Keywords: Ablation laser, Plasma induit par laser, Laser-induced breakdown spectroscopy (LIBS), Calibration free LIBS, Spectrométrie optique, Analyse qualitative, Analyse quantitative, Matériel organique, Produit agroalimentaire Laser ablation, Laser-induced plasma, laser-induced breakdown spectroscopy (LIBS), Calibration free LIBS, Optical spectroscopy, Qualitative analysis, Quantitative analysis, Organic material, Agricultural product

IV V

Résumé

Ce travail de thèse a été consacré à la compréhension du plasma induit par laser sur des matériaux organiques et à l'application de la technique de laser-induced breakdown spectroscopy (LIBS) à l'analyse quantitative de ces matériaux. L'ensemble des travaux contribue donc à approfondir notre connaissance sur les mécanismes physiques impliqués dans l'interaction laser-matière, dans la génération du plasma et dans l'évolution de celui-ci au cours de son expansion dans le gaz ambiant avec la spécificité de s'adresser à des plasmas induits sur des cibles organiques. Ces travaux visent également à améliorer la performance de la LIBS pour l'analyse de matériaux organiques. La spécificité concernant la cible organique répond au besoin actuel de la communauté internationale travaillant sur le développement de la LIBS, de mieux maîtriser le plasma induit sur ce genre de matériau qui présente des propriétés optiques bien spécifiques par rapport à des matériaux mieux connus pour l'ablation laser tels que des métaux. Elle répond également au besoin grandissant d'utiliser la technique LIBS aux matériaux organiques pour des applications dans les domaines environnementaux, agroalimentaires, ou encore biomédicaux.

Conformément à la nature de cotutelle de cette thèse, les travaux ont été réalisés à l'Université Lyon 1, au Laboratoire de Spectrométrie Ionique et Moléculaire et également à l'East China Normal Univesity au State Key Laboratory of Precision Spectroscopy. Néanmoins la majorité des travaux originaux de cette thèse ont été réalisés à Lyon. Les travaux à Shanghai consistaient essentiellement en un transfert de compétences acquises à Lyon qui conduit au démarrage d'une activité de recherche similaire à Shanghai.

Ce mémoire de thèse a été rédigé selon l'organisation suivante. Après l'Introduction Générale qui précise les contextes scientifiques et technologiques, le Chapitre I rappelle les principes de base nécessaires à la compréhension du phénomène de génération de plasma par ablation laser, et de l'évolution de celui-ci dans un gaz ambiant. L'accent a été mis sur l'ablation des matériaux organiques. Les procédures et les techniques de diagnostic du plasma induit par laser sont ensuite présentées en insistant sur la nature transitoire et inhomogène d'un plasma en expansion. Le chapitre II s'intéresse à la génération et l'évolution du plasma induit sur la peau d'une pomme de terre, un échantillon typique de produit agroalimentaire. La caractéristique du plasma induit sur une cible organique molle et humide, comme une pomme de terre fraîche était quelque chose d'inconnu au démarrage de la thèse et constituait une base nécessaire à l'analyse quantitative des éléments métalliques en traces et ultra-traces contenus dans un tel échantillon. A l'issue de cette caractérisation, les données analytiques semi-quantitatives ont été extraites des spectres LIBS correspondant à la peau d'une pomme de terre. Le Chapitre III se situe dans la continuité du Chapitre II pour l'application de la LIBS à des matériaux organiques. Une étude comparative d'analyse de la poudre de lait par la LIBS et par l'ICP-AES permet une évaluation de la performance d'analyse quantitative de la LIBS pour des échantillons organiques, et une validation de la procédure CF-LIBS. A la différence des Chapitres II et III où les éléments de traces métalliques étaient au centre de notre attention, le Chapitre IV étudie le comportement des éléments majeurs qui composent la matrice d'un matériau organique, qui sont les 4 éléments organiques, H, C, O, N. A la décomposition d'un matériau organique par ablation laser, ces éléments peuvent se présenter sous la forme de fragments moléculaires, ou encore se recombiner en des espèces moléculaires. Nous étudions alors dans ce Chapitre l'évolution de ces espèces en fonction des paramètres du laser utilisé, et notamment la longueur d'onde. Le mémoire se termine par une conclusion générale et des perspectives.

VI

General Introduction

Laser-induced breakdown spectroscopy (LIBS) corresponds to an atomic emission spectroscopy (AES) that uses laser-induced plasma (LIP) to vaporize, atomize and excite material to be analyzed. The optical emission from a LIP is thus used for chemical analysis purpose. Generally, a LIBS experiment consists of two main parts: plasma generation and signal collection. In the plasma generation process, an intense pulsed laser beam is focused onto the surface of a sample, where high energy density is delivered within short time duration. Consequently, a small volume of material of the target is heated and evaporated into the surrounding gas, producing a material plume above the target surface. The plume can continue to absorb laser energy becoming further ionized into the state of plasma. The optical emission of the plasma is then collected to a spectrometer. The obtained emission spectrum recorded by a photo-detector can thus be used for qualitative and quantitative analyses of the target.

Brief historical review of the development of LIBS technique

Laser-induced spark emission can be considered as the precursor of LIBS, which was first performed in 1962, where a laser beam was used to produce a vapor from a solid target and an electrical spark was subsequently used to excite the ablated plume [START_REF] Brech | Opticalmicroemission stimulated by a ruby maser[END_REF]. At that time, the laser was used primarily as an ablation source with cross-excitation in combination with an electric discharge. The first analytical use of LIP for spectrochemical analysis of surface was reported in France in 1963 [START_REF] Debras-Guédon | De l'utilisation du faisceau issu d'un amplificateur à ondes lumineuses par emission induite de rayonnement (laser à rubis), comme source énergétique pour l'excitation des spectres d'emission des éléments[END_REF]. Since then, LIP was used not only as a sampling tool but also as an emission source [START_REF] Runge | Spectrochemical analysis using a pulsed laser source[END_REF]. In addition, LIBS became a technique for direct spectrochemical analysis and had shown its huge potential for fast multi-elemental analysis. From 1964 to 1967, the first commercial instruments based on LIBS were manufactured by Jarrell-Ash Corporation (USA) and VEB Carl Zesis (Germany) [START_REF] Moenke | Laser Micro-SpectrochemicalAnalysis[END_REF]. During the 1970s, the development continued in several directions over several countries [START_REF] Ready | Effects of High-Power Laser Radiation[END_REF]. On the one hand, the direct ablation, excitation and observation of the spark on surfaces were significant advantages for spectrochemists. On the other hand, LIBS mostly provided physicists a mean for fundamental investigations of breakdown in gases [START_REF] Radziemski | From LASER to LIBS, the path of technology development[END_REF].

After the first wave of enthusiasm in the early 1970s, the interest in LIBS slowly declined with the stagnation of the development of commercial LIBS instruments. The instrumentation with LIBS was quite expensive and unreliable, whereas the accuracy and precision could not compete with other developed analytical techniques, such as electro-thermal atomization -atomic absorption spectrometry (ETA-AAS) or inductively coupled plasma-atomic emission spectrometry (ICP-AES) [START_REF] Radziemski | From LASER to LIBS, the path of technology development[END_REF].

Starting in the early 1980s, a renewed interest in LIBS emerged along with the significant improvements in laser and, more importantly, in sensitive imaging optical detectors, such as the intensified charge-coupled device (ICCD) [START_REF] Radziemski | From LASER to LIBS, the path of technology development[END_REF]. These detectors allowing time-resolved spectral measurements in a wide spectral window perfectly matched the emission properties of the LIP, which has promoted a huge development of the LIBS technique. Such development provided laboratories with reliable and relatively inexpensive instruments for research on LIBS technique. One of the most representative groups at Los Alamos National Laboratory deserves to be mentioned for the application of LIBS in detection of hazardous gases and vapors in air [START_REF] Radziemski | Laser-induced breakdown spectroscopy: time-resolved applications[END_REF][START_REF] Cremers | Detection of chlorine and fluorine in air by laser-induced breakdown spectrometry[END_REF] and small amounts of beryllium in air or on filters [START_REF] Radziemski | Detection of beryllium by laser-induced breakdown spectroscopy[END_REF][START_REF] Cremers | Direct detection of beryllium on filters using the laser spark[END_REF]. It was also this research group at first coined the acronym LIBS for Laser-induced breakdown spectroscopy in Ref [START_REF] Radziemski | Time-resolved laser-induced breakdown spectrometry of aerosols[END_REF]. Further development of the technique turned to very practical problems, such as monitoring environmental contaminations [START_REF] Wisbrun | Detector for trace elemental analysis of solid environmental samples by laser plasma spectroscopy[END_REF][START_REF] Ciucci | Trace pollutions analysis in a soil by a time-resolved laser-induced breakdown spectroscopy technique[END_REF][START_REF] Gornushikin | Determination of cobalt in soil, steel, and graphite using excited-state laser fluorescence induced in a laser spark[END_REF][START_REF] Hilbk-Kortenbruck | Analysis of heavy metals in soils using laser-induced breakdown spectrometry combined with laser-induced fluorescence[END_REF], industrial applications of controlling material processing [START_REF] Aragon | Determination of carbon content in molten steel using laser-induced breakdown spectroscopy[END_REF][START_REF] Aguilera | Determination of carbon content in steel using laser-induced breakdown spectroscopy[END_REF][START_REF] Sabsabi | Quantitative analysis of aluminum alloys by laser-induced breakdown spectroscopy and plasma characterization[END_REF], and sorting of materials to put them in proper scrap bins. [START_REF] Sattmann | Laser-induced breakdown spectroscopy for polymer identification[END_REF][START_REF] Mönch | Laser identifies steel grades: A new approach to the automatic inspection of pipe fittings[END_REF][START_REF] Fink | Analysis of recycled thermoplasts from consumer electronics by laser-induced plasma spectroscopy[END_REF].

As we entered the new millennium, LIBS was attracting more and more attention. This was stimulated by the large range of applications of qualitative and quantitative analysis in various domains, such as analysis of metal alloys for metallurgy industry and precious stones for jewellery [START_REF] Garcia-Ayuso | Characterization of jewellery products by laser-induced breakdown spectroscopy[END_REF][START_REF] De Giacomo | ns-and fs-LIBS of copper-based-alloys: A different approach[END_REF][START_REF] Elhassan | Nanosecond and femtosecond Laser Induced Breakdown Spectroscopic analysis of bronze alloys[END_REF]; analysis of art works and cultural heritages [START_REF] Burgio | Pigment identification in paintings employing laser induced breakdown spectroscopy and Raman microscopy[END_REF][START_REF] Bicchieri | Characterization of azurite and lazurite based pigments by laser induced breakdown spectroscopy and micro-Raman spectroscopy[END_REF][START_REF] Colao | Laser-induced breakdown spectroscopy for semi-quantitative and quantitative analyses of artworksapplication on multi-layered ceramics and copper based alloys[END_REF][START_REF] De Giacomo | Laser Induced Breakdown Spectroscopy methodology for the analysis of copper-based-alloys used in ancient artworks[END_REF]; inspection of environment-related samples such as soils, rocks, sediments or water [START_REF] Barbini | On board LIBS analysis of marine sediments collected during the XVI Italian campaign in Antarctica[END_REF][START_REF] De Giacomo | Laser induced breakdown spectroscopy on meteorites[END_REF][START_REF] Senesi | Heavy metal concentrations in soils as determined by laser-induced breakdown spectroscopy (LIBS), with special emphasis on chromium[END_REF]; measurements of pollutant elements in foods such as vegetables and cereals [START_REF] Juvé | Space-resolved analysis of trace elements in fresh vegetables using ultraviolet nanosecond laser-induced breakdown spectroscopy[END_REF][START_REF] Lei | Time-resolved characterization of laser-induced plasma from fresh potatoes[END_REF][START_REF] Ferreira | Determination of Ca in breakfast cereals by laser induced breakdown spectroscopy[END_REF]; and so on.

As a result of the rapid development of the LIBS technique and the exponential growth of the number of scientific publications devoted to it since the middle of the 1990s [START_REF]Laser-induced breakdown spectroscopy: Fundamentals and applications[END_REF][START_REF] Cremers | Handbook of Laser-Induced Breakdown Spectroscopy[END_REF], a scientific community specialized in LIBS has emerged during the last decade. The first international conference devoted to LIBS was organised in 2000 in Pisa, providing an excellent snapshot of the status of LIBS research, development and commercialization at the beginning of the new millennium. Since then, the international LIBS conference takes place every two years, with in the interval, the holding of regional LIBS conferences: EMSLIBS (Euro Mediterranean Symposium on Laser-Induced Breakdown Spectroscopy) and NASLIBS (North American Symposium on Laser-Induced Breakdown Spectroscopy) [START_REF] Hahn | Laser-Induced Breakdown Spectroscopy (LIBS), Part I: Review of Basic Diagnostics and Plasma-Particle Interactions: Still-Challenging Issues Within the Analytical Plasma Community[END_REF].

LIBS, an analytical technique with unique features

What renders so wide the range of application of LIBS is preliminarily its unique and attractive features. LIBS, like other analytical techniques based on AES, presents some advantages compared with other techniques, for instance the ability to detect all elements and the capability of simultaneous multi-elemental detection. In addition, LIBS has many specific advantages compared with conventional AES-based techniques, thanks to the use of the laser radiation-induced spark rather than a physical device such as a pair of electrodes to create the plasma.

Any kind of substance (in gas, liquid and solid state) can be analyzed with simple or even without sample preparation in air, in vacuum, under water, and in extreme conditions such as high temperature and pressure [START_REF] Noda | Detection of carbon content in a high-temperature and high-pressure environment using laser-induced breakdown spectroscopy[END_REF][START_REF] Michel | Laser-induced breakdown spectroscopy of bulk aqueous solutions at oceanic pressures: evaluation of key measurement parameters[END_REF]. It is worth mentioning that LIBS shows its unique advantages when femtosecond laser is used as the ablation source. First of all, the accuracy and the precision of sampling are remarkably with significant improvement compared to ablation with nanosecond laser [START_REF] Samek | Sampling of material using femtosecond pulses[END_REF]. This improvement is directly linked to the changes in laser-material interaction. A proposed application of fs-LIBS has been tested successfully for in-depth profiling [START_REF] Margetic | Depth profiling of multi-layer samples using femtosecond laser ablation[END_REF]. Considering the minimized thermal damage of the sample, fs-LIBS has been used for analyzing biological samples with high spatial resolution [START_REF] Assion | Femtosecond laser-induced-breakdown spectrometry for Ca2+ analysis of biological samples with high spatial resolution[END_REF], where caters with diameter of 3 m were reported. To improve the spatial resolution, near-field technique was applied to further decrease the size of the probed volume [START_REF] Zorba | Optical far-and near-field femtosecond laser ablation of Si for nanoscale chemical analysis[END_REF]. In such way, a 600 nm crater can be obtained with a 775 nm IR laser [START_REF] Samek | Ultra-short laser pulse ablation using shear-force feedback: Femtosecond laser induced breakdown spectroscopy feasibility study[END_REF]. Another remarkable feature of fs-LIBS is the excellent performance of measurement at a distance without contacting the sample directly, namely standoff or remote LIBS. An important characteristic of remote LIBS is the maximum distance at which the measurement can be carried out. This distance is mainly limited by the divergence of the laser beam. With femtosecond laser pulse, the divergence can be overcome by self-focusing or self-trapping effect. For this application, fs-LIBS is not limited to a conventional LIBS experimental setup. A more recent configuration that has been investigated is the use of filaments by the Teramobile team with the contribution of the research team in Lyon 1 University [START_REF] Stelmaszczyk | Long-distance remote laser-induced breakdown spectroscopy using filamentation in air[END_REF]. The advantage of using filaments is that no focusing optics is needed and, depending on the femtosecond beam profile, the filament can be formed in air. UV filaments at 248 nm have been used to distinguish different stone samples at 6 m [START_REF] Tzortzakis | Ultraviolet laser filaments for remote laser-induced breakdown spectroscopy (LIBS) analysis: applications in cultural heritage monitoring[END_REF]. Fs-LIBS spectra of metallic targets have been obtained at 90 m with NIR filaments (795 nm) [START_REF] Rohwetter | Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes[END_REF]. The record of the distance has been made, in the Teramobile team, to be 180 m [START_REF] Rohwetter | Filament-induced remote surface ablation for long range laser-induced breakdown spectroscopy operation[END_REF].

Besides, high speed analysis and remote sensing capabilities offer a strong potential of using compact and portable LIBS instruments for in situ [START_REF] Goujon | A compact and portable laser-induced breakdown spectroscopy instrument for single and double pulse applications[END_REF][START_REF] Bousquet | Development of a mobile system based on laser-induced breakdown spectroscopy and dedicated to in situ analysis of polluted soils[END_REF], standoff [START_REF] Salle | Laser-Induced Breakdown Spectroscopy in open-path configuration for the analysis of distant objects[END_REF], and/or online analyses and process control [START_REF] Boue-Bigne | Laser-induced breakdown spectroscopy applications in the steel industry: Rapid analysis of segregation and decarburization[END_REF]. The integration by the NASA and the ESA of a LIBS module in their space probes for the analysis of the soil of Mars highlights the application of LIBS for space exploration [START_REF] Knight | Characterization of laser-induced breakdown spectroscopy (LIBS) for application to space exploration[END_REF][START_REF] Colao | Investigation of LIBS feasibility for in situ planetary exploration: An analysis on Martian rock analogues[END_REF][START_REF] Sirven | Feasibility study of rock identification at the surface of Mars by remote laser-induced breakdown spectroscopy and three chemometric methods[END_REF]. In addition, laser pulse induces a limited and localized damage on the sample surface by removing a small amount of material in the order of tens to hundreds of nano-grams. Such property is appropriate for the analysis of art works and cultural heritages for their conservation or renovation. Finally, LIBS can be easily coupled with other spectroscopic techniques, for example Raman spectroscopy or laser-induced fluorescence (LIF) [START_REF] Hilbk-Kortenbruck | Analysis of heavy metals in soils using laser-induced breakdown spectrometry combined with laser-induced fluorescence[END_REF][START_REF] Dreyer | Study of sub-mJ-excited laser-induced plasma combined with Raman spectroscopy under Mars atmosphere-simulated conditions[END_REF].

Although LIBS has demonstrated its versatility and attractive features, from the analytical point of view, the performance of quantitative analysis may be considered as its Achilles' heel [START_REF] Hahn | Laser-Induced Breakdown Spectroscopy (LIBS), Part I: Review of Basic Diagnostics and Plasma-Particle Interactions: Still-Challenging Issues Within the Analytical Plasma Community[END_REF]. A major factor affecting LIBS quantitative performance is the matrix effect. Obviously, such effect also exists for other plasma sources for atomic emission spectroscopy such as ICP, but it is more severe for LIP due to the high density of material within the small laser plasma. Moreover, in terms of detection limit, LIBS is in general significantly less competitive than established laboratory methods for analytical chemistry.

Normally, these established techniques reduce a sample to be analyzed to a solution in which the analyte concentration is measured in μg/l. While LIBS may exhibit a greater degree of detection for an element in its native matrix (e.g., in soil) compared to the methods including a dilution of the elements by reducing the sample into a solution. However, it is still instructive to compare the limit of detection (LOD) of LIBS with more conventional analytical methods. A comparison of detection limits obtained using LIBS, atomic absorption (AA), ICP, and X-ray fluorescence (XRF) is shown in Table 5 of Ref [START_REF] Cremers | Laser-Induced Breakdown Spectroscopy-Capabilities and Limitations[END_REF]. Generally, ICP-mass spectrometry (IPC-MS) has the lowest detection limit, typically 5-50 ppb (parts per billion), followed by graphite furnace-atomic absorption (GF-AA), ~0.5 ppm (parts per million), and flame-AA ~5-50 ppm. These three techniques are laboratory based, so samples need to be collected in the field and transported back to laboratory. Both LIBS and XFR are adaptable for field-portable instruments. If we compare the detection limits of LIBS and XFR, LIBS tends to have somewhat lower limits (~0.1 to hundreds of ppm), than XFR (tens to hundreds of ppm) for many elements.

Quantitative analysis with LIBS

Classically like for other analytical techniques, quantitative analysis with LIBS involves the use of a calibration curve that relates the concentrations of analytes to the corresponding line emission intensities observed in a spectrum. However, the emission intensity of a specific line of a specific element depends not only on the concentration of the element but also on the properties of the plasma, which can be strongly affected by the laser-matter interaction responsible of the plasma generation. In other words, a same concentration of a given species in different materials can correspond to different emission intensities in emission spectra. Such effect is called matrix effect. The matrices of reference samples used to establish the calibration curve have to match those of unknown samples to be analyzed. Unfortunately, it is not always possible to have matrix-matched reference samples because the property of the matrices of the samples to be analyzed can be unknown or the needed reference sample might be unavailable.

In order to go round the matrix effect, a calibration free method was proposed by assuming that the local thermodynamic equilibrium (LTE) was reached in the plasma [START_REF] Ciucci | New Procedure for Quantitative Elemental Analysis by Laser-Induced Plasma Spectroscopy[END_REF]. This method is called calibration-free laser-induced breakdown spectroscopy (CF-LIBS).

However, the accuracy of CF-LIBS critically depends on the associated assumptions, such as stoichiometric ablation (the composition of the plasma under observation is representative of that of the sample); the plasma volume under observation is in LTE state; and the spectral lines used to determinate concentration are optically thin [START_REF]Laser-induced breakdown spectroscopy: Fundamentals and applications[END_REF]. The application of the CF-LIBS procedure needs therefore drastic requirements on the state of a plasma and on its optical emission. Accurate values of temperature and electron density must be determined in the plasma. The emission lines of all the elements contained in a sample must be detected, which requires to record spectra with high signal-to-noise ratio over a wide spectral range. In addition, almost no real validation of LTE assumption can be achieved in most of the cases due to the complex transient nature and the spatial inhomogeneity of the plasma. As a result, a full spatial and temporal diagnosis of the plasma is necessary for quantitative analysis with the CF-LIBS procedure. Finally, the influence of the optical thickness of the plasma has to be considered in order to get good accuracy of the measurement. Here and below, the accuracy means the degree of closeness of measurements of a quantity to that quantity's actual (true) value.

Application of LIBS in analysis of organic materials

Nowadays, it is generally admitted that in its state of actual development, LIBS combines great potential and severe limitations as mentioned above. The analytical performance of LIBS sensitively depends on the nature of the material to be analyzed. Generally speaking and due to the different interaction mechanisms with laser radiation, two large classes of materials can be distinguished: metals and organic materials. It is recognized that the application of LIBS to metallic alloys tends to give more accurate analytical results than for organic materials [START_REF] Tognoni | Calibration-Free Laser-Induced Breakdown Spectroscopy: State of the art[END_REF]. From the ablation point of view, photothermal ablation dominates the ablation of metallic target while both photothermal and photochemical ablation play important roles for organic samples. Due to the similar structure of the metallic targets, it is much easier to obtain a partial stoichiometric ablation among metallic elements. While a full stoichiometric ablation is certainly much more difficult to obtain for organic samples, due to the divergences among complex molecular bond energies. In addition, plasmas composed of metallic elements satisfy the McWhirter criterion at low electron density values, while non-metallic elements require higher electron density values [START_REF] Tognoni | Calibration-Free Laser-Induced Breakdown Spectroscopy: State of the art[END_REF]. This is related to the electronic configuration and in particular to the higher density of excited levels in the low energy range in metals. Besides, plasma composed of non-metallic elements need longer time to reach LTE than that composed of metallic elements, because organic elements typically have larger energy differences between excited and de-excited energy levels than metallic ones. Finally, metallic samples normally have a better homogeneity compared to organic samples, which makes measurements of metallic samples more repeatable and more controllable with respect to organic ones.

When an intense laser pulse is focused on an organic material, atoms and molecules are vaporized from the material. Therefore, elemental analysis is in principal possible as for metals. For example in pharmaceutical industry, examples of specific elements to be analyzed are chlorine, sulfur, fluorine or bromine as part of the drug; magnesium as part of the lubricant (i.e. magnesium stearate); sodium as part of the disintegrant (i.e. croscarmellose sodium); or titanium in the form of titanium oxide in the coating. From the elemental analysis point of view, both organic and metallic samples use the same LIBS analytical protocol. However, in many other applications, the organic matrix itself has to be determined. Such applications include detection and analysis of biomedical samples [START_REF] Hamzaoui | Quantitative analysis of pathological nails using laser-induced breakdown spectroscopy (LIBS) technique[END_REF], polymers [START_REF] Sattmann | Laser-induced breakdown spectroscopy for polymer identification[END_REF], or organic explosives [START_REF] Lucena | New challenges and insights in the detection and spectral identification of organic explosives by laser induced breakdown spectroscopy[END_REF]. Two approaches have been investigated for the extension of LIBS to the analysis of organic materials. The first one is based on the use of chemometric procedures for the treatment of LIBS spectra of organic materials. Such procedures allow the extraction of the most significant information from the whole spectral range containing emission lines and especially the interrelation between the emission intensities from the different elements or molecules to provide and enhance the specific spectral feature of an organic material for its identification [START_REF] Duchene | Chemometrics and Laser Induced Breakdown Spectroscopy (LIBS) Analyses for Identification of Wall Paintings Pigments[END_REF]. For instance, the determination of intensity ratios between line emissions from the organic elements C, H, O and N can provide valuable information about the chemical structure and composition of organic targets [START_REF] Anzano | Classification of polymers by determining of C-1 : C-2 : CN : H : N : O ratios by laser-induced plasma spectroscopy (LIPS)[END_REF][START_REF] Tran | Determination of C : H : O : N ratios in solid organic compounds by laser-induced plasma spectroscopy[END_REF]. Especially, the C/H ratio was found to be particularly important for the discrimination [START_REF] Sattmann | Laser-induced breakdown spectroscopy for polymer identification[END_REF][START_REF] Anzano | Laser-induced plasma spectroscopy for plastic identification[END_REF][START_REF] Gondal | Identification of different kinds of plastics using laser-induced breakdown spectroscopy for waste management[END_REF]. Another approach consists in the detection of characteristic molecules or radicals in the laser-induced plasma from an organic material. In some experimental conditions, such molecular or radical species can be transferred directly from the sample to the plasma. This part of molecule can be described as native ones [START_REF] Baudelet | Spectral signature of native CN bonds for bacterium detection and identification using femtosecond laser-induced breakdown spectroscopy[END_REF], which can be detected with time-resolved LIBS. Emission of small native diatomic fragments present in the plasma can provide important information about the chemical structure of organic material, such as CN or C 2 . However, diatomic molecules can also be formed due to the interaction between the vaporized species and the ambient gas. Therefore, investigation of the molecular formation mechanism is very important for LIBS application for the analysis of organic samples.

Overall it is still challenging to apply the LIBS technique to organic and biological materials, such as polymers, vegetables, or more generally to foods, compared to metals.

There are several reasons: firstly, laser ablation process is more complicated for organic samples with respect to metallic ones. Secondly, in the majority of the situations biological materials are rather inhomogeneous media, where the matrix effect is accentuated. In addition, trace elements in biological materials are often close to or below the limit of detection of LIBS in its actual state of development. Finally, it is more difficult to prepare matrix-matched reference samples than for metallic samples [START_REF]Laser-induced breakdown spectroscopy: Fundamentals and applications[END_REF]. However the importance of the application recently has been attracting many attentions on the extension of LIBS to organic materials, and makes the application in the analysis of organic materials one of the major actual development directions of LIBS.

Previous works on LIBS applied to the analysis of organic materials by the team from Lyon 1 University

In the previous works of the research team from Lyon 1 University, the application of LIBS to organic materials has been investigated in the framework of two PhD theses [START_REF] Baudelet | Propriétés physico-chimique du plasma induit par laser en régime nanoseconde et femtoseconde: Application analytique aux bactéries et aux produits agroalimentaires[END_REF][START_REF] Boueri | Laser-induced plasma on polymeric materials and applications for discrimination and identification of plastics[END_REF]. These works were focused on the demonstration of the feasibility of LIBS for discrimination and identification of bacteria [START_REF] Baudelet | Spectral signature of native CN bonds for bacterium detection and identification using femtosecond laser-induced breakdown spectroscopy[END_REF][START_REF] Baudelet | Discrimination of microbiological samples using femtosecond laser-induced breakdown spectroscopy[END_REF], detection of metallic elements in fresh vegetables [START_REF] Juvé | Space-resolved analysis of trace elements in fresh vegetables using ultraviolet nanosecond laser-induced breakdown spectroscopy[END_REF], and discrimination and identification of polymers [START_REF] Boueri | Identification of Polymer Materials Using Laser-Induced Breakdown Spectroscopy Combined with Artificial Neural Networks[END_REF]. For the detection of trace metallic elements in vegetables, an extensive number of 27 elements was detected in a typical vegetable such as potato [START_REF] Juvé | Space-resolved analysis of trace elements in fresh vegetables using ultraviolet nanosecond laser-induced breakdown spectroscopy[END_REF], including organic elements, nonmetallic elements and trace metallic elements. However, only qualitative analysis was performed, which represents the first step towards quantitative analysis of trace or ultra-trace elements in fresh vegetables. In addition, the qualitative analysis of bacteria and polymers showed the potential of LIBS technique for material identification [START_REF] Baudelet | Spectral signature of native CN bonds for bacterium detection and identification using femtosecond laser-induced breakdown spectroscopy[END_REF][START_REF] Boueri | Identification of Polymer Materials Using Laser-Induced Breakdown Spectroscopy Combined with Artificial Neural Networks[END_REF]. In these works for identification of organic materials, the diatomic molecules CN and C 2 formed in plasma were considered as important indications. The importance of characterization of the plasma induced on an organic material was also emphasized in these works.

Objective of the present thesis

The objective of my thesis is to go further in the understanding of the plasma induced on organic materials and in the development of LIBS technique for organic materials. This thesis aimed at the improvement of the application of LIBS to organic materials for both qualitative and quantitative analyses in the continuity of the previous works realized in our group.

My work therefore was first focused on the characterization of the plasma induced from an organic material. Using time-resolved emission spectroscopy, the evolution of the plasma was studied in terms of its electron density and temperature. Such characterization allowed us verifying the LTE condition of the plasma. In the second step, the CF-LIBS procedure was applied to an organic sample, milk powder for quantitative determination of the concentrations of contained metallic elements. In the last part of my work in Lyon, I investigated, with time-and space-resolution the behavior of molecules fragments, such as CN and C 2 in a plasma induced on a polymer. This work contributes to the understanding of the behavior of molecules in a plasma as fingerprints of polymers for their classification and identification.

Structure of the manuscript

My thesis manuscript is divided into four Chapters. In Chapter I, theoretical backgrounds of laser-induced plasma, and especially those induced from organic materials are introduced. We discuss then the principle of LIBS with a special focus on the CF-LIBS procedure. Such procedure is compared with the classical calibration curve method. In Chapter II, the results of time-resolved diagnostics of the plasma induced from a fresh potato are presented. The temporal evolution of electron density determined using the Stark effect of the hydrogen H line at 656 nm, together with the temperature calculation using Saha-Boltzmann plot method (SBP) is presented. The LTE state of the plasma is validated by comparing atomic, ionic and molecular temperatures. Simultaneously, the signal-to-noise ratio is also measured as a function of the delay after the impact of the laser pulse on the sample. Chapter III is devoted to the comparative measurement of the concentrations of mineral elements in milk powders with LIBS and ICP-AES, which provides assessment and validation of the CF-LIBS procedure that we developed. The matrix effect was directly observed from the measured electron density and temperature. Its influence on analytical measurement is subsequently revealed by the quantitative results from the calibration curve method. The CF-LIBS procedure is used to overcome the matrix effect, in order for improving the accuracy and the precision of the analysis with respect to the calibration curve method. In Chapter IV, timeand space-resolved diagnostics allow studying the behavior of molecular species, C 2 and CN, during the expansion of a plasma induced on a PVC sample. Such behavior is correlated to the ablation mechanism and the formation of molecules in plasma.

Chapter I Theoretical backgrounds of laser-induced plasma and laser-induced breakdown spectroscopy on organic materials

In this chapter, the complex processes of laser ablation, plasma initiation, and subsequent propagation and evolution of the generated plasma are considered as the basis of the LIBS technique. Interaction mechanisms between laser radiation and matter depend on the parameters of the laser as well as the physical and chemical properties of the material. When a short laser pulse (nanosecond in the first part of thesis) with an irradiance reaching a certain threshold (e.g. > 1 GW/cm 2 typically, depending on the target composition) is focused on the sample surface, a significant material vaporization occurs, leading to a vapor plume formed above the substrate surface. Such process is called laser ablation. When laser ablation occurs in an ambient gas, the vapor plume expands into the ambient gas. The interaction of the plasma with the ambient gas represents a complex gas-dynamic process due to the implication of several physical processes such as formation of shock wave, deceleration of the plasma propagation, thermalization of the ablated species, gas-vapor inter diffusion, recombination, molecule and cluster formation [START_REF] Harilal | Internal structure and expansion dynamics of laser ablation plumes into ambient gases[END_REF].

If the ablation is stoichiometric, the resulting plasma has the same elemental composition as the target, so quantitative analysis of the target can be retrieved from the analysis of the plasma. Furthermore, if the plasma is in local thermodynamic equilibrium (LTE), the calibration-free LIBS procedure can be applied. However, the laser-induced plasma is intrinsically a transient and inhomogeneous medium, which makes the diagnostics still challenging. Temporal and spatial resolutions are needed for a complete characterization of the plasma.

In order to understand the generation and the evolution of laser-induced plasma, in this chapter, we recall the theoretical backgrounds of laser-induced plasma from its generation to its propagation in a background gas. The specificity of laser ablation of organic materials will be emphasized. Our focus is on the understanding of the physical processes leading to a plasma useful for LIBS application. Simple theoretical models are therefore used to describe the process as complex as laser-induced plasma. The principal of plasma diagnostics using emission spectroscopy will then be presented. The factors influencing the accuracy of quantitative analytical results will be especially discussed, such as matrix effect, self-absorption, departure from the LTE condition and so on.

I.1 Modeling of laser ablation and plasma generation in a background gas

Detailed interaction mechanisms between pulsed laser and solid state materials depend on both the laser pulse with its characteristic parameters, and the physical and chemical properties of the material. A general description does not exist today due to the complexity of the phenomenon. Simplified models have been established in the literature to describe the generation of a plasma due to laser ablation and the propagation of the plasma into the background gas. In general, nanosecond laser ablation of solid materials is treated according to the three following simplified models: photothermal ablation, photochemical ablation and photophysical ablation [START_REF] Bauerle | Laser processing and chemistry[END_REF]. In photothermal ablation, electronic excitation due to photon absorption is thermalized in a very short timescale (picoseconds typically) and accumulated heat can lead to thermally activated lattice degradation and bond breaking. On the other hand, in photochemical process, electronic excitation can result in direct lattice degradation and bond breaking without heating the material. When both thermal and nonthermal processes play a role, the process is more generally described by photophysical ablation. The nanosecond ablation of metal is a typical case where the photothermal process dominates. Actually most of the numerical models for laser-solid interaction and laser ablation are based on the photothermal process: heating of the solid followed by melting and evaporation, which has been justified for ns laser ablation, especially on metal surface [START_REF] Bogaerts | Laser ablation for analytical sampling: what can we learn from modeling?[END_REF]. Therefore in the following, the photothermal process will be introduced first to provide a general understanding of the initiation of the plasma. However, for organic materials, both photothermal and photochemical ablations play a role. And according to the specific ablation condition, one can be dominated with respect to the other or vice versa. This is why after the introduction on thermal ablation model for metal, we will present in more detail in this section the state of the art of the understanding and the modeling of laser ablation of organic materials.

The photochemical ablation is typically a dominant process for ablation of polymer materials by UV laser pulse.

I.1.1 Plasma generation through photothermal ablation

The first step of laser ablation is laser energy absorption by target, which leads to heating, melting and evaporation of the material touched by the laser pulse. In metal, the laser energy is first absorbed by free electrons inverse Bremsstrahlung, followed by electron fast energy relaxation, thermal diffusion, and energy transfer to the lattice [START_REF] Fantoni | Methodologies for laboratory Laser Induced Breakdown Spectroscopy semi-quantitative and quantitative analysis-A review[END_REF]. To describe the optical absorption properties of the material, it can be characterized by an absorption coefficient, α.

Due to the absorption, an incident laser with irradiance of at the sample surface becomes after travel through a path length in the sample. Optical transmission is given by Beer-Lambert's Law [START_REF] Vogel | Mechanisms of pulsed laser ablation of biological tissues[END_REF] α

• (I.1)
where R s is the surface reflectivity.

Here we assume that the light energy absorbed by the medium is totally transformed into heat, so the temperature distribution in the medium can be calculated with the heat conduction equation. In the case of aluminum sample, the absorption coefficient α=1.25×10 6 cm -1 , which corresponds to a penetration depth in target of in the order of 8 nm [START_REF] Bauerle | Laser processing and chemistry[END_REF]. The fact that the penetration depth is much smaller than the size of the focused spot of the laser beam (typically 100-500 m), so the lateral heat flow can be ignored and the temperature distribution in z-direction can be described by a one-dimensional heat equation:

(I.2)
The first term of the right side of equation (I.2) expressed the heat conduction, whereas the second term indicates the energy coming from the laser energy absorption. T represents the temperature in the target, U describes the additional energy per unit volume and time that is required or provided if phase transition occurs, z is the distance measured from the target surface, t is the time, , c p and ρ denote the thermal conductivity, heat capacity and mass density of the target material respectively, values of which are listed for various materials in the ref. [START_REF] Bauerle | Laser processing and chemistry[END_REF] (Page 759, Tab. II).

When the surface temperature T s exceeds the melting point T m of the sample, melting starts at the surface. Subsequently, T s increases much slower or not at all, due to the consumption of the absorbed laser energy not only on heating, but also on melting. During the time that phase change takes place, the local temperature remains constant. If the irradiance of the incident laser is high enough, the surface temperature becomes so high that vaporization becomes significant. Here we determined I v the threshold of laser irradiance which causes significant vaporization of the substrate surface.

The surface evaporation of a semi-infinite solid at temperature T can be approximated by the Hertz-knudsen equation [START_REF] Bauerle | Laser processing and chemistry[END_REF]:

(I.3)
where J i (species/cm 2 s) is the flux, m i is the mass of species i that leaves the surfaces, S 1 is a correction factor, which is often denoted as the evaporation or condensation coefficient, and P i is the partial pressure of molecules at infinity.

The saturated vapor pressure at the surface can be calculated from the Clausius-Clapeyron relation [START_REF] Bogaerts | Laser ablation for analytical sampling: what can we learn from modeling?[END_REF]:

(I.4)
where P 0 =1 atm, ΔH v is the latent heat of evaporation, T b is the normal boiling point at 1 atm, R is the gas constant.

The expansion dynamic of the evaporated material can be described by the Euler equations of hydrodynamics. For the sake of simplicity, one-dimensional equations of hydrodynamics can be used to express the conservation of mass, momentum and energy, respectively [START_REF] Balazs | Expansion of Laser-Generated Plumes near the Plasma Ignition Threshold[END_REF]:

(I.5) (I.6) (I.7)
where ρ is the mass density, ρv is the momentum, ρv 2 /2 is the kinetic energy density, P is the local pressure, ρE is the internal energy density. The product ε abs denotes the local laser energy absorption due to the inverse Bremsstrahlung, photo-excitation and photo-ionization; whereas ε rad is the amount of energy emitted by the vapor per unit volume and time, which means a loss for the internal energy of the vapor. It should be mentioned that the equations (I.5) to (I.7) describe the expansion in vacuum, where only the evaporated material need to be considered. Compared to the expansion in vacuum, the interaction of plume with an ambient gas is a more complicated gas-dynamic process. However, for the plume expansion into a background gas at 1 atm, the same hydrodynamic model can be used with adding the contribution of surrounding gas [START_REF] Chen | Laser ablation of Cu and plume expansion into 1 atm ambient gas[END_REF]. The spatial confinement and the slowing down of the expanding plume are considered as the general effect of the background gas.

A specific feature of nanosecond pulsed laser ablation is that the pulse duration is significantly longer than the initiation time of the plasma which is commonly considered as the interval between the initial impact of the laser pulse on the target and the appearance of evaporated material over its surface. Followed by the ablation of the material, the evaporated plume expands into the ambient and compresses (or shocks) the surrounding gas. Typically this time scale is in the order of ~100 ps [START_REF] Mao | Initiation of an early-stage plasma during picosecond laser ablation of solids[END_REF]. The expanding vapor plume as well as the compressed (or shocked) gas can thus absorb energy from the incoming laser pulse.

Consequently, the evaporated plume turns to be ionized and sustained by inverse bremsstrahlung absorption during collisions among sampled atoms and ions, electrons, and the gas species. The violent collisions among atoms, ions, electrons, and species are especially efficient in ambient pressure background, in which the vapor plume is efficiently slowed down and confined leading to plasma shielding. As a result of the violent collision, thermal ionization can occur in the shocked gas, increasing the absorption rate of the gas. In the hot vapor excited species, ions and free electrons interact with the laser light, leading to further heating and ionization. This feed-back mechanism may or may not result in a breakdown, i.e. the generation of a fully ionized plasma, which depends on the laser pulse energy. With laser irradiance increasing to a threshold value I p , the vapor becomes substantially ionized and is then described as plasma. This threshold irradiance I p for plasma ignition was discussed in detail in ref. [START_REF] Vertes | Threshold conditions of plasma ignition in laser ionization mass spectrometry of solids[END_REF]. In the typical LIBS condition, single ionization dominates in the plasma formation process. Therefore the generated plasma is usually composed of atoms, single ionized ions and molecules. Frequent collisions between these particles can result in dynamic equilibrium, where different species can be described in the same parameters, i.e. electron density and temperature. The ionization degree, fraction of electrons and ions, can be described by the Saha-Eggert equation, which will be discussed later in this chapter for plasma diagnostics.

As stated above, the laser-solid interaction starts from the absorption of laser energy by the solid, followed by melting, evaporation and ionization. The photothermal ablation and initiation of the plasma are sketched in Fig I .1. Photothermal ablation is typically a dominant process for ablation of metals. For organic materials which will be studied in the following subsection, the mechanism of ablation can be very different due the absence of initial free electrons. Laser ablation of organic materials can be due to chemical bond breaking, leading to evaporation of elemental and/or molecular fragments from the target. Bond breaking can be thermally activated, if the relaxation of electronic excitation is faster than bond breaking in the electronic excited state. In such case, the ablation is dominated by the photothermal process. In the case where bond breaking takes place because of optical absorption bringing a molecule into a dissociative electronic excited state, ablation can be caused by direct bond break without rise of temperature in the material. Such process corresponds to photochemical ablation. Photochemical ablation can be a dominate process in certain conditions for ablation of organic materials. In a molecular solid, an optically excited molecule is in close contact with other molecules, the vibrational relaxation takes place in a very short timescale of less than 1 ps [START_REF] Fox | Optical Properties of Solids[END_REF]. And the released energy ends up as heat. Then the molecule in its new vibrational equilibrium position emits a fluorescence photon and returns back to its ground electronic state. Again the Franck-Condon principle leads its departure from the vibrational equilibrium position in the ground electronic state and non radiative relaxation occurs as for absorption.

The typical fluorescence lifetime is about 1 ns which is much longer than the non radiative relaxation. One encounters here a similar situation as in the case of nanosecond laser ablation of metal, the laser pulse acts as a heat source that induces a rise of the temperature in the irradiated material through the cycle of absorption-relaxation. Such temperature rise in molecular solid can lead to dissociation of a molecule from its ground electronic state when its vibrational state is so highly excited to break the bond.

Photochemical ablation of organic materials

In 1982, two articles reported on the intense pulsed UV-laser ablation on synthetic polymer surfaces without evidence of thermal or mechanical damage to the remaining material [START_REF] Srinivasan | Self-Developing Photoetching of Poly(Ethylene-Terephthalate) Films by Far Ultraviolet Excimer Laser-Radiation[END_REF][START_REF] Kawamura | Effective Deep Ultraviolet Photoetching of PolyMethyl Methacrylate by an Excimer Laser[END_REF].

To explain these distinct ablation characteristics, mechanisms of UV laser radiation should be considered. As shown in ref. [START_REF] Vogel | Mechanisms of pulsed laser ablation of biological tissues[END_REF], photon energies available from common UV laser sources (4-6.5 eV) are larger than many organic molecular bonds. It is hence possible that the UV photons cause direct bond breaking of the absorbing molecular chains in organic samples, leading to photochemical decomposition [START_REF] Sutcliffe | Dynamics of Uv Laser Ablation of Organic Polymer Surfaces[END_REF]. This direct non-thermal bond breaking may be an important or even dominant mechanism in polymer ablation by means of deep UV laser light.

As Let us consider the simplest photochemical reaction [START_REF] Bityurin | Models for Laser Ablation of Polymers[END_REF] (I.8)

where M i stands for initial molecule, and M p denotes the product molecule of photochemical reaction. The kinetic of modification caused by eq. (I.8) can be expressed by the following equations:

(I.9)
where N i and N p are the number densities of M i and M p species, respectively, I is the light intensity (W/cm 2 ), η i is the quantum yield, i and p are the absorption cross-sections, α is the absorption coefficient, and N 0 is constant. This model describes irreversibly induced darkening (for i p ) or bleaching (for i p ). In darkening process the absorption coefficient increases with light intensity, with inverse situation for bleaching [START_REF] Luk'yanchuk | The role of excited species in ultraviolet-laser materials ablation III. Non-stationary ablation of organic polymers[END_REF]. The initial and boundary conditions are

N i(z, 0)=N0, Np(z, 0)=0, I(0, t)=IS(t) (I.10)
where I S (t) can be an arbitrary function of time [START_REF] Bityurin | Models for Laser Ablation of Polymers[END_REF].

When we consider a more general model consisting of two successive photochemical reactions, the process (I.8) can be replaced by the following reaction:

(I.11)
Comparing to process (I.8), this model can describe a non-monotonous change of the absorption coefficient. Then the kinetic modification expressed by (I.9) can be replaced by (I.12)

The initial and boundary conditions are in the same form of equation (I.10) with an additional condition N p2 (z, 0)=0.

In the similar way, three, four, five, etc., successive or branching reactions can be taken into account for describing the modification of the photochemical ablation process.

I.1.3 Molecular fragments in laser-induced plasma from organic material

In some experimental conditions, molecular or radical species can be transferred directly from the sample to the plasma by photochemical process for example and can be observed using time-resolved detection [START_REF] Baudelet | Spectral signature of native CN bonds for bacterium detection and identification using femtosecond laser-induced breakdown spectroscopy[END_REF][START_REF] Boueri | Identification of Polymer Materials Using Laser-Induced Breakdown Spectroscopy Combined with Artificial Neural Networks[END_REF]. However, molecules can also be formed due to the interaction between the vaporized species and the ambient gas. Therefore, investigation of the molecular formation mechanism is very important for LIBS application for analysis of organic samples.

Evaporated form an organic target and expanding into the background gas, plasma plume gives rise to numerous chemical reactions involving reactant species originated from the target as well as the background gas. C 2 and CN are among the most frequently observed and studied diatomic molecules in laser-induced plasma from organic material. [START_REF] Ma | Kinetic model of atomic and molecular emissions in laser-induced breakdown spectroscopy of organic compounds[END_REF] for the formation of CN radials in laser-induced plasma, the reaction

(I.14)
is generally considered as the principal one for CN formation [START_REF] Vivien | A study of molecule formation during laser ablation of graphite in low-pressure nitrogen[END_REF][START_REF] St-Onge | Carbon emissions following 1.064 m laser ablation of graphite and organic samples in ambient air[END_REF] in a plasma induced from an organic material in a background containing nitrogen, because of large concentration of nitrogen molecules available from the background and the slightly exothermic nature of the reaction Molecules observed in plasma induced from organic materials have attracted much attention for LIBS application to organic materials (polymers, explosives, biological samples…). In the previous works of the team in Lyon 1 laboratory, the native CN bonds were used for bacteria detection and identification [START_REF] Baudelet | Spectral signature of native CN bonds for bacterium detection and identification using femtosecond laser-induced breakdown spectroscopy[END_REF]. In this work, the authors have demonstrated that the CN molecular bands observed in femtosecond ablation regime are due to CN bonds directly ablated from the bacteria and can be distinguished from the contribution due to recombination with ambient gas. The same authors also used CN and C 2 molecular band heads for identification of polymers [START_REF] Boueri | Identification of Polymer Materials Using Laser-Induced Breakdown Spectroscopy Combined with Artificial Neural Networks[END_REF].

I.2 Transient and space-inhomogeneous nature of laser-induced plasma

As stated above, when the vapor from the target is substantially ionized, it is described as a plasma. All the vaporization and ionization process results from the absorption of a laser radiation, which shows both temporal and spatial properties. As a result, generated plasma undergoes fast temporal evolution of their characteristic parameters together with significant spatial gradients. It is hence important to perform time-and space-resolved investigation of the plasma for a good LIBS measurement. In order to have a time-resolved detection of the emission from plasma, the detector is synchronized to laser Q-switch or the laser pulse using a photodiode in such way the signal is collected with a certain delay after the impact of the laser pulse on the target. Spatial resolution is usually provided using an imaging system which allows obtaining an amplified image of the plasma. There are usually two methods to obtain space-resolved detection of the emission from a plasma: 1) the image of the plasma is coupled to the entrance slit of a spectrometer equipped with a CCD camera; 2) a fiber, connected with a spectrometer, is used to scan the image plane.

I.2.1 Temporal evolution of the plasma

The temporal history of a pulsed laser-induced plasma emission is illustrated schematically in Fig I .5. At the beginning, the plasma light is dominated by a continuum emission, which is caused by bremsstrahlung and recombination emissions from the plasma. The bremsstrahlung emission is sometimes referred to as free-free radiation, which is created by charged particles that are free both before and after the acceleration that causes the emission. And the recombination emission corresponds to capture of free electrons by ions. Subsequently, emission lines from ions, atoms and molecules come out as the plasma cools down. If the plasma emission is integrated over the entire plasma evolution time, the continuum can seriously interfere with the detection of weaker transition emissions. For this reason, LIBS measurements are normally carried out with time-resolved detection. Two detection systems for plasma temporal characterization were reported in 1983: photomultiplier tube (PMT) equipped with boxcar averager and gated integrator and time-gated photodiode arrays (PDA) [START_REF] Radziemski | Time-resolved laser-induced breakdown spectrometry of aerosols[END_REF]. In addition, both non-intensified CCD and intensified CCD (ICCD) have been frequently used as detectors. PMT is a single element detector, which restricts the number of emission lines that can be simultaneously detected. It is less frequently employed in LIBS application. However, its high sensitivity in the visible spectral region makes it useful to specific application [START_REF] Huang | The correlation between ion production and emission intensity in the laser-induced breakdown spectroscopy of liquid droplets[END_REF][START_REF] Gomba | Spectroscopic characterization of laser induced breakdown in aluminium-lithium alloy samples for quantitative determination of traces[END_REF]. Comparing with PMT, both PDA and CCD combine a large number of sensors (also called pixels) in one device, allowing plasma emission being acquired within a wide range of wavelength. Among these available detectors, ICCD detectors have probably been the most exploited for LIBS applications [START_REF] Carranza | Comparison of nonintensified and intensified CCD detectors for laser-induced breakdown spectroscopy[END_REF]. Generally, detector choices for LIBS depend on various factors, including data acquisition rates and types of signal processing (single-shot or ensemble averaging), analytical sensitivity, spectral bandwidth, and overall system cost.

In this thesis, LIBS signal are recorded using a Mechelle spectrometer equipped with an The most frequently used technique to obtain spectral and spatial resolutions is imaging plasma onto a spectrometer slit, named as spectrometer slit imaging method. It is based on imaging the laser plume onto an entrance slit of a spectrograph which is equipped with a CCD camera. The slit can be moved using a spiral motorized setup equipped with the spectrometer, with which the slit can be moved without moving the spectrometer. In this way a two dimension image of the plasma can be obtained. An imaging lens (ref. [START_REF] Aragon | Two-Dimensional Spatial Distribution of the Time-Integrated Emission from Laser-Produced Plasmas in Air at Atmospheric Pressure[END_REF]) or a pair of lenses (ref. [START_REF] Chaleard | Correction of matrix effects in quantitative elemental analysis with laser ablation optical emission spectrometry[END_REF]) is disposed with its axis perpendicular to the laser beam axis to get the plasma image. This spectrometer slit imaging set up is shown in Fig I .10. In such setup, the observed zone is a slice in the plasma, with the width depending on the slit width of the spectrometer and the height being limited by the sensitive area of the detector. Generally, the plasma can be imaged on the slit of the spectrometer in two directions, with laser incident axis parallel or perpendicular to the slit depending on the requirements of experiments. two-dimensional grid of the plasma emissions by varying the position of the fiber in the image plane of the plasma [START_REF] Corsi | Three-dimensional analysis of laser induced plasmas in single and double pulse configuration[END_REF]. A similar setup is used in this thesis for the study of plasma morphology, which will be discussed in §IV.3.

ICCD

I.3 Diagnostics of a plasma and validation of local thermodynamics equilibrium

Plasma diagnostic is considered as the basis of LIBS. That is because most of LIBS information comes from atomic and ionic lines emitted by the plasma. From such information, we can determine the electron density and the temperature, which are considered as two important parameters for the characterization of the plasma. There are several methods to determine the electron density, including Stark broadening and shift, Saha equation. For the determination of the temperature, there are also several choices such as line-to-continuum ratio, Boltzmann plot (BP), Saha-Boltzmann plot (SBP) and so on. The use of these methods is justified when the plasma is in the LTE state.

I.3.1 Determination of the electron density

Among the methods based on optical emission spectroscopy (OES) for electron density determination, the broadening of emission lines due to the Stark effect has been the most widely used. This method is based on the collisional Stark effect and becomes efficient for electron density determination when such effect is the dominant line broadening mechanism, compared to Doppler, instrumental or pressure broadening mechanisms. This consideration is generally justified in most of the situations in LIBS experiments [START_REF] Harilal | Electron density and temperature measurements in a laser produced carbon plasma[END_REF].

In general, the Stark effect leads to the following relation between the half width at half maximum (HWHM) of an emission line, , and the electron density .

(I.15)

where A and w are the ion broadening parameter and the electron impact (half) width respectively; is a reference electron density, usually of the order of 10 16 or 10 17 cm -3 , at which the parameters A and w are measured or calculated; R is the ratio of the mean distance between ions and Debye radius. This equation is valid only in the range A ≤ 0.5, R ≤ 0.8.

Additionally, it is valid for neutral emitters; for singly ionized emitters, the term 0.75R should be replaced by about 1.2R. The coefficients or parameters for electron density determination can be found in refs. [START_REF] Griem | Spectral line broadening by plasmas[END_REF][START_REF] Griem | Plasma spectroscopy[END_REF]. The parameter A is in general much smaller than 1, and for typical plasma for LIBS the Stark broadening is mainly due to electrons, so the contribution of the ion, the second term in eq. (I.15), can be ignored [START_REF] Griem | Spectral line broadening by plasmas[END_REF][START_REF] Bekefi | Principles of laser plasmas[END_REF] .

(I.16)

For hydrogen and hydrogenic atoms or ions, the linear Stark effect leads the following equation [START_REF] Griem | Spectral line broadening by plasmas[END_REF]:

(I.17)
where Δ s is the full width at half maximum (FWHM) of the Stark profile of the considered emission line in angstrom and the reduced Stark width w slightly dependent on the electron density (N e ) and the temperature (T).

For an accurate determination of electron density, several factors have to be considered.

Firstly, the selected line must be isolated and optically thin to avoid any additional broadening due to neighbor lines or self-absorption. Secondly, the uncertainty of the reference Stark coefficients or parameters must be as small as possible, since the main error source of the electron density determination comes from such uncertainty [START_REF] Aragon | Characterization of laser induced plasmas by optical emission spectroscopy: A review of experiments and methods[END_REF]. As the theoretical calculation is more accurate for lines from the hydrogen and hydrogenic atoms, these lines should be used whenever possible [START_REF] Griem | Spectral line broadening by plasmas[END_REF][START_REF] Bekefi | Principles of laser plasmas[END_REF]. On the other hand, the technique used to extract Stark broadening from the experimental line width plays an important role in the accuracy of the determination. As reported in ref. [START_REF] Cristoforetti | Influence of ambient gas pressure on laser-induced breakdown spectroscopy technique in the parallel double-pulse configuration[END_REF], it is possible that the main error of electron density results from the uncertainty of fitting of the line profile and of the instrumental width.

The Stark effect yields a Lorentzian broadening, whereas the Doppler and instrument broadening present Gaussian profile. As a result, the Voigt profile, which is a convolution of the Lorentz and the Gaussian profiles, is used to extract the Stark broadening of the line from experimental spectrum.

The electron density may also be extracted from spectral line shift due to the Stark effect.

The total Stark line shift can be estimated with the following formula [START_REF] Griem | Plasma spectroscopy[END_REF]:

(I.18)
where d is electron-impact shift parameter. The modification of this equation concerning the factor A for singly ionized emitters is the same as described above for equation (I.16).

Comparing to the electron-impact broadening parameter, the theoretical calculation of the electron-impact shift parameter has larger uncertainty. Therefore the Stark shift method is not recommended when the broadening method is possible. However, in case that the self-absorption is important and unavoidable, the broadening method involves too much overestimation of the electron density. Therefore the estimation of the electron density using the line shift is preferred, since the Stark shift effect is not affected by the self-absorption [START_REF] Iida | Effects of Atmosphere on Laser Vaporization and Excitation Processes of Solid Samples[END_REF].

When the plasma is sufficiently close to the LTE state, the electron density can also be derived from the emission intensity ratio of two lines corresponding to different ionization stages of a same element. Considering both Saha and Boltzmann equations, the electron density can be calculated using the following equation:

(I.19)
where the parameters will be introduced in §I.3.2. Typically, the electron density of plasma in LIBS analysis is from 10 18 to 10 16 cm -3 .

I.3.2 Measurement of plasma temperature

First of all, plasma temperature is meaningless without validation of the LTE condition.

Normally, there are several temperatures to characterize the plasma, including excitation temperature T ex characterizing the Atomic State Distribution Function (ASDF) among different excited energy level, electron temperature T e characterizing the electron velocity distribution function, and temperature of heavy particles T H , i.e. atoms, ions and molecules.

For a plasma in LTE, the three temperatures merge together, so the plasma can be described with a single temperature T, which will be discussed in detail in the next part when the LTE state of a plasma is validated.

Boltzmann plot

Provided that the LTE hypothesis is fulfilled, the plasma temperature can be calculated from the ratio of a pair of spectral lines from the same element with the same ionization state.

Assuming that the populations in excited levels of a given species obey the Boltzmann distribution, the population density of the excited level i of species s can be described with the following equation [START_REF]Laser-induced breakdown spectroscopy: Fundamentals and applications[END_REF]:

(I.20)
where g i , E i are the statistical weight and the excitation energy of the level, n s is the total number density of the species s in the plasma, k is the Boltzmann constant and U s (T) is the internal partition function of the species at temperature T:

(I.21)
Therefore the line intensity I ij (number of transitions per unit volume per unit time)

corresponding to the transition between the upper level i and lower level j is given by [START_REF]Laser-induced breakdown spectroscopy: Fundamentals and applications[END_REF] (I. [START_REF] Garcia-Ayuso | Characterization of jewellery products by laser-induced breakdown spectroscopy[END_REF] where A ij is the transition probability from level i to j.

Considering two lines, ij and mn , of the same species at different upper energy levels (E i ≠ E m ), the plasma temperature can be calculated with the so-called Boltzmann two-line method by the following equation:

(I.23)
For a typical LIBS plasma, the temperature is in the order of 10 4 K.

As the Boltzmann two-line method has the advantage of simplicity, it could be used in the cases where just few transitions are detected for a given species in the considered spectral range. However, since just two lines are used in this method, it may lead to considerable uncertainty of the determined temperature. By taking the variation of the equation (I.23), this uncertainty can be derived by the following expression:

. (I.24)

From equation (I.24), we can see that the uncertainty comes from the error of the intensity ratio of the two lines.

The accuracy of temperature determination can be improved, if the Boltzmann equation is applied to a series of lines from different excitation states of the same species. If we take the natural Logarithm of both sides of equation (I.22), the familiar form of the Boltzmann plot equation is obtained:

. (I.25)
It is easy to understand that if we consider the left side of the equation (I.25) as a function of the upper energy level E i , a straight line with slope of -1/kT is obtained. Therefore, the plasma temperature can be derived from the linear regression, which is called the Boltzmann plot method for the plasma temperature determination. Fig I .12 is an example of the Boltzmann plot constructed using a set of atomic Ca I lines for the temperature determination of a plasma induced on a potato skin at a delay of 1380 ns, the details of the experimental parameters and used lines will be described in §II.3.3.

Fig I.12. Boltzmann plot for temperature determination for plasma induced on potato skin using a set of Ca I lines

It can be deduced from equation (I.25) that the excited energy levels should cover a large range to improve the accuracy of temperature determination. Unfortunately, in most of the situations, the extension range of E i for a single ionization state is not large enough for the linear regression in Boltzmann plot method. As shown in Fig I .12 the difference among the excited energies is about 1.5 eV. Therefore a combination of Saha ionization and Boltzmann excitation distributions is sometimes used to measure the plasma temperature in order to enhance the effective energy difference. Significant accuracy improvement is obtained if lines of successive ionization stages of the same element are compared to each other, because the extension of E i is now enlarged by the ionization energy, which is much larger than the thermal excitation energy [START_REF] Aragon | Characterization of laser induced plasmas by optical emission spectroscopy: A review of experiments and methods[END_REF].

Saha-Boltzmann plot

The Saha equation relates the densities of the species of subsequent ionization degrees for a considered element as following:

(I.26)
where the superscript z refers to the ionization stage (z=0 for neutral atom, z=1 for As shown in equation (I.29), the ordinate value depends on temperature as ln(T 3/2 ), which is slower than 1/T, the temperature can be hence determined through a iterative algorithm.

Provided that N e is known, equation (I.27) allows plotting a straight line similar to Boltzmann plot to obtain the plasma temperature from its slope. This method is named as Saha-Boltzmann plot.

Multi-element Saha-Boltzmann plot

The above mentioned methods for temperature determination use emission lines from one element. For a plasma resulting from a stoichiometric ablation of the target with known elemental concentrations, the Saha-Boltzmann plot method can be applied to lines of different elements from the target. Such extension of the Saha-Boltzmann plot was first proposed in ref.

[109] and known as multi-element Saha-Boltzmann plot (MESBP). Similar to the extension from Boltzmann plot to Saha-Boltzmann plot, the generalization of Saha-Boltzmann plot to multi-element Saha-Boltzmann plot requires a correction of the formalism by taking into account the concentrations of the involved elements. However, the equation (I.27) cannot be used directly in multi-element Saha-Boltzmann plot method, because of the difference between the ionization ratio n 1 /n 0 , which is given by Saha equation. For the implementation of multi-element Saha-Boltzmann plot, equation (I.27) has to be modified with the following considerations.

Firstly, for a typical LIBS plasma, the temperature and electron density are typically of the order of 10 000 K and 1×10 17 cm -3 Only single ionization needs to be considered due to low number densities of the higher order ionized ions (z 2). Therefore the number density of the element α is given by:

. (I.31)
So the neutral atom number density can be related to the total number density by:

(I.32)
where is the number density ratio of the ionic to the neutral atom, which can be derived from equation (I.26) with z=1.

Then, the equation (I.27) can be rewritten to a similar expression:

(I.33)
where n is the total number density of all elements in the plasma

. (I.34)

Here D α (T, N e ) can be expressed with the follow formula:

(I.35)
which is different for different elements but identical for the different ionization states of a given element. C α =100n α /n (%) is the concentration of the element in the target. Also, the abscissa value of ions have to be modified with respect to the corresponding element, which has the same expression as the equation (I.30) when z=1.

Generally, the multi-element Saha-Boltzmann is proposed to determine plasma temperature, because the consideration of different elements helps to confirm the validation of LTE of the plasma. In addition, the temperature obtained from the multi-element Saha-Boltzmann plot represents an average temperature for all the used elements, which is more closed to the real temperature of the plasma. However, the concentrations of the used elements should be given for establishing the multi-element Saha-Boltzmann plot. In the situation where the elemental concentration is unknown, the Saha-Boltzmann plot is preferred to Boltzmann plot. The reason is because the accuracy of the determination is improved by using a larger range of upper energy level for Saha-Boltzmann plot. However, in some situation, Saha-Boltzmann plot method cannot be used due to just atomic or ionic lines are observed. Then Boltzmann plot can be used for the determination. In addition, Boltzmann plot is also proposed when equilibrium between ions and atoms cannot be reached, where the Saha equation cannot be used to describe the equilibrium between atoms and ions.

Line to continuum intensity ratio

Besides the methods stated above, there is another method to calculate the plasma temperature based on the ratio of emission line intensity to continuum intensity [START_REF] Bastiaans | The Calculation of Electron-Density and Temperature in Ar Spectroscopic Plasmas from Continuum and Line Spectra[END_REF]. Assuming LTE is validated, the emissivity ε l of a neutral atomic line can be related to the continuum emissivity ε ,c by the following formula [START_REF] Aragon | Characterization of laser induced plasmas by optical emission spectroscopy: A review of experiments and methods[END_REF]:

(I.36)
where A 21 , g 2 and E 2 are the transition probability, upper energy level degeneracy and upper energy level of the neutral atom transition, U i (T) is the partition function for the ion, c and l are the continuum wavelength and the central wavelength of the neutral atom line, respectively, ε 0 is the permittivity of the free space, e is elementary charge, G is the free-free Gaunt factor and is the free-bound correction factor.

It is clear that the line-to-continuum ratio method is suitable for the diagnostic of the early stage of the plasma, where the continuum and line intensities are of comparable magnitude [START_REF] Liu | Early phase laser induced plasma diagnostics and mass removal during single-pulse laser ablation of silicon[END_REF]. As the plasma evolves, the continuum intensity reduces dramatically while the ionic and atomic line intensities increase, the Boltzmann plot, Saha-Boltzmann plot and multi-element Saha-Boltzmann plot methods are most considered for temperature determination. With the further evolution of the plasma, it continues to cool down. Molecular lines will dominate the plasma emission spectrum, then the plasma temperature can be determined from molecular emissions.

Temperature determination with molecular emission

Various procedures exist for temperature determination using molecular emission from the plasma, such as Boltzmann plot and fitting of experimental spectrum.

Temperature determination using molecular lines based on Boltzmann plot applied to the vibrational band head intensities provides the vibrational temperature. With this method, the temperature is extracted from the Boltzmann plot of the vibrational band intensity against the vibrational energy using the following expression [START_REF] Harilal | Time resolved study of CN band emission from plasma generated by laser irradiation of graphite[END_REF]:

(I.37)
where ' and '' are the vibrational quantum numbers corresponding to the upper and lower electronic state respectively, is the wavelength corresponding to each transition ( ', '') and G( ') is the vibrational term value of the upper electronic state, C 1 is a constant and T vib is the vibrational temperature. Temperature can also be determined by fitting of experimental molecular emissions. The rotational temperature (T rot ) of the excited molecules corresponds roughly to the temperature of the neutrals, whereas the vibrational temperature (T vib ) is indicative of vibrationally excited species that are chemically reactive [START_REF] Acquaviva | Simulation of emission molecular spectra by a semi-automatic programme package: the case of C-2 and CN diatomic molecules emitting during laser ablation of a graphite target in nitrogen environment[END_REF]. In addition, determinations of T rot and T vib for ejected species are useful for probing the LTE state of the plasma. Simulation of molecular emission spectrum allows retrieving T rot and T vib . In this section, a procedure of computing synthetic diatomic molecular spectrum will be presented.

Before going into the details of the computation, the molecular spectroscopic constants are given by the ensemble of parameters as shown in Table I.2. All these parameters for C 2 Swan band and CN violet band can be found in Refs [START_REF] Acquaviva | Simulation of emission molecular spectra by a semi-automatic programme package: the case of C-2 and CN diatomic molecules emitting during laser ablation of a graphite target in nitrogen environment[END_REF][START_REF] Tatum | The Interpretation of Intensities in Diatomic Molecular Spectra[END_REF][START_REF] Danylewych | Intensity Measurements and Transition Probabilities for Bands of the CN Violet (B 2 ∑ X 2 ∑) Band System[END_REF].

Parameters

Table I.2. Molecular spectroscopic constants

The rotational term can be written as

(I.38)
and the R-, P-, and Q-branch wave numbers are compiled, depending on the studied case (singlet, doublet or triplet).

Here only the 2 ∑-2 ∑ transition will be discussed in detail. In this case, each "line" of the P-and R-branches are doublets, since they separates in two sublevels with J=N (1/2).

Therefore, the P-and R-branches are obtained with the following wave number, with i=1, 2 (1 for J=N+1/2; 2 for J=N-1/2):

(I.39) (I.40)
In the Born Oppenheimer approximation and assuming the existence of thermodynamic equilibrium between rotational and vibrational states, the emission intensity of a molecular band is obtained by the formula [START_REF] Acquaviva | Simulation of emission molecular spectra by a semi-automatic programme package: the case of C-2 and CN diatomic molecules emitting during laser ablation of a graphite target in nitrogen environment[END_REF]:

(I.41)
where C em is a emission constant, n the principal quantum number, J the maximum rotational quantum number, the rotational partition function , the transition wave number with the corresponding R, P and Q expression, G 0 (υ)=G(υ)-G 0 (0) with

(I.42)
Theoretical line intensities for both P-and R-branches with corresponding wavelengths can be calculated with equation (I.41).

The spectrum computation was conducted with a program developed using LabView. In order to verify the computation results, parameters similar to those used in ref. [START_REF] Acquaviva | Simulation of emission molecular spectra by a semi-automatic programme package: the case of C-2 and CN diatomic molecules emitting during laser ablation of a graphite target in nitrogen environment[END_REF] were chosen for computing theoretical intensities of P-and R-branches for CN violet system Δυ=0.

The results shown in Fig I .15 with input parameters T rot =20 000 K, T vib =9000 K and J=100 are in good agreement with those in ref. [START_REF] Acquaviva | Simulation of emission molecular spectra by a semi-automatic programme package: the case of C-2 and CN diatomic molecules emitting during laser ablation of a graphite target in nitrogen environment[END_REF].

I.3.3 Validation of local thermodynamic equilibrium for a transient and inhomogeneous plasma

Generally, a laser induced plasma expends into the ambient gas with typical values of temperature and electron density in the range of respectively, 20000 K and 10 19 cm -3 at the beginning of its expansion and 5000-6000 K and 10 17 cm -3 at the late stages of its evolution [START_REF] Gaudiuso | Laser Induced Breakdown Spectroscopy for Elemental Analysis in Environmental, Cultural Heritage and Space Applications: A Review of Methods and Results[END_REF]. During its lifetime (~10 s in air), radiation escapes from plasma which affects the thermodynamic equilibrium of the plasma. However, if the loss of the radiative energy is small compared to energy exchanges between material particles in the plasma, the fast collisional process can bring the plasma to a state of local thermodynamic equilibrium. In such state, the velocities of the particles are distributed according to the Maxwell law, the population among the excited states of a given specie is given by the Boltzmann law, while the population ratio between different ions of a same element is provided by the Saha equation [START_REF] Vandermullen | Excitation Equilibria in Plasmas -a Classification[END_REF]. In this case, a single temperature can be used to characterize the three laws mentioned above. For a transient plasma, which is the case of laser-induced plasma, the LTE is still possible, because the characteristic time of collisional process is much smaller than the time constant of the evolution of the plasma. The LTE state is a crucial concept for plasma diagnostics and for spectroscopic application based on plasma. Its realization for a laser-induced plasma is not however automatic and requires some drastic conditions. In the following part of this sub-section we will discuss the conditions of validation of the LTE state for laser-induced plasma.

McWhirter criterion

As mentioned above, the validity of LTE is important for diagnostics of the plasma and consequently for the quantitative analysis by LIBS. A preliminary condition of LTE is that the electron energy distribution function (EEDF) is a Maxwell-Boltzmann distribution. This means that the distance between the thermal electrons must be much larger than the de Broglie wavelength of the electron, which imposes that the number density of electrons must be much smaller than a critical value as shown in the following formula [START_REF] Hahn | Laser-Induced Breakdown Spectroscopy (LIBS), Part I: Review of Basic Diagnostics and Plasma-Particle Interactions: Still-Challenging Issues Within the Analytical Plasma Community[END_REF]:

. (I.43)
In the opposite case, quantum effects have to be considered, the Fermi-Dirac statistics have to be used. For most of LIBS plasmas, the electron density remains smaller than this critical value, i.e., 10 21 cm -3 for T e = 6000 K and 6.7×10 21 cm -3 for T e = 20000 K.

For a classical ionized gas, a basic criterion used for LTE validation is the so-called

McWhirter criterion, which defines the minimum electron number density to ensure enough collisions for the existence of LTE [START_REF]Laser-induced breakdown spectroscopy: Fundamentals and applications[END_REF]:

(I.44)
where ΔE (eV) is the energy of the most energetic transition of the species for which the LTE state is evaluated. This criterion is deduced under the assumption that collisional population rates for all excited levels of an atom are at least ten times larger than the radiative depopulation rate. In this condition, the collisional process prevails over the radiative process, which ensures that the energy exchange between the elementary species is larger than the energy lose due to the radiation.

Supplementary condition for a transient and inhomogeneous plasma

It is worth to note that the McWhirter criterion is a necessary condition for LTE, but for a transient plasma it is not a sufficient condition. Considering the spatiotemporal evolution of the plasma, two additional criteria have to be fulfilled to validate the LTE condition. In the time domain, the temporal variations of T e and N e have to be slower than the time taken to establish excitation and ionization equilibrium:

; (I.45)
where rel is the relaxation time of the plasma [START_REF] Hahn | Laser-Induced Breakdown Spectroscopy (LIBS), Part I: Review of Basic Diagnostics and Plasma-Particle Interactions: Still-Challenging Issues Within the Analytical Plasma Community[END_REF]. If this condition is not fulfilled, the evolution of the plasma is so fast that the electrons and atoms/ions do not have time to reach thermodynamic equilibrium. In the spatial domain, a similar criterion must be satisfied, which requires that the diffusion length of atom or ion during the relaxation time should be shorter than the variation length of the temperature and electron number density in the plasma as expressed by the following formula:

; (I.46)
where x is the local position, is the diffusion length during the relaxation time. Obviously, for the both criteria (I.45) and (I.46), the relaxation time rel and the diffusion length need to be estimated. The relaxation time can be approximated as the reciprocal of the excitation/de-excitation rate as follow [START_REF] Cristoforetti | Local Thermodynamic Equilibrium in Laser-Induced Breakdown Spectroscopy: Beyond the McWhirter criterion[END_REF] (I. [START_REF] Rohwetter | Remote LIBS with ultrashort pulses: characteristics in picosecond and femtosecond regimes[END_REF] where 12 is the cross section of inelastic collisions form the ground state "1" to the first excited state "2" which can be described with

(I.48) v i (cm -1
) is the incident velocity of electron, f 12 (dimensionless) is the absorption oscillator strength of the transition, (dimensionless) is an effective Gaunt factor. While the calculations of the diffusion length of atoms and ions are quite complex due to the requirement of cross sections of several collision processes and of the absolute atom and ion number density. Therefore some approximations have to be used for a rough estimation of the order of magnitude of . Since the diffusion lengths of atoms are typically larger than those of ions, and impose more restrictive limit to the establishment of LTE, only diffusion length of atom needs to be considered. In addition, only resonant collisions with ions are considered to affect the diffusion coefficient for atoms. Under these conditions, the diffusion length can be expressed as [START_REF] Cristoforetti | Local Thermodynamic Equilibrium in Laser-Induced Breakdown Spectroscopy: Beyond the McWhirter criterion[END_REF] (I. [START_REF] Goujon | A compact and portable laser-induced breakdown spectroscopy instrument for single and double pulse applications[END_REF] where D (cm 2 s -1 ) is the diffusion coefficient, M A is the relative mass of the species considered (M H =1), and kT and ΔE are expressed in eV. Typically, the characteristic variation length in the plasma d T(x)(dT(x)/dx) -1 should be at least ten times larger than this diffusion length to validate the LTE condition. Attention should be paid to the fact that in a multi-element plasma, the diffusion length is generally larger than the one given by equation (I.49), especially for trace elements whose diffusion length can be one to two orders of magnitude larger.

In order to give an intuitive understanding of the relaxation time rel of the plasma, we consider here the cases of copper, oxygen and hydrogen in a plasma characterized by N e =5•10 16 cm -3 and kT=1 eV. In the case of neutral copper ( =324.8/327.4 nm, ΔE 3.78 eV, f 12 1.37), a value of rel ~ 3.8•10 -9 s can be calculated according to equation (I.47).

Considering the typical decay time of plasma temperature and electron density in the range of 10 -5 -10 -6 s [START_REF] Cristoforetti | Local Thermodynamic Equilibrium in Laser-Induced Breakdown Spectroscopy: Beyond the McWhirter criterion[END_REF], the criteria expressed by (I.45) are easily fulfilled for copper. However, the criterion can be critical or not fulfilled at all for elements characterized by higher values of ΔE.

As an example, the relaxation times of oxygen and hydrogen ( , ; , ), calculated in the same conditions as above, are rel ~ 1.6•10 -4 s and 1.2•10 -4 s, respectively. The values are much larger than the typical decay times of plasma. For illustration of the diffusion length , we consider here the cases of copper, iron, nickel, oxygen and hydrogen in a plasma with the same T and N e . The diffusion lengths can be calculated for different elements Cu I 1.9•10 -3 mm, Fe I

I.4 Quantitative analysis with LIBS

All the above descriptions, including the initiation and diagnostics of the plasma, and the validation of LTE condition, provide the basis of quantitative analysis using LIBS. The quantitative analysis can be performed with either calibration curve method or calibration free LIBS (CF-LIBS) procedure [START_REF] Lei | Comparative measurements of mineral elements in milk powders with laser-induced breakdown spectroscopy and inductively coupled plasma atomic emission spectroscopy[END_REF]. For the calibration curve method, the matrix effect is considered as the one of the severest limitations. Concerning the CF-LIBS procedure, there are several factors influencing the performance such as departure from LTE, bad signal-to-noise ratio, self-absorption, and so on. Traditionally, a quantitative measurement is based on a calibration curve that relates the concentration of an analyte to the observed intensity of the spectroscopic signal. In this case, the reference samples used for establishing the calibration curve have to be matrix-matched to the unknown materials to be analyzed.

Unfortunately, in some applications, it is impossible to build such suitable calibration curve because of the lack of matrix-matched reference samples. To pass around the matrix effect, the CF-LIBS procedure was proposed, allowing determination of the concentration without calibration curve. This procedure has been applied to various materials and especially in analysis of metals with good performances [START_REF] Tognoni | Calibration-Free Laser-Induced Breakdown Spectroscopy: State of the art[END_REF]. However, it is still challenging considering the accuracy of the quantitative results is affected by many factors, such as departure of the plasma from LTE conditions, optical thickness of the plasma and so on. In this part, two kinds of LIBS quantitative analysis protocol will be introduced, including calibration curve and CF-LIBS.

I.4.1 Calibration curve and Matrix effect

The most common approach to quantitative LIBS analysis relies on the use of calibration curves generated from measurements of standards with certified compositions. Normally, calibration procedure implies three steps: the first step is to measure signal intensities using samples with known concentration in order to construct the calibration curve; the second step consists of measurement of the signal intensity of an unknown sample; the last step is to deduce the concentration of the analyte from the calibration curve using the measured signal intensity of the unknown sample. When more than two standards are used, a regression procedure must be carried out to build the calibration curve. The regression may be of the linear or quadratic type and normally is based on the least-squares method (LSM), which minimizes the sum of the squares of the differences between the experimental data and the computed values [START_REF] Mermet | Calibration in atomic spectrometry: A tutorial review dealing with quality criteria, weighting procedures and possible curvatures[END_REF]. In most of the favorable cases, the linear calibration curve is chosen, considering the intensity of a specific line is related with the corresponding concentration by equation (I.22). As shown in Fig I .17, the calibration curve built with line Na I 330.3 nm exhibits a linearity with coefficient R 2 of 0.991. This calibration curve was developed with a series of laboratory-prepared reference samples consisting of certified milk powder (BCR063 from IRMM) and cellulose, the detail of which will be described in §III.3. CF-LIBS was first proposed in 1999 [START_REF] Ciucci | New Procedure for Quantitative Elemental Analysis by Laser-Induced Plasma Spectroscopy[END_REF] to overcome the so-called matrix effect, and to avoid the calibration procedure when reference samples are missing. Before going to details of the implementation of this procedure, the three important assumptions for CF-LIBS have to be emphasized. Firstly, the plasma composition is representative of the elemental composition in the material to be analyzed. This condition is also named stoichiometric ablation assumption. Secondly, the plasma in the temporal detection window has to be in LTE state, or more realistically as close as possible to LTE. Finally, the plasma radiation source has to be optically thin, or at least self-absorption can be neglected for lines chosen for CF-LIBS procedure. Under these assumptions, the integrated intensity corresponding to the transition i to j can be described with equation (I.22). Considering the efficiency of the optical collection system in an experimental measurement, the measured intensity can be rewritten as

(I.50)
where F is an experimental parameter that takes into account the optical collection efficiency of the collection system as well as the total number density in the plasma and the volume of the plasma covered by the detection system; C s is the concentration of the corresponding atomic emitting species s. Similar to the equation (I.25), we can rewrite the Boltzmann plot equation as

. (I.51)

It is easy to deduce from this equation that the slope of the plot is related to the temperature, while the intercept is proportional to the logarithm of the species concentration. Then we can calculate the corresponding ionic species concentration using Saha-equation (I.26), and subsequently the elementary concentration C α considering equations (I.31) and (I.32).

If all the elements contained in the material to be analyzed can be detected using such protocol, the parameter F can be determined with the normalization of the concentrations of all the elements by (I. [START_REF] Boue-Bigne | Laser-induced breakdown spectroscopy applications in the steel industry: Rapid analysis of segregation and decarburization[END_REF] In some situations, all the elements cannot be detected due to low concentration or emission line with wavelength out of the spectral range of the detection system. Therefore, only relative concentrations can be calculated using CF-LIBS with the following equation:

(I.53)
where the subscript "ref" represents the referenced element, M is the atomic weight and D denotes the intercept of Boltzmann or Saha-Boltzmann plots. Attention should be paid that, the choice of referenced element plays an important role for the accuracy of the calibration, which will be discussed later in Chapter II.

A large number of works using the CF-LIBS procedure have been published since it was proposed. Most of them focused on the application to metallic alloys, such as aluminum [START_REF] Ciucci | New Procedure for Quantitative Elemental Analysis by Laser-Induced Plasma Spectroscopy[END_REF][START_REF] Tognoni | A numerical study of expected accuracy and precision in Calibration-Free Laser-Induced Breakdown Spectroscopy in the assumption of ideal analytical plasma[END_REF][START_REF] Herrera | Comparative study of two standard-free approaches in laser-induced breakdown spectroscopy as applied to the quantitative analysis of aluminum alloy standards under vacuum conditions[END_REF][START_REF] Lednev | Plasma stoichiometry correction method in laser-induced breakdown spectroscopy[END_REF], steel and iron [START_REF] Tognoni | A numerical study of expected accuracy and precision in Calibration-Free Laser-Induced Breakdown Spectroscopy in the assumption of ideal analytical plasma[END_REF][START_REF] Bulajic | A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy[END_REF][START_REF] Herrera | Semi-quantitative analysis of metal alloys, brass and soil samples by calibration-free laser-induced breakdown spectroscopy: recent results and considerations[END_REF][START_REF] Sun | Correction of self-absorption effect in calibration-free laser-induced breakdown spectroscopy by an internal reference method[END_REF], and copper [START_REF] Herrera | Semi-quantitative analysis of metal alloys, brass and soil samples by calibration-free laser-induced breakdown spectroscopy: recent results and considerations[END_REF][START_REF] Burakov | Calibration-Free Laser Spectral Analysis of Glasses and Copper Alloys[END_REF][START_REF] Aguilera | Application of calibration-free laser-induced breakdown spectroscopy to radially resolved spectra from a copper-based alloy laser-induced plasma[END_REF]. The interests on alloys can be mainly attributed to the facility of commercially available reference samples which provide assessment and validation of the CF-LIBS procedure. On the other hand, the relative simple matrix and good homogeneity make the plasma induced on metallic alloys exhibiting characteristics close to an ideal plasma. Some other applications of the CF-LIBS procedure are reported for oxide materials [START_REF] Praher | Calibration free laser-induced breakdown spectroscopy of oxide materials[END_REF], coral skeletons [START_REF] Pandhija | In situ multielemental monitoring in coral skeleton by CF-LIBS[END_REF], fruits [START_REF] Rai | Application of LIBS in Detection of Antihyperglycemic Trace Elements in <i>Momordica charantia</i&gt[END_REF], soils and rocks [START_REF] Colao | Investigation of LIBS feasibility for in situ planetary exploration: An analysis on Martian rock analogues[END_REF][START_REF] Wang | Controlled calibration method for laser induced breakdown spectroscopy[END_REF][START_REF] Pandhija | Contaminant concentration in environmental samples using LIBS and CF-LIBS[END_REF], human hairs [START_REF] Corsi | Application of laser-induced breakdown spectroscopy technique to hair tissue mineral analysis[END_REF] and so on.

I.4.3 Factors influencing the performance of CF-LIBS

Factors influencing the performance of the CF-LIBS procedure can be classified into three groups, corresponding to the departures of the actual plasma state from the three assumptions mentioned in §I.4.2.

Departure from the stoichiometric ablation

Departure of the elemental composition of the plasma from the stoichiometric composition of the original material is a severe limitation of CF-LIBS. The situation is different from the case of calibration curve method where the fractionation is also mentioned as an open issue. With the calibration curve method, matrix-matched standards and the unknown sample behave in a similar way during the ablation process, which leads to the compensation of the fractionation effects between the reference standards and the sample to be analyzed. In CF-LIBS however, analytical results are extracted directly from the emission spectrum of the plasma. Therefore, non-stoichiometric ablation or incomplete atomization will severely degrade the final accuracy of the analytical result [START_REF] Tognoni | Calibration-Free Laser-Induced Breakdown Spectroscopy: State of the art[END_REF]. Generally speaking, organic samples suffer more from the non-stoichiometric ablation with respect to the metallic ones. That is firstly due to different ablation mechanisms. Photothermal ablation dominates the ablation of metallic target while both photothermal and photochemical ablation play important roles for organic samples. For metallic samples, it is much easier to obtain a stoichiometric ablation among metallic elements, due to the similar structure of the metallic targets. For organic samples, a stoichiometric ablation is much more difficult to obtain, because the divergences among complex molecular bond energies result in different ablation efficiencies for different elements. On the other hand, due to the large difference in ionization potentials between organic and metallic elements, it is easier to obtain a partial stoichiometric ablation among metallic elements. While a full stoichiometric ablation, metallic and organic elements included, is certainly much more difficult to realize.

Departure from the LTE state

The assumption of LTE is particularly important for CF-LIBS, since the Boltzmann distribution law and Saha equation are used for the determination of the concentrations. If LTE is not validated, the CF-LIBS will provide unreliable result. The deviation from LTE is usually described by the parameter b(p), which is defined using the following equation [START_REF] Hahn | Laser-Induced Breakdown Spectroscopy (LIBS), Part I: Review of Basic Diagnostics and Plasma-Particle Interactions: Still-Challenging Issues Within the Analytical Plasma Community[END_REF]:

(I.54)
where N(p) and N SB (p) is the population of the level actually measured and the value calculated using the Saha-Boltzmann equilibrium. The fact that the parameter b(p) is greater or smaller than unit indicates a plasma characterized by ionization or recombination states.

However, the determination of b(p) is not easy in most of the situations, since it requires the actual population of the level which is difficult to determine in the plasma. Therefore, a different procedure is used in this work for the validation of LTE before the implementation of CF-LIBS.

In addition to the method discussed above, self-consistent check of the LTE state is introduced below and will be implemented in Chapter II for a plasma induced from a fresh vegetable. Such self-consistent check is suitable for a transient plasma evolving towards the LTE state. For a given element, the Boltzmann distribution is assumed to be verified by the population distributions of the atom and of the corresponding ion respectively. The Boltzmann plot of atomic lines leads to the excitation temperature of the atom, T atm . While the Boltzmann plot of ionic lines allows the deduction of the excitation temperature of the ion, T ion . In parallel, the molecular vibrational temperature T v can be deduced using the Boltzmann plot applied to molecular vibrational bands. If the three temperatures merge together, T atm =T ion =T v , the LTE state is reached for the concerned element. On the other hand, the Boltzmann or Saha-Boltzmann plot can be applied to different elements in the plasma, if all the plots exhibit a same slop, the LTE state is verified for all elements in the plasma.

Moreover, since the Stark effect does not depend on the LTE state of the plasma, it can be used for electron density determination whatever the thermodynamic state of the plasma.

At the same time, the electron density can also be calculated using the intensity ratio between atomic and corresponding ionic lines of the same element as expressed in equation (I. [START_REF] Sattmann | Laser-induced breakdown spectroscopy for polymer identification[END_REF]).

Then the difference in the values of the electron density calculated from the two methods can be used to evaluate the departure from the LTE state. Alternatively, the electron density calculated using the Stark effect can be substituted into equation (I. [START_REF] Sattmann | Laser-induced breakdown spectroscopy for polymer identification[END_REF]) for the determination of temperature. The result can be compared with the temperature obtained from Saha-Boltzmann plot for the evaluation of the LTE condition.

Self-absorption in an optically thick plasma

The hypothesis made for deriving the McWhirter criterion is that the plasma is optically thin.

In fact, plasma created by laser ablation is often optically thick for some particular wavelengths. In this case, the effective radiative population rate of the ground state is reduced by a factor. The factor is in the order of the ratio of the actual intensity to the corresponding intensity that the line would have if self absorption is absent. This leads to a corresponding reduction of the electron number density needed for LTE by the same factor. When Stark broadening method is used for the determination of the electron number density, line shape distortion due to self-absorption leads to an overestimation of the electron density. On the other hand, including self-absorbed lines in Boltzmann plot or Saha-Boltzmann plot leads to erroneous estimation of the slope and the intercept, subsequently affects the accuracies of the temperature and the concentration. Therefore, it becomes important to estimate the expected line intensity in the case of optically thin plasma so to improve the reliability and precision of the quantitative evaluation of the material composition.

When light is emitted from plasma, it has to travel from some part in the interior of the plasma source to the outside. Considering the absorption of the radiation emitted by atoms in a plasma by other atoms of the same element, the integrated intensity of the emission line is

given by [START_REF] Bulajic | A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy[END_REF]:

(I.55)
where α c is a constant factor which accounts for the response of the detection instrument, l is the absorption length, and k( ) is the frequency dependent absorption coefficient (m -1 ) which is given by

(I.56)
with k 0 , a, and x are defined as follows:

(I.57)

(I.58) (I.59) (I.60)
where f is the transition oscillator strength (dimensionless), and Δ N , Δ L , and Δ D represent the natural, Lorentzian, and Doppler line half-widths (Hz), respectively. Then the total absorption A t can be described as

(I.61)
where k(x) will be replaced by k if homogeneous plasma is considered.

The curve of growth (COG) method is often used to estimate the self-absorption behavior.

The curve of growth is usually constructed experimentally by measuring the integrated line intensity as a function of the analyte concentration. The theoretical curve of growth is a double-logarithmic plot of A t /2b versus n 0 fl/b. Normally, it has two asymptotes with slopes of 1 in the linear zone and 1/2 in the strong self-absorbed zone [START_REF] Gornushkin | Curve of growth methodology applied to laser-induced plasma emission spectroscopy[END_REF].

As stated above, self-absorption leads to overestimation of the line width and underestimation of the line intensity, which obviously affects the accuracy of CF-LIBS procedure. Therefore, the optical thin lines have to be used whenever possible in the CF-LIBS procedure. Although the self-absorption can be corrected considering the equations (I.55) to (I.61) [START_REF] Bulajic | A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy[END_REF], the correction is usually limited to a homogenous plasma. Empirically, in order to minimize self-absorption effects, firstly no resonant lines are used for electron density and temperature determinations, secondly lower level of a transition with energy higher than 6000 cm -1 for elements with high concentration not be selected [START_REF] De Giacomo | Laser induced breakdown spectroscopy on meteorites[END_REF].

I.5 Summary of the chapter

This chapter presented theoretical background of LIBS from plasma generation to its diagnostic, with the main line of three hypotheses including stoichiometric ablation, local thermodynamics equilibrium and optically thin plasma. Laser ablation of the target was first introduced in this chapter, from laser material interaction and plume evaporation to plasma generation. Considering organic sample was focused in this thesis, the ablation of organic target was emphasized, including photochemical ablation and molecular fragment generation.

Obviously, the most important for LIBS is the analysis of plasma. As a consequence, the spatiotemporal distribution was presented from both theoretical and experimental point of view. Since electron density and temperature are two important parameters of plasma, different methods were introduced in details for the determinations. Considering the hypothesis of local thermodynamic equilibrium is unavoidably discussed in plasma diagnostic, it was subsequently introduced with different validation processes. After the presentation of diagnostics of plasma, quantitative analysis methods were introduced, including calibration curve and CF-LIBS. Finally, factors affecting the quantitative result were discussed. For calibration curve method, the inaccuracy result is mainly due to the matrix effect. For CF-LIBS procedure, it is mainly due to the departures of three important hypotheses, including non-stoichiometric ablation, departure of local thermodynamic equilibrium and optically thick plasma.

Chapter II Time-resolved characterization of laser-induced plasma from a fresh vegetable and quantitative determination of trace elements

As mentioned above, my thesis aims at the improvement of the application of LIBS to organic materials for both qualitative and quantitative analyses in the continuity of the works realized in the team in Lyon 1 University. In the previous works of this team, LIBS qualitative analysis of the potato skin showed the presence of a large number of elements, including organic elements, nonmetallic as well as metallic elements which are contained in a potato as trace element [START_REF] Juvé | Space-resolved analysis of trace elements in fresh vegetables using ultraviolet nanosecond laser-induced breakdown spectroscopy[END_REF]. Such work gives us a clue for the capacity of LIBS to provide sensitive analysis of trace or even ultra-trace elements contained in agricultural products for in situ or online detection. The qualitative analysis was the first step towards the quantitative analysis, which is precisely the objective of the present chapter. In this chapter, I will first present the experimental setup and protocol that optimize the plasma generation on the surface of a fresh vegetable, potato. The temporal evolution of the plasma was investigated using time-resolved LIBS. In particular, the electron density and the temperatures in the plasma were measured as a function of the decay time. The comparison between temperatures of the different species in the plasma validated the local thermodynamic equilibrium (LTE) in the specific case of fresh vegetable ablated in a typical LIBS condition. The evolution of the signal-to-noise ratio of the emission spectrum also provided practical indication for an optimized detection of trace elements. Finally, under optimized experimental parameters the calibration-free LIBS procedure was applied to determine the concentrations of trace elements in a fresh vegetable.

II.1 Motivation of this work

Nowadays, there is an increasing need for sensitive and reliable techniques that enable the detection and the analysis of trace elements in food. This is especially true for vegetables that are in direct contact with pollutants present in soil and in air [START_REF] Miquel | Les effets des métaux lourds sur l'environnement et la santé[END_REF]. Such analytical techniques provide useful assessments for safe and healthy consumption of foods and in particular of fruits and vegetables [START_REF] Leblanc | Etude de l'alimentation totale française, Mycotoxines, minéraux et éléments traces[END_REF]. They may also provide control and monitoring of the pollutants in the surrounding environment (soil, water, and air) to which vegetables, or more generally agricultural products, are in direct contact [START_REF] Delibacak | Trace element and heavy metal concentration in fruits and vegetables of the Gediz River region[END_REF][START_REF] Voutsa | Trace elements in vegetables grown in an industrial area in relation to soil and air particulate matter[END_REF]. Among available elemental analysis techniques, LIBS exhibits attractive features, such as a capacity for multi-elemental detection, rapid response, easy sample preparation, possibility of in situ or online analysis, and high sensitivity. Quantitative measurements can be achieved with LIBS either with calibration, using reference samples, or by performing the calibration-free LIBS (CF-LIBS) procedure.

It is however still a challenging task to apply the quantitative analysis using LIBS, traditionally and commonly used for inorganic sample analysis (alloys, minerals…), to the analysis of vegetables or more generally foods. Several works have reported the use of LIBS for qualitative analysis of trace elements in plants [START_REF] Assion | Femtosecond laser-induced-breakdown spectrometry for Ca2+ analysis of biological samples with high spatial resolution[END_REF][START_REF] Sun | Zn, Mg, and Fe in plant materials by laser-induced breakdown spectroscopy[END_REF][START_REF] Trevizan | Evaluation of laser induced breakdown spectroscopy for the determination of micronutrients in plant materials[END_REF], and in particular in leaves [START_REF] Samek | Femtosecond laser spectrochemical analysis of plant samples[END_REF][START_REF] Bossu | Femtosecond laser-induced breakdown spectroscopy for detection of trace elements in sophora leaves[END_REF][START_REF] Pouzar | LIBS analysis of crop plants[END_REF]. Quantitative measurements can be achieved with LIBS either with calibration curves, using reference samples, or by performing the CF-LIBS [START_REF] Ciucci | New Procedure for Quantitative Elemental Analysis by Laser-Induced Plasma Spectroscopy[END_REF][START_REF] Tognoni | A numerical study of expected accuracy and precision in Calibration-Free Laser-Induced Breakdown Spectroscopy in the assumption of ideal analytical plasma[END_REF]. As mentioned above, matrix-matched references samples are needed for the establishment of a useful calibration curve. Such requirement is particularly difficult to fill for fresh vegetable. It is why the CF-LIBS approach has been chosen in our work as the tool to extract analytical data.

In order to implement the CF-LIBS procedure for LIBS analysis of fresh vegetable, a detailed investigation of the characteristics of the laser-induced plasma from such sample is still required to optimize the experimental protocol for plasma generation and for validating of the LTE condition of the resulted plasma. The result of such an investigation is the first step towards the quantitative determination of trace elements using the CF-LIBS procedure.

In the literature, even though a number of studies have been published on plasma induced from metallic materials with extensive studies on the LTE [START_REF] Aragon | Characterization of laser induced plasmas by optical emission spectroscopy: A review of experiments and methods[END_REF][START_REF] Barthelemy | Investigation of the state of local thermodynamic equilibrium of a laser-produced aluminum plasma[END_REF][START_REF] Galmed | Temporal follow up of the LTE conditions in aluminum laser induced plasma at different laser energies[END_REF], the characteristics of plasma induced from fresh vegetable are still unknown. Detailed research is needed to put forth the dependence of such characteristics with the ablation condition (laser parameters, sample preparation) as well as with its temporal evolution during plasma decay.

In this chapter, I will present the results on the investigation of the characteristics of the plasma induced from the skin of a potato, a typical root vegetable. The investigations are based on space-integrated and time-resolved plasma emission spectroscopy. The experimental setup and the experimental protocol will first be described. Then the physical parameters of the plasma, i.e. the electron density and the temperatures, will be measured with time-resolved LIBS for different laser fluences. The standard LIBS data processing methods, based on Stark broadening and Boltzmann or Saha-Boltzmann plots, will be used to extract the electron density and the excitation temperatures. The vibrational temperature will also be retrieved from the band head emission of CN molecules. The validation of the LTE will be checked for the specific case of plasmas induced from a fresh potato, where a large number of trace elements can be detected [START_REF] Juve | Space-resolved analysis of trace elements in fresh vegetables using ultraviolet nanosecond laser-induced breakdown spectroscopy[END_REF]. The temporal evolution of the signal-to-noise ratio will also be presented for different trace elements as well as ultra trace elements. Therefore a time window with high signal-to-noise ratio can be found, within which trace elements detected in the plasma are in LTE. With these conditions, the calibration-free procedure can thus be applied. Finally, the CF-LIBS procedure will be applied for the determination of the concentrations of trace elements detected in the potato sample. I will finally specify the condition and the limitation of such approach.

II.2 Experimental setup, sample preparation, and measurement protocol

The experimental setup is schematically shown in Fig II .2. A quadrupled Nd:YAG laser (wavelength 266 nm) with a 10 Hz repetition rate was used in our experiments in order to get better detection sensitivity thanks to the efficient UV laser-induced ablation of organic materials [START_REF] Baudelet | Time-resolved ultraviolet laser-induced breakdown spectroscopy for organic material analysis[END_REF]. The used energy ranged from 5 to 20 mJ. Laser pulses were focused on the skin of a potato using a bi-convex quartz lens with a 50 mm focal length. The focused spot size was estimated to be 100 μm in diameter using microscopic pictures of ablation craters.

The laser fluence used in our experiments ranged thus from 64 to 250 J/cm 2 . Optical emission from the plasma was collimated into a coupling fiber (50 μm core diameter) using a combination of two parabolic mirrors, offering an efficient and achromatic light collection [START_REF] Yu | Unité d'excitation lumineuse d'un échantillon et de collection de la lumière émise par ledit échantillon excité[END_REF]. The used fiber presented a good transmission from 200 to 850 nm. It was connected to an Echelle spectrometer (spectral range: 220 nm to 821 nm, spectral resolution: /Δ =5000)

coupled with an ICCD camera to record the spectra (Mechelle and iStar from Andor Techology). The wavelength calibration of the spectrometer was done with a mercury argon lamp (HG-1 from Ocean Optics). The spectral intensity calibration was performed using a deuterium tungsten halogen light source (DH-2000-CAL from Ocean Optics), which is very important to the temperature determination and will be discussed in detail later in this chapter.

The ICCD camera was synchronized to the Q-switch trigger of the laser. A detection window was opened for the camera after a time delay which avoids the strong continuum emission immediately after the impact of the laser pulse on the sample. The detection window could also be sequentially delayed in a series of time-resolved detections of the plasma emission. In this case, the width of the detection window was adjusted to get suitable signal-to-noise ratio (SNR) as the time delay increases. The emission intensity was then normalized to a reference gate width. Each spectrum represents an accumulation of 500 laser pulses. The sample was moved quickly using a step motor during the spectrum accumulation in order for each laser shot having a fresh sample surface.

Sample potatoes came from a local market. Our previous work showed a larger concentration of metallic elements in the potato skin compared to its inside region due to the direct contamination by the soil [START_REF] Juvé | Space-resolved analysis of trace elements in fresh vegetables using ultraviolet nanosecond laser-induced breakdown spectroscopy[END_REF]. The skin was therefore chosen for the experiment.

II.3 Experimental results and discussion

II.3.1 Temporal evolution of the optical emission from the plasma

To record the temporal evolution of the optical emission from the plasma induced on the skin of a potato, a delayed detection window with an increasing width was used to compensate for the decreasing signal. The used detection gate widths for different delays are indicated in Table II.1. Each spectrum represents an accumulation of 500 laser pulses. In Fig II .3 four spectra are chosen to show the time evolution of the optical emission from the plasma for a delay going from 100 ns to 2980 ns. For short delays, the continuum emission significantly contributes to the total emission. As the delay increases, this emission, essentially due to the radiative recombination between electrons and ions and bremsstrahlung emission, drops significantly as a result of the decay of the plasma. After 500 ns, the spectrum is dominated by spectral emission lines associated to optical transitions between discrete states of different species, ions, atoms and molecules. Spectrum narrowing was observed with increasing delay as the consequence of decrease of the electron density. In a potato, a large number of elements could be identified in the spectrum [START_REF] Juve | Space-resolved analysis of trace elements in fresh vegetables using ultraviolet nanosecond laser-induced breakdown spectroscopy[END_REF]. Besides the organic elements (H, C, O, N), which constitute the matrix of vegetable samples, the trace elements including Na, Mg, K and Ca are distinguished. Ultra trace elements are also detected by LIBS in typical potato samples and may include Li, Al, Si, Ti, Mn, Fe, Cu, Zn, Sr and Ba as shown in our previous work [START_REF] Juve | Space-resolved analysis of trace elements in fresh vegetables using ultraviolet nanosecond laser-induced breakdown spectroscopy[END_REF].

Delay

II.3.2 Electron density

The plasma emission spectra recorded as a function of the detection delay, allow us to study the temporal evolution of the electron density in the plasma during its expansion and decay.

The electron density was determined using the Stark broadening of the Hydrogen line at 656 nm. The H α line appeared to be a good choice for electron density determination since it is well isolated and quite intense due to the high hydrogen concentration present in the sample.

In addition, this line is strongly affected by the linear Stark effect due to the degeneracy of the transition as mentioned above [START_REF] Griem | Spectral line broadening by plasmas[END_REF]. Its use for electron density determination has been extensively reported for the diagnostics of laser ablation plasma [START_REF] Ashkenazy | Spectroscopic Measurements of Electron-Density of Capillary Plasma Based on Stark-Broadening of Hydrogen Lines[END_REF][START_REF] El Sherbini | Measurement of electron density utilizing the H alpha-line from laser produced plasma in air[END_REF]. In our work, the equation (I.17) was used to relate the electron density and the Stark line broadening.

In order to extract the Stark line width, the LIBS spectra were fitted using the Voigt profiles. The used Lorentzian width was identified to the Stark broadening width, while the Gaussian width was fixed according to the instrumental line width. This width was determined by fitting visible Hg lines emitted from a mercury light source and was measured to be 0.14 nm at 656 nm. This corresponds quite well to the spectral resolution power of The temporal evolution of the electron density was determined for ablation energies of 5, 10 and 20 mJ. As shown in Fig II .5, the electron density decreases from about 10 18 cm -3 at short delays to about 10 16 cm -3 at longer delays. The error bars estimated for each delay take into account the accuracy of 10% of the reduced Stark width, and the statistical error calculated from 4 independent measurements. As expected the electron density increases with increasing laser pulse energy. The most remarkable feature is that the electron density decay lifetime increases significantly with increasing ablation laser pulse energy, while the difference in initial electron densities remains relatively small for different laser energies. We specify here that the self-absorption of the line H α was considered as negligible in our calculation of the electron density. For this line, it has been shown that the self-absorption only starts to appear for electron densities higher than 3×10 18 cm -3 [START_REF] Ashkenazy | Spectroscopic Measurements of Electron-Density of Capillary Plasma Based on Stark-Broadening of Hydrogen Lines[END_REF], which supports our approximation. After 400 ns at 5 mJ, 600 ns at 10 mJ and 1000 ns at 20 mJ, the H α line became undetectable with respect to the noise, and the evaluation of the electron density with this line impossible. In laser-induced plasma, for the LTE to be reached, the electron density has to be high enough to ensure that collision process dominates the radiative process. This condition is generally described by the McWhirter criterion as discussed in §I.3.3, which provides the lowest value of the electron density necessary for the plasma to reach the LTE. According to this criterion, if we consider the largest energy ΔE=4 eV and a typical plasma temperature of T = 7000 K, the equation (I.44) results in a minimal electron density of N e =8.6×10 15 cm -3 . In delays up to the range between 1.5 and 2 μs (we consider a power law extrapolation of N e for delays beyond 1 μs). Such a long period should be quite enough for the establishment of the LTE in the plasma. In the following section for the presentation of the results of plasma temperature measurement, only the case of ablation with 20 mJ laser pulse will be considered since it better fulfils the condition on electron density for the establishment of the LTE.

II.3.3 Measurement of temperatures

For plasma characterization, the excitation temperature of a given species (given element and given ionization degree) is in general retrieved using Boltzmann plot method as mentioned in §I.3.2. The temperature of this species is deduced from the slope of such plot. In practice, a careful line selection must be processed when performing Boltzmann plots. Self-absorption or self-reversing can greatly influence the result if the concerned lines are not correctly chosen.

Used lines should be measured with suitable signal-to-noise ratio. They should be well isolated without interference with other transitions. Intensity calibration of the detection system must also be performed especially for the case where the selected lines extend over a large spectral range. In order to increase the accuracy of the calculation, the range of E i should be as large as possible. The specificity and the advantage of the plasma induced from a vegetable such as potato are that the optical emissions from a large number of elements/species are detected in a LIBS spectrum. The conditions for a precise determination of the temperature are in general satisfied when working with transition metals, such as Fe or Ti, or alkaline earth metals, such as Ca, for which a large number of transitions are available in the visible spectral range. However, the temperature determination can be more difficult for other elements, alkali metals, non metallic elements or especially organic elements for which only a few emission lines are detected in the spectral range sensitive for usual ICCD detector.

In our work concerning the plasmas induced on the skin of a fresh potato, calcium appears to be the most suitable element for temperature determination, taking into account the considerations discussed above. A supplementary reason is also that Ca is a trace element which is omnipresent in vegetables with a relatively high concentration. We can also mention that since the temperature is evaluated in our work for quite short delays after laser impact, the strong continuum emission observed for these delays prevents us from using transition metals, such as Fe or Ti, for temperature evaluation, because their line emissions are in general much weaker than those of Ca. More precisely, Table II the line set (1) was used, which includes three strong neutral and ionized Ca transitions for Saha-Boltzmann plot. For longer delays (from 480 to 2980 ns), the line set (2) was used with 11 weaker neutral and ionized Ca lines for Saha-Boltzmann plot. Indeed, these last lines were observed with suitable signal-to-noise ratios for these longer delays, while the lines in the set

(1) exhibit line shape distortions which indicate self absorptions after 400 ns. For these delays, a Boltzmann plot was also performed with the listed neutral Ca lines in the set (2). An excitation temperature of neutral atoms has been extracted from this plot. Typical Saha-Boltzmann plots are shown in Fig II .6 for different delays of 580 and 980 ns. These two plots exhibit an excellent linearity (R 2 0.9997 and 0.999 respectively) with statistical errors associated to the retrieved temperature less than 100 K. Good agreements are especially observed between the atomic (left side) and ionic (right side) transitions. This agreement indicates a thermodynamic equilibrium between neutral and ionized calcium. These plots also show the improvement in the precision of the temperature determination using Saha-Boltzmann plots, which allows the plot to be performed over a wide range of energy.

Specie ji (nm) A ji (10 The observed kinetic behavior of the different temperatures shows that for 20 mJ laser ablation on the skin of a fresh potato, the produced initial electron density is high enough to ensure a collision rate necessary to establish LTE in the plasma. Such equilibrium is reached in the plasma about 700 ns after laser impact. After this delay, the plasma can be described with a single temperature in the framework of the LTE approach. Furthermore by considering the McWhirter criterion, the electron density is high enough to ensure the LTE up to the range of 1.5 to 2 μs in delay. We can also remark that after the delay of 700 ns, the temporal evolution of the plasma temperature becomes much slower compared to the initial evolution.

From the point of view of the analytical applications, the CF-LIBS procedure for retrieving elemental concentrations can be therefore applied within the temporal window between 700 ns and 1.5 μs. In addition, we will see in the following section that with our experimental configuration, this temporal window fits well with that one which optimizes the signal-to-noise ratios (SNRs) for the detection of trace as well as ultra trace elements.

II.3.4 Evolution of the signal-to-noise ratio of the spectral lines

In our experiments, the signal-to-noise ratio of a spectrum was determined for trace, as well as ultra trace elements in order to see whether the detection delay for optimized SNR is Such SNRs allow all of these elements to be quantified with the LIBS technique. We remark also that the LTE condition holds for the observed delays which optimize the SNR. In fact, for delays greater than about 700 ns, which are necessary for the LTE to be established, all measured SNRs exhibit reasonably high values. Therefore, in practice, with the experimental configuration used in the present work, we can integrate the LIBS spectrum from a potato using a detection window starting at 700 ns after laser impact. The choice of the width of the detection window is fixed by the McWhirter criterion applied to the electron density in order to ensure the LTE. In our case the detection window can be extended upper to a delay in the range of 1.5 to 2 μs.

II.3.5 Determination of the elemental concentrations using CF-LIBS

In the following section, integrated spectra were recorded with a detection window opened from 700 ns to 1.2 μs after the laser impact. Such integrated spectra present good SNR for the detection of a large number of trace and ultra trace elements according to Fig II. The application of the equation (I.53) together with the temperatures presented in Table II.3 lead to the determination of the relative number densities in the plasma of the detected elements with respect to a reference element. Among the detected elements, Ca appears to be a suitable reference element, because of its relatively high concentration in vegetables, and because its relatively homogenous distribution in a vegetable as was observed in our previous work [START_REF] Juve | Space-resolved analysis of trace elements in fresh vegetables using ultraviolet nanosecond laser-induced breakdown spectroscopy[END_REF]. The experimental relative concentrations of Al, Mn, Fe, Ti and Mg with respect to Ca are shown in Fig II .11. For comparison, the minimum and maximum values form Refs [START_REF] Anderson | Determining the Geographic Origin of Potatoes with Trace Metal Analysis Using Statistical and Neural Network Classifiers[END_REF][START_REF] Bibak | Concentrations of 50 Major and Trace Elements in Danish Agricultural Crops Measured by Inductively Coupled Plasma Mass Spectrometry. 3. Potato (Solanum tuberosum Folva)[END_REF] have also been included. We can see that the experimental values are located between the minimum and maximum value presented in refs for Al, Mn, Ti and Mg. However, the relative concentration of Fe/Ca is twice lower than the minimum value.

Fig II.11. Relative concentrations of Al, Mn, Fe, Ti and Mg with respect to Ca in potato, comparison between CF-LIBS results and values from

Refs. [START_REF] Anderson | Determining the Geographic Origin of Potatoes with Trace Metal Analysis Using Statistical and Neural Network Classifiers[END_REF][START_REF] Bibak | Concentrations of 50 Major and Trace Elements in Danish Agricultural Crops Measured by Inductively Coupled Plasma Mass Spectrometry. 3. Potato (Solanum tuberosum Folva)[END_REF].

For the purpose of the assessment of security or nutrition quality of fresh vegetables, it is interesting to have a measurement of the relative concentrations of toxic elements such as Al, Ti, and heavy metals such as Pb, Hg, As or Cd, as well as those of oligo-elements such as Ca, Mg, Fe, or Mn [START_REF] Leblanc | Etude de l'alimentation totale française, Mycotoxines, minéraux et éléments traces[END_REF]. Besides Ca of which the concentration in a potato is quite high, some trace elements can also be considered as reference, for example Fe, with the advantage that such reference elements present similar concentrations compared to those of toxic or oligo-elements particularly important for the application in food security and food quality assessment.

The importance and the relevance of the relative concentrations in the analysis of the samples such as potatoes are due to their complexity in composition including a large number of elements of different natures and different concentrations. In fact, our observations reveal that the optical spectroscopic diagnostics of the plasma can be applied relatively easily to metallic elements. However, the use of the same procedure to organic elements (C, H, O, N which are the major elements in an organic material) seems to be difficult. This is due the fact that only a limited number of emission lines are observed in the usual spectral range covered by a typical LIBS measurement. More precisely, in our experiment, we observed 1 line for C (247.8 nm), 1 line for H (656.3 nm), 1 triplet for O (777 nm) and 5 lines for N (742.4 nm, 744.2 nm, 746.8 nm, 818.4 nm and 818.8 nm). In order to apply the calibration free procedure to these elements, one has to assume that they have actually the same temperature as trace metallic elements. Any discrepancy of such thermal equilibrium leads to imprecision on the calculations of the concentration of organic elements. In addition some ultra trace elements may have concentrations below the detection limit of the experimental setup. It is therefore practically impossible to realize the multi-elements Saha-Boltzmann plots for all elements contained in a vegetable sample such as potato. Without taking into account the contribution of the totality of the elements, it is impossible to normalize with precision the total concentration in a full CF-LIBS procedure [START_REF] Ciucci | New Procedure for Quantitative Elemental Analysis by Laser-Induced Plasma Spectroscopy[END_REF]. Another important aspect for the quantitative analysis of a fresh vegetable sample with LIBS concerns the stoichiometric ablation. Due to the large difference in ionization potentials between organic and metallic elements, it is much easier to obtain a partial stoichiometric ablation among metallic elements. While a full stoichiometric ablation, metallic and organic elements included, is certainly much more difficult to realize.

An estimation of the limit of detection may be obtained for example, by comparing with other quantitative measurement techniques, such as ICP-MS. In this thesis, we limit ourselves to a comparison to typical data available in the literature since calibrated reference samples are not available. According to the data published in Ref [START_REF] Leblanc | Etude de l'alimentation totale française, Mycotoxines, minéraux et éléments traces[END_REF], for the 4 elements presented In order to guarantee the accuracy in the measurement of the relative line intensities, the spectral response calibration of the detection system (Andor Technology) was performed using a deuterium tungsten halogen light source (DH-2000-CAL from Ocean Optics) according to the standard procedure provided by Andor Company. The deuterium tungsten halogen light source used for the calibration provided absolute spectral intensity in W/cm 2 /nm at the fiber output port from 220 to 850 nm. The calibration data of the light source is provided by Ocean Optics which allows about 50 hours of operation before each calibration. Therefore, the spectrum obtained in our experiment has a real intensity at the input of the fiber, taking into account the weighted instrument function, including grating efficiency, transmittance, and detector sensitivity. This calibration procedure confirmed accurate relative line intensity in all the wavelength range, which subsequently allowed accurate temperature calculation.

On the other hand, the accuracy of the temperature can be improved by increase the difference between the upper energy levels for the used transition lines. In the case of Saha-Boltzmann plot, the difference of the upper energy level is modified by the ionization energy. This value is enlarged to be about 10 eV as shown in Fig II .6, so a 10% uncertainty of the relative line intensity will only involve 1% uncertainty of the calculated temperature, assuming T=11600 K as mentioned above. However, we found in our experiment that higher excitation temperature is obtained with ionic lines with respect to that obtained with the atomic lines. A possible explanation of the difference is the absence of LTE in the plasma.

Another explanation is the use of spatial integrated measurement in an inhomogeneous laser-induced plasma. We know that the emissivity of a line of a species is proportional to the population of the upper level of the transition, which in turn is proportional to the corresponding Boltzmann factor and to the number density of the species. The spatial variation of the plasma temperature, together with the different location of the number density distributions, leads to a difference in the location of the upper level population distributions for neutral atom and ion transitions. In addition, the emissivity of the ionic lines is produced generally in the middle of the plasma with high temperature considering the higher upper energy level involved. On the contrary, the atomic emission, on the average, comes from the low-temperature region where the neutral atom density is higher. Therefore, the Boltzmann plot using the neutral atomic lines provides a lower temperature value compared to that obtained using ionic lines.

Strictly speaking, the temperature provided by fitting both atomic and ionic lines in a single straight line can be considered as an apparent ionization temperature of the whole plasma. In our experiment, the uncertainty of the temperature was obtained from the statistic error of the Saha-Boltzmann plot slopes, which has a considerable dependence on the lines included in the plot. Therefore, the selection of the lines for constructing Saha-Boltzmann plot is crucial for the precision of the temperature determination. It should be taken into account several factors, such as self-absorption, overlapping with neighbor emission lines, low signal-to-noise ratio and so on. For investigating the effect of self-absorption, it is better to use the curve of growth method in order to make sure that the selected line has a linear response to the elemental concentration in the sample. Unfortunately, this was not done in this work due to the absence of reference potato skin with certified elemental concentration. The curve of growth method will be used for the selection of lines in the work for milk powder analysis. In this work, firstly an empirical selection of lines was conducted to construct a Saha-Boltzmann plot. In the case where a large number of lines can be used, the line with the largest departure from the Saha-Boltzmann plot was abandoned. A new Saha-Boltzmann plot was constructed with the rest of the lines until a good linearity was obtained. With this method a low uncertainty of temperature was obtained for Ca and Fe as shown in Table II.3, considering a number of lines can be used for the two elements. Because limited number of lines can be selected for the other elements, the corresponding uncertainties are higher for Mg, Mn and Al.

We assumed here a better linearity with a lower uncertainty of temperature should be obtained if a spatially resolved measurement was conducted with the selection of lines confirmed by the curve of growth method. As reported in ref. [START_REF] Aguilera | Characterization of a laser-induced plasma by spatially resolved spectroscopy of neutral atom and ion emissions.: Comparison of local and spatially integrated measurements[END_REF], a Saha-Boltzmann plot was obtained with a set of atomic and ionic lines of Fe, which indicates a excellent correlation ( R 2 =0.9993) and temperature 13160 K.

Choice of the internal reference element

As mentioned in Chapter I, a full CF-LIBS procedure requires that all the elements can be detected to obtain the experimental parameter F that takes into account the optical collection efficiency of the collection system. This parameter will be determined with the normalization of the concentrations of all the elements by equation (I.52). However, in most of the situations all the elements cannot be detected due to low concentration or emission lines with wavelength out of the spectral range of the detection system. Therefore, only relative concentrations were determined in this work using CF-LIBS with the help of the equation (I.53), using an internal reference element. This approach is also called controlled CF-LIBS procedure [START_REF] Wang | Controlled calibration method for laser induced breakdown spectroscopy[END_REF].

The choice of this internal reference element plays an important role in the analysis.

Generally, there should be a reasonably high and homogeneous concentration of the reference element in each sample. In our case, calcium has a relative high concentration and homogeneous distribution in a potato as discussed in our previous work [START_REF] Juvé | Space-resolved analysis of trace elements in fresh vegetables using ultraviolet nanosecond laser-induced breakdown spectroscopy[END_REF]. On the other hand, a large number of transitions are available in the visible spectral range for Ca, which allows easier selection of reference lines with high signal-to-noise ratio and upper energy levels as close as possible to those of the analyte. In addition, the analyte and the internal reference element should have comparable ionization energy and similar atomic weight [START_REF] Hahn | Laser-Induced Breakdown Spectroscopy (LIBS), Part II: Review of Instrumental and Methodological Approaches to Material Analysis and Applications to Different Fields[END_REF].

As shown in Table II.4, the atomic weight of Ca is similar to the average atomic weight of the 6 elements analyzed in this work. Although Ti has an ionization energy closest to the average value, it is not selected as the reference element due to other criteria that should also be considered as discussed above.

II.4 Conclusion of the chapter

In the work presented in this chapter we have investigated the laser-induced plasma on the skin of a fresh potato, a typical root vegetable. The purpose of this work was to optimize the procedures concerning the experimental setup and protocol as well as the spectroscopic data analysis methods for the quantitative measurement of trace elements in fresh vegetables using the LIBS technique. We are especially interested in the calibration-free LIBS approach, which is based on the assumption that plasma is in the local thermodynamic equilibrium. The experimental observation was carried out using time-resolved optical emission spectroscopy, which provided a detailed diagnostics of the transient plasma. The data treatment has been performed using the classical procedures based on the Stark effect, the Boltzmann and Saha-Boltzmann equations. The obtained results showed the temporal evolution of the electron density and the temperatures within the plasma. More precisely, we showed that the electron density in the ablation plasma generated on the skin of a potato allows the LTE to be realized according to the McWhirter criterion. However a high enough electronic density does not automatically correspond to the LTE since this criterion represents a necessary but not sufficient condition. The temperature measurement showed that a time interval is required for the different temperatures (ionic, excitation and molecular temperatures) to converge to an equivalent value. It is therefore better to use a high ablation energy (20 mJ in our experiment)

to ensure a high enough electron density over a long period of time for the establishment of the LTE within the plasma. In our experimental conditions, the electron density in the ablation plasma generated on the skin of a potato fulfils the McWhirter criterion from the initiation of the plasma up to a delay of about 2 μs. A LTE regime was indeed observed for a period starting from 700 ns after laser impact. A study of the temporal evolution of the signal-to-noise ratios for trace and ultra-trace elements showed that the above mentioned time period from 700 ns to 1.2 μs was also compatible for an optimized detection of line emissions from these elements. The emission spectrum was thus integrated in the time window from 0.7 to 1.2 μs in order to increase the sensitivity of the detection. Saha-Boltzmann or Boltzmann plots were then constructed for oligo-elements (Mg, Al, Ca, Ti, Mn, Fe) detected in the sample. Such plots lead to the determination of the relative concentrations of these elements in the sample with respect to calcium which is chosen as reference element.

We specify here that all our results presented in this chapter are obtained with a space-integrated detection. This means that the inhomogeneity of the plasma during its expansion has been neglected in our study. In a more satisfactory way, time-as well as space-resolved observations should be carried out to fully characterize the plasma. The temporal and space evolutions of the plasma are indeed correlated each other for the laser-induced plasma which is by nature a transient and inhomogeneous medium. Finally, we point out the specificities for the implementation of the full CF-LIBS procedure to quantitatively determine the elemental composition of a fresh vegetable. Such specificities are due to the complexity of the sample rather to the principal of the CF-LIBS procedure which has been developed for the laser-induced plasma in its ideal case. It is practically impossible to represent the organic elements (C, H, O, N) in a multi-element Saha-Boltzmann or Boltzmann plot with a number of points sufficiently large to get a precise measurement of their temperatures. The calculation of their concentrations needs necessarily the assumption of their thermodynamic equilibrium with trace metallic elements. Any discrepancy with respect to such equilibrium leads to imprecision in the determination of the concentrations of organic elements and in consequence, renders the normalization procedure required in the full CF-LIBS procedure difficult to be realized. It also seems difficult to achieve a full stoichiometric ablation for a sample containing organic as well as metallic elements, such as fresh vegetable, because of the large discrepancies in ionization potentials. A realistic plan for the application of the LIBS technique for fresh vegetables is, therefore, to provide the measurement of relative concentrations of metallic trace and ultra-trace elements with respect to a reference element with a similar ionization potential, calcium or iron for examples. Such measurement together with all the advantages proposed by the LIBS technique as stated above promise important applications in the control and the assessment of the security and the nutrition quality of the food.

Chapter III Quantitative analysis of mineral elements in milk powder with ICP-AES and LIBS: assessment and validation of the CF-LIBS procedure

In the last chapter, the CF-LIBS has been applied to determine the relative concentrations of trace metallic elements contained in a fresh potato. The obtained results have been compared

to typical concentrations reported in the literature, which provided an indication of the validity of the CF-LIBS procedure for analysis of organic materials. More convincing validation and more detailed assessment are however expected with comparison to an established quantitative analytical technique. This is precisely the purpose of the present chapter.

In this chapter, I will present our results on quantitative analysis of inorganic elements contained in commercially available milk powders, with on the one hand ICP-AES, and on the other hand LIBS. Such direct comparison of the analytical results, provides an assessment of the performance of LIBS, and especially of the procedure of CF-LIBS, to deal with organic samples such as milk powders. In our experiments, the matrix effect was clearly observed affecting the analytical results each time laser ablation was employed for sampling.

Such effect was in addition directly observed by calculating the electron densities and the temperature of the plasmas induced on different samples and with the images of the craters on the surface of the pellets of different types of milk. The CF-LIBS procedure was implemented to deduce the concentrations of detected mineral elements from the LIBS spectra. The good results obtained with the CF-LIBS procedure demonstrate its capacity to take into account the difference in physical parameters of the plasma in the calculation of the concentrations of inorganic elements, which allows a significant reduction of the matrix effect related to laser ablation. I will finally discuss the way to optimize the implementation of the CF-LIBS procedure for the analysis of organic materials.

This work has been performed within a collaboration with Nicole Delepine-Gilon and her colleagues from the team ANALISS of the Laboratoire des Sciences Analytiques at Lyon 1 University, who ensured sample preparation and analysis with ICP-AES.

III.1 Motivation of the work

Quantitative analytical with LIBS has been demonstrated for metallic alloys thanks to a good understanding of the plasma generated from metallic matrix [START_REF] Cremers | Laser-Induced Breakdown Spectroscopy-Capabilities and Limitations[END_REF][START_REF] Gaudiuso | Laser Induced Breakdown Spectroscopy for Elemental Analysis in Environmental, Cultural Heritage and Space Applications: A Review of Methods and Results[END_REF][START_REF] Bulajic | A procedure for correcting self-absorption in calibration free-laser induced breakdown spectroscopy[END_REF][START_REF] Corsi | A fast and accurate method for the determination of precious alloys caratage by Laser Induced Plasma Spectroscopy[END_REF]. Reliable calibration curves can be established with reference samples which are easily available commercially [START_REF] Gornushkin | Curve of growth methodology applied to laser-induced plasma emission spectroscopy[END_REF][START_REF] Mohamed | Improved LIBS limit of detection of Be, Mg, Si, Mn, Fe and Cu in aluminum alloy samples using a portable Echelle spectrometer with ICCD camera[END_REF]. Compared to metallic alloys, stronger matrix effects are unfortunately expected for organic samples, which makes the preparation of matrix-matched reference samples very difficult [START_REF] Eppler | Matrix effects in the detection of Pb and Ba in soils using laser-induced breakdown spectroscopy[END_REF][START_REF] Gornushkin | Effective normalization technique for correction of matrix effects in laser-induced breakdown spectroscopy detection of magnesium in powdered samples[END_REF]. One of the solutions to be explored for quantitative analysis of organic materials with LIBS is the use of the CF-LIBS procedure. The success of this procedure for metallic alloys [START_REF] Tognoni | Calibration-Free Laser-Induced Breakdown Spectroscopy: State of the art[END_REF] allows us to expect its good performance for organic samples and especially for taking into account the corrections made necessary by the matrix effect, in the calculation of the concentrations. The question however concerns the LTE in a plasma induced on an organic sample. In Chapter II, through the characterization of the plasma induced on an organic sample, such as a potato, we have demonstrated that the LTE can be established over a certain period after the laser impact on the sample [START_REF] Lei | Time-resolved characterization of laser-induced plasma from fresh potatoes[END_REF]. It is therefore possible to apply the CF-LIBS procedure to an organic sample by detecting the plasma emission in this time interval. The aim of the work presented in this chapter is thus to develop a quantitative analysis procedure for inorganic elements contained in milk powders with CF-LIBS. The obtained quantitative analysis results will be compared with a classical quantitative analytical using ICP-AES. Such direct comparison provides an assessment of the performance of the procedure of CF-LIBS to deal with organic materials such as milk powder.

There are several reasons to choose milk powder for our study. Milk powder is an essential foodstuff for which it is important to develop sensitive and rapid elemental analysis techniques. Elemental composition in milk needs to be controlled for health reason, especially for infant formulae which contain essential nutrients necessary for childe growth. Milk powder can be easily digested using classical procedures with nitric acid and microwave heating to obtain solution for quantitative analysis using ICP-AES. Milk powder can be also easily prepared into pellets for LIBS measurements, with or without binder. In addition, milk powder for infant and adults are commercially available and provided often with indication of concentrations of many inorganic elements. It must be however noticed that the commercial milks are not reference samples in the sense of analytical science. Nevertheless the indicative concentrations are generally quite reliable. The determination of the concentrations of inorganic elements in milk powders with ICP-AES is a well established procedure since 1980s [START_REF] Schramel | Consideration of inductively coupled plasma spectroscopy for trace element analysis in the bio-medical and environmental fields[END_REF][START_REF] Nobrega | Direct determination of major and trace elements in milk by inductively coupled plasma atomic emission and mass spectrometry[END_REF][START_REF] Mckinstry | The determination of major and minor elements in milk and infant formula by slurry nebulisation and inductively coupled plasma optical emission spectrometry (ICP-OES)[END_REF]. Very recently, LIBS technique was applied to milk powders for the determination of calcium concentration using the calibration curve method with a validation by ICP-AES [START_REF] Ferreira | Determination of Ca in breakfast cereals by laser induced breakdown spectroscopy[END_REF]. Some recent works report the direct comparison between ICP-AES and LIBS for analysis of organic samples such as plant materials [START_REF] Trevizan | Evaluation of laser induced breakdown spectroscopy for the determination of micronutrients in plant materials[END_REF][START_REF] Pouzar | LIBS analysis of crop plants[END_REF]. Comparing the analytical performances of these different techniques for the quantitative analysis of inorganic elements in milk powders is also the motivation of the present work.

In this Chapter, after a brief presentation of the analyzed samples, the used setups and measurement protocols, the calibration curves established with reference samples for ICP-AES, and LIBS will be presented. The calibrations curves will be then applied for quantitative analysis of the concentrations of inorganic elements in commercial milk powders using LIBS technique. Observed large discrepancies between the measured concentrations and the nominal values given by the providers of the milks suggest a strong matrix effect. The matrix effect is further confirmed by the determinations of the electron density and the temperature of the plasma and the observation of laser-induced craters. The analytical results

with the CF-LIBS procedure will be finally presented. The validation of CF-LIBS results using either the nominal concentrations or the measurements from ICP-AES will be conducted to demonstrate the reduction of the matrix effect using the CF-LIBS procedure. We will compare finally the analytical performance of CF-LIBS to that of ICP-AES associated to a digestion step, and point out the possible optimizations of the experimental setup to improve the implementation of the CF-LIBS procedure for analysis of organic materials.

III.2 Sample preparations, experimental setups and measurement protocols

Samples and pellets preparation

Different milk powders were analyzed in this work, including 8 commercially available products and a certified reference sample (BCR063 from IRMM). Among the 8 commercial products shown in Fig III .1, there were 7 formulae for baby (Gallia, Guiggoz, Lemiel, Milupa, Novalac Bleu, Novalac Rose and Nutricia) and a skimmed milk powder for adult (Auchan) all bought from a local supermarket. In addition, we prepared secondary reference samples by mixing certified reference sample and powder of pure cellulose (lot: 04227BE-296 from Sigma Aldrich, St Quentin Fallavier, France) with grain size ~20 μm at different percentages.

The mixed powders were pressed to obtain pellets with 13 mm diameter using a hydraulic press (10 tons during 3 minutes). Pellets with different percentages of certified milk were used as standards for establishing the calibration curve for LIBS measurements. The same procedure of pellet preparation was used also for the commercial milk powders.

Analysis with ICP-AES

The commercial milk powders contain a wide range of elements including, Na, Mg, P, K and Ca, with concentrations larger than tens of mg/kg. The optimized digestion procedure allowed quantitative recoveries for Mg, K and Ca (Table III.2). Overestimation was observed for Na and P, a vessel contamination was suspected in this case. The following study was therefore focused on the three elements Mg, K and Ca. According to the developed digestion protocol, their concentrations in the infant formulae and the adult milk powder were determined as presented in Table III

Setup and protocol for LIBS measurements

A typical LIBS experimental setup was used in the present investigation as sketched in Fig III .2. The ablation source was a Q-switched Nd:YAG laser (Quantel Brillant) operating at 355 nm with repetition rate of 10 Hz, pulse duration of 5 ns, and pulse energy of 50 mJ. The laser beam (about 8 mm diameter) was focused on the sample surface using a quartz lens of 5 cm focal length to generate a plasma. The sample pellet was moved during the spectral accumulation in such way that each laser shot had a fresh sample surface. The beam size on the sample surface was estimated to be 500 μm by measuring the crater on the sample surface.

The fluence on the sample surface was thus 25.5 J/cm 2 corresponding to a maximum irradiance of 5.1 GW/cm 2 without considering the absorption by the plasma. The emission from the plasma was collimated by a pair of parabolic mirrors which focused the emission into the entrance of an optical fiber of 50 μm core diameter. The fiber coupled the plasma emission into an echelle spectrometer (Andor Technology, Mechelle) equipped with an ICCD (Andor Technology, iStar). The detection system offered a spectral range between 240 and 820 nm and a resolution power of /∆ = 5000. The spectrum was recorded by accumulating 60 laser shots. And for each sample, 10 spectra were measured to evaluate the standard deviation. During the experiment, the lens-to-sample distance was controlled with the use of a laser pointer and a CCD camera. In order to have a plasma in the LTE condition and at the same time a high signal-to-noise ratio, the delay of the detection window was optimized for from 1000 to 4000 ns after the impact of the laser pulse. This point will be discussed in details later in this chapter.

III.3 Experimental results and discussions

III.3.1 Calibration curves for ICP-AES and LIBS measurements

As an example we show in Fig III .3, the calibration curves with the Ca II 317.9 nm line for ICP-AES and LIBS measurements established using the secondary reference samples that we prepared. The calibration curve for ICP-AES obtained with digested samples showed an excellent linearity with a coefficient of determination R 2 of 0.9996. Similar results were obtained for other elements, R 2 0.9995 for Mg and 0.996 for K. The calibration curve for LIBS exhibits a linearity but with a smaller coefficient of determination of R 2 0.98 as shown in Fig III .3b. The degradation of the coefficient of determination can be related to the inhomogeneity of the prepared pellets. It could also be attributed to the fluctuations of the properties of the plasma in terms of the electron density, temperature and the stoichiometry.

These behaviors indicate that the material-dependent interaction between laser and sample (the matrix effect) strongly affected the physical-chemical properties of the plasma and subsequently the analytical signal. In Fig III .3b, the points measured from the commercial milk samples are also plotted. We will come back later for detailed comments of these points.

III.3.2 Direct observations of the matrix effect for laser ablation

In order to confirm our hypothesis of matrix effect to explain the systematic deviations of the concentrations measured for commercial milks with respect to the nominal ones, we have measured the physical parameters of the plasma, electron density and temperature, for all the analyzed samples. The electron density was determined using the Stark broadening of the H α line at 656 nm, and the temperature was extracted with the Saha-Boltzmann plot using a set of calcium lines. The use of the H α line for electron density determination has been extensively reported because it is well isolated and broadened by strong linear Stark effect [START_REF] Griem | Spectral line broadening by plasmas[END_REF][START_REF] El Sherbini | Measurement of electron density utilizing the H alpha-line from laser produced plasma in air[END_REF].

The self-absorption is assumed to be absent in our measurements for this line. For temperature determination, the used lines have to be not affected by self-absorption. We used in this work, growth curves to check the linearity of the intensities of the chosen calcium lines in the spectra obtained with the laboratory-prepared reference samples as functions of the calcium concentration. Fig III. [START_REF] Ready | Effects of High-Power Laser Radiation[END_REF] shows the growth curves of several calcium lines used for the temperature calculation. Here, the intensity corresponds to the surface under an emission line.

We can see that all the chosen calcium lines have a linear response to the concentration within the range from 0 to 14 mg/g. Such range overlaps the calcium concentrations in all the analyzed samples. We can therefore use these lines for temperature calculation without influence of self-absorption. Finally for the pure cellulose sample, the vibrational temperature extracted from the emission band heads of CN molecule was used for the temperature of the plasma. average and a corresponding standard deviation of 8600±160 K. Electron density for these samples shows a regular increase (from ~ 2.2×10 17 to ~ 3.9×10 17 cm -3 ) as a function of the concentration with an average and a standard deviation of (3.1±0.5)×10 17 cm -3 . For the commercial milks, except the "Auchan" sample, a similar temperature is observed, 8000±230 K. This temperature is significantly lower than those of the reference samples. Concerning the electron density, a similar value of (1.8±0.3)×10 17 cm -3 is observed for all commercial milks except the "Auchan" one. Again the electron density observed is significantly lower than those of the reference samples. The "Auchan" sample is thus an exception among the commercial milks. The temperature and the electron density measured for it, 8670 K and The matrix effect was further directly observed from the images of the craters on the different samples as shown in Fig III .7. We observe similar craters at the surface after ablation between reference samples (certified one and cellulose) and the "Auchan" sample. However the surface of the "Guigoz" sample, one of the commercial milks for baby, exhibits a totally different aspect after ablation. The total destruction of the surface with the disappearance of distinguished individual craters indicates a surface mechanical resistance against laser ablation much weaker than that of the reference samples. Such weaker mechanical resistance can lead to a resulted plasma with lower electron density and temperature as observed in our experiments.

Fig III.7. Photos of pellets after ablation with craters for different samples.

Consequently, the matrix effect has to be considered in order to achieve accurate and precise analysis. In practice, matrix-matched reference samples need to be prepared. Our experiments show however the difficulty to have such reference samples especially for organic materials. Even for a same type of matrix, milk powders for instance the matrix effect

Cellulose Certified reference

Auchan Guiggoz

Cellulose Certified reference

Auchan Guiggoz is obvious, leading to the impossibility to apply the calibration curves. The origin of the matrix effect can have multiple physical and chemical reasons. For organic materials, it can be in particular related to the mineral elements present in small concentrations in the matrix, as we observed in our experiments. Optical absorption coefficient of an organic material can be significantly increased with the presence of mineral elements. These elements can be easily ionized by laser radiation leading to free electrons available for further absorption of laser radiation. The correction of the matrix effect can be very complex. However, as we show here, it can be measured with the electron density and the temperature of the plasma, its effect may therefore be taken into account in the calculation of the concentrations. This is precisely the idea of the CF-LIBS procedure where the plasma parameters, in particular the temperature, are used for the calculation of the concentrations.

III.3.3 Quantitative measurement using controlled CF-LIBS with an internal reference element

Deduction of the concentrations of Mg and K

As mentioned in §I.4.2, the concentrations of the elements can be retrieved using an internal reference element with known number density. In our experiments, due to its relative high concentration in all the samples and a large number of detected lines, calcium was chosen as the internal reference element. In addition, proper choice of lines for CF-LIBS procedure is very important. These lines must be well isolated without interference with other emissions.

They need to be detected with good signal-to-noise and without significant self-absorption.

And finally their spectroscopic data are available. For Ca, several lines were chosen, including two Ca I lines at 428.3 and 518.9 nm and three ionic lines Ca II 315.8, 317.9 and 373.6 nm lines. For Mg and K, 517.8 nm and 404.7 nm lines was used respectively. All these lines were checked to be not self-absorbed by the linearity of the growth curves measured with the reference samples. These lines, together with the electron density and temperature In our experiments, a detection window from 1000 to 4000 ns after the impact of the laser pulse was chosen for all LIBS measurements as mentioned above. Such detection window was chosen after the verification procedure specified in our previous works [START_REF] Lei | Time-resolved characterization of laser-induced plasma from fresh potatoes[END_REF]. The certified We can see that the temperature retrieved from Boltzmann plots of ionic lines and that retrieved from the Saha-Boltzmann plots merged together after 750 ns. In addition, the molecular temperature retrieved from the vibration temperature of CN molecules (violet bands) exhibits the same tendency after the same delay. Before this delay, the ionic and molecular temperatures cannot be determined with enough precision in our experiments. However, our previous work [START_REF] Lei | Time-resolved characterization of laser-induced plasma from fresh potatoes[END_REF] clearly showed the difference among these temperatures in shorter delays. We can thus according our observations form Fig III.9, consider a LTE state of the plasma for delays beyond 750 ns. However the plasma continues to evolve with the LTE temperature which decreases in time. It was thus necessary to choose a time interval beyond the delay for LTE, where the plasma temperature can be considered as quasi stationary. The interval from 1000 to 4000 ns was therefore chosen also to have enough good signal-to-noise ratios for spectral line detections. We can easily remark that unfortunately in this interval the temperature varied from ~ 8500 to ~ 6500 K. The integration of the LIBS signal over this interval only provides an approximation of a stationary plasma in LTE, and introduces inaccuracy in the determination of elemental concentrations with CF-LIBS as we observed.

Future improvements of CF-LIBS for organic materials

Firstly, more accumulations of the laser shots at different positions of the sample surface can be conducted to average the inhomogeneity of the sample. Beside a better homogeneity of the sample, the optimization of the detection system seems us crucial to improve the performance of the CF-LIBS procedure for organic materials. According to the above discussions, the approximation of a stationary LTE plasma is more difficult to realize when the LIBS signal is integrated over a long time interval. In addition, the search for a time interval where the plasma is in LTE with a temperature decreasing enough slowly to be considered as constant leads often to a too long delay and too narrow detection window for an optimized signal-to-noise ratio to be detected. A short integration interval is in principal favorable for a more accurate measurement with the CF-LIBS procedure. However a short integration time automatically degrades the signal-to-noise of the LIBS signal. The attempt to have a stationary LTE plasma restricts necessarily the effective detection of plasma emission in a limited time interval. Such restriction intrinsically reduces the sensitivity of the CF-LIBS and makes its application more difficult and even non adequate for trace elements. It is why up to now the most successful applications of the CF-LIBS procedure concern the detection of major elements in metallic alloys [START_REF] Tognoni | Calibration-Free Laser-Induced Breakdown Spectroscopy: State of the art[END_REF].

In order to improve the performance of the CF-LIBS for the analysis of mineral elements in organic materials, it is thus necessary to increase the sensitivity of the detection system. In our experiment, an echelle spectrometer was used. It offered a larger spectral range with high resolution. This type of spectrometer generally suffers from a mediocre detection sensitivity due to a small entrance port of tens μm aperture. The large spectral range of an echelle spectrometer is interesting for plasma diagnostics since it can detect simultaneously many lines emitted from various elements, which facilitates the simultaneous determinations of the electron density and the temperatures. However its use is not suitable for a sensitive detection.

The ideal detection system for the implementation of the CF-LIBS may consist of two parallel and simultaneous detection channels. A first channel, said diagnostics channel with a large spectral range, provides the simultaneous detections of the H α line for electron density measurement and a large number of lines of a major element, calcium for example for organic materials, for the precise determination of the temperature. A second channel, said measurement channel with a large throughput, allows the specific line emissions from desired trace elements to be detected with high sensitivity. Our experiment shows that the diagnostics channel can be a combination of an echelle spectrometer and an ICCD, which provides satisfactory plasma diagnostics. For the measurement channel, a Czerny-Turner spectrometer is more suitable for a higher detection sensitivity with its high throughput. The use of a spectrometer with a narrow spectral range has also the advantage to optimize the detection for weak lines without saturation of stronger lines. It is especially important for the detection of certain alkali metals, sodium for example. There is such big difference of the intensities between the most intense lines and other less intense ones for sodium, when the detection is set to not saturate the most intense lines, it becomes generally no sensitive enough for weaker lines.

III.4 Conclusion of the chapter

In the work presented in this chapter, we have measured the concentrations of mineral elements, in particular calcium, magnesium and potassium, in milk powders with ICP-AES and LIBS. The comparison of the results from these different techniques have allowed us to have an assessment and a validation of the CF-LIBS procedure applied to organic samples, such as milk powder. Our results showed obvious matrix effects each time laser ablation was involved for sampling. Compared to metallic alloys, organic materials suffer much more from the matrix effect as their optical absorption property depends sensitively on their concentrations in mineral elements. Firstly, the laser sampled interaction is more complicated compared to metallic samples which can bring different ablation mechanism and efficiency as well as vaporization rates from element to elements. Secondly, the plasma evolution should be more complicated due to the chemical reaction with the surrounding gas. We have observed in our experiments clear correlations between electron density/temperature of the plasma and the concentrations of mineral elements (Ca, K for example) in the sample. Such matrix effect made the established calibration curves difficult to be used for precise quantitative analysis unless matrix-matched reference samples are available, a difficult task especially for organic materials.

Our results show furthermore that the plasma diagnostics provides a quantitative indication of the matrix effect in terms of the variations in electron density and temperature of the plasma. It is therefore expected that the CF-LIBS procedure contributes to the reduction of the matrix effect by taking into account the plasma parameters in the calculation of the concentrations. Such efficient compensation of the matrix effect has been demonstrated in our experiments for the case of the determinations of the concentrations of magnesium and potassium with respect to that of calcium in commercial milk powders. The quantitative analytical results obtained from the CF-LIBS procedure remain however significantly less accurate and less precise than those obtained with ICP-AES. We point out that this situation is partially due to the intrinsic requirement of the CF-LIBS to work with a quasi stationary LTE plasma. Such requirement restricts the effective detection within a limited time interval often much smaller than the total radiative lifetime of the plasma and situated at a rather long delay, where the emissions from elements are significantly decreased. It is why the limit of quantification of the CF-LIBS is often much higher than the standard LIBS.

It is certainly possible to improve the experimental setup dedicated to an implementation of CF-LIBS for organic materials. The ideal setup may consist of two parallel and simultaneous detection channels. A first one, said diagnostic channel, offering a large spectral range and not necessarily very sensitive, determines the electron density from H α line for example, and the temperature from lines of a major element, calcium for example. The second one, said measurement channel, corresponding to a narrow spectral band but high sensitive detection system, is optimized for the sensitive detection of one or a few trace elements to be analyzed. Such optimized configuration should be able to provide more accurate, more precise measurements with limits of detection comparable to those of the standard LIBS technique.

Chapter IV Influence of ablation photon energy on the distribution of molecular species C 2 and CN in laser-induced plasma from a polymer under atmospheric pressure

In the last two chapters, quantitative analysis of inorganic trace elements in organic sample using LIBS has been considered. It has been demonstrated that the CF-LIBS procedure can be applied for elemental concentration analysis in organic samples, with the optimization of experimental protocol and spectroscopic analysis. The comparison of the results from different techniques, LIBS, CF-LIBS and ICP-AES, have allowed us to have an assessment and a validation of the CF-LIBS procedure applied to organic samples, such as milk powder.

However, the analysis concerned inorganic elements, like Mg, Ca, K and so on. In some situations, the analysis of the matrix of the organic material becomes more important. This is the case for example for discrimination of plastic waste for their classification before recycling. Such matrix is composed in the most of the case by the 4 organic elements C, H, O, and N.

In this chapter, we will focus on a different approach of analysis of organic materials, which consists in the study of the correlation between the molecular structure of a polymeric material and the time-and space-resolved emission from the characteristic molecules or radials, such as C 2 or CN, in the laser-induced plasma. We will demonstrate especially that the existence of such correlation allows potential applications for detection and identification of organic compounds. The techniques of time-and space-resolved emission spectroscopy and fast spectroscopic imaging are used in this study. The advantage of such techniques for the detection of specific feature of molecular emission in the plasma will be therefore emphasized.

IV.1 Motivation of this work

LIBS has been attracting more and more interests for a large variety of applications for detection and analysis of organic materials including biological samples (tissues [START_REF] Santos | Evaluation of Femtosecond Laser-Induced Breakdown Spectroscopy for Analysis of Animal Tissues[END_REF], teeth [START_REF] Singh | Potential of laser-induced breakdown spectroscopy for the rapid identification of carious teeth[END_REF], bones [START_REF] Kasem | Influence of biological degradation and environmental effects on the interpretation of archeological bone samples with laser-induced breakdown spectroscopy[END_REF] , and bacteria [START_REF] Baudelet | Discrimination of microbiological samples using femtosecond laser-induced breakdown spectroscopy[END_REF]), polymers [START_REF] Sattmann | Laser-induced breakdown spectroscopy for polymer identification[END_REF][START_REF] Boueri | Identification of Polymer Materials Using Laser-Induced Breakdown Spectroscopy Combined with Artificial Neural Networks[END_REF][START_REF] Lasheras | Identification of polymers by libs using methods of correlation and normalized coordinates[END_REF], landmines [START_REF] Harmon | LIBS for landmine detection and discrimination[END_REF], explosives [START_REF] Gottfried | Laser-induced breakdown spectroscopy for detection of explosives residues: a review of recent advances, challenges, and future prospects[END_REF], pharmaceutical products [START_REF] St-Onge | Quantitative analysis of pharmaceutical products by laser-induced breakdown spectroscopy[END_REF], and so on. However, as compared to traditional applications of LIBS for metallic alloys, its routine use for analysis of organic materials still remains a challenge. Such challenge mainly arises from the fact that compounds to be analyzed are all similar from the point of view of elemental composition. Four basic elements, C, H, O and N are omnipresent and provide the common basis of organic materials. An efficient strategy for discrimination and identification of organic materials is based on the determination of emission intensity ratios between spectral lines from organic elements [START_REF] Anzano | Classification of polymers by determining of C-1 : C-2 : CN : H : N : O ratios by laser-induced plasma spectroscopy (LIPS)[END_REF][START_REF] Tran | Determination of C : H : O : N ratios in solid organic compounds by laser-induced plasma spectroscopy[END_REF]. For example, the C/H ratio was found to be particularly important for discrimination [START_REF] Sattmann | Laser-induced breakdown spectroscopy for polymer identification[END_REF][START_REF] Anzano | Laser-induced plasma spectroscopy for plastic identification[END_REF]. In addition, it has been shown that a certain number of diatomic molecular fragments, such as C 2 and CN, also provide useful indications for identification of organic materials [START_REF] Lucena | New challenges and insights in the detection and spectral identification of organic explosives by laser induced breakdown spectroscopy[END_REF][START_REF] Baudelet | Spectral signature of native CN bonds for bacterium detection and identification using femtosecond laser-induced breakdown spectroscopy[END_REF]. As it has been pointed out in our previous works, due to the complex physical and chemical processes in the plasma and in particular the recombination with compounds from the background gas, molecular or radical species detected in the plasma can have different origins. Determination of the mechanisms leading to the formation of a specific molecular species is crucial for the establishment of the correlation between its observation in the plasma and the molecular structure of the ablated target [START_REF] Baudelet | Spectral signature of native CN bonds for bacterium detection and identification using femtosecond laser-induced breakdown spectroscopy[END_REF]. Such correlation is a determinant factor for identification of organic materials using LIBS. Time-resolved emission spectroscopy has been used to study the formation mechanisms of molecules C 2 and CN in the plasma [START_REF] Baudelet | Time-resolved ultraviolet laser-induced breakdown spectroscopy for organic material analysis[END_REF]. On the other hand, molecule formation in laser-induced plasma represents also an important issue for pulsed laser deposition (PLD) [START_REF] Kushwaha | C 2 and CN dynamics and pulsed laser deposition of CN x films[END_REF][START_REF] Abdelli-Messaci | CN emission spectroscopy study of carbon plasma in nitrogen environment[END_REF]. In the context of PLD of carbon nitride films CN x , emission spectroscopy has been used for the study of the spatiotemporal evolution of laser ablation plume and the formation of molecular species C 2 and CN [START_REF] Kushwaha | C 2 and CN dynamics and pulsed laser deposition of CN x films[END_REF][START_REF] Thareja | Interaction of ambient nitrogen gas and laser ablated carbon plume: Formation of CN[END_REF][START_REF] Acquaviva | High-resolution investigations of C 2 and CN optical emissions in laser-induced plasmas during graphite ablation[END_REF][START_REF] Kushwaha | Effect of ambient nitrogen pressure on the formation and spatio-temporal behaviour of C 2 and CN[END_REF][START_REF] Trusso | Pulsed laser ablation of SiC in a nitrogen atmosphere: formation of CN[END_REF]. Most of these works were conducted at a residual background pressure, in contrast with LIBS measurements usually carried out in the atmosphere condition.

In this Chapter, the influence of ablation photon energy on spatial profile of molecular species, C 2 and CN, in laser-induced plasma from a PVC target in the atmospheric air is studied. Two wavelengths in near UV range of 266 nm and 355 nm were therefore used for ablation, representing in the first case a photon energy of 4.66 eV exceeding the bond energies of the chemical bonds in the target and in the second case a photon energy of 3.49

eV smaller than or in the same range of the involved bond energies. Spatial profiles of the molecular species and their evolution will be presented for ablation with the two wavelengths.

Temperature profile in the plasma will be further presented in order to correlate with emission profiles of the molecules. Observed different behaviors for ablation with the two wavelengths will be emphasized and studied in terms of different molecule formation mechanisms.

Photothermal or photochemical ablation models are used to understand the different molecule formation channels relevant to interpret the observed phenomena. Finally observation of morphology of ablation craters left on the target surface confirms the specific ablation regime for each used laser wavelength.

IV.2 Theoretical backgrounds for laser ablation of polymer and molecule formation in plasma

Laser ablation of polymer material represents a complicated process, result of complex interaction between laser radiation and organic molecule chains. Discussion on the involved mechanisms remains still controversial today three decades after the first reports of the phenomenon in 1982 and despite the spectacular development of the applications since then [START_REF] Srinivasan | Self-Developing Photoetching of Poly(Ethylene-Terephthalate) Films by Far Ultraviolet Excimer Laser-Radiation[END_REF][START_REF] Kawamura | Effective Deep Ultraviolet Photoetching of PolyMethyl Methacrylate by an Excimer Laser[END_REF][START_REF] Urech | Photoablation of Polymer Materials, Photochemistry and Photophysics of Polymer Materials[END_REF]. The standard description is based on the three simplified models of photothermal, photochemical or photophysical processes [START_REF] Bauerle | Laser processing and chemistry[END_REF]. In photothermal ablation, electronic excitation due to photon absorption is thermalized on a picosecond timescale leading to thermally activated bond breaking. On the other hand, in photochemical process, the electronic excitation results in direct bond breaking. When both thermal and nonthermal processes play a role, photophysical process is more suitable to describe the phenomenon. In However, as a result of the strong continuum emission, the molecular emission was invisible at short delay (before 500 ns in this work) with this kind of experimental setup. Therefore, a second experimental setup, dual wavelength fast spectroscopic imaging was used to analyze the plasma in the early expansion.

was sequentially delayed in a series of time-resolved detections of the plasma emission. In this case, the width of the detection window was adjusted to get a suitable SNR as the time delay increased. In order to get a suitable SNR for C 2 and CN molecular lines and related atomic lines, three delays at 500, 2000 and 5000 ns were chosen for ablation with 266 nm pulses. For ablation with 355 nm pulses, the chosen detection windows were with delays of 1500, 3000 and 6000 ns. The shortest delay investigated was fixed by the fact that the continuum emission decreased and the line emissions from molecules grew enough allowing correct spectroscopic measurements. At a given position of the fiber and a delay of detection, each spectrum was accumulated for 60 laser pulses. During spectrum recording, the target was moved using a stepper motor in order for each laser shot to have a fresh target surface.

The target used was a piece of PVC commercially available as construction material. It presented a well polished surface and a gray color due to charges mixed into pure PVC resin for the manufacture of the material.

Setup for dual wavelength fast spectroscopic imaging

The setup is schematically shown in Fig IV .3. Plasmas were produced in the atmospheric air using quadrupled (266 nm) Nd:YAG laser with a pulse duration of 5 ns at a repetition rate of 10 Hz. Laser pulses, were perpendicularly focused on a sample by a quartz lens of focal length of 50 mm. The sample was mounted on motorized stages providing its precise 3D positioning. A beam shutter was used to control the delivery of laser pulse on the sample. An imaging system, composed by two lenses of focus length f 1 =7.5 cm and f 2 =20 cm respectively was installed along an axis perpendicular to the laser beam. It provided a magnification of about 2.7 of the plasma. The optical axis, parallel to the sample surface, was set to be very close to it. The resulted image of the plasma was recorded using an ICCD camera (iStar, Andor technology) positioned on the image plane of the two-lens system. The final spatial resolution was 5 μm per pixel determined using a ruler at the place of the plasma. A band-pass filter was mounted between the two lenses where the captured light from the plasma was collimated. The ICCD camera was synchronized to Q-switch trigger of the laser, which allowed detection with a precise temporal resolution of about 5 ns with respect to the impact of the laser pulse on the sample. In order to avoid perturbation by direct breakdown of the air induced by laser, the laser beam was focused under the sample surface at a depth of about 550 μm.

This distance was kept constant during experiment using a trigonometric surface positioning system. Such system was based on combination of a laser pointer focused obliquely on the sample surface and a monitoring camera used to image the laser spot on the sample surface.

Fig IV.2. Principal of trigonometric surface positioning system

The laser energy was also kept constant and regularly measured. Images were recorded with different delays after the impact of laser pulse on the sample. To increase signal-to-noise ratio of the images, especially for long delays, each image was accumulated with 100 laser shots on 10 different sites on the sample surface (10 shots per carter). The resulting craters were analyzed with a confocal laser scanning microscope and showed a diameter and a depth of about 100 μm with a near Gaussian depth profile. A transparent pure PVC sample was used to investigate the formation of CN and C 2 molecules.

Fig IV.3. Schematic experimental setup for spectroscopic imaging

Compared to the classical spectroscopic imaging technique for laser-induced plasma, we used a differential spectroscopic imaging with a pair of band pass filters. The center of one of these filters is centered at an emission line of a species, elemental or molecular, to be studied in the plasma ( on ), while that of another one is shifted to a neighboring wavelength ( off )

where emission from the specie is negligible. Wavelength shift between the two filters should remain however small enough to avoid any change in continuum emission and background passing through them. For typical laser-induced plasma, we observed for spectrum recorded at a short delay (~ 10 ns), no significant difference on continuum emission for a wavelength shift in a range of 30 nm. Besides, experimental conditions (laser energy, surface position…) must be stable and reproducible enough during the period where the double images are recorded to guarantee the representability of the image taken with off filter for the background (including the continuum and backgrounds of different natures) and of the image taken with the on filter. In addition to above mentioned conditions, transmission curves of the filters were normalized with a calibrated white light source in such way the subtraction between the two images can be correctly processed. The resulting image corresponds to that of the plasma taken with emission from the species under study. With respect to the classical We can see a groove with clear boundaries for 266 nm ablation, characteristic of photochemical cleavage of material. While for 355 nm ablation, the groove exhibits irregular boundaries, which is characteristic of thermal effect in mass removing.

IV.5 Validation of molecule distribution at short delays with fast spectroscopic imaging

In order to complete the results obtained with time-and space-resolved emission spectroscopy on the evolution of the molecular species at long time delays, the evolution of the plasma at short delays has been studied using dual wavelength differential spectroscopic imaging technique as described above.

In this study, evolutions of 4 different species were investigated: carbon and nitrogen as elemental species, CN and C 2 as molecular species. The pairs of filters chosen for these species are listed in Table IV.1. Series of band pass filters with bandwidth in the range of 10 nm commonly available in the market were chosen for these species. Central wavelengths of the filters were carefully chosen according to LIBS spectrum of the samples in order to avoid any interference with other species. Notice that UV filters for carbon were more difficult to be purchased and that it is why its bandwidth was larger than other filters.

Species

IV.6 Spatiotemporal profiles of a femtosecond laser-induced plasma: investigation with C2 and CN molecules

The original idea of using femtosecond laser for this investigation comes from its different way to ablate material and produce plasma with significantly different properties compared to nanosecond laser. As mentioned above, the significant different spatial distribution of CN and C 2 in the plasma can be due to the different ablation regimes under two laser wavelengths.

Therefore, ablation with femtosecond laser was supposed to have a different influence on the diatomic molecular formation mechanism. In addition, works in our group in Lyon 1 university have demonstrated that fs-LIBS provides a sensitive detection of a large number of trace elements contained in a biological medium [START_REF] Baudelet | Discrimination of microbiological samples using femtosecond laser-induced breakdown spectroscopy[END_REF]. On the other hand, the association of significant and relevant molecular spectral information with atomic spectral information makes femtosecond LIBS a powerful analytical tool to address organic or biological samples [START_REF] Baudelet | Spectral signature of native CN bonds for bacterium detection and identification using femtosecond laser-induced breakdown spectroscopy[END_REF][START_REF] Baudelet | Femtosecond time-resolved laser-induced breakdown spectroscopy for detection and identification of bacteria: A comparison to the nanosecond regime[END_REF]. I mention here this work was conducted in Shanghai and just a preliminary result was obtained.

The used experimental setup was similar to that described in §IV. Since rotational level population densities are easier than vibrational ones to reach the equilibrium with the colliding particles, due to smaller energy gap between rotational levels, the rotational temperature can be assumed to be identical to the gas kinetic temperature. Unfortunately, we don't know how to explain our experimental results using femtosecond.

It seems difficult to correlate the temperature distribution with the CN and C2 formation mechanism as for nanosecond laser. This work was just started in Shanghai, where we need more efforts to obtain better results.

IV.7 Conclusion of the chapter

General conclusion and outlook

This thesis work is the continuation of the research activity that has been initiated by the research team in Lyon 1 University since 2005 on LIBS. There were accumulated efforts of the PhD thesis works of Matthieu Baudelet and Myriam Boueri [START_REF] Baudelet | Propriétés physico-chimique du plasma induit par laser en régime nanoseconde et femtoseconde: Application analytique aux bactéries et aux produits agroalimentaires[END_REF][START_REF] Boueri | Laser-induced plasma on polymeric materials and applications for discrimination and identification of plastics[END_REF]. The first one was devoted to the application of LIBS to the detection and the identification of bacteria. And the second one interested in the discrimination of plastics. Although the capacity of qualitative analysis of organic materials with LIBS has been demonstrated with these two theses, the quantitative analysis of trace metallic elements contained in such materials was not treated in the former works of the team in Lyon. The purpose of my work is precisely to explore the quantitative analysis capacity of LIBS for organic materials.

With the given objective, an analysis of the state of the art at the moment when my thesis started clearly showed that the major difficulty for the extension of quantitative analysis with LIBS to organic materials was certainly the matrix effect. This is because of the molecular nature of the matrix, which leads to more complex ablation mechanism. This is also due to large inhomogeneity and heterogeneity that can be found in many organic materials such as plant stuff or biological tissues. A pronounced matrix effect makes the establishment of calibration curve very difficult. And certified reference samples for organic materials are not commercially available. Our strategy is therefore to develop the calibration free LIBS procedure for quantitative analysis of organic materials. With respect to the literature, such approach was totally new at the beginning of my thesis because of the lack of the detailed description of the plasma induced on an organic material.

As a consequence in my thesis the first step of the implementation of CF-LIBS procedure for quantitative analysis of organic materials consisted of the study of the plasma induced on the skin of a fresh potato with time-resolved emission spectroscopy. Fresh potato was chosen for our study because of the easiness to obtain a flat sample surface for ablation and its representability for a large range of important organic materials such as plant stuff and biological samples. The purpose of my work was therefore to optimize experimental setup and procedure for taking LIBS spectrum of the skin of a fresh potato. Classical procedures of plasma diagnostics using plasma emission spectrum allowed us to extract the most important parameters of the plasma, the electron density and the temperature, and to study their evolution. More precisely, we showed that the electron density in the ablation plasma generated on the skin of a potato allows the LTE to be realized according to the McWhirter criterion. However a high enough electronic density does not automatically correspond to the LTE since this criterion represents only a necessary condition. The temperature measurement showed that a time interval is required for the different temperatures (ionic, excitation and molecular temperatures) to converge to an equivalent value. It is therefore better to use a high ablation energy (20 mJ in our experiment corresponding to 250 J/cm 2 ) to ensure a high enough electron density over a long period of time for the establishment of the LTE within the plasma. In our experimental conditions, the electron density in the ablation plasma generated on the skin of a potato fulfils the McWhirter criterion from the initiation of the plasma up to a delay of about 2 μs. However temperatures corresponding to different species in the plasma are observed in different values at the beginning of the plasma expansion and merge into a unique value after a delay of 700 ns. A LTE regime was therefore observed for a interval from 700 ns to 2 μs after the impact of the laser pulse on the sample. The emission spectrum can thus be integrated in a typical time window from 0.7 to 1.2 μs in order to increase the sensitivity of the detection. Boltzmann and Saha-Boltzmann plots were then constructed for oligo-elements (Mg, Ca, Mn, and Fe) as well as toxic elements (Al and Ti) detected in the sample. Such plots lead to the determination of the relative concentrations of these elements in the sample with respect to calcium which is chosen as reference element.

The CF-LIBS procedure that we have implemented for quantitative analysis of organic materials needs however a validation with an established quantitative analytical technique. It is why in the second step of my thesis work, comparative measurements have been performed

between LIBS and ICP-AES, a standard analytical technique frequently used in analytical chemistry. Milk powder, especially those for child, was chosen for this study, because it can be easily prepared in pellet for LIBS measurement as well as in solution using a wet digestion procedure for ICP-AES measurement. It is therefore an organic sample which can be easily analyzed in parallel using two independent techniques. The concentrations of mineral elements, in particular calcium, magnesium and potassium, were measured. Our results showed obvious matrix effects each time laser ablation was involved for sampling. Compared to metallic alloys, organic materials suffer much more from the matrix effect as their optical absorption property depends sensitively on their concentrations in mineral elements. We have observed in our experiments clear correlations between electron density and temperature of the plasma and the concentrations of mineral elements (Ca and K for example) in the sample.

Such matrix effect made the established calibration curves difficult to be used for precise quantitative analysis. Our results show furthermore that the plasma diagnostics provides a quantitative indication of the matrix effect in terms of the variations in electron density and temperature of the plasma. The CF-LIBS procedure can thus be used to reduce the matrix effect by taking into account the plasma parameters in the calculation of the concentrations.

Such efficient compensation of the matrix effect has been demonstrated in our experiments for the case of the determinations of the concentrations of magnesium and potassium with respect to that of calcium in commercial milk powders. The quantitative analytical results obtained with CF-LIBS remain however significantly less accurate and less precise than those obtained with ICP-AES. This situation is partially due to the intrinsic requirement of the CF-LIBS to work with a quasi-stationary LTE plasma. Such requirement restricts the effective detection of plasma emission spectrum within a limited time interval often much shorter than the total radiative lifetime of the plasma and situated at a rather long delay, where the emissions from the elements are significantly decreased. It is why the limit of detection of CF-LIBS is often much higher than the standard LIBS.

The last part of my work in Lyon was devoted to the analysis of the matrix of organic materials which is essentially composed by the 4 principal organic elements, H, C, O, and N.

During the decomposition of an organic material by laser ablation, these elements can be found in the form of molecular fragments, or recombine into molecular species. The study of the mechanisms of formation of molecular fragments in plasma can therefore provide information of the molecular structure of the sample. Molecules C 2 and CN in laser-induced plasma from a PVC target have been observed for ablation with 266 nm and 355 nm laser radiations. The originality of this study with respect to our former works consists in the use of time-and space-resolved emission spectroscopy to monitoring the evolution of the molecules.

Influence of ablation photon energy on molecule formation in the plasma is thus studied. Our Finally as we can see through this thesis document, the application of LIBS to qualitative and quantitative analysis of organic materials remains still challenging. However the huge potential presented by such development attracts much attention and encourages continuous efforts in this field of research. The results obtained in this PhD thesis work contribute to a better understanding of the plasma induced on these materials and makes progress, we hope, in the direction of a successful use of LIBS for qualitative as well as quantitative analysis of organic materials.

For the future, continuous efforts need still to be made to improve the performance of LIBS for analysis of organic materials for quantitative trace element analysis as well as for qualitative analysis for identification and classification of organic matrix. The results obtained in the framework of my thesis allow us to consider some perspectives. The improvements of the accuracy and the limit of detection seem us to be the most important factors for routine use of LIBS for analysis of organic materials. From the experimental point of view, it is possible to improve the performance of CF-LIBS using a setup, including two parallel and simultaneous detection channels. A first one, said diagnostic channel, offering a large spectral range and not necessarily very sensitive, determines the electron density from H α line for example, and the temperature from a set of lines from a major element, calcium for example.

The second one, said measurement channel, corresponding to a narrow spectral band but highly sensitive detection system, is optimized for the sensitive detection of one or a few trace elements to be analyzed. On the other hand, spectrum simulation can be helpful for take into account the transient nature and the inhomogeneity of the plasma. For example, the Abel inversion can be used for extracting the emissivity of the plasma from the detected spectra, which is integrated from inner to outer part of the plasma. In addition, spectrum simulation can be conducted with the consideration of optical thickness and inhomogeneity of the plasma, and overlapping between lines from different transitions. Finally, the electron density and the temperature, as two of the computational parameters, could be retrieved by iterative comparisons between synthetic and measured spectra [START_REF] Hermann | Système et procédé d'analyse quantitative de la composition élémentaire de la matière par spectroscopie du plasma induit par laser (LIBS)[END_REF].

Concerning identification of organic materials using molecular emission, different kinds of ambient gases with controlled pressures can be used in the experiments to control the reactions between the evaporated species and those from the ambient gas. In addition, the time-of-flight mass spectrometry can be used for the determination of the clusters formed in the plasma with different sizes. Cluster dissociation mechanism in the plasma can be investigated. More generally, the combination of optical and mass spectroscopies can be helpful to study the evolution of the plasma induced from an organic target, and especially the transformation from a plasma into a molecular then particular gas as the plasma recombines and recondenses.

Fig I. 1 . 1 . 2

 112 Fig I.1. Schematic presentation of the thermal ablation processes

Fig I. 2 .

 2 Fig I.2. Energy-level diagram for the ground and an excited state of a diatomic molecule as a function the internuclear distance r. Optical absorption and emission as well as relaxations of vibrational energy are indicated by arrows. Reproduced from ref. [84]. Copyright © 2010 Oxford University Press.

Fig I. 3 .

 3 Fig I.3. Potential energy curves for the ground and excited states of a diatomic molecule as a function the internuclear distance. Different configurations of optical dissociation are shown and discussed in the text. Reproduced from ref. [74]. Copyright © 2000 Springer-Verlag.

Fig I. 4 .

 4 Fig I.4. Energy level diagram illustrating various pathways for photochemical bond-breaking. Reproduced from Ref [77]. See the text for details.

Fig I. 5

 5 Fig I.5 Typical temporal evolution of the plasma emission and optimal gating of the detector for atoms and ions.

Fig I. 7 .

 7 Fig I.7. Time-integrated photo of the plasma initiated on an aluminum target.

Fig I. 8 .Fig I. 9 .

 89 Fig I.8. Direct imaging system for spatially resolved diagnostics of plasma

Fig I. 10

 10 Fig I.10 Spectrometer slit imaging setup

Fig I. 11 .

 11 Fig I.11. Set-up for two dimension space-resolved emission spectroscopy with the detection using an optical fiber for point by point scanning of the image of a plasma.

  singly-charged ion), m e and h represent the electron mass and Plank constant respectively, E ion and ΔE ion denote the ionization energy and the correction of this quantity due to the interaction in plasma. Therefore the number density n z for the ionized species (z ≥ 1, only z=1 is considered in this thesis because in the temperature range of a LIBS plasma the high level ionizations are negligible) can be deduced from n z-1 from equation (I.26). Consequently the integrated intensity of lines for all ionization states can be obtained in a similar way to equation (I.22)[START_REF] Yalcin | Influence of ambient conditions on the laser air spark[END_REF]:. (I.27)where the superscript "*" refers to the correction for the ionized species with respect to the Boltzmann plot. Equation (I.27) allows plotting both neutrals and single ionized species on a same graph, by taking into account the following corrections of the ordinates:

  Fig I.13 is an example of Saha-Boltzmann plot for temperature determination for a plasma induced from the skin of a potato at 1380 ns after the laser impact under the experimental condition described in Chapter II. Comparing Fig I.12 and Fig I.13, we can see that a larger range of excited state energy of 8 eV is obtained. An improvement of linear regression is also observed from the comparison between Fig I.12 and Fig I.13, which indicates that Saha-Boltzmann plot improves the accuracy of determined plasma temperature.

Fig I. 13 .

 13 Fig I.13. Saha-Boltzmann plot for temperature determination for plasma induced on potato skin using a set of atomic and ionic lines of Ca

  Fig I.14. Boltzmann plot applied to band head intensities of the violet band of CN radicals in the emission spectrum of a plasma induced from a target of PVC.

  the equilibrium position α e and γ e corrections to the rotational constant up to the second-order D e centrifugal constant at the equilibrium A split coupling constant ω e vibrational frequency of the harmonic oscillator χ e ω e , y e ω e and z e ω e first-, second-and third-order corrections of the enharmonic vibration

Fig I. 15 .

 15 Fig I.15. Synthetic spectrum calculated for CN violet system Δυ=0, with Trot=20 000 K, Tvib=9000 K and J=100

Fig I. 17 .

 17 Fig I.17. Calibration curve for Na I 330.3 nm built with prepared reference samples which consist of certified milk powders and cellulose

Fig II. 1

 1 shows the potato sample before and after preparation.

Fig II. 1 .

 1 Fig II.1. Photo of sample before and after the sample preparation (see the text for the details)

Fig II. 2 .

 2 Fig II.2. Schematic representation of the experimental setup.

Fig II. 3 .

 3 Fig II.3.Temporal evolution of optical emission of the plasma induced on the skin of a potato for different detection delays of 100, 580, 1980, and 2980 ns.

/

  Fig II.4. Hydrogen Hα line used for electron density determination for 20 mJ ablation energy and at different detection delays of 100, 280, 580 and 980 ns. Experimental spectra for different delays were normalized (scatters) and fitted with the Voigt profile (lines).

Fig II. 5 .

 5 Fig II.5. Electron density in the plasma induced on the skin of a fresh potato for different ablation laser energies (5, 10 and 20 mJ) retrieved from the Stark width measurement of Hα line. Error bars were estimated by considering the accuracy of 10% of the reduced Stark width and the statistical fluctuation of 4 independent measurements.

Fig II. 5 ,

 5 Fig II.[START_REF] Ready | Effects of High-Power Laser Radiation[END_REF], we see that for the plasmas induced by all the three laser energies, the measured initial electron densities are larger than this value. That provides the necessary condition for the plasmas to reach the LTE. However we see that the electron density drops rather rapidly for the plasmas induced by 5 and 10 mJ laser pulses. These short plasma decay times may not

Fig II. 7 .

 7 Fig II.7. Time evolutions of the temperatures (extracted from Ca lines for SBP and BP, CN band heads for Vibrational) as functions of the delay after the laser impact on the potato skin.

  Fig II.8. Illustration for signal-to-noise ratio determination

Fig II. 9 .

 9 Fig II.9. Signal-to-noise ratios for major and trace (a), as well as ultra trace (b) elements in potato skin as a function of the detection delay.

  9. Saha-Boltzmann plots were performed for a number of elements including traces, Ca and Mg, as well as ultra traces such as Ti, Fe and Mn to extract the corresponding temperatures. For Al, no ionic line was detected. Boltzmann plot was thus used to extract the temperature with a set of four atomic lines. The Saha-Boltzmann plots and Boltzmann plots performed for Mg, Al, Ca, Ti, Mn and Fe are shown in Fig II.10. The resulted temperatures are presented in

7 ,

 7 the temperatures continue to change in such period, although with reduced rates of change. This can introduce bias in the concentrations extracted using the CF-LIBS procedure with averaged temperature. A detailed model should take into account the temperature change together with those of the SNRs in order to improve the accuracy of the extracted concentrations.

in Fig II. 10 ,

 10 Al, Mn, Ca, and Mg the averaged concentration in a typical potato are respectively 0.59, 1.43, 156, 208 mg/kg of dried matter. This comparison allows us to situate the range of the detection limits of the method presented in this thesis in the range from the ppm to hundreds of ppm.II.3.6 Discussion on the temperature calculation and the choice of the internal reference elementTemperature calculation with the Saha-Boltzmann plotThe temperature is a crucial parameter that, if the plasma is in LTE, determines the population distribution among the levels through the Boltzmann equation and the ionization equilibrium through the Saha equation. For simplicity, a Boltzmann two-line method was considered for the determination of temperature. Then the relative error of the determined temperature can be estimated to correlate with the uncertainty of the relative line intensity by the equation (I.24) .Taking, the difference between the upper energy level for two atoms for Ca as shown in Fig II.6, a 10% uncertainty of the relative line intensity results in 5% uncertainty of the calculated temperature. In order to improve the accuracy of the temperature calculation, efforts can be made either to improve the accuracy of the relative line intensity or to increase the difference between the upper energy levels.

Fig III. 1 .

 1 Fig III.1. Photos of commercial products of milk powders.

Fig III. 2 .

 2 Fig III.2. Schematic representation of the experimental setup.

Fig III. 3 .

 3 Fig III.3. Calibration curves with Ca II 317.9 nm line for (a) ICP-AES and (b) LIBS.

Fig III. 5 .

 5 Fig III.5. Growth curves of the calcium lines used for the temperature calculation.

3 .

 3 7×10 17 cm -3 are in the ranges of the values measured for reference samples. We can remark from Fig III.6 and Table III.2 that the electron density and the temperature of the plasma are directly correlated to the concentrations of mineral elements, Ca and K for instance, in milk samples. These observations can be now used to explain the results shown in Fig III.3b and Fig III.4, where we remarked that the measured spectral intensities for the given nominal concentrations or the measured concentrations deduced from the calibration curves are systematically and significantly lower than the excepted values for the commercial milks. In fact the parameters of the plasma are different for these samples compared to the values of the laboratory-prepared reference samples which were used to establish the calibration curves.These deviations are however reduced for the "Auchan" sample (Fig III.4b, c). This exception can be now understood because the temperature and the electron density of this sample are different from those of the other commercial milks and lie in the ranges of the reference samples.

Fig III. 6 .

 6 Fig III.6. Electron densities and temperatures of the laser-induced plasma measured for different samples. The laboratory-prepared reference samples are indicated by the percentages of certificated milk powder in cellulose. The commercial milk samples are indicated by their mark.

  Fig III.8. Concentrations of Mg and K extracted using the CF-LIBS procedure and using Ca as the internal reference compared to the corresponding nominal (or certified) values and the measurements with ICP-AES

  milk sample was used to study the evolution of the plasma. First the McWhirter criterion, which requires a minimal electron density of Ne=1.23×10 16 cm -3 (calculated for ΔE=4 eV and T=10 000 K) to ensure the necessary condition of the LTE, was checked with the evolution of the H α line. Our measurement showed an electron density larger than this value up to a delay of 6000 ns. The sufficient condition of the LTE for a transient plasma was checked by calculating different temperatures associated to the different species in the plasma. Atomic and ionic lines of calcium and molecular lines from cyano radicals CN were used in this study. The evolutions of the different temperature are shown in Fig. III.9.

Fig III. 9 .

 9 Fig III.9. Evolution of the temperatures of the different species in the plasma.

3

 3 photon. Experimental observation showed clear wavelength dependence of ablation behavior for used laser fluence near ablation threshold[START_REF] Küper | Threshold behavior in polyimide photoablation: Single-shot rate measurements and surface-temperature modeling[END_REF]. Especially the photochemical ablation was identified for 193 nm UV radiation, while the photothermal model fitted better for ablation with longer wavelengths. More generally at higher fluence, coupled influences between laser wavelength and laser fluence can lead to much more complicated situation depending on the detailed molecular structure of the ablated polymer. It is however a good indication to consider that the photochemical process is activated once the ablation photon energy exceeds bond energies in the matrix. When ablation photon energy drops below the bond energies, it is more likely that the photothermal processes becomes dominant. In the present work, the ablated target was a PVC plate. It consists of chains of vinyl chloride monomers, (-CH 2 -CHCl) n . Included chemical bonds are C-H, C-C and C-Cl with respectively average bond energy of 4.26, 3.59 and 3.39 eV [182]. Ablation at 266 and 355 nm, with corresponding photon energy of 4.66 and 3.49 eV, therefore allowed us to distinguish two cases with photon energy significantly exceeding the bond energies with 266 nm and below or in the same range of value of the bond energies with 355 nm.

Fig IV. 1

 1 Fig IV.1 Schematic representation of the experimental setup.

For better understanding the

  principal of the trigonometric surface positioning system, a schematic figure is given in Fig IV.2. Considering the pointer laser incident angle was fixed during our experiment, when the sample surface position moves from A to B with a height variation of ΔH, the position of the laser spot on the sample surface horizontally moved from O A to O B , ΔX=ΔH/tan . So the position of the laser spot on the control camera as shown in Fig IV.3 represents a direct monitoring of the lens-to-target distance. With our system, the surface of the sample can be fixed with respect to the focusing lens with an accuracy of ±25 m.

Fig IV. 4 .IV. 4 . 2 IV. 4 . 3

 44243 Fig IV.4. Axial profiles of C 2 , CN, C and N in plasma induced by 266 nm pulses at different delays of 500 ns (a), 2000 ns (b) and 5000 ns (c). Electron temperature, T, is also shown in the same figures for correlation study.

Fig IV. 6

 6 Fig IV.6 Ablation grooves on the target surface with ablation of (a) 266 nm and (b) 355 nm lasers.

Fig IV. 7

 7 Fig IV.7 shows a part of spectrum of pure PVC centered at the emissions of C 2 swan system. As shown in Fig IV.7, no emission line was detected in the band pass wavelengthrange of the filter off , which confirmed that only background information was collected with the off filter. We emphasize here that PVC sample used must be pure without impurity in

  3 as schematically shown in Fig IV.1. The same PVC sample was used for the analysis. The difference is that the laser used here is a Ti:Sapphire laser system at 800 nm, with a 50 fs pluse duration, 1 kHz repetition rate, and 1.8 mJ of pulse energy. Fig IV.10 shows the temporal evolution of fs-LIBS spectrum between 380 to 400 nm. Compared to the case of nanosecond laser, fs-LIBS signal shows different behavior. No significant continuum emission was observed at the beginning of the plasma evolution at delay of 40 ns as shown in Fig IV.[START_REF] Cremers | Direct detection of beryllium on filters using the laser spark[END_REF]. This is mainly due to the lower temperature of the plasma induced by femtosecond laser pulse with respect to the nanosecond laser case. In addition, the plasma induced by femtosecond laser had a shorter lifetime than that induced with nanosecond laser. We can see that the line intensity of ionic calcium increases with time from 40 to 100 ns and decreases after 100 ns. Almost no line emission was observed after 500 ns. In contrast, the maximum line intensity was observed at the delay of 1980 ns and the emission lines vanished after about 10 s for nanosecond laser-induced plasma as shown in Fig II.3. Femtosecond laser-induced plasma has thus a significantly shorter lifetime compared to that of induced with nanosecond laser. This difference can be explained by the heating of the expanding plasma by the trailing part of a ns laser pulse.

Fig IV. 10 .

 10 Fig IV.10. Temporal evolution of fs-LIBS signal on PVC sample

Fig IV. 12 .

 12 Fig IV.12. Spatial distribution of temperatures determined with Boltzmann plot of CN emission band heads, T_BP; with simulation of CN molecular emissions T_rot and T_vib at different detection delays (a) 20 ns, (b) 80 ns, and (c) 150 ns

  Distribution of molecular species, C 2 and CN, in laser-induced plasma from a PVC target has been observed for ablation with 266 nm and 355 nm laser radiations. The influence of ablation photon energy on molecule formation in the plasma is thus studied. Our results show distinguished molecule profiles in the two ablation regimes. The interpretation can be given in terms of the different formation channels of C 2 molecules. For 266 nm ablation, the channel of molecule formation through recombination of atomic carbon emitted from the target dominates. Such recombination is more efficient around the front of the plasma in contact with the background gas where the temperature is lower. For 355 nm, both recombination between atomic carbon and fragmentation from carbon cluster significantly contribute to the observed C 2 molecule populations. Due to the different energetic property of the two channels, molecules formed by recombination are located around the front of the plasma, while those formed by fragmentation are found near the target surface where the temperature is higher.The distribution of CN molecules are often correlated to that of C 2 . This suggests the reaction as the principal channel for CN formation in the plasma with the help of nitrogen molecules from the background. This consideration does not however exclude other reaction channels. The ensemble of possible channels makes the detailed description of CN molecule formation in plasma still quite complicated at the actual state of our understanding.Different molecule formation mechanisms are related to the different photonic processes involved in laser ablation of polymer. Our results strongly suggest a transition of ablation regime from photothermal to photochemical when the laser wavelength passes from 355 nm to 266 nm. Such transition corresponds to a threshold effect when the ablation photon energy exceeds the bond energies in the polymer. The change of ablation regime is further confirmed by the change observed in the morphology of the ablation craters. The distribution of the different species in the plasma provided by the differential imaging method has moreover validated the results from time-and space-resolved emission spectroscopy at very short delays.Existence of molecular species in the plasma, such as CN and C 2 , has been observed at very short delays after plasma initiation. In addition, space segregation of different species inside of the plasma has been clearly established. Finally although our qualitative arguments appear satisfactory for understanding the observed phenomena, further detailed modeling and numerical simulation will provide more complete description of involved mechanisms in such processes as complex as laser ablation of polymer and molecule formation in a laser-induced plasma.

  results show distinguished molecule profiles for the two used wavelengths. The interpretation can be given in terms of the different formation channels of C 2 molecules. For 266 nm ablation, the channel of molecule formation through recombination of atomic carbon emitted from the target dominates. Such recombination is more efficient around the front of the plasma in contact with the background gas where the temperature is lower. For 355 nm, both recombination between atomic carbon and fragmentation from carbon cluster significantly contribute to the observed C 2 molecule populations. Due to the different energetic property of the two channels, molecules formed by recombination are located around the front of the plasma, while those formed by fragmentation are found near the target surface where the temperature is higher. The distribution of CN molecules are often correlated to that of C 2 . This suggests the reaction as the principal channel for CN formation in the plasma with the help of nitrogen molecules from the ambient air. This consideration does not however exclude other reaction channels. The ensemble of possible channels makes the detailed description of CN molecule formation in plasma still quite complicated at the actual state of our understanding. Different molecule formation mechanisms are related to the different photonic processes involved in laser ablation of polymer. Our results strongly suggest a transition of ablation regime from photothermal to photochemical when the laser wavelength passes from 355 nm to 266 nm. Such transition corresponds to a threshold effect when the ablation photon energy exceeds the bond energies in the polymer.

  UV photon, as the bond extends, the electronic configuration A+B * can acquire the repulsive character of a dissociative state. In other words, as the molecule reconfigures following the electronic excitation, the nearby vibrating nuclei follow either the bound or the repulsive potential considering the extended geometry. Those following the former route execute another molecular vibration, but those taking the latter route continue to separate from one another, forming atomic fragments.

	mentioned above, two generic types of photochemical dissociation pathways of a
	diatomic molecule, AB, are illustrated in Fig I.4 [77]. The first possibility, shown in Fig I.4a,
	is that the molecule is directly promoted into a dissociative electronic state resulting in a
	direct dissociation into its constituent atoms A+B. The second possibility, shown in Fig I.4b,
	represents the case where the electronic excitation promotes the molecule into a bound excited
	state, A+B * , which is matched to a dissociative electronic state. Therefore, while the molecule
	is promoted into a bound vibrational level within the excited electronic state due to the
	absorption of a

Delay (ns) Gate width (ns)

		camera from Andor Technology. Fig I.6 shows typical temporal evolution of LIBS
	signal from a copper sample recorded with our experimental setup. The used gate widths for
	different delays are indicated in Table I.1. We can see that at the beginning of plasma
	evolution (before 70 ns), a continuum emission dominates the spectrum. With time evolution,
	the line emission intensity increases with the reduction of the continuous emission (from 70 to
	500 ns). However, the emission line intensities reduce after a certain delay with the cooling
	down of the plasma (after 500 ns). It is hence important to choose a suitable detection time
	window to detect a specific line with a good signal to continuum ratio.
		Fig I.6. Temporal evolution of LIBS spectrum from a copper sample
	I.2.2	50, 70	30
		100	50
		200	80
		500	200
		1000	500
		2000	1000
		5000	2000
		Table I.1. Used gate widths for different detection delays

Spatial distribution in a plasma and space-resolved diagnostics

	Fig I.7 is a photo of a plasma initiated on an aluminum target by a nanosecond pulsed laser at
	266 nm. We can see that the plasma has a spatial extension. Spatial characteristic of the
	plasma is often called plasma morphology. Such morphology may be related to various
	plasma properties, such as profiles of its electron density and temperature. The morphological
	data can be applied to indicate the distributions of atomic and molecular species at various
	locations in the plasma and subsequently to improve LIBS analytical feature.

  Fe and Ni. Generally, organic elements have higher values of ΔE with respect to the metallic elements, which leading to the relaxation time and diffusion length are usually larger than those of metallic ones. In a typical LIBS plasma, the criterions expressed by equations (I.45) and (I.46) are normally fulfilled for metallic elements, but difficult for organic elements. That is also why LIBS is still a challenge for analysis of organic samples, especially for the organic elements.

1•10 -2 mm, Ni I

2•10 -2 mm, O I 0.2 mm and H I 0.7 mm. Typically, the characteristic variation length in the plasma d is in the order of 1 mm. It is clear that the diffusion length criterion is verified only for Cu,

Table II

 II

	(ns)	Gate width (ns)
	70-130	30
	130-280	50
	280-580	100
	580-780	200
	780-1780	500
	1980-2980	1000
	1980-3980	2000

.1. Detection gate widths for increasing detection delays used for time-resolved emission spectroscopy of the plasma.

  8 s -1 ) E j (eV) g j Line set greater than 580 ns. This equilibrium is further demonstrated by the calculation of the excitation temperature of neutral Ca using the Boltzmann plot method for delays greater than 580 ns. We see in Fig II.7, the temperatures extracted from Boltzmann plot tend to merge with those extracted from Saha-Boltzmann plot for delays greater than 780 ns. At the same time for these delays, the vibrational temperature extracted from emission band heads of CN molecule exhibits the same tendency which becomes identical to those of the neutral or ionized Ca.

	Ca I	422.673	2.18	2.93 3
	Ca II	393.366	1.47	3.15 4	(1)
	Ca II	396.847	1.40	3.12 2
	Ca I	458.147	0.04	5.23 5
	Ca I	487.813	0.19	5.25 7
	Ca I	504.162	0.33	5.17 3
	Ca I	610.272	0.10	3.91 3
	Ca I	644.981	0.09	4.44 5
	Ca I	647.166	0.06	4.44 7	(2)
	Ca I	649.965	0.08	4.43 5
	Ca II	315.887	3.10	7.05 4
	Ca II	317.933	3.60	7.05 6
	Ca II	370.603	0.88	6.47 2
	Ca II	373.690	1.70	6.47 2
	Table II.2. Spectroscopic data of lines used for temperature calculation. Two line sets have
	been used to perform Saha-Boltzmann plots at different delay ranges: sets (1) for 70 to 380
	ns and (2) for 480 to 2980 ns. The atomic lines in the set (2) are further used to perform
	Boltzmann plot in the corresponding delay range.

Table II . 3

 II3

	Element	T(K)	ΔT (K)	D	ΔD
	Mg	8100	180	1	0.25
	Al	7400	450	-1.4	0.4
	Ca	7700	150	0.0	0.2
	Ti	8100	230	-4.0	0.4
	Mn	7800	170	-1.4	0.25
	Fe	8600	100	-3.8	0.1

. Fig II.10. Saha-Boltzmann plots for Mg, Al, Ca, Ti, Mn, and Fe.

Table II

 II

.3. Temperatures and the intercepts (D) with corresponding statistic errors of the considered elements in potato skin extracted from Saha-Boltzmann or Boltzmann plots.

Our result show that the temperatures for the considered elements are in the range of 7400 to 8600 K. This range represents a dispersion of the results which is 15% of the average temperature. The uncertainties of temperatures ΔT shown in Table

II

.3 represent the statistical errors retrieved from the linear fit. The observed large dispersion of the temperatures corresponding to the different elements can be due to the imprecision of the available spectroscopic data. Taking into account imprecision, we can reasonably consider that all detected elements are in local thermodynamic equilibrium within the time range during which the spectrum was integrated. We recall here that the Saha-Boltzmann or Boltzmann plots presented in Fig II

.

10 together with the temperatures extracted in Table

II

.3 are the results of an average over a time period (from 700 ns to 1.2 μs after the laser impact in our case).

According to Fig II.

Table II .

 II

		Atomic weight	Ionization energy (eV)
	Mg	24.31	7.65
	Al	26.98	5.99
	Mn	54.94	7.43
	Ca	40.08	6.11
	Ti	47.97	6.83
	Fe	55.85	7.90
	Average	41.69	6.99

[START_REF] Moenke | Laser Micro-SpectrochemicalAnalysis[END_REF]

. Atomic weight and ionization energy for different elements: Mg, Al, Mn, Ca, Ti and Fe, and the average values for these elements.

Table III .

 III

1. Operation conditions of the ICP-AES.

Table III

 III .2. The retrieved concentrations are in good agreement with the indicative values (nominal values).

	Concentra		Mg	K			Ca		Na	P
	tion	Nomi	ICP-A	Nomi	ICP-A	Nomi	ICP-A	Nomi	ICP-A	Nomi	ICP-A
	(mg/g)	nal	ES	nal	ES	nal	ES	nal	ES	nal	ES
	Bcr 063r	1.26 1.34 17.68 17.38 13.49 14.51 4.37 14.51 11.10 11.20
	Gallia	0.42 0.41 4.92 4.96 3.86 4.35 2.00 1.11 2.67 2.39
	Guigoz	0.54 0.57 6.45 6.53 5.35 5.93 2.00 2.37 3.60 2.84
	Lemiel	0.55 0.63 5.80 5.73 5.60 5.92 1.40 1.42 3.30 2.41
	Milupa	0.33 0.34 4.15 3.62 4.22 4.67 1.39 0.90 2.32 1.54
	Novalac-B 0.45 0.53 4.70 4.80 3.80 4.24 1.50 1.80 2.30 2.98
	Novalac-R 0.45 0.48 6.25 6.75 5.00 5.61 1.50 1.86 3.65 3.87
	Nutricia	0.60 0.60 6.30 6.74 5.50 6.25 1.60 1.150 3.50 2.88
	Auchan	1.14 1.19	-	17.48 12.60 13.35 12.60 5.22 9.80 9.96

.2. Elemental concentration in milk powders obtained after wet digestion and ICP-AES determination.

Vibrational temperature is also determined with CN molecular band emission heads. The CN molecular emission is indeed commonly detected in LIBS spectra of organic materials [START_REF] Baudelet | Time-resolved ultraviolet laser-induced breakdown spectroscopy for organic material analysis[END_REF]. The vibrational temperature is extracted using the method described in §I.3.2. The obtained vibrational temperatures have been further confirmed by using the temperature calculation by the spectrum simulation with the LIFBASE software [153]. For temperature ranging from 5000 to 20000 K, the comparison showed good agreements with a typical accuracy of 5-10%.

Wet digestion procedure

For the digestion of milk powders, a microwave assisted nitric acid digestion procedure was developed using a microwave system, Mars Xpress (CEM μWave S.A.S, Orsay, France). For the analysis of the major elements (Na, Mg, K and Ca), 100 mg of powder was placed in a closed vessel with nitric acid. For the analysis of trace elements (P), 1 g of sample was used.

Five replicates were prepared for each sample in order to check the repeatability of the mineralisation procedure. In order to evaluate possible contaminations of the vessel, a nitric acid blank was also analysed in several replicates. The optimisation of the digestion was made using the reference material, BCR063. The optimized temperature program was as the following: during the first 15 minutes the temperature rose from the room temperature to 200 °C which was kept for another 15 minutes. The optimal recovery was obtained for a power of 400 W. After cooling, the digests were diluted up to 50 ml with deionized water.

The same dilution protocol was successfully employed in our previous works to obtain calibrants for LIBS and LA-ICP-MS [START_REF] Stankova | Comparison of LA-ICP-MS and LA-ICP-OES for the analysis of some elements in fly ashes[END_REF][START_REF] Stankova | A simple LIBS method for fast quantitative analysis of fly ashes[END_REF].

ICP-AES operation conditions

Measurements were made using an ICP-AES, JY 138 ultrace (Jobin Yvon Horiba, Longjumeau, France) modified for axial viewing. Experimental parameters are listed in Table II. 1. results, we can see first, the standard deviations of the LIBS measurements are in general much larger than those of ICP-AES measurements. The averaged error bars across all the samples were respectively 3.2%, 3.6% and 4.0%, for Mg, K and Ca for ICP-AES measurements, while these values become 17%, 9.6% and 5.8% for raw LIBS measurements.

Measurement repeatability is thus degraded with LIBS analysis. This mediocre repeatability for LIBS can be considered as due to its high sensitivity to experimental fluctuations, such as laser energy fluctuation or sample inhomogeneity, since the ablation process is highly nonlinear. We can also remark that the concentrations determined by LIBS are systematically smaller with respect to the nominal values, with an averaged bias across all samples of 52.8% for Mg, 42.3% for K and 38.0% for Ca. These deviations are significantly larger than those observed in ICP-AES measurements, 6.2% for Mg, 4.9% for K, and 10% for Ca, which is consistent with dispersions of concentrations in commercial milks. The observed systematical deviation of the LIBS measurements to significantly smaller values with respect to the measurements with ICP-AES suggests a strong matrix effect which leads to significant differences in plasma property for the commercial milks compared to the laboratory-prepared reference samples. This matrix effect is also observed in Fig III .3b, where the LIBS intensities (Ca II 317.9 nm) for the 8 commercial milks are plotted against their calcium concentration (the stars in Fig III .3b). It is clear that all the obtained points lie under the calibration curve with significant deviations. concentrations of magnesium and potassium in these samples with calcium as the internal reference. In order to determine the uncertainties of the measurements, the relative concentrations are calculated for each of the 5 lines of calcium mentioned above, which allows us to extract an averaged concentration for magnesium and potassium with corresponding standard deviations.

The retrieved concentrations are shown in Fig III .8. We see that the concentrations for magnesium and potassium extracted using the CF-LIBS procedure are now in good agreement with the concentrations reported by the producer within the measurement uncertainties. With respect to the nominal values, the averaged errors of the CF-LIBS measurements across the all samples are 17.6% and 12.1% for Mg and K respectively, while the corresponding deviations for the LIBS measurement with calibration curves are 52.8% for Mg and 42.3% for K as shown above. Such improvement highlights an efficient compensation of the matrix effect using the CF-LIBS procedure as expected. The bias of the measurements with CF-LIBS remains however significantly larger than those of the measurement with ICP-AES, 6.4% for Mg and 4.4% for K with respect to the nominal values. In addition when comparing the precision of the measurements, for ICP-AES the averaged error bars across all the sample are 4.1% for Mg and 4.4% for K, while these values are respectively 24% for Mg and 16% for K for CF-LIBS measurements.

Setup for time-and space-resolved emission spectroscopy

The used experimental setup is showed in Fig IV .1. A tripled (wavelength 355 nm) and quadrupled Nd:YAG laser (wavelength 266 nm) with a 10 Hz repetition rate was used respectively to ablate the PVC sample in our experiments. Laser pulses were focused on the sample surface using a bi-convex quartz lens with a 50 mm focal length. The focused spot size was estimated to be 300 and 200 μm for the laser at 355 and 266 nm respectively in diameter by measuring the crater sizes. The lens-to-target distance was chosen in such way that the spark formed in the ambient air totally disappeared. The laser fluence used in our experiments was controlled to be identical, estimated to be 60 J/cm 2 , for both of lasers for the comparison. To perform space-resolved emission spectroscopy of the plasma, we used a 4-f optical imaging system with the optical axis parallel to the sample surface. Two quartz lens, with focus length 100 and 50 mm, provided a magnification of 0.5 for a (reversed) plasma image. The optical axis of the imaging system passed very close to the sample surface so that the plasma as the object was placed near the optical axis of the imaging system. The plasma emission was collected using an optical fiber of 50-μm core diameter positioned on the image plane. The fiber could be translated in the image plane (x-z plane) using a micrometric stage.

The fiber was coupled to an Echelle spectrometer (spectral range from 220 nm to 800 nm with a spectral resolution power of /Δ =5000) equipped with an ICCD camera with 1024×1024 pixels (Mechelle and iStar from Andor Technology). The wavelength calibration of the spectrometer was done with a mercury argon lamp (HG-1 from Ocean Optics). The spectral intensity calibration was performed using a deuterium tungsten halogen light source (DH-2000-CAL from Ocean Optics).

The emission from the plasma was recorded with space resolution by translating the fiber in the middle of the plasma (x=0) along the laser incidence axis (z axis) from the target surface (z=0) up to the top of the plasma. The ICCD camera was synchronized to the laser pulse. A detection window was opened after a time delay which avoided the strong continuum emitted immediately after the impact of the laser pulse on the target. The detection window spectroscopic imaging, the advantage of the developed method is able to perform emission images at very short delays where strong continuum can be emitted from the plasma. similarly to the case of ablation with 266 nm laser. However other channels of CN formation cannot be totally excluded, for example , although its endothermic nature requires external energy supply for the reaction to take place. At longer delays, we observe the disappearance of emission from atomic carbon and the long lifetime emissions from the molecules similar to the case of ablation with 266 nm.

IV.4 Experimental results and discussion