ORIGINAL PAPER

Kinetic model of atomic and molecular emissionsin laser-induced breakdown spectroscopyof organic compounds

Qianli Ma & Paul J. Dagdigian

Received: 10 November 2010 /Revised: 13 December 2010 /Accepted: 16 January 2011 /Published online: 1 February 2011# Springer-Verlag 2011

Abstract A kinetic model previously developed to predictthe relative intensities of atomic emission lines in laser-induced breakdown spectroscopy has been extended toinclude processes related to CN and C2 molecular emis-sions. Simulations with this model were performed topredict the relative excited-state populations. The resultsfrom the simulations are compared with experimentallydetermined excited-state populations from 1,064 nm laserirradiation of organic residues on aluminum foil. The modelreasonably predicts the relative intensity of the molecularemissions. Significantly, the model reproduces the vastlydifferent temporal profiles of the atomic and molecularemissions. The latter are found to extend to much longertimes after the laser pulse, and this appears to be due to theincreasing concentration of the molecules versus time.From the simulations, the important processes affectingthe CN and C2 concentrations are identified.

Keywords Laser-induced breakdown spectroscopy .

Plasmas . Laser ablation . Kinetic model

Introduction

Laser-induced breakdown spectroscopy (LIBS) has beendemonstrated to be a powerful tool of chemical analysis,with little or no sample preparation required [1, 2]. LIBS is

also attractive as a potential standoff detection technique indefense and security applications [3–5]. Despite the widerange of application of LIBS, the technique has a highdetection limit compared with other well-established tech-niques such as inductively coupled plasma optical emissionspectroscopy [6]. It would thus be desirable to have a betterunderstanding of the physical and chemical processesgoverning the intensity of the optical emission signals inLIBS.

Several of the processes contributing to the LIBS event,such as material ablation, plasma formation, plasmaexpansion, and collisional excitation of atoms have beeninvestigated in detail by a number of groups [7–11]. Ourgroup has been developing a full chemical and physicalkinetic model for various systems in order to understand indetail the processes leading to the observable spectroscopicsignatures in a LIBS experiment [12, 13]. We have includedin the model electron-impact (de)excitation, radiative decay,collisional quenching, collisional ionization, three-bodyrecombination, and chemical reactions involving smallmolecules and molecular ions.

We have presented in a previous paper [13] a kineticmodel to describe the intensities of C/H/N/O atomicemissions in LIBS of organic compounds. These calcula-tions were compared with observed LIBS intensities for355 nm laser irradiation of organic residues on aluminumfoil. Reasonably good agreement was found for the relativeexcited-state concentrations and their time profiles. In thepresent study, we expand this model to describe CN and C2

molecular emissions. These species are usually observed inLIBS of organic molecules and provide additional infor-mation for molecular identification [14, 15]. In order tovalidate the model, we compare results of kinetic modelingwith experimentally determined excited-state atomic andmolecular populations, measured as a function of time after

Published in the special issue Laser-Induced Breakdown Spectroscopywith Guest Editors Jagdish P. Singh, Jose Almirall, Mohamad Sabsabi,and Andrzej Miziolek.

Q. Ma : P. J. Dagdigian (*)Department of Chemistry, The Johns Hopkins University,Baltimore, MD 21218-2685, USAe-mail: pjdagdigian@jhu.edu

Anal Bioanal Chem (2011) 400:3193–3205DOI 10.1007/s00216-011-4687-y

the laser pulse. The kinetic model is used to elucidate theprimary processes generating and removing ground andelectronically excited CN and C2.

Two organic compounds, perylene and adenine (whosestructures and chemical formulas are given in Fig. 1), werechosen as representative organic compounds for study.Perylene is a polycyclic aromatic hydrocarbon; strong C2

emission is usually observed for such compounds in LIBSexperiments [15]. Adenine is rich in nitrogen with bothsingle C–N and multiple (aromatic) C–N bonds. Hence, CNmay be directly formed by fragmentation of adenine. Ofcourse, for both compounds, CN can be formed in air buffergas, by reaction involving fragments of the organicmolecule and the entrained air.

The observation and interpretation of the molecularemissions in LIBS is also of considerable interest. Anumber of groups have reported time-resolved measurementof molecular emissions, involving laser ablation of graphite[16–19], organic compounds [20], or polymers [21]. Unfor-tunately, information on the plasma temperature was notavailable in these experiments because of the lack ofemission lines suitable for a reliable Boltzmann analysis.Although the comparison of the observed rotational–vibra-tional structure of the molecular emissions with simulatedspectra could yield rotational and vibrational temperatures[22], these temperatures provide a lower limit to the plasmatemperature and are unsuitable for time-resolved determina-tion of plasma temperature. In our experiments, deposition oforganic residues on aluminum foil allows determination ofthe plasma temperature from the relative intensities of Allines. The plasma temperature is a critical parameter in akinetic simulation.

Kinetic model

We have extended the kinetic model previously developed[12, 13] to include a description of the molecular CN andC2 emissions. The expanded model now includes reactionsinvolving air oxidation and plasma chemistry, thermaldecomposition of small organic molecules, and the productionand removal of excited atomic and molecular levels. Severalatomic energy levels are listed in Table 1, and we will use the

notation in the table for the rest of the paper. A complete listof atomic energy levels included in the kinetic model can befound in our previous paper [13]. Al atomic levels are notincluded in our current model since we have previouslyobserved that the Al mole fraction required to representproperly the observed Al*4S signal was too low to affect thechemistry of the light atoms.

Table 2 shows the new molecular processes we haveadded to our model. The spontaneous decay rates of CN(B)and C2(d) states were taken from the experiments ofJackson [23] and Naulin et al. [24], respectively. For therates of collisional quenching of molecules, we used theroom-temperature rate constant for quenching of CN(B) byCO from Jackson [23] and that for quenching of C2(d) byCH4 from Wang et al. [25]. We assume that the quenchingrate constants are independent of temperature and are thesame for other molecular collision processes. The availabledata on the electron-impact excitation and de-excitationprocesses are limited. Halmova et al. [26] have computedthe cross section for electron-impact excitation of C2 out ofthe ground X1Σ+

g and low-lying a3Πu states as a functionof collision energy. We used their data for the d3Πg←a3Πu

transition to compute thermal rate constants for electron-impact excitation of C2. They computed a much smallercross section for excitation to the d3Πg state out of theground state. The d–a rate constants should provide areasonable estimate for C2 electron-impact excitation. TheC2(a) state lies only 716 cm−1 above the C2(X) state [27]and has an electronic degeneracy of 9. The rate constant forthe reverse de-excitation processes was computed bydetailed balance. No experimental or theoretical informationis available for electron-impact excitation of CN. We assumethat the CN electron-impact (de)excitation rate constants arethe same as for C2. We note that we have assumed thatelectron-impact excitation is the only process for formationof an excited, emitting level.

The Chemkin Pro (Release 15083 by Reaction Design,San Diego, California, USA) package was employed tosolve the system of kinetic equations numerically andsimulate the time-dependent population densities of differentspecies. We ignore spatial variation of the concentrations andthe physical parameters such as temperature and pressure andhave employed a closed homogeneous reactor model withconstant pressure (taken as 1 atm) and constrained tempera-ture. For consistency with the required input data format, allrate constants of the included processes were fitted to thefunctional form k=ATnexp(−Ea/RT), where T is the plasmatemperature in K and R is the gas constant, while A, n, andEa are fitted parameters. A total of 125 species and 1,509processes (with forward and reverse processes listed sepa-rately) were included in the kinetic model. A list of theprocesses, kinetic parameters, and the sources for theparameters can be obtained from one of the authors (PJD).

Fig. 1 Chemical structure of perylene (C20H12, left) and adenine(C5H5N5, right)

3194 Q. Ma and P.J. Dagdigian

Integration of the rate equations requires specification ofthe species initial concentrations which arise from thelaser–matter interaction and the temporal profile of thetemperature. We describe in the “Results and discussion”section the various assumptions made for the initialconcentrations. The temperature was computed from theratio of the time-dependent intensities of the Al 308.22 and394.40 nm lines observed in our experiments and theassumption of local thermodynamic equilibrium (LTE). It iswell known that LTE is not established immediately afterthe laser pulse [28], but our derived temperatures shouldprovide reasonable estimates for our kinetic simulation.

Experimental setup

The apparatus used in this work is similar to that we haveemployed in previous studies [13, 14]. A brief descriptionof the apparatus is provided here. A Nd:YAG laser(Continuum Powerlite 8000 operated at 10 Hz repetitionrate) was used to generate 1,064 nm (Nd:YAG fundamen-tal) radiation. The laser beam was reflected off an 800-nm

dichroic mirror to reduce the pulse energy. The radiationwas then passed through a mechanical shutter and focusedusing a 75 mm focal length fused silica lens onto thesample, which was mounted on a motorized translationstage. The position of the lens above the substrate wasadjusted to maximize the intensity of the Al*4S lines. Afresh area of substrate was irradiated in ambient air on eachlaser shot, and the translation stage was moved betweenshots. The emission from the laser-induced plasma wasfocused by a pair of 30° off-axis parabolic mirrors (focallength 25.4 mm) onto a UV-transmitting optical fiber(50 μm core) and transmitted to an echelle spectrometer(Andor Mechelle 5000) equipped with a gated, intensifiedcharge-coupled device (ICCD; Andor DH734-18-03). TheICCD was synchronized with the emission from the plasmausing a digital delay generator (Stanford Research SystemsDG535), which was triggered by a photodiode detecting theemission. For most of our experiments, the gate width ofthe ICCD was fixed at 100 ns and delays from 20 ns to 2 μswere employed. The wavelength-dependent sensitivity ofthe apparatus was determined using the spectra of calibrateddeuterium and tungsten-halogen lamps, and the spectra of

Table 1 Atomic energy levels (upper levels only) of lines studied in this work

Notation Element Levela Energy (cm–1)b Emission line studied (nm) Radiative decay rate (s–1)c

H*3 Hydrogen n=3 97492 656 4.41×107

C*5 Carbon 2s22p3s(1P°) 61982 248 3.40×107

N*10 Nitrogen 2p23p(4S°) 96750 742–6 3.77×107

O*5 Oxygen 3p(5P) 86629 777 3.69×107

Al*4S Aluminum 3s24s(2S) 25348 394/396 1.47×108

a The levels listed are the upper levels of the emission linesb The energies are averaged over the fine-structure levelsc Calculated from the radiative decay rates (Aij) provided in the NIST atomic spectra database [43], assuming the populations of different J levels are in theratio of their degeneracies

Table 2 New molecular processes included in the kinetic model

Reaction A (mol, cm, s)a n Ea (cal mol−1) Reference

C2+e− → C2(d)+e

− 1.23×1017 –0.30 58600 b

C2(d)+e−→C2+e

− 3.63×1017 –0.40 3870 c

CN+e−→CN(B)+e− 1.23×1017 –0.30 58600 d

CN(B)+e−→CN+e− 3.63×1017 –0.40 3870 d

C2(d)→C2 9.82×106 0 0 [24]

CN(B)→CN 1.52×107 0 0 [23]

C2(d)+M→C2+M 2.2×1013 0 0 [25]

CN(B)+M→CN+M 3.7×1013 0 0 [23]

a Rate constant k in (mol, cm, s) is expressed in Chemkin format as ATn exp(−Ea/RT)b Calculated from the reaction cross section reported in reference [26]c Calculated using detailed balance from the rate constant for electron excitationd Used the same fitted parameters as the reactions involving C2

Kinetic model of atomic and molecular emissions 3195

the samples were corrected for the varying sensitivity as afunction of wavelength.

Two organic compounds, adenine and perylene (Sigma-Aldrich), were studied in this work. The compounds weredispersed in a solvent (water–ethanol mixture with avolume ratio of 6:1 for adenine, and toluene for perylene)to form a suspension with a concentration of 0.02 g/mL A0.15 mL aliquot of the suspension was delivered to a pieceof aluminum foil (99.99% on metal basis, 50 mm×50 mm,0.1 mm thick, Alfa Aesar) which was previously sonicatedfor 20 min in methanol to remove the organic residue onthe foil. The suspension was then allowed to dry in thehood, resulting in a foil covered with a thin layer of organiccompound. The coverage was estimated to be ∼13 μg/cm2.

The atomic line intensities were computed from the areaunder the line profile above any background, and therelative excited-state populations were determined from theintegrated intensities by dividing by the radiative decayrates (given in Table 1). An extra correction was performedto improve the accuracy of CN and C2 emissions, whichrequired integration over a wider wavelength range. Foreach spectrum of an organic residue on aluminum foil, aspectrum of the bare foil was taken under the sameexperimental conditions. The intensities in the bare foilspectrum were then multiplied by a series of factors andwere used as background to correct the spectrum of thesample. The corrected spectra using different multiplicationfactors were compared, and the spectrum with minimalbackground artifacts was used to calculate the molecularline intensities. The determination of molecular lineintensities and excited-state populations will be discussedfurther in the “Molecular emissions” subsection.

Results and discussion

Bare aluminum foil

We first present our results for bare aluminum foil, which asa substrate will provide important information on theassumptions we make in the model. The LIBS spectra wererecorded with a gate width of 100 ns and various gatedelays. Figure 2a shows the determined time-dependentexcited-state populations. We clearly see a rapid decay ofthe excited-state populations for all observed atomic lines.The C*5 emission at 248 nm was found to be very weak orabsent. The nitrogen and oxygen lines indicate theentrainment of environmental air. We also observe a strongH*3 signal at 656 nm (Hα Balmer line), which may comefrom the moisture in the ambient air, water moleculesadsorbed on the surface of the aluminum foil, and/orhydroxyl groups bonded to aluminum atoms on the surfaceof the foil. The oxidized surface of the aluminum foil may

contribute to the O*6 emissions as well. Note that hydrogensignal was not significant in our previous study [13]. In thiswork, we use foils of higher purity and clean the foil tominimize the carbon emissions from the foil, which allowsus to study the molecular emission from the organiccompounds with better precision. This process, however,may contribute to the adsorption of small molecules orhydroxyl groups on the surface of aluminum foil.

Figure 2b shows the plasma temperature determinedfrom the ratio of the intensities of Al 308.22 and 394.40 nmlines. Since self reversal in both lines is observed in someexperiments, as was also observed in 355 nm LIBS in ourprevious study [13], we fit the wings of the peaks to Voigtprofile using the method of least squares to determine theintegrated intensities of the two Al lines. We then assume aBoltzmann distribution for the two excited states ofaluminum and calculate the plasma temperature. Thetemperature profile is fitted to the form of T=Ae−Bt, whereT is the plasma temperature, t is the gate delay, and A and B

Fig. 2 LIBS of bare aluminum foil in ambient air for 1,064 nm laserirradiation (pulse energy 10 mJ). a Relative populations of excitedatomic states determined from the measured intensities (corrected forthe wavelength-dependent detection sensitivity). b Plasma temperaturederived from the relative intensities of the Al 308.22 and 394.40 nmlines. c Electron density derived from the Stark broadening of the Al394.40 nm line

3196 Q. Ma and P.J. Dagdigian

are fitted parameters. This fitted temperature profile [solidline in Fig. 2b] is used as input in our kinetic model.

As we noted previously [13], the Al lines are broad atshort gate delays, and the widths decrease with increasingdelay. This broadening is the result of Stark broadening andprovides a spectroscopic measure of the electron density.We computed the time-dependent electron densities fromthe broadening of the Al 394.40 nm line, using thepreviously determined relationship between Al line widthand electron density [29, 30]. Parigger et al. [31] havereported a recent determination of the Al 394/396 nm Starkbroadening parameters, by comparing Al and H broadening.The broadening parameters are ∼40% larger than those of theearlier studies [29, 30] and are much less precise. We chooseto use the latter in our data analysis. Use of the parameters ofParigger et al. with our measured line widths wouldyield ∼40% smaller computed electron densities.

Figure 2c presents the derived time-dependent electrondensities for LIBS of bare aluminum foil. We see that theelectron density in our experiments is in the range of 1017

to 1018 cm−3. To confirm our result, we measured the Starkwidth of hydrogen Hα Balmer line at 656 nm for theshortest delay. We estimate the Stark width as 4.3 nm,which corresponds to an electron density of ∼7×1017 cm−3

[32, 33], in reasonable agreement with the electron densitycalculated from the Al line. Unfortunately, H*3 signaldecays much faster and is noisier than Al*4S signal, and wewere unable to determine the electron density accuratelyfrom the Stark broadening of the Hα line.

Figure 3a shows the results of our simulation of excited-state populations for laser irradiation of bare aluminum foil.For the reason described in the “Kinetic model” section, wedo not include aluminum in the kinetic simulation. Takinginto account all sources of hydrogen and oxygen is verydifficult. Lazic et al. [34] observed in LIBS experimentsthat the hydrogen signal decreases in intensity for subse-quent shots of a moving sample and suggested that sincethe shock wave can reduce the local air humidity, wateraerosol droplets in air are the primary source of hydrogenlines in LIBS experiments. In our experiments, however,the fluctuations of the H*3 signal are not significantlygreater than those of other atomic emissions [shown inFig. 2a]; hence, we cannot assume ambient moisture as thesingle source. Considering also the oxidation of aluminumand species on the surface of the aluminum foil, we simplyadd some hydrogen and oxygen atoms in equal quantity inthe initial mixture. For the purpose of a qualitativesimulation, we assume the mole ratio of air, hydrogenatoms, and oxygen atoms to be 2:1:1. As in our previousstudy [13], we assume complete atomization and 10% ofinitial ionization of N. Figure 3b shows the computedexcited-state populations (shown in Fig. 3a) averaged over100 ns windows to provide a direct comparison with the

experimentally determined excited-state populations (Fig. 2a).The simulation reasonably represents the time-dependentexcited-state populations of the light atoms and the electrondensity. If we assume no atomization or ionization initially,the maximum electron density will appear several hundrednanoseconds after the shot and is inconsistent with ourexperimental observations. We will make similar assump-tions in later simulations for organic compounds onaluminum foil.

Molecular emissions

CN emission The CN violet bands (B2Σ+–X2Σ+ bandsystem) are observed for both compounds studied. Thestrongest emission was observed at 388 nm, whichcorresponds to the (0, 0) band of the Δv=0 progression. Asample spectrum is shown in Fig. 4. To calculate therelative excited-state CN(B) concentrations, we first dividethe integrated intensity of the Δv=0 progression by 69.7%

Fig. 3 Plots of the computed time-dependent concentrations of theexcited emitting atomic levels and electron densities for a mixture ofair, hydrogen atoms, and oxygen atoms (air:H:O mole ratio 2:1:1),computed with the kinetic model described in the “Kinetic model”section and the temperature profile plotted in Fig. 2b. We assumecomplete atomization and 10% initial ionization of Ninitial mole ratios : N; 6:3; Nþ; 0:7; e�; 0:7; O; 8;H; 5ð Þ. a Computedmole fraction; b mole fraction averaged over 100 ns windows

Kinetic model of atomic and molecular emissions 3197

to obtain the emission intensity in all progressions. This isthe fraction of the CN emission that occurs in the Δv=0progression, derived from analysis of a high-quality LIBSspectrum provided by J. B. Spicer. We then use thiscorrected intensity and the known radiative decay rate(see Table 2) to calculate the relative CN(B) concentration.We note that an artificial hole is observed in our CN spectranear 384 nm (see Fig. 4), which is caused by the change ofdiffraction order of the echelle spectrometer. We correct thespectra with the spectra of standard lamps and barealuminum foil, as described in the “Bare aluminum foil”subsection, under the same experimental conditions tomake sure the hole is insignificant compared with the CNB–X bands, but our correction is not perfect and the holecan be a potential source of error in determining theintegrated intensity.

C2 emission The C2 Swan bands (d3Πg–a3Πu band system)

are observed in some of our experiments. The strongestemission was observed at 516 nm, which corresponds to the(0, 0) band of the Δv=0 progression. A sample spectrum isshown in Fig. 5. The Δv=1 progression is also wellresolved (not shown in Fig. 5). However, the emission inthis progression is much weaker and hence is not favorableto use in determining the C2 excited-state population. Asfor CN, we correct the C2 intensity in the Δv=0 progressionby dividing by 48.2% to determine the emission intensity inall progressions. This factor was again obtained by analysisof a high-quality LIBS spectrum. The relative C2(d)concentration was computed from the integrated intensityby dividing by the radiative decay rate shown in Table 2.

Perylene

Figure 6a presents the experimentally determined timedependence of the relative concentrations of the excited,

Fig. 5 Spectrum of the C2 Swan bands d3Πg � a3Πu;Δv ¼�

0 progressionÞ taken with 7 μs gate length and 20 ns gate delay after1,064 nm laser irradiation of perylene residue on aluminum foil inambient air. The spectrum was corrected with the spectrum of barealuminum foil as background (see the “Experimental setup” sectionfor details)

Fig. 4 Spectrum of the CN violet bands B2Σþ � X 2ΣþΔv ¼ð0 progressionÞ taken with 7 μs gate length and 20 ns gate delay after1,064 nm laser irradiation of perylene residue on aluminum foil inambient air. The spectrum was corrected with the spectrum of barealuminum foil as background (see the “Experimental setup” section fordetails)

Fig. 6 LIBS of perylene residue on aluminum foil in ambient air for1,064 nm irradiation (pulse energy 10 mJ). a Relative populations of theexcited levels determined from the measured emission intensities(corrected for the wavelength-dependent detection sensitivity). The scalesfor the atomic and molecular populations are on the left- and right-handsides, respectively, of the plot. b Plasma temperature derived from therelative intensities of the Al 308.22 and 394.40 nm lines

3198 Q. Ma and P.J. Dagdigian

emitting states of the light atoms, Al, CN, and C2 for1,064 nm laser ablation of perylene residue on aluminumfoil. The atomic emissions show a similar pattern of timedependence, namely strong signals at short delays anddecaying rapidly. The H*3 level is seen to have the highestconcentration. The populations of CN(B) and C2(d),however, remain significant at long gate delay. We observethe concentrations of CN(B) and C2(d) are similar at shortgate delays, but the ratio of CN(B) and C2(d) is roughly 3:1at long delays. Figure 6b shows the time dependence of theplasma temperature determined from the ratio of Al lines.The plasma temperature is similar to that plotted in Fig. 2b,except that at longer delay the determined plasma temperatureis somewhat lower.

Figure 7 shows the computed excited-state concentrationsof the light atoms and diatomic molecules for the mixture ofperylene, air, hydrogen atoms, and oxygen atoms. In aprevious paper [13], we found that for anthracene (C14H10)residue on aluminum foil with a coverage of ∼25 μg cm−2,the assumption of a 1:5 to 1:10 anthracene–air ratio gavereasonable representation of the experimental results. Sinceperylene is a larger molecule and the coverage used in thecurrent experiment is only ∼13 μg cm−2, we assume aperylene–air ratio of 1:20. For the reason discussed in the“Bare aluminum foil” subsection, we add some additionalhydrogen and oxygen atoms to the initial mixture of oursimulation (air:H:O ratio 2:1:1). The simulation presented inFig. 7a was run with the assumption of complete atomizationand 10% initial ionization of N. The simulation describeswell the overall time dependence of the CN and C2 excited-state populations but underestimates the populations at shortdelay.

Several previous LIBS studies [16, 35, 36] haveobserved that C2 emission is more intense from compoundscontaining C–C bonds, especially aromatic compounds.Portnov et al. [15] observed that the C2/CN ratio forpolycyclic aromatic hydrocarbons rises with increasingmolecular size. All these workers stated that C2 may bereleased directly in the laser–matter interaction. In addition,St-Onge et al. [16] has observed prompt C2 emission. It istherefore reasonable to include in our kinetic simulations asmall concentration of C2 in the initial mixture. Figure 7bshows the result of a simulation with 0.1% of carbonpresent initially as C2. We see the initially high C2(d)concentration decreases rapidly, and at longer delays itsconcentration is essentially identical to the simulation inFig. 7a, for which no initial C2 was assumed. The CN(B)concentration is seen in Fig. 7b to rise very rapidly at shortdelays. To provide a direct comparison between theexperiment and our modeling, we present in Fig. 7c theexcited-state concentrations in Fig. 7b averaged over 100 nstime intervals, which was our detection gate width. Ourmodel successfully predicts the relative concentrations of

H*3, O*6, and N*10. However, the simulated C*5population is significantly higher than observed experimen-tally. Part of the reason can be attributed to the low UVsensitivity of our spectrometer-ICCD combination, whichcan lead to an uncertainty in the corrected C*5 emission at

Fig. 7 a and b Plots of the computed time-dependent concentrationsof the excited atomic and molecular levels for a mixture of perylene,air, hydrogen atoms, and oxygen atoms at a mole ratio of 1:20:10:10,computed with the kinetic model described in the “Kinetic model”section and the temperature profile plotted in Fig. 6b. The assumedinitial conditions are as follows: a complete atomization and 10%ionization of N initial mole ratios : C; 20;H; 22; N; 12:6; Nþ; 1:4; e�;ð1:4;O; 16Þ and b incomplete atomization with 0.1% of C existing asC2 and 10% ionization of N initial mole ratios : C; 19:98; C2;ð0:01;H; 22; N; 12:6;Nþ; 1: 4; e�; 1:4;O; 16Þ. c Time-dependent con-centrations of the excited atomic and molecular levels shown in b,averaged over 100 ns windows. The scales for the atomic andmolecular populations are on the left- and right-hand sides, respec-tively, of the plot

Kinetic model of atomic and molecular emissions 3199

248 nm. The simulation plotted in Fig. 7c also gives areasonable representation of the time-dependent popula-tions of CN(B) and C2(d), in particular their timedependence and the ratio of the populations of the twoexcited states. Moreover, the computed ratio of the atomicand molecular excited-state populations are in reasonableagreement with our observations. We discuss the slightdiscrepancies between experiment and simulation in the“Adenine” subsection.

To explain the long-lasting emission of CN and C2, wepresent in Fig. 8 the simulated ground-state populations ofthe light atoms, and CN and C2, computed with the initialconditions given in Fig. 7b. We observe that the populationsof the light atoms remain approximately constant over theplotted time domain. However, the electron density andplasma temperature decrease rapidly with time (see Fig. 2).The reduction in these parameters with time leads to therapid decay of atomic emissions. On the other hand, the CNand C2 concentrations both increase with time. This increasecompensates for the decrease of electron density and plasmatemperature and contributes to the long-lasting molecularemissions. We will discuss the formation of CN and C2

further in the “Formation of the diatomic molecules”subsection.

Adenine

We present in Fig. 9a the experimentally determined timedependence of the relative concentrations of the excited,emitting states of the light atoms, Al, CN, and C2 for1,064 nm laser ablation of adenine residue on aluminumfoil. The populations of the excited atomic states are similar

to that plotted in Fig. 6a for perylene, except for a much lowerC*5 population. This difference can be simply explained bythe relatively small carbon content in adenine. For thissample, CN(B) population starts high and decays slowly overtime, while C2(d) emission is barely observable. Actually, wewere unable to determine the time dependence of C2(d)concentration with confidence, especially for short gatedelays (indicated by the large error bars). Figure 9b showsthe time-resolved plasma temperature. The temperatureprofile is similar to that plotted in Fig. 2b.

Kinetic simulations of mixtures of adenine, air, hydrogenatoms, and oxygen atoms were carried out, using proce-dures similar to those described in the “Kinetic model”section. Adenine is a smaller molecule than perylene.Hence, we assumed a larger initial mole fraction of adenineand used the mole ratios 1:10:5:5 for adenine, air, hydrogenatoms, and oxygen atoms, respectively. Figure 10a showsthe computed excited-state concentrations of the light atomsand diatomic molecules with the assumption of completeatomization and 10% ionization of N initially. Thesimulation reasonably describes the emission from theexcited states of the light atoms except for C*5. However,a high CN(B) concentration was not obtained at the shortestdelays. As we did for perylene, we investigated the possible

Fig. 9 LIBS of adenine residue on aluminum foil in ambient air for1,064 nm irradiation (pulse energy 10 mJ). a Relative populations ofthe excited levels determined from the measured emission intensities(corrected for the wavelength-dependent detection sensitivity). Thescales for the atomic and molecular populations are on the left- andright-hand sides, respectively, of the plot. b Plasma temperaturederived from the relative intensities of the Al 308.22 and 394.40 nmlines

Fig. 8 Time-dependent concentrations of the ground-state lightatoms, CN, and C2 for a mixture of perylene, air, hydrogen atomsand oxygen atoms computed with the initial conditions given in thecaption of Fig. 7b. The scales for the atomic and molecularpopulations are on the left- and right-hand sides, respectively, of theplot

3200 Q. Ma and P.J. Dagdigian

role of molecular fragments produced through laserirradiation by adding a very small portion of CN to theinitial mixture. The result is shown in Fig. 10b. We see alarge CN(B) concentration at very short delays, which is

computed to decay rapidly. At longer delays, the CN(B)concentration is very similar to that computed without theassumption of CN in the initial mixture. We note that nostudies on the relationship between the presence of C–Nbonds and CN emission in LIBS has been published, butstrong CN emission is often observed shortly after the laserirradiation [20, 21]. This emission can hardly be explainedby the plasma chemistry since the formation of CN is slow,as shown in Fig. 10a. It is therefore reasonable to considerthat laser irradiation of adenine releases CN although ourcomputed initial time dependence of the CN(B) concentrationagrees poorly with our observations.

We present in Fig. 10c the computed mole fractions as afunction of time of the excited states averaged over 100 nstime intervals for direct comparison with our observations.The model properly predicts the long-lasting emission ofCN. The concentration of C2(d) predicted by the model isalmost constant and negligible compared with that of CN(B), in agreement with experiment. Nevertheless, the modeldoes not predict well the time evolution of the CN(B)concentration as plotted in Fig. 9a. Moreover, the simulationsignificantly underpredicts the ratio of the molecular toatomic emissions. Various factors can contribute to thisdeviation between the simulations and our measurements.First, we observe that the spectra taken with short gate delaysare noisy because of the background continuum emission, asshown in Fig. 11. Despite the similar signal intensity, thespectra taken at short gate delays are noisier. This makes thedetermination of molecular excited-state populations for shortgate delays extremely difficult and inevitably leads to a largeuncertainty. One of largest uncertainties in our modeling isour assumption of the initial concentrations after the laser–matter interaction. Unfortunately, these concentrations are not

Fig. 10 a and b Plots of the computed time-dependent concentrationsof the excited atomic and molecular levels for a mixture of adenine,air, hydrogen atoms, and oxygen atoms at a mole ratio of 1:10:5:5,computed with the kinetic model described in the “Kinetic model”section and the temperature profile plotted in Fig. 9b. The assumedinitial conditions are as follows: a complete atomization and 10%ionization of N initial mole ratios : C; 5;H; 10; N; 10:8; Nþ; 1:2; e�;ð1:2;O; 8Þ and b incomplete atomization with 0.1% of C and acorresponding amount of N present as CN and 10% ionization of Ninitial mole ratios : C; 4:995; CN; 0:005; H; 10; N; 10:795; Nþ; 1:2;ðe�; 1:2;O; 8Þ. c Time-dependent concentrations of the excited atomicand molecular levels shown in b, averaged over 100 ns windows. Thescales for the atomic and molecular populations are on the left- andright-hand sides, respectively, of the plot

Fig. 11 Time-resolved emission spectra of the CN B2Σþ �X 2ΣþΔv ¼ 0 progression progression after 1064 nm laser irradiationof adenine residue on aluminum foil in ambient air. Each spectrumwas taken with a 100 ns gate width

Kinetic model of atomic and molecular emissions 3201

amenable to direct measurement. A laser-induced plasma isactually more complicated than that described in our model,and it would be desirable to combine our kinetic model witha full description of the ablation process and the plasmahydrodynamics.

Formation of the diatomic molecules

Kinetic modeling offers an opportunity to investigate thechemical reactions contributing to the molecular emissions.As an illustration, we present the rates of production of CN(B) and C2(d) from our simulation for 1,064 nm laserablation of perylene on aluminum foil. The other simulationswe have run show a very similar plasma chemistry and are notpresented here.

We first present in Fig. 12a the computed rates ofproduction of CN(B) by various processes. In our model,there are three major processes related to the excitation of CN,which include electron-impact excitation and de-excitation

CNþ e� $ CNðBÞ þ e�; ð1Þ

radiative decay

CNðBÞ ! CNþ hn; ð2Þand collisional quenching

CNðBÞ þM ! CNþM: ð3Þ

The forward direction of Reaction 1 is the only processin our model generating excited CN. We see from Fig. 12that the rate of electron-impact excitation is greater than thereverse de-excitation process. The domination de-excitationprocess is Reaction 3. The radiative decay rate is smallerthan the other de-excitation processes.

Figure 12b shows the computed rates of production ofC2(d). The processes are similar as those shown inReactions 1, 2 and 3 and are not written explicitly. Again,electron-impact excitation is the only process we include inthe model that forms C2(d), and we observe that radiativedecay is the smallest de-excitation process. Note that wehave included a small amount of C2 in our initial mixture, itis thus reasonable to have a high initial rate of productionfor the electron-impact excitation and de-excitation process.For both CN(B) and C2(d), we see a large initial rate ofproduction, because of the presence of the diatomicmolecules at short delays (see Fig. 7b).

It is interesting to study the formation of ground-statemolecules, since the increasing concentration of CN and C2

over time is responsible for the long-lasting molecularemissions (discussed in the “Adenine” subsection).Figure 13a shows the computed rates of production forCN. To illustrate our results better, we have combined bothdirections of a reaction, i.e., each line in Fig. 13 representsthe net rate of production of the forward and reservereaction. A positive value indicates the reaction favors theformation of CN, while a negative value indicates net lossof CN. We find that only five overall reactions make amajor contribution to the formation of CN. The major CNforming processes are the reaction of carbon atom anddiatomic molecules, i.e.,

Cþ NO $ CNþ O; ð4Þand

Cþ N2 $ CNþ N: ð5Þ

However, the right-hand side of the reaction

COþ N $ CNþ O; ð6Þis the same as that of Reaction 4. Reaction 6 favors to theleft-hand side and actually consumes more CN thanReaction 4 produces at longer gate delay. The forwarddirection of Reaction 5 is the major process responsible forthe increase in the CN concentration over time.

Fig. 12 Plots of the rates of production of a CN(B) and b C2(d) for amixture of perylene, air, hydrogen atoms, and oxygen atoms computedwith the initial conditions given in the caption of Fig. 7b

3202 Q. Ma and P.J. Dagdigian

Some workers [16, 37–40] argue that the formation ofCN occurs through the four-center reaction

C2 þ N2 ! 2CN; ð7Þwhere nitrogen comes from ambient air. This argument isinconsistent with the results of experiment and oursimulations. First, the four-center reaction has a largeactivation energy (1.8 eV) [41] and could hardly explainthe strong CN emission at shortest gate delays. Second, inour experiments with adenine residue on aluminum foil andin other studies, C2 emission is weak or not present, whilethe CN emission can be quite strong. It is very unlikely thatCN is formed from a reaction involving C2 in these cases.Also, we have run kinetic simulations without Reaction 7and observed that the difference in the CN(B) concentrationis very small (not observable if plotted in a same graph witha simulation in which Reaction 7 is included). This furtherillustrates that Reaction 7 is insignificant in our experiment.We therefore conclude that Reaction 7 is unimportant in thegeneration of CN. Several other groups [18, 42] have also

cast doubt on the role Reaction 7 plays in LIBS plasmachemistry.

The computed rates of production for C2 are shown inFig. 13b. At short delays, the major formation process is theforward step of

COþ C $ C2 þ O; ð8Þ

while at longer delays the most important C2 formationprocesses become the reaction of C with CN and CH:

CNþ C $ C2 þ N; ð9Þand

Cþ CH $ C2 þ H: ð10ÞSome workers [17, 19] state that the recombination of

carbon atoms

Cþ CþM $ C2 þM ð11Þis an important process forming C2. However, in oursimulations this recombination plays an insignificant role.Still, we note that these investigations [17, 19] focused onthe ablation of graphite in ambient air. Hydrogen wasabsent in these experiments, and hence the chemistry couldbe different.

It is also interesting to look at the interconversion of CNand C2 (Reaction 9). CN is thermodynamically more stablethan C2, but surprisingly, in our simulation the net result ofthis process is the formation of C2. This can be explainedby the large amount of air entrainment in our experiments.The high concentration of nitrogen enhances the formationof CN from Reaction 5, leading to a higher CN concentrationthan that of C2. The difference in the CN and C2

concentrations further enhances the formation of C2 fromCN.

Our model requires a considerable number of rateconstants, and their dependence upon temperature and, insome cases, upon pressure. The rate parameters can eithercome from experimentally determined rate constants orcomputed reaction cross sections. However, the experimentaldata were mostly taken at a much lower temperature than ischaracteristic of a LIBS plasma. The extrapolation of the rateconstants to the temperature of the plasma can lead tosignificant uncertainties in the rate constants. Nevertheless,such kinetic modeling has proven to be an important tool inunderstanding the processes in the LIBS plasma leading to theobservable spectroscopic signatures.

Conclusion

We have presented a kinetic model describing the complexchemistry occurring in a laser-induced plasma, in particular

Fig. 13 Plots of the rates of production of a CN and b C2 for amixture of perylene, air, hydrogen atoms, and oxygen atoms computedwith the initial conditions given in the caption of Fig. 7b. Note thateach line in the plot represents the net rate of formation of the forwardand reverse reaction

Kinetic model of atomic and molecular emissions 3203

the processes involving the generation of the spectroscopicsignatures. We have compared the excited-state concen-trations predicted by this model with experimentallydetermined relative concentrations in LIBS of two organiccompounds, perylene and adenine, which were prepared asresidues on aluminum foil. The simulation could qualita-tively represent the relative concentrations of the excitedlevels of both atoms and molecules. We were also able toelucidate the major chemical processes responsible for thelong-lasting molecular emissions observed in LIBS experi-ments. It was demonstrated that the often cited four-centerreaction C2+N2→2CN is very unlikely to be the major CNforming process in our and other LIBS experiments. Rather,the reaction of C and N2 appears to be responsible for theincreasing CN concentration at longer gate delays while thereaction of C with CO or CN appears to be responsible forthe increasing C2 concentration. The resulting increase ofground-state concentrations of CN and C2 with timecompensates the rapid decrease of electron density andplasma temperature and ultimately leads to the long-lastingmolecular emissions. The difference in the duration of theatomic and molecular emissions should affect an experi-menter’s choice of the width of the detection gate in a LIBSexperiment.

Our kinetic model depends on two types of inputparameters in addition to the matrix of rate constants.These include the temperature profile as a function of timeand the initial composition of the plasma. The temperatureprofile we used came from Boltzmann analysis of experi-mentally determined Al emission line intensities. For theinitial composition, we have made various assumptions sothat the model could reasonably predict the promptformation of atomic emission. To provide a completepicture describing the LIBS process, this kinetic modelneeds to be combined with other theoretical treatments,such as a model for the ablation process and the plasmahydrodynamics that can provide these two types of inputparameters.

Acknowledgments This research has been supported by the U.S.Army Research Office under the Multidisciplinary University ResearchInitiative ProjectW911NF-06-1-0446. We are grateful to James B. Spicerfor providing a high-quality LIBS spectrum containing CN and C2 bands.

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