and is in agreement with previous findings as discussed above. [ 55 ] It clearly sh ows in increased signal and sensitivity of the LIBS signal to the particulate phase as compared to the gaseous phase. Figure 3 4 LIBS calibration curves for 90% gas phase carbon (left) a nd 10% gas phase carbon (right) for both sin gle pulse and double pulse configurations. Error bars represent one standard deviation. Analytically, there is a marked difference in roles between the peak to base ratio and the signal to noise ratio. The former quantity is a self normalization of the signal to the plasma continuum emission and is therefore a useful parameter for calibration, while the latter better reflects the quality of the signal and is more useful in the context of detection limits.
65 The SN R values are presented in Fi gure 3 5 as a function of percent gaseous carbon for a fixed total carbon concentration of 5.8 g/L. Note that the data points at about 10% and 90% gas phase carbon correspond to the spectral data of Figure 3 3 As expected, the signal to noise ratio increases as the percentage of solid phase carbon increases (gas phase carbon decreases). This trend is in agreement with the calibration curve data reflecting the enhanced analy te response with the solid phase as compared to the gaseous phase. In contrast to the P/B data, the SNR is greater for the single pulse LIBS data than for double pulse data at any given gas phase concentration. This trend was consistent for all gas/soli d mixtures and all concentrations, and is in qualitative agreement with the spectral data of Figure 3 3 which reveals a greater amount of spectral noise in the continuum emission relative to the signal level of the carbon line. While the P/B ratio does correctly reflect the value of atomic emission intensity relative to the continuum emission intensity, the overall signal levels were greatly diminished with the double pulse configuration. Hence the spectral signals are moving to ward the noise limited regime with the double pulse configuration, which is reflected with the diminished SNR values. As a summary of the overall data and trends, Figure 3 6 presents the slopes of the individual calibration cur ves (e.g. Figure 3 4 ) as a function of the gas phase percentage for both D P and S P experiments. The plot shows that for all of the gas phase carbon percentages investigated, the slopes of the D P LIBS calibration curves are grea ter than their respective S P calibration slopes, as discussed above, and reflects the enhanced atomic emission relative to the continuum emission with the D P approach, noting the
66 reduced intensity levels as reflected in the SNR values. In addition, it i s observed that the calibration curve slopes decrease as the gas phase percentage increases for both pulse configurations, reflecting the decrease in sensitivity of gas phase species relative to particulate phase species. Both curve fits show high linearit y, with the single exception being the approximately 50% gas/solid mixture for the D P configuration. No explanation is apparent for the departure of this particular value, but it was excluded from the linear fit for the D P data. Fi gure 3 5 Signal to noise ratio as a function of the percentage of gaseous carbon for a fixed total carbon concentration of 5.8 g/L Error bars represent one standard deviation In light of the trends highlighted above, the ratio of the slopes of the D P LIBS calibration curves to that of the S P was calculated as a function of the gas phase carbon percentage over the full range o f experimental values. This ratio was also calculated using the two linear trend lines of Figure 3 6 which enables calculation of a
67 continuous ratio function rather than the discrete experimental values. The results are present ed in Figure 3 7 Figure 3 6 Slopes of the calibration curves as a function of percent gas phase carbon for the single pulse and double pulse LIBS configuration s. Error bars are based on the average standard deviation over all concentrations for each respective calibration curve. Using the linear trend lines to generate the continuous ratio reveals a monotonically increasing function, in which the ratio of the D P to S P LIBS response does correlate with the percentage of gas phase analyte. This finding is rather novel in that it is the first time that a LIBS methodology has been demonstrated as a means to discriminate between gas phase and particulate phase fra ctions of the same elemental species in an aerosol. Caution is noted, however, in that the superposition of the individual data measurements at each gas phase percentage reveals considerable scatter, notably so with the approximately 50% gas/solid fractio n data point, which is
68 clearly affected by the reduced slope of the D P calibration curve at this fraction, as noted in the discussion of the Figure 3 6 data. The response of the D P to S P ratio, as measured by the slope of th e Figure 3 7 curve, is observed to increase as the percentage of gas phase carbon is increased. This makes sense in view of the overall differences in response of the gas phase and solid phase analytes. As the analyte fraction a pproaches 100% gas phase, the addition of a small fraction of solid phase analyte can appreciably alter the double to single pulse ratio response. However, at the lower overall gas phase carbon percentages, nearly all solid phase analyte, the signal becom es dominated by the solid phase, resulting in poor overall sensitivity to changes in the gas phase. This behavior can be interpreted as the asymptotic behavior at the lower gas phase percentages, as observed in Figure 3 7 Figure 3 7 Ratio of double pulse to single pulse LIBS calibration curve slopes as a function of the p ercentage of gas phase carbon. The solid line represents a ratio of the linear trend lines as sh own in Figure 3 6 The discrete data represent the experimental values at each gas phase concentration. Error bars are based on the formal propagation of error from Figure 3 6 for each respective gas phase concentration.
69 Conclusions As per Asgill et al., [ 74 ] t he overall signal response, as reported in earlier studies, [ 55 ] for the double pulse plat form is greater for the solid phase analyte fraction in an aerosol system, which is considered to be rooted in the rarefaction of gas phase analyte species within the ensuing laser induced plasma. In addition, the D P response, as measured by the P/B ratio is greater than that of a S P system, though inherently noisier. More importantly, the enhancement is also related to the phase of the analyte. We have then considered the ratio of the double pulse to single pulse response as a means to combine the ef fects of analyte phase on the LIBS response (both double pulse and single pulse) with a goal of differentiating between the analyte phases. The present results do show a dependence of the LIBS response on the phase of the analyte as based on the double pu lse t o single pulse response although the response curve is not particularly steep at low gas phase percentages, and is characterized overall by scatter in the individual data sets.
70 CHAPTER 4 I NVESTIGATION OF THE POLARIZATION EFFECTS OF LIBS Recently, concern was raised over possible polarization effects in LIBS plasmas. Liu et al. [ 77 ] found c onsiderably diminished continuum radiation when placing a polarizer before their detector in the ablation of silicon. They used a D P, non gated femtosecond system to measure the spectral polarization by fitting the data to the Malus function; A non neglig ible amount of polarization was discovered, with minima in the polarization value directly corresponding to atomic emission peaks. Further studies by this group and others corroborated their findings: Zhao et al. [ 78 ] with a D P fs system on copper and graph ite; Penczak et al. [ 79 ] with a S P fs system on aluminum; Liu et al. [ 80 ] with a ns system; and Majd et al. [ 81 ] with a ns system on copper. Typical LIBS experiments use a temporal delay and detector gate when collecting data. This serves the dual purpose of p reventing saturation of the optics and to shield the data from the highly non equilibrium plasma formation process. It is possible that this delay could prevent detection of a short lived polarizing condition. The aforementioned papers at tributed the polar ization to an inherent anisotropy in the thermal velocity distribution of free elections, which would not affect atomic emission. [ 80 ] Previous derivations and calculations do show angular dependent polarization in plasmas [ 82 ] [ 83 ] but those works involve the assumption of anisotropy or inherently anisotropic plasmas, such as tokamak plasmas. None support the hypothesis of an inherently polarized continuum or atomic emission without a driving force for said anisotropy, such as a constant magnetic field. Sharma and Thareja [ 84 ] do report strong polarization of the atomic emission of a doubly ionized aluminum transition at 569.6 nm for ablation under reduced pressures, which they attribute to self generated magnetic
71 fields (and corr esponding level splitting) at the plasma gas interface resulting from Rayleigh Taylor instability. [ 85 ] As discussed in previous chapters, laser induced plasmas are in a non equilibrium state with non Maxwellian electron distributions at short times after fo rmation but those conditions do not necessitate anisotropy. This study explores polarization for both the continuum and selected atomic transitions in gaseous and solid media using temporally and spectrally resolved measurements. Experimental Methods This section follows the presentation by Asgill et al. [ 85 ] The experiments utilized a Q switched Nd:YAG laser (10 ns pulse width ) operating at its fundamental wavelength of 1064 nm and a frequency of 1 Hz. The pulse energy was set to 225 mJ/pulse for analysis of gases and 40 mJ/pulse for analysis of solids. A schematic of the system is provided in Figure 4 1 The laser was spatially oriented such that it passed through the central axis of a standard 5 way vacuum cross sample chamber (15.2 cm across, 3.5 cm ID) The plasma was created in the center of the sample chamber using a 50 mm diameter, 100 mm focal length plano convex lens (1064 nm AR coating). A UV grade quartz window sealed the chamber betwe en the lens and the focal point. E mission from the plasma was collected using two distinct configurations: (1) backscatter on axis with the la ser through a pierced mirror as shown, and (2) orthogonal to the laser (denoted as side scatter) using a single lens positioned at a distance 2 f from the plasma, thereby forming an image of unity magnification on the fiber optic or directly on the phototube (not shown). For all measurements, the sample chamber window for side scatter collection was removed to avoi d any potential polarization effects in the quartz.
72 For spectral measurements, the light was coupled through a non polarization preserving fiber optic bundle into the spectrometer. Two film polarizers, in series, were placed between the collection lens a nd the fiber optic. When crossed, the two polarizers had an extinction value greater than 200:1. For all experiments, measurements were made with both polarizers set either perpendicular to the horizontal plane (denoted as vertical polarization) or both set parallel to the horizontal plane (denoted as horizontal polarization). The polarization sta te of the laser was horizontal. The light was dispersed by a 0. 3 m spectrometer ( 600 grooves/mm ), and recor ded by an intensified CCD array that was synchronize d to the laser using the Q switch. Three different iCCD delay and gate widths were used, namely, 0/100 ns (delay/width), 1.0/0.5 s, and 5.0/3.0 s for analysis of both nitrogen and the solid target. The early delay (denoted as zero delay) was selected su ch that the ICCD gate included the entire laser pulse and the first tens of nanoseconds of plasma emission, as shown in Figure 4 2 The spectral data collected for the solid target used a spectral region centered at 465 nm, wherea s the spectral window was centered at 490 nm for analysis of gaseous nitrogen. All spectral data were recorded using the sum of 50 consecutive laser shots. Experiments were all done in duplicate, alternating the polarization state between horizontal and vertical for each recorded sum. For the temporally resolved measurements, a digital oscilloscope (2 Gsample/sec) and two fast response phototubes ( Hamamatsu 200 ps rise tim e) were used to capture the reference laser waveform and the plasma emission. Neu tral density filters were used as necessary to ensure detector linearity for all measurements, and the oscilloscope was triggered using the laser pulse. Temporal data was collected over
73 different spectral windows using various band pass filters placed dir ectly in front of the phototube, which was positioned in place of the fiber optic location depicted in Figure 4 1 The specific filter bandwidths included 396/3 nm (denoting center wavelength/bandwidth), 488/10 nm, 546/10 nm and 687/10 nm, 447/60 nm, 510/70 nm, and 575/20 nm. As with the spectral data, temporal data was recorded for both vertical and horizontal polarization states. Temporal emission profiles were recorded by averaging 50 consecutive laser shots, alternating betw een vertical and horizontal polarization after each 50 shot sequence. Figure 4 1 Experimental apparatus for spectral LIBS measurements. The primary schematic depicts breakdown in pure nit rogen, while the inset shows breakdown on the solid target in both normal and oblique incidence. For temporal measurements, the fiber optic, spectrometer and ICCD are replaced by a fast rise time phototube and digital oscilloscope. Two different samples we re investigated. For gaseous breakdown, pure nitrogen (99.7% N 2 <32 ppm H 2 O) was used as the analyte species, with a flow rate of 10 lpm through the sample chamber. For the solid targets, a 4.7x4.7 mm square piece of Beam Dump Pierced Mirror Fiber Optic Nd:YAG Laser Spectro meter ICCD P olarizers Window Plasma Side scatter Backscatter Laser Solid Target
74 keystock (1018 low carbon steel) was used. Prior to measurements, the rod was sanded to remove any surface effects and carefully cleaned with acetone. The rod was positioned vertically, and oriented either normal to the incident laser or tilted at various angles of incidence. The chamber was also purged with a flow of 10 lpm nitrogen for analysis of the solid. All gaseous flow s were passe d through a HEPA filter and metered with a mass flow controller Figure 4 2 The earlie st ICCD gate (0/100 ns) for the spectral data along w ith the reference laser pulse. This corresponds to the zero delay used for analysis of the nitrogen and the steel samples Results and Discussion The section follows the work of Asgill et al. [ 85 ] For both spectral and temporal measurements, data for the pure gaseous system is presented first, which is independent of surface effects such as angle of incidence or surface reflectivity. This is followed by the dat a for the solid s ample
75 Spectral Data Emission data for breakdown of pure nitrogen was collected in both side scatter and backscatter, with representative spectra shown in Figure 4 3 for two different delay times following breakd own. In side scatter, emission collection was orthogonal to the incident laser direction with line of sight directly to the plasma without the aid of any reflective surfaces. In contrast, emission collected in backscatter was reflected off the pierced mi rror oriented at 45 to the laser beam axis (see Figure 4 1 ). Examination of Figure 4 3 spectra reveals two major trends. Firstly, for side scatter emission collection, the horizontal and vertical polar ization spectra fall exactly on each other, and the H/V polarization ratio, defined as the horizontal spectrum divided by the vertical spectrum for a given delay and orientation, is exactly one for both delay times. This indicates that free standing plasm a (i.e. pure gaseous breakdown with no solid surface interactions) has no polarization associated with either the continuum or the atomic emission; it has a spectrally flat polarization ratio despite prominent atomic emission features. The same trend was observed for the 5 s delay. Secondly, for the backscatter emission off the pierced mirror, the H/V polarization ratio is also constant (spectrally flat) but equal to about 0.9 for both delay times. Since mirrors generally exhibit some polarization effe cts, the 45 reflectivity of the pierced mirror was measured independently using a 632 nm He:Ne laser for both polarization states, and the H/V reflectivity ratio was found to be 0.90. As a result, the backscatter polarization ratio observed in Figure 4 3 is attributed solely to polarization dependent reflectivity of the pierced mirror. In summary, the spectral data examined for the
76 nitrogen plasma reveals no polarization effects inherent in the plasma continuum or atomic emission Figure 4 3 Spectral data recorded for breakdown of pure nitrogen gas, as recorded at a delay of zero (left) and 1 s (right) with respec t to the incident laser pulse. For each delay, sp ectra were recorded using both backscatter and side scatter (as noted), with the polarizers set to either vertical or horizontal orientation. The side scatter data fall nearly exactly on top of each other, hence are difficult to distingui sh. The polarizati on ratio (bottom two traces) represents the ratio of the horizontal spectrum to the vertical spectrum for each orientation pair, and is labeled for each orientation. Spectra for each vertical/horizontal polarization pair have the identical intensity scale; however, the backscatter pair and the side scatter pair do not have the same intensity scale. Figure 4 4 displays spectral data from the solid steel target at normal and oblique (45) incidence zero and 1 s after breakdown, al l in side scatter collection. For zero delay, it is seen that at oblique incidence, and therefore oblique plasma collection, the horizontally polarized spectrum has a slightly reduced intensity than that of the vertically polarized spectrum. This reducti on, however, is spectrally flat, as observed in the
77 constant H/V polarization ratio of 0.96. In contrast, the spectra collected at normal incidence have identical intensity, revealing a spectrally flat polarization ratio of unity. At a delay of 1 s, the spectra at both incident angles display no polarization dependency, as seen by the constant polarization ratio of one. Similar results were observed in the backscatter plasma emission, although with the additional contribution of the pierced mirro r. Specifically, the polarization ratio at zero delay and oblique incidence was spectrally flat at a value slightly less than unity but was equal to unity for all other spectral pairs after correcting for the polarization introduced by the pierced mirror. Figure 4 4 Spectral data recorded in side scatter for breakdown of the steel target at a delay of zero (left) and 1 s (right) with respect to the incident laser pulse. For each delay, spectra were recorded with the target oriented either normal (i.e. perpendicular) or tilted 45 o with respect to the incoming laser beam (as noted), with the polarizer set to either vert ic al or horizontal orientation. The normal incidence data fall nearly exactly on top of each other, henc e are difficult to distinguish. The polarization ratio (bottom two traces) represents the ratio of the horiz ontal to the vertical spectrum for each orient ation pair, and is labeled for each orientation. Spectra for each vertical/horizontal polarization pair have the identical intensity scale; however, the normal incidence pair and the 45 o pair do not have the same intensity scale.
78 The minor polarization dep endency discussed above for oblique incidence at zero delay time, is attributed to effects associated with viewing the plasma emission at an angle oblique to the surface normal. Fresnel theory clearly shows that surface reflectivity is polarization depend ent and can be highly dependent on the viewing angle. For example, the Brewster angle is simply the angle of incidence when the reflectivity for horizontally polarized light approaches zero, yielding reflected light that is perfectly vertically polarized. It is hypothesized that in the first few tens of nanoseconds, the plasma size and spatial position is such that a percentage of collected plasma emission is reflected off of the target surface, with this reflected portion displaying some polarization du e to Fresnel effects. This dependence on Fresnel reflectivity would, however, not be linked to the origin of plasma emission; hence any induced polarization would be identical for both the continuum and atomic emission in a given spectral region. This la tter point would account for the spectrally flat nature of the observed polarization effects with the solid target at oblique incidence. At delays of 1 and 5 s, any signs of polarization dependence are gone, suggesting that the percentage of plasma light reflected off the sample surface, and thus subject to the Fresnel effect, is temporally dependent and affected by the size, optical density and spatial location of the plasma. In their fs laser study, Lui et al. [ 77 ] report ed strong effects of angle of incidence on plasma polarization, finding very weak polarization for normal incidence and orthogonal collection As an illustration of the above discussio n, the Fresnel reflectivity [ 86 ] for vertically and horizontally polariz ed light is plotted in Figure 4 5 as a function of the angle of incidence based on the optical properties of iron (m = 2.8 3.3i) at 600 nm and copper
79 (m = 1.48 2.0i) at 400 nm [ 87 ] Both polarized states show strong angular dep endence for light reflected off such a target surface. The exact optical properties of any real material are difficult to predict, as they are dependent on the physical state of surface, and therefore dependent on parameters such as surface roughness and the presence of contaminants such as oxide layers. Furthermore, during plasma formation and growth, the nature of the target surface is highly dynamic, resulting in time dependent optical properties and thus time dependent reflectivity. Nonetheless, th e data present in Figure 4 5 are consistent with the polarization of plasma emission when reflected from a target surface at non normal angles of incidence. The overall polarization of the collected plasma emission depends on the fraction of light emitted directly from the plasma and the fraction reflected from the target surface, is itself a dynamic process. It is also noted that no polarization effect is seen at normal incidence in Figure 4 5 which is in nice agreement with the normal incidence experimental data. Figure 4 5 The Fresnel reflectivity values for horizontal and vertical polarization states for pure copper and iron surfaces as a function of the angle of incidence.
80 Additional measurements were recorded using a fixed side scatter collection while varying the angle of incidence from 25 to 60 degrees, in 5 o steps, for plasma delay times of zero and 5 s. The data trends were in ex cellent agreement with the above results; namely, the polarization ratio for non normal incidence varied from about 0.85 to 0.99 over the spectral band from 420 520 nm (similar to Figure 4 4 ), although no clear trend was observed with angle of incidence or plasma delay time. Importantly, for all cases, the data were spectrally flat, revealing no difference in polarization between atomic and continuum emission. Temporal Data The temporal data is now explored to provide a more detai led view of the early plasma lifetime, with focus the plasma emission that is synchronous with the laser pulse. As noted above, during overlap with the laser pulse, the high intensity electric field could potentially affect the polarization state of emitt ed radiation, in particular continuum, free free, radiation due to interactions of the free electrons with the induced field. As before, data were collected for both the gaseous nitrogen and the solid steel target using the first laser platform. Data wil l first be discussed for the pure gas sample. Figure 4 6 shows the temporal evolution of nitrogen plasma emission as collected in side scatter (488/10 nm filter) and in backscatter (447/60 nm filter). A range of spectral bandw idths were used, all yielding similar results. Overall, the temporally resolved results for gaseous nitrogen are in excellent agreement with the spectrally resolved data. Specifically, the traces recorded in side scatter for both polarization orientation s yielded a temporally constant polarization ratio of unity.
81 There is considerable noise in the polarization ratio for the first few nanoseconds of the laser pulse, during which the polarization ratio is observed to drop to about 0.75. This trend is dif ficult to quantify definitively given the steep slope of the emission data in this region; for example, a slight shift of 0.5 ns (the digitization rate) due to a change in the oscilloscope trigger point, could easily account for this feature. Alternativel y, there may be a slight polarization effect during the first 2 3 ns of breakdown while the laser pulse is still engaged and the free electron density is rapidly growing. Overall, however, the trend is one of no polarization with regard to the temporally resolved emission from the peak of the incident laser pulse forward. Similar to the spectrally resolved results, the plasma emission collected in backscatter shows the slight polarization attributed to the pierced mirror, which is constant with time, as discussed above. An interesting feature of the Figure 4 6 nitrogen data is the local minimum observed in the plasma emission about 10 ns following the laser pulse. This is attributed to a non optically thin plasma during the fi rst few ns of plasma lifetime, which shields plasma emission from the inner plasma core for the freely expanding gas breakdown. Together, the temporally and spectrally resolved emission data for the breakdown of a pure gaseous sample shows no sign of po larization in the continuum or atomic emission features. The importance of the gaseous experiments are that all surface plasma interactions are removed, allowing careful and accurate assessment of the actual plasma emission.
82 Figure 4 6 Temporal data recorded for breakdown of pure nitrogen gas corresponding to collection in backscatter and side scatter, along w ith the reference laser pulse. For each orientation, emission was rec orded with the polarizer set to either vert ical or horizontal orientation. The polarization ratio represents the ratio of the horizontal trace to the vertical trace for each orientation pair (as noted). Traces for each vertical/horizontal polarization pair have the identical intensity scale; however, the backscatter pair and the side scatter pair do not have the same scale. Temporal measurements were then repeated for the steel target oriented both normal and at 45 o to the incident laser beam, as performed for the spectral measurements. Figure 4 7 shows the temporal evolution of steel initiated plasma emission as collected in side scatter (488/10 nm filter) and in backscatter (510/70 nm filter). It is seen that in about the first 100 ns of plasma lifetime, there is distinct, measurable polarization of the plasma emission for the oblique angle of incidence, after which the effect tends to dissipate. Specifically, the 45 o angle of incidence polarization
83 ratio has an average value o f 0.91 and 0.92 in side scatter and backscatter, respectively, during the first 100 ns. As with the spectrally resolved measurements, this polarization effect is not readily observed for the case of normal incidence. For the backscatter dat a some polariz ation is attributed to the pierced mirror. Figure 4 7 Temporal data for breakdown of steel target, as recorded in side scatter (left) and back scatter (right) with respect to the incident laser pulse. For each orientation, spectra were recorded with the target oriented either normal (i.e. perpendicular) to the incoming laser beam or with the target tilted 45 o with respect to the incoming laser beam, with the polarizer set to either verti ca l or horizontal orientation. The polarization ratio represents the ratio of the horizontal trace to the vertical trace for each orientation pair, and i s labeled for each orientation. Traces for each vertical/horizontal polarization pair have the identical intensity scale; however, the normal incidence pair and the 45 o pair do not have the same intensity scale. The temporal data firmly support the conclusions reached above with the spectral data, namely, that plasma inception and initial growth is strongly c oupled to the sample surface, after which the plasma expands away from the surface, and that such surface interactions can give rise to some degree of polarization for non normal collection angles. In particular, the degree to which the plasma emission is also reflected from the sample surface and subsequently collected for analysis is expected to be a complex
84 process that is temporally dependent. While none of the results in the present study have shown any polarization that is preferentially linked to e ither plasma continuum or atomic emission, others have reported such data for nanosecond plasma emission [ 80 ] noting that the emission in that study was collected at non normal incidence and temporally unresolved. The appa rent contradiction in results between that nanosecond study and the current study may be explained in the overall evolution of plasma emission. It is well known that atomic emission is pronounced only after some inception time, or delay time, which is re quired for the continuum emission to decay from it s initial, dominant intensity. It is plausible that temporally unresolved plasma emission, with no temporal gating, may show some polarization in the fraction of light corresponding to early times due to Fr esnel reflects when the plasma is positioned near the surface, while such an effect might diminish for the fraction of plasma emission recorded at later plasma times. Temporal changes in optical thickness may also affect the partitioning of direct and ref lected plasma emission. Since the fraction of light stemming from early times is heavily weighted to continuum emission, while the fraction of light arising from latter lifetimes may be strongly weighted to atomic emission, it could appear that the contin uum is selectively polarized as compared to the atomic emission when the emission is viewed in aggregate temporally. Conclusion s As per Asgill et al., [ 85 ] the polarization of nanosecond laser induced plasma emission has bee n carefully studied for both gaseous and solid analyte samples. By resolving the plasma emission both temporally and spectrally, coupled with investigation of the angle of incidence for solid targets, a consistent set of trends was observed. For
85 breakdow n of a pure gas phase sample at atmospheric pressures, for which the plasma emission is uncoupled from any surface interactions, no evidence of any inherent polarization was found in the plasma emission, including both continuum and atomic emission, for th e transitions selected in this study. The results for the analysis of solid surfaces did reveal slight polarization (~10%) of the plasma emission, but only for the special case of non normal surface orientation with respect to the incident laser and ang le of collection. Perhaps of greatest significance, the polarization that was recorded was in all cases spectrally flat, meaning that no differences were observed for continuum emission as compared to atomic emission. Based on the aggregate results, the slight polarization recorded for LIBS of obliquely oriented solid surfaces is attributed to the time dependent interactions of the plasma light and the solid surface resulting from polarization dependent Fresnel reflectivity. Because of the highly dynamic nature of the plasma evolution, it is expected that the contribution of total plasma light collected will contain fractions of plasma light emitted directly and plasma light reflected off of the target surface, and that the relative percentages of these t wo components may vary greatly with time. Plasma non homogeneity may also play a role.
86 CHAPTER 5 O BSERVATION OF THOMSO N S CATTERING IN GASEOUS PLASMAS The laser induced breakdown and plasma formation process has an impact on the properties of the plasma and thus on the LIBS signal; as such, it is beneficial to gain a better understanding of the formation of a LIBS plasma. However, many spectroscopic techniques used to analyze plasma properties are not available at the time scales of plasma formation. Thomson scattering is one of the exceptions. The goal of this experiment is two fold : (1) t o con firm the validity of Thomson scattering as an effective tool to analyze formation of LIBS plasmas, i.e. to confirm that conditions in the early times of the formation of LIBS plasmas are sufficie nt to induce Thomson scattering and (2) to identify the locat ion of Thomson scattering satellite peaks if feasible, and use that information to determine the temporal profile of both plasma temperature and electron density during the plasma formation process. Experimental Methods The experiments utilized two Q swit ched Nd:YAG pulsed lasers, both operating at 5 Hz. The first laser (Continuum Electro Optics Inc. Precision II 8000), denoted Laser 1, was used to generate the plasma. It operated at its fundamental wavelength of 1064 nm with pulse energy of 150 mJ/pulse a nd was focused using a 50.8 cm diameter, 100 cm focal length biconvex lens (Newport KBX 154 AR 33). The second laser (Big Sky Laser 230A8000), denoted Laser 2, was used as the probe laser for the scattering measurements. It operated at a frequency doubled wavelength of 532 nm with a pulse energy of either 45 mJ/pulse, on the edge of the plasma, or 80 mJ/pulse, closer to the center, and was focused using a 50.8 cm diameter, 300 cm focal length biconvex lens (Newport KBX 172 AR 14). The pulse energy was such that there was no breakdown in
87 air from Laser 2. Since Laser 2 was originally horizontally polarized, a quarter wave plate was used to make the beam vertically polarized; according to Rayleigh scattering theory, the scattering cross section of horizontall y polarized light at a viewing angle of 90 is zero. The two lasers were aligned collinearly such that the probe laser passed through the center of the plasma, as shown in Figure 5 1 The flash lamp of Laser 1 was used to trigger the flash lamp of Laser 2; this trigger was used for all time resolutions. In addition, in order to reduce jitter, the Q switch of Laser 2 was externally triggered off its flash lamp at a fixed delay of 46.77 s, nominally equal to its normal internal delay. The timing of the two lasers was accomplished using a delay generator (Stanford Research Systems DG 535) and monitored using a digital oscilloscope (LeCroy Waverunner LT 372, 4 GSamples/s). The oscilloscope was triggered by the 1064 nm laser beam using a phototube (Hamamatsu R1193U 51) with a 630 nm high pass filter in place to prevent triggering the oscilloscope with the green laser pulse at short delays. As shown in Figure 5 1 below, the scattering signal was collected perpendicular to both laser beams using a photo multiplier tube, PMT (Products for Research Inc. PR 1402CE). Two apertures were placed, in series, before the PMT to ensure that it only captures light from the plasma. A lens was placed at twice its focal distance from the plasma and between the two apertures in order to image the entire scattering volume on to the PMT. In addition, two 532 nm line filters (10 nm and 2 nm widths) were used in series befo re the apertures to ensure that only a small wavelength range, centered polarizer was placed in front of the aforementioned collection optics to reduce the
88 amount of plas ma light captured. Lastly, neutral density (ND) filters were used as needed to ensure signal linearity. Figure 5 1 Expe rimental apparatus for Thomson s cattering temporal measurements. To achieve spatial resolution, the 1064 nm focusing lens was mounted on a translational stage; movement of the stage changed the location of the plasma that was imaged onto the PMT. Data was collected at the nominal plasma center, denoted as 0.0 mm, and at 0.3 mm intervals moving away from the center, namely 0.3 mm, 0.6 mm, 0.9 mm, and 1.2 mm from the plasma center. The plasma was formed within a flow of pure nitrogen ( Praxair 99.7% N 2 <32 ppm H 2 O ) at 8.89 lpm, except for stray light measurements, which re quired the use of nitrogen and ultra high purity methane non concurrently. The plasma was formed within an enclosure, to minimize stray light entering the system, with access orifices for each laser and for the collection optics. At each spatial position, data was collected at different temporal delays, referring to the delay of the green laser pulse with respect to the plasma formation as observed Laser 1 Nd:YAG 1064 nm Oscilloscope Laser 2 Nd:YAG 532 nm PMT 532 nm Line Filters ND filters Polarizer Double Aperture Tube Lens Aperture 1 Aperture 2
89 on the oscilloscope, as well as one set of data without a green laser pulse (plasma only). The delays used wer e 100, 0, 10, 20, 30, 40, 50, 70, 100, 150, 200, 300, and 500 ns. Together, they comprise one temporal sweep. There were three temporal sweeps per set and three sets per spatial position, resulting in 9 unique data points for each time step at each positi on; this is with the exception of the 1.2 mm position in which had only 6 unique data points for each time step. Each data point corresponds to the average of 100 different plasma events. Data collection for each spatial position was completed over several days. Stray light measurements were taken before and after each set. All signals were normalized to the same neutral density (ND=0), adjusted to the same pulse energy of 45 mJ/pulse, according to and corrected for stray light. There were some individual data points that were noise dominated, that is, the measured signal was less than the stray light calculated for that set; these points were discarded. In addition, a few data points with very low signals, less than three standar d deviations lower than the average signal for their respective time step, were discarded. In total, 14 data points were discarded out of the 546 total unique data points gathered. Stray light calculations were done using nitrogen and methane as reference scatterers according to the following equation: [ 88 ] ( 5 1 ) where and are the differential scattering coefficients for methane and nitrogen, respectively, and are the measured scattering
90 signa ls of methane and nitrogen, respectively, and SL is the amount of stray light scattering. This simplifies to ( 5 2 ) A value of 2.17 was used for R ref at 532 nm. [ 88 ] The plasma only signal in each te mporal sweep served as a reference and was subtracted from the signal at each time step to yield the green scattering signal, as shown in Figure 5 2 All green scattering signals were then compared to the signal at 100 ns, before the presence of the plasma, to attain a scattering gain, Lastly, the differential scattering coefficient of the plasma (cm 1 sr 1 ) was also calculated using the following equation: [ 88 ] ( 5 3 ) where I o is the incident laser intensity, is the efficiency of the collection optics, V is the scattering volume and is the solid angle of observation. By taking the ratio of the scattering signal to that of a reference scatterer, CH 4 the calculation of the constants is avoided, yielding ( 5 4 ) A value of 3.33E 8 cm 1 sr 1 was used for [ 88 ] The resulting trends in the differential scattering coefficient mirror those of the scattering gain. This plasma
91 differential scattering coefficient represents the sum of differential scattering coeffi cients from atoms, ions, and electrons. Figure 5 2 Sample spectra showing the extraction of the green probe signal. The laser waveform is given as a reference. The scales of the Plasma + Green s ignal and the Plasma Only signal are offset for clarity. For spectral measurements, the PMT was replaced by a fiber optic connected to a spectrometer (Acton Research Corporation Spectra Pro 275) and iCCD (Princeton Instruments ICCD 1224 MLDS E/1). The 532 nm line filters were replaced with a 532 nm razor high pass filter. The iCCD was triggered off the flash lamp of Laser 2; its delay width. Several spectral windows were u sed, centered at 532 nm, 560 nm, 588 nm, and 616 nm. Two 1000 shot averaged spectra were collected with Laser 2 active and again with Laser 2 inactive (with and without the scattering laser) with the latter subtracted
92 from the former in an attempt to obser ve the red shifted Thomson scattering satellite peak. Results and Discussion The data presented here is the average of the differential scattering coefficient for each time period. The first thing that is observed is the presence of a multiple peaks in the differential scattering coefficient as seen in Figure 5 3 The first peak occurs at very early delays, 10 to 50 ns, and is seen to be strongest at the plasma center where the electron density is temporally and spa tially strongest; thus, this first peak is suspected to be caused by Thomson scattering. The second peak appears at delays of 100 150 ns, the time scale needed for full plasma expansion, and is stronger closer to the edge of the plasma; this suggests the s econd peak is caused by scattering off the edge of the plasma. Secondly, the times at which the peaks occur vary slightly with location within the plasma. As seen in Figure 5 4 the farther from the plasma center, the sooner the scattering peaks are observed. This can be due to the plasma being optically thick for a longer time period at the center due to higher electron densities, causing the observation of scattering to be delayed. To ensure that the changes in te mporal peak occurrence were not due to scattering off a traveling shockwave, the potential velocity of such a shockwave was calculated for both maxima. This was done by fitting a linear curve to the data in Figure 5 4 and using the inverse of the slope to calculate the corresponding to the spatial positions with a distinct second peak, namely 0.9 mm through 1.2 mm. All five points we re used in the fit of the first local maximum. Wave speeds of approximately 27,200 m/s and 12,000 m/s were found for the first and second
93 local maxima, respectively; in comparison, the speed of sound for an ideal gas at 20,000K is about 2,800 m/s. This rul es out the possibility of scattering off a traveling shockwave within the plasma, thus supporting the conclusion of the sharp t ransient scattering as Thomson s cattering. Figure 5 3 Differential s cattering coefficients versus delay at all distances from the peak in the early tens of nanoseconds and the second at 100 150 ns. The ken, the more the first peak dominates the second. Lastly, it is observed that closer to the plasma center, the peak differential scattering coefficient associated with plasma scattering decreases while that associated with Thomson scattering increases, a s noted in Figure 5 5 Because the green probe meets the plasma end on, the plasma scattering is strongest at the edges of the plasma. As the more central parts of the plasma are analyzed, the electron density incr eases, causing the amount of Thomson scattering to rise as well.
94 Figure 5 4 Times at which the local maxima occur. The shaded data points refer to the absolute maxima at each spa t ial posi tion. It is observed that the farther from the center of the plasma, the sooner the peaks are observed. Figure 5 5 Differential scattering coefficient for both local maxima at each spatial position. It can be clearly seen that closer to the center of the plasma, the first maximum becomes more pronounced and the second decays. The shaded data points refer to absolute maxima.
95 The Thomson s cattering satellite peaks could not be observed in t he spectral data. As shown in Figure 5 6 the plasma data with the green probe laser showed an overall higher intensity than the data with the plasma only. However, when the two were subtracted, there were no addit ional spectral structures that would suggest the presence of a satellite peak. This trend held for all four spectral windows used. This can be attributed to a decrease in spatial resolution; the iCCD is less sensitive than the PMT, requiring larger solid a ngles for fiber optic coupling as compared to direct PMT imaging. Figure 5 6 Thomson s cattering spectra showing the signals for the plasma with the green probe laser, plasma only, and the subtra cted green laser only. Thomson s cattering satellite peaks were not observed at any of the windows used.
96 Conclusions The LIBS plasma was probed temporally, spectrally, and spatially at very early times, 500 ns and less, in order to better understa nd plasma conditions immediately following breakdown. Temporal probing revealed two different scattering phenomena: scattering off the edge of the plasma and scattering at the center, with minimal scattering in between. The scattering at the edge of the pl asma peaks at about 150 ns following breakdown an d is believed to be simple Mie s cattering due to the steep property gradient along the plasma boundary. The scattering near the plasma center peaks earlier at about 50 ns following breakdown and is believed to be Thomson scattering, confirming the presence of the high electron densities necessary to produce the effect. Unfortunately, spectral measurements failed to identify the Thomson scattering satellite peaks. As such quantitative analysis of plasma proper ties, temperature and electron density, could not be accomplished.
97 CHAPTER 6 M ULTI COMPONENT AEROSOL ST UDY As mentioned in previous chapters, the rates of heat and mass transfer within a laser induced plasma are finite and on the same scale as the plasma emission. When particles are present within a plasma, they draw energy from their immediate surroundings in order to vaporize and ionize. Because of these finite transfer rates, the energy used by the particles is not quickly replaced by the bulk plasma, causing the local plasma about the particles to be cooler. As such, the particles emit radia tion at a lower temperature than the bulk plasma. The goal of this study is to calculate the bulk and local plasma temperature and electron density, using gaseous analytes and particulate metals within the plasma, respectively, in order to observe this tem perature difference and find the point of equilibrium within the plasma. Also, this study hopes t o determine if the presence of large quantities of a matrix element within the aerosol particles can significan tly alter the local plasma conditions ; this matr ix element is not expected to affect the bulk plasma properties Experimental Methods The system used for this experiment is identical to that reported in Chapter 2 for the upper size limit study and is shown in Figure 2 1 Briefl y, a 1064 nm Q switched Nd:YAG laser operating with 300 mJ pulse energy, 10 ns pulse width, and 5 Hz pulse repetition rate was used as the plasma source. An expanded, 12 mm diameter beam was focused inside a six way vacuum cross using a 75 mm UV grade pla no convex lens. The plasma emission was collected along the incident beam in a backward direction and separated using a 50 mm elliptically pierced mirror. The collected plasma emission was launched into an optical fiber bundle, coupled to a spectrometer (2400
98 grove/mm grating, 0.12 nm optical resolution), and recorded with an intensified charge coupled device, iCCD, array ( Princeton Instruments ICCD 1224 MLDS E/1) Neutral density, ND, filters were used as necessary to prevent saturation of the detector. Argon, nitrogen, and hydrogen were used for the bulk plasma analysis. For hydrogen, ultra purified deionized water was nebulized with 5 lpm of purified, dry air. This hydrogen nebulization stream was mixed in a co flow of argon and purified, dry air at a r ate of 21 lpm each. For the aerosol particles, the nebulized water was replaced with an aqueous solution of aluminum, manganese and lutetium (SPEX CertiPrep ICP grade). 10,000 g/mL of each aluminum and manganese were diluted down to 2,000 g/mL with deion ized water and mixed, in equal amounts, with 1,000 g/mL of lutetium; the final mixture had a resulting concentration of 666.67 g/mL of both aluminum and manganese and 333.33 g/mL of lutetium. In the elemental matrix experiments, 10,000 g/mL of ICP grad e sodium was added in equal amounts to the above mentioned solutions, resulting in a mixture containing 500 g/mL aluminum and manganese, 250 g/mL lutetium, and 2,500 g/mL sodium. Transmission electron microscopy, TEM, was p erformed on a sample of aeroso l particles gathered from the sample chamber. The presence of roughly spherical particles between 50 and 500 nm was confirmed as seen in Figure 6 1 Energy Dispersive x ray Spectroscopy (EDS) confirmed the presence of Al, Lu, Mn, and Na within the particles; a representative EDS spectrum is shown in Figure 6 2 These tests confirm t hat the aerosol stream, and by extension the plasma contains sub micron, multi element aerosol particles; the particle sizes are well below published limits for complete dissociation.
99 Figure 6 1 Sample TEM images of aerosol particles formed in aerosol stream during particulate analysis. Particles ranged in size from 50 500 nm. Figure 6 2 Sample EDS spectrum for the sodium matrix experiment. EDS confirms the presence of multi element aerosols, with all four elemental matrix components pre sent. Copper is from the TEM grid. 200 nm Matrix 200 nm Matrix + Na
100 Eight different spectral windows where used throughout the experiment to capture the emission lines of the various elements. For the purely gaseous plasma, four windows were used, centered about 415, 480, 500, and 656 nm. For the aerosols, including the aerosols in the sodium matrix, four other windows were used, centered about 260, 310, 350, and 400 nm. In each window, spectra were collected in a range of temporal delays between 0.1 and 250 s; not all delays were used in each window. Specifically, the delays used were 0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1.0, 1.5, 2.0, 3.0, 5.0, 7.5, 10, 15, 25, 40, 65, 100, 150, and 250 s. At each delay, six sets of data were collected, over multiple days, with each set comprising the average of 600 different plasma events. Table 6 1 Range of delays used in each spectral window Window (nm) Temporal r ange ( s) 260 0.5 150 310 0.1 250 350 0.1 100 400 0.1 150 415 0.1 10 480 0.1 10 500 0.1 5 656 1.0 40 Intensity Normalizaton A calibrated lamp source (Oriel tungsten halogen, 250 2400 nm, 1000 watts) operating at 7.82 amps and 102.8 volts was used to correct for the instrumen t function. At each wavelength used, the measured irradiance from the lamp was compared to the actual irradiance as given by the calibration equation; this resulted in an irradiance correction factor at each wavelength that was then applied to the spectra gathered.
101 Because the intensity of the calibrated lamp source was much lower at lower wavelengths, see Figure 6 3 a stray light correction was performed for the 260 and 310 nm windows before their irradiance corre ction factors were calculated. The spectral intensities at these windows using a 355 nm high pass filter were compared to those without the high pass filter with the true lamp emission taken as the difference between the two. It was found that stray light accounted for about 70% of the calibrated lamp intensities in the 260 nm window and about 33% in the 310 nm window without the filter. The true neutral density of the ND filters used was also calculated using the calibrated lamp at each spectral window; th e measured irradiance without ND filters was compared to that with ND filters and the true ND backed out of the data. It is important to note that only two ND filters were tested, in total: one with neutral density of 1 and the other 0.6; the filters used were of varying neutral densities (0.3, 0.6, 1.0, 2.0), with multiple filters of each. It was then assumed that the other true neutral densities were multiples of the ones tested, i.e. the true ND of a nominally 0.3 ND filter is half that of the nominally 0.6 ND filter, etc. Neutral density corrections were then applied to all data, as needed, bringing all data to the same relative intensity. There were two other, more specific, corrections done. The first correction was in the 310 nm window. At certain tim es, the intensities within that window seemed abnormally high. This resulted in the calculated plasma temperatures using that window to be much higher than temperatures calculated without the use of the 310 window. Upon further investigation, it was found that the start and duration of the anomaly corresponded perfectly with a recorded change in the ND filter used during the data collection. It is believed that the recorded neutral density, ND =1.6, differed from the
102 actual one used, ND =1.3. Acting on this assumption, when the ND was corrected using the true neutral densities calculated above, the temperature data using the 310 nm window at these times fell in perfectly with that from other windows. The second correction was in the 260 nm window. The Boltzm ann plot for Mn II emissions contained lines from three different spectral windows (260, 310, and 350 nm) including the resonance lines at 259.37 and 260.57 nm. The slope of that Boltzmann plot was found to be positive at most time delays, corresponding to an impossible negative temperature. It is believed that this was the result of unavoidable errors in the calculation of the irradiance correction factors in that window. Since the calibrated lamp intensity at that window was noise dominated, more noise th an measured signal, small errors in the stray light correction can lead to larger errors in the correction factors. In addition to that, the window is at the very edge of the calibration of the lamp intensity, see Figure 6 3 a calibration that was in itself several years old, which can create even more uncertainty in the correction factor. An additional correction factor was needed for the 260 nm window. The additional 260 nm correction factor was found using the M n II and Lu II Boltzmann temperature data; the Lu II Boltzmann temperature was derived using lines wholly contained in the 350 nm window. At a specific temporal delay, it was assumed that the Mn II Boltzmann temperature was equal to that of Lu II. The slop e of the Mn II Boltzmann plot needed to achieve this temperature was then calculated. Holding the Mn II data in the other windows (310 and 350 nm) constant, the necessary intensities of the 259.37 and 260.57 nm lines were calculated and compared to those t hat were measured. The ratio of the desired intensity for the assumed temperature and the
103 measured intensity then yielded a correction factor for that window. This exercise was repeated for six different delays, delays at which the Boltzmann plot of Lu II had correlations of 0.99 and above. These correction factors ranged from 2.36 to 4.86 and averaged out to 3.74. The average 260 nm correction factor was then applied to the entire 260 nm window data set at all times. Figure 6 3 Calibrated lamp source i rradiance as a function of wavelength. [ 89 ] Plasma Diagnostics Once all the above corrections were applied and all data brought to the same relative intensity, the plasma temperature was calcu lated using the Boltzmann plot method, as shown in Chapter 1, for gaseous species, corresponding to bulk plasma conditions, and particulate species, corresponding to local plasma conditions. Since the same relative intensities were used, Boltzmann plots us ing lines from different spectral windows could be utilized. Temperatures were calculated using Ar II, N II, N I, Lu II, Mn II and Mn I.
104 Figure 6 4 Sample spectra These plots corresp ond to Lu II at various times Electron densities were also calculated using Stark broadening for H alpha and Ar II. A mercury argon lamp (Ocean Optics, model HG 1) was used to find the instrument width (FWHM); the instrument width was then subtracted from the measured full width half maximums to obtain the Stark broadening width. For the H alpha electron density calculation, a series of stark widths (nm) was calculated for electron densities of 1E15 to 1E18 cm 3 [ 90 ] From that data, a p 2/3 v n e was drawn and [ 91 ] [ 92 ] ( 6 1 )
105 where is the fractional half width of the reduced Stark profile, e is the electron charge (4.8032E 10 esu), and C 1 is the slope of the linear fit which is weakly dependent on electron density and temperature. This process was done for temperatures of 10,000K and 20,000K, with the fits shown in Figure 6 5 below. The H alpha electron density calculated from the two different fits was then averaged to get the reported electron density. Figure 6 5 Sample spectra for the H alpha line at various times (left) and l inear fits used to determine Stark broadening of the H alpha line (right) For the electron density using argon, the Stark broadening equation shown in Chapter 1 was used. ( 6 2 ) Using published values for the stark broadening width and electron density at different temperatures, between 10,880 and 13,880 K, [ 93 ] C 2 was determined at each temperature; the C 2 values were then averaged, resul ting in a value of 3.67E18 cm 3
106 nm 1 and used to determine the Ar II electron density. The various lines used to calculate electron temperature and density are shown below in Table 6 2 Table 6 2 Elemental lines used for temperature and electron density calculations, along with their respective spectral windows and the properties each line was used to determine. Element Lines (nm) Spectral w indows (nm) Pro perties d etermined Al I 308.21, 309.27, 309.28, 394.4, 396.15 310, 400 T e Ar II 354.56, 355.95, 385.06, 392.86, 487.99, 506.20 350, 400, 480, 500 T e 484.78 480 n e H I 656.28 656 n e Lu II 339.71, 350.74, 355.44 350 T e Mn II 259.37, 260.57, 293.31, 29 3.93, 344.20, 346.03 260, 310, 350 T e Mn I 403.08, 403.31, 403.45, 404.14, 404.87 400 T e N II 343.71, 504.51 350, 500 T e N I 413.76, 414.34, 415.15, 467.07 415, 480 T e Results and Discussion Once all irradiance corrections were applied as described a bove, all windows had comparable intensities, as shown in Figure 6 6 Especially noteworthy are the overlapping windows, 400 & 415 nm and 480 & 500 nm, which show excellent agreement with one another and the 260 nm window whose shape is skewed due to a
107 uniform scaling of the whole window as opposed to a more ideal wavelength dependent scaling. Except for the 260 nm window, the spectral emission curve of the plasma can easily be pictured in the plot. Figure 6 6 All spectral windows used after all irradiance corrections have been applied. Shown here are the spectral windows at a delay of 1.5 s. From these data, the intensities, full peak integration, of the lines mentioned above in Table 6 2 were calculated; Boltzmann plots were then generated from these intensities. The number of peaks used for the se plots varied between 2, for N II only, and 6; the R values for the linear fits were mostly 0.98 or greater, with all but one fit, R=.81, having an R value of at least 0.9. A representative plot is shown below in Figure 6 7
108 Figure 6 7 Boltzmann plot of Ar II. From these Boltzmann plots the plasma temperature was derived for the aforementioned species. The temperature plot from Ar II, d isplayed in Figure 6 8 below, exhibited some oscillation in early times, less than 1 s, but remained relatively flat until it terminates at 3 s. The N II temperature, also displayed in Figure 6 8 showed similar oscillatory behavior at early times but with an overall trend of decrease by its termination at 1 s. Both showed temperatures around 10,000 K. In contrast, the temperature derived from N I, showed a monotonic expo nential decay over its range, 3 10 s, with no oscillations but with temperatures around 25,000 K.
109 Figure 6 8 Bulk p lasma temperature calculated from Ar II (left) and N II (right). For th e particulate species, the temperatures were measured over a longer time period, up to 100 s, and were generally decreasing with time. However, the rate of decrease of the plots is not constant. In the Lu II temperature plot, shown below in Figure 6 9 the rate of cooling is almost linear between 5 and 25 s, at which point the plot adopts an exponential rate of decrease. The same trend is seen in the Mn II data in which the slope is nearly flat between 2 and 15 s but then converts to an exponential decay. This behavior is in perfect agreement with that seen in previous studies [ 23 ] [ 52 ] [ 53 ] [ 54 ] This change in the slopes of the temperature curves is attributed to heat from the bulk plasma diffusing into the locally cooled plasma about the emitting particles, thereby slowing the rate of net energy loss to the surroundings, i.e. the room. The Mn I temperature data, begins at 25 s, after this slope shift phenomenon is observed, but does show a monotonic exponential decay in temperature. The Al I data shares the same time frame as th at of Mn I and exhibits temperatures between 4,000
110 trends of the other three elements and is counter to what is expected to occur physically. The values of the temperature a re in good agreement with each other for all three particulate species. Figure 6 9 Local plasma temperature as determined by Lu II (left) and Mn II (right). Figure 6 10 below shows representative error bars for the temperature data. These error bars were determined by calculating the y axis of the Boltzmann plot (i.e. ln( I/gA) ) for all six sets of data as well as that of their average spectrum; from this data, the standard deviation was also calculated. It was then assumed that the data on the y axis follows a normal distribution centered about the value calculated from the average spectrum and with a standard deviation equal to the one calculated. For each time, a value for the y axis for each peak used in the Boltzmann plot was then selected at random, with the probability of selection equal to that of a normal distribution, and th e slope of the plot calculated; this process was repeated five thousand times. The average slope of all five thousand calculations was very close to the slope determined using the averaged spectrum, indicating a sufficiently large
111 sampling population. The standard deviation of the population was then assumed to be equal to the standard d eviation of the slopes of the Boltzmann plots. The temperature was then calculated using the slope plus one standard deviation and the slope minus one standard deviation and the difference between the two calculated. For the Lu II data, this difference was between 9% and 35% of the average temperature and for Mn II, it was between 15% and 56% of the average temperature. The error bars in Figure 6 10 represent 1 of the average temperature derived from all six data sets. Figure 6 10 Local plasma temperature as determined by Lu II (left) and Mn II (right) with representative error bars ( 1 Figure 6 11 below shows all the te mperature data on the same plot; there are multiple phenomena of interest that can be observed. The first is that the temperature calculated from N I is much higher than all other temperatures observed; no explanation is offered for this phenomenon. Second ly, there is fairly good agreement in temperature at the intersection of the gaseous and particulate data, at around 1 s. Thirdly, at early times the temperature calculated from Mn II is notably lower than that from Lu II; this
112 may be due to the differences in the ionization energies of the two elements. Manganese, with a first ionization energy of 717.3 kJ mol 1 require s more energy to ionize than lutetium, which has a first ionization of 523.5 kJ mol 1 ; this difference in ionization energies can result in a greater local cooling effect for manganese compared to the lutetium, thereby lowering the observed temperature. Th e final thing of note is that the temperatures calculated from all three particulate species converge at very long times. This suggests that over time, the different degrees of cooling experienced by each species become negated as the locally cooled region s absorb energy from the bulk plasma, causing all species to emit at the same bulk plasma temperature. Figure 6 11 Temperatures derived from all species. Open symbols refer to gas species (bulk plasma properties) and solid symbols to particulate species (local plasma properties). The full temporal range is shown on the left and a close up view of the first 15 s on the right. Figure 6 12 below presents the same data as Figure 6 11 above but on a log log scale. In this presentation of the data, the slope shift point of the temperature curve is clearly visible between 15 and 2 5 s, marking the end of internal temperature gradients within the plasma and start of emission at a single bulk plasma temperature.
113 It was the intent of this study to compare the electron density calculated from the gaseous species to those from the par ticulate species in a similar manner to the temperature plots above. However, the FWHMs of the particulate species were at or below the instrument width measured using the Hg Ar lamp. As a result, Figure 6 13 below only shows the bulk plasma electron density calculated using the H line and Ar II 484.78 nm line. The two data agree extremely well, except at the 5 and 7.5 s points, which correspond to much a smaller Ar II peak and thus more inaccuracy in the calculation of the FWHM due to a lesser degree of broadening of the Ar II l ines as compared to the H line. Figure 6 12 Temperatures derived from all species on a log log scale. The slope shift point at 15 25 s is clearly evident in this presentation.
114 In order to compare the effects of the matrix on plasma properties, the plasma temperature from Lu II in the normal matrix was compared to that in the heavy sodium matrix; the results are shown below in Figure 6 14 The temperatures show two major differences. Firstly, the temporal region of local plasma cooling is shorter in the sodium matrix than in the non sodium matrix; this may be due to a reduced overall plasma temperature due to the presence of additional mass within the plasma. Secondly, once equilibrium is reached, the rate of cooling of the sodium matrix is slower than that of the non sodium matrix; this can again be attributed to the presence of additional thermal mass in the plasma which causes more energy to be present for a given temperature. This in turn can reduce the rate of cooling in the plasma. Figure 6 13 Bulk plasma electron density as measured by the H and Ar II 484.78 nm lines, on a semi log scale Full error bars denote one standard deviation.
115 Figure 6 14 Comparison of the local plasma temperature using Lu II in normal matrix vers us the heavy sodium matrix. Conclusions The goal of this study was two fold: it aimed to compare bulk and local plasma properties in order to find their equilibrium time and to determine if the presence of large quantities of a matrix aerosol within the pl asma can significan tly alter the plasma conditions. It successfully revealed changes in the temperature profile of particle derived species, confirming the effect of local cooling on plasma properties. The intersection of the local, gas species, temperatur es and the local, particle derived temperature were in general agreement but since the gas species emission was short lived, it did not form a good basis of comparison with the particulate emission. It was found that the matrix of the particle affected the duration of the reheating of the local plasma as well as the rate of temperature loss for particle derived species.
116 CHAPTER 7 S UMMARY AND FUTURE WO RK Up to this point, many important LIBS related phenomena have been noted. Previous work has identified a finite upper particle size limit for complete dissociation in the range of several microns with the actual limiting value dependent on the thermo physical properties of the particle. It has also been shown that the time scales for mass diffusion from an aerosol particle to the bulk plasma and the time scales for heat diffusion from the plasma to the particle are on the same order of magnitude as the LIBS analytical time frames This in turn may create significant matrix effects related to local cooling of the plasma about the emitting species. Differences were also highlighted in the LIBS respo nse of solids and gases of the same mass concentration, with solids showing greater response and sensitivity partially attributed to the rarefaction of the gases during plasma expansion. The current studies, as detailed above, have added to this pool of k nowledge and are summarized below. 1) Particle Size s tudy : The aerosol particle size study revealed that even with increased residence time in the plasma, aerosol particles do not overcome their upper size limits for c omplete dissociation and linear, i.e. atomic number density dependent, response This is important in that it shows that the heat transfer rate within the plasma is sufficiently slow that by the time the local plasma temperature is restored to bulk conditions, the radiative energy transfer rat e from the bulk plasma has cooled the plasma to the point where it is no longer capable of dissociating particles and producing a linear analyte response This exemplifies the idea of the heat and mass diffusion within the plasma and radiative decay of the plas ma occurring simultaneously and on the same timescale as atomic emission.
117 2) Analyte phase s tudy : The carbon phase study showed that it is indeed possible to differentiate between different analyte sources using a LIBS signal. This stands in stark co mparison to the assumption of independence of the LIBS signal on analyte source and highlights the importance of matrix effects. In this scenario, the effect results from rarefaction of gaseous species caused by the expansion shock of the plasma. This effe ct is similar to aerosol upper size limits in that it does not require the presence of any other species and reflects only the interaction of the plasma with the analyte. The overall sensitivity of the routine still requires temporal optimization 3) Polar ization s tudy : The polarization study found some polarization when analyzing solids at o blique collection angles but revealed nothing that was spectrally dependent. This counters the idea of a polarization matrix in the continuum emission and preserves the concept of a uniformly emitting plasma. The discovery of possible polarization effects at very early times, attributed to Fresnel reflectivity, around plasma inception, serves to emphasize the idea of delaying data collection in order to minimize matrix e ffects. 4) Thomson scattering s tudy : Temporal probing of a LIBS plasma at early times, 500 ns and less, revealed two different scattering phenomena: scattering off the edge of the plasma and scattering at the center, with minimal scattering in between. Th e scattering near the plasma center is believed to be Thomson scattering, confirming the presence of the high electron densities necessary to produce the effect. Unfortunately, spectral measurements failed to identify the Thomson scattering satellite peaks As such quantitative analysis of plasma temperature and electron density could not be accomplished. However, quantitative Thomson scattering coefficients measured in this
118 study will be useful in combination with a model of the effective Thomson scatteri ng cross section, to be determined in future work. 5) Plasma properties time scale and matrix effect s tudy : The multi component aerosol study revealed changes in the temperature profile of particle derived species, highlighting the effect of local cooling on plasma properties. The matrix of the particle affected the duration of the reheating of the local plasma as well as the rate of temperature loss for particle derived species. The intersection of the gas species temperatures, measured at early times, and the temperature of particle derived species, measured at later times, were in general agreement. Overall, the current set of experiments has enhanced our knowledge of the dependence of the LIBS signal on plasma particle interactions and highlights the nee d for a complete understanding of this phenomenon. The most significant finding is the need for sufficient residence time, on the order of 10 to 20 s, for dissociation, heat and mass transfer, and equilibration of analyte species within the plasma, condit ions promoting accurate quantitative analysis. However, more work still needs to be done to better understand the plasma particle interactions and their resulting mat rix effects. Key among these are exploring element specif ic behavior, measuring Thomson s c attering satellite peaks, and exploiting plamsa particle interactions to enhance the LIBS response. 1) In inductively coupled plasma mass spectrometry, ICP MS, different elements have shown different degrees of matrix effects. It would be beneficial to ass ess whether thermo physical properties, such as elemental mass, atomic diffusion rates, ionization
119 potential, and volatility, have an effect on the LIBS response and if so, the nature of th ose effect s 2) The Thomson s cattering experiment in this work was unable to identify the satellite peaks. These peaks can be used to obtain useful information about the plasma properties at very early times, such as electron temperature and number density. As such it is proposed that the spectral portion of the experime nt be repeated with better spatial resolution. This can be done using a spectrometer in monochromator mode with a PMT as the detector, instead of a CCD and scannin g through different wavelengths. This method can significantly improve SNR, making observati on of the satellite peaks possible. 3) Lastly, new hybrid techniques, such as LA LIBS, should be developed and explored. These techniques attempt to take advantage of our knowledge of plasma analyte interactions to improve analyte response and matrix indep endence. Such developments are in the best interest of the entire optical spectroscopy community.
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128 BIOGRAPHICAL SKETCH Michael Asgill was born in Freetown, Sierra Leone to Michael Asgill and Evelyn Williams. He graduated from Apopka Hig h School in Apopka, Florida in May 2005. Upon completion, he began his undergraduate studies at the University of Florida in Gainesville, Florida. He completed his Bachelor of Science in Mechanical Engineering in May 2008 and immediately began his PhD. stu dies under the direction of Professor David W. Hahn in the same discipline. He earned his Master of Science degree (non thesis) from the University of Florida in August 2009. The work presented here is the culmination of the research carried out during his PhD. s tudies at the University of Florida.