Energy transfer in combustion diagnostics : Experiment andmodeling

Andreas Brockhinke* and Katharina Kohse-Ho� inghaus

Physikalische Chemie I, Chemie, Bielefeld, 25,Fakulta� t fu� r Universita� t Universita� tsstr.D-33615 BieleÐeld, Germany. E-mail : brockhinke=pc1.uni-bielefeld.de

Received 5th March 2001First published as an Advance Article on the web 9th October 2001

Laser induced Ñuorescence (LIF) of OH (A 2&`) is measured in severalatmospheric-pressure Ñames using a short-pulse laser system (80 ps duration) inconjunction with an intensiÐed streak camera. The two-dimensional signal-detectiontechnique allows one to simultaneously monitor rotational and vibrational relaxation aswell as electronic quenching. Rotationally-resolved LIF spectra a†ected by energy transferare compared with the results of a rate-equation model and are found to be in reasonablygood agreement. It is shown that a signiÐcant contribution of Ñuorescence detected bybroad-band techniques is due to levels populated by vibrational energy transfer (VET).Implications for picosecond LIF techniques for the time-resolved, quench-free detection ofOH are discussed. A detailed analysis is presented for Ñuorescence spectra originatingfrom levels populated by VET after excitation of states in the OH (A 2&`, v@\ 2) level.

1 IntroductionEnergy transfer is an ubiquitous process in chemistry. Considering the possibilities of motion of amolecule and its interactions with its environment, energy redistribution on the microscopic scaletakes place, depending on the quantum states and degrees of freedom of the molecule and thenature of its surroundings. Reaction kinetics may need information on inter- and intramolecularenergy transfer, often concerning electronic ground states. In contrast, energy transfer in and fromthe excited electronic state is considered in the present contribution, where the inÑuence of col-lisional processes on the LIF detection of small molecules in high-temperature combustion isinvestigated. The OH radical is the most exhaustively studied diatomic radical in this respect,because of its importance in combustion and atmospheric chemistry, therefore, its spectroscopy isvery well-known.1h3 Many of the numerous combustion studies presented at the biannual Interna-tional Combustion Symposia4,5 have used LIF of OH in characterizing Ñame structures, in mea-suring temperatures or in providing experimental data for kinetic model validation. Typically, anexcited-state population in a speciÐc quantum state is prepared using a pulsed laser, and theOH-LIF signal is detected in the AÈX band to measure OH concentrations or to monitor theÑame temperature. Depending on the chemical composition, temperature and the pressure of thecombustion environment, collisional processes lead to a redistribution of the energy and popu-lation during the lifetime of the excited electronic level.6

Quantitative OH-LIF measurements in Ñames at atmospheric pressure using nanosecond laserstypically require, at least, information on electronic quenching as a function of the excited statequantum numbers and collision partner mixtureÈa requirement not easily met in turbulent com-bustion studies. Even broadband detection schemes which are often used in two-dimensional

DOI: 10.1039/b102058g Faraday Discuss., 2001, 119, 275È286 275

This journal is The Royal Society of Chemistry 2001(

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imaging experiments will need information on the spectral structure of the signal. Here, quenchingcompetes with vibrational (VET) and rotational energy transfer (RET), processes which alsodepend on the quantum states, temperature, pressure and chemical composition. In order to keeptrack of all individual state-to-state transfer steps, hundreds of respective rate coefficients mayeasily be involved. Often, experimental strategies are thus employed which are thought to mini-mize the inÑuence of collisions, including saturated LIF and predissociative LIF.7h11 However,both approaches may be a†ected strongly by energy transfer in the ground state.11,12

Recently, the use of picosecond lasers has been suggested for quench-free measurements13h17with the idea being to either excite and detect the Ñuorescence in a very short time interval withrespect to typical collision times (of the order of 100 ps in atmospheric pressure Ñames) or toobserve the complete temporal decay of LIF signals. Picosecond OH concentration measurementswere performed in turbulent, non-premixed Ñames.18 Also, some energy transfer coef-CH4/H2/N2Ðcients for OH have been measured by Nielsen et al.19 and Beaud et al.20 for the A 2&`, v@\ 2and v@\ 1 vibrational states, respectively, using picosecond LIF. In this context, Beaud et al.20have been the Ðrst to report polarization-dependent energy transfer coefficients in OH-LIF.Whereas an early paper21 had already analyzed polarization e†ects in OH-LIF spectra observedin an atmospheric pressure Ñame, the inÑuence of polarization has largely failed to attract furtherattention in LIF combustion measurements, with only a few exceptions.7,22 An interesting ques-tion in picosecond OH-LIF studies using polarized excitation or detection is thus the collisionally-induced reorientation or depolarization process,19,22,23 a potential additional complication. In acollision-free environment, polarization ratios for individual lines may be calculated following ref.21 and Ñuorescence intensity distributions may be derived which are una†ected by collisions.However, it is intuitively clear that collisions will tend to destroy any preferential orientation, andagain, this process may depend on the chemical nature of the collisional environment and on thequantum states involved.

In an attempt to analyze potential collisional inÑuences for typical LIF experiments in com-bustion diagnostics, we have been using a combined approach of experiment and simula-tion.22,24h31 A computer code (LASKIN) has been developed which uses kinetic equations todescribe state-to-state energy transfer in the OH A 2&` state.28,29,31 After experimental investiga-tion of RET in v@\ 0 and v@\ 125,27 and VET30 between these two levels for some combustion-relevant collision partners, we have recently been able to satisfactorily simulate the predominanttrends observed in OH-LIF experiments under a wide range of conditions.31 In spite of the com-paratively large available data base existing for OH, remaining key questions were identiÐed inthis study. These include a lack of information on energy transfer in the higher vibrational levels,v@\ 2 and v@\ 3, from which branching ratios for VET with one or more vibrational quantacould be derived ; also, the interdependence of vibrational and rotational relaxation, i.e. the““nascent ÏÏ rotational distribution associated with a VET step, is not well known.

In view of these open questions and the unresolved question of collisional depolarization, wehave recently developed a novel experimental approach using, simultaneously, time-, wavelength-and polarization-resolved picosecond OH-LIF.22 With a further improved apparatus and sensi-tivity, the present study will report the Ðrst rotationally-resolved energy transfer measurementsexciting the OH (A 2&`, v@\ 2) state in a well-deÐned combustion environment. In conjunctionwith the simulation by the LASKIN program, the inÑuence of VET and RET in typical rotation-ally resolved and broadband LIF combustion diagnostics experiments will be discussed.

2 ExperimentalThe experimental set-up used for the experiments described in this paper basically consists of twoparts : a picosecond laser and a detection system basing on a streak camera. Both are shownschematically in Fig. 1. The system consists of a tunable Ti : sapphire oscillator (Spectra Physics,““Tsunami ÏÏ) and a three-stage ampliÐer (Spectra Physics, model TSA-50). The oscillator is pumpedby an argon ion laser and runs at a repetition rate of 80 MHz. Pulse durations of nominally 3 or80 ps may be selected ; the resulting line width is close to the Fourier transform limit. The ampli-Ðer system consists of one regenerative ampliÐcation stage and two double-pass travelling-waveampliÐers ; two frequency-doubled Nd : YAG lasers running at a repetition rate of 10 Hz are usedas pump sources. The ampliÐed output, also at 10 Hz repetition rate, can then be frequency

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Fig. 1 Experimental set-up. The oscillator is a mode-locked Ti : sapphire laser. Ar` pump laser ;P1 : P2 , P3 :Nd : YAG pump laser ; THG: frequency tripling unit ; P : polarizer ; L : lens ; B : burner ; M: mirror ; Sp :spectrograph ; SC: streak camera ; CCD: detector camera ; PC: computer. The inset shows the geometry oflaser and signal polarization directions.

doubled, tripled and quadrupled. In order to reach frequencies other than those obtainable byharmonic generation, a Raman shifter (10 bar is used. Thus, nearly the complete wavelengthH2)range from 200 to 900 nm can be covered. With the 80 ps pulse length option, pulse energies up to5 mJ are achievable in the UV.

The UV laser beam is mildly focused into the Ñame using a 2 m focal length lens with the focalpoint located 20 cm downstream of the observation location to further reduce the power densityand to avoid saturation. In some experiments, the polarization purity of the beam is enhanced bya Rochon-type polarizer (Laser Components ; air-spaced UV quartz version) located before thelens. The LIF signal is collected by a large aperture ( f number : f/1), spherical, concave mirror with

coating, in the usual 90 degrees excitationÈdetection geometry. The mirror is aligned toAl : MgF2image the laser focal region onto the spectrograph entrance slit. A GlanÈThompson polarizer(Halle ; selected calcite crystal, cut angle optimized for UV wavelengths) is mounted in a rotationstage directly in front of the entrance slit assembly.

The spectrograph is a 275 mm focal length, f/4 aperture model (Spectra Pro 275, ActonResearch) equipped with a set of three gratings mounted on a turret. In this work, the gratingswith 1800 and 3600 grooves mm~1 were used. The spectrograph is mounted with the entrance slitoriented parallel to the laser beamÏs propagation direction. The exit plane is imaged onto theentrance slit of a streak camera (Hamamatsu Model C2830) so that the slit is parallel to thewavelength axis. On the output side of the camera, a gated microchannel plate image intensiÐer ismounted. Streak ranges between 0.5 and 10 ns are selectable. The spectrally and temporally dis-persed signal is eventually detected with a cooled, slow-scan CCD camera which provides a 12 bitdynamic range. The raw data consists of a two-dimensional image, where the dimensions corre-spond to the wavelength and timescales. The spectral system response of the detection system wascalibrated using deuterium and halogen lamps.

For some experiments, the spectrometer was substituted with a set of colored glass Ðlters (UG11and WG305) which form a bandpass from 295 to 395 nm and the streak camera was rotated by90¡ so that its entrance slit was oriented parallel to the laser beamÏs propagation direction. Thisgeometry allows line-wise concentration measurements along a 5 mm line.

Two di†erent burner types are used to generate OH radicals : A Hencken burner (squarematrix, 25 mm ] 25 mm) was used for Ñames. It provides a relatively uniform Ñow Ðeld,H2/airhas little heat transfer to the burner body and is thus easy to characterize. A commercial welding

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Fig. 2 Time- and wavelength-resolved raw image obtained in a Ñame after excitation of the AÈX (1È0)H2/O2transition (image already corrected for background and detection efficiency).R1(7)

torch was used for hydrogen/oxygen Ñames. This o†ers the advantage of much higher temperatureand a correspondingly larger OH number density, at the expense of less well-deÐned conditions.

Using an input pulse of nominally 80 ps duration, the temporal resolution of the detectionsystem was tested by observing Rayleigh scattered light. Averaging over 1200 pulses results in asignal of about 90 ps FWHM, indicating a jitter of *t O 30 ps. For the experiments performedwith the 3600 g mm~1 grating, the temporal signal is broadened to about 140 ps due to di†erentpath lengths in the spectrometer ; this e†ect is described in detail in ref. 22. Overall, the temporalresolution of the complete system is very well matched to the typical time between collisions inatmospheric pressure Ñames ps). The laser bandwidth was checked with excitation scans(qc B 100of di†erent lines. Typical line widths are about 1 cm~1 in the UV, or 0.33 cm~1 with respect to theTi : sapphire fundamental frequency scale. Doppler broadening (about 0.3 cm~1) contributes tothis linewidth. The present laser system is thus well suited to the resolution of individual lines inthe OH spectrum.

For the measurements described in this paper, only a part of the laser energy (0.3 to 1 mJ) wasused in order to avoid saturation. The entrance slit of the spectrograph is set at 150 lm width, thestreak camera entrance slit is opened up to 200 lm width, and the streak range is set to 5 ns. Withthese settings, typical acquisition times are 5È15 min (3000È9000 laser pulses). For calibration, theRayleigh signal scattered from room air is recorded to provide the ““ t \ 0ÏÏ point, and a measureof temporal resolution. Additionally, the dark signal of the camera is acquired at regular intervals.

Fig. 2 shows a typical time- and wavelength-resolved raw image obtained in a ÑameH2/O2after excitation of the (1È0) line. The background is already subtracted, and the image hasR1(7)been corrected for the varying detection efficiency of the camera. Intensities are given in a lineargrey scale. Fluorescence from the directly populated levels can be clearly discerned by the highintensity at the time of the excitation laser pulse. As time progresses, additional lines from levelspopulated by energy transfer (both RET and VET) appear.

3 Results and discussion3.1 Rotationally resolved LIF spectra

For a more detailed study of energy transfer processes, Fig. 3 shows wavelength-resolved spectraextracted from the raw data in Fig. 2 for two di†erent time intervals (top : [120 \ t/ps \ 80,

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Fig. 3 Fluorescence spectra for di†erent time intervals after excitation of the (1È0) line (solid) andR1(7)comparison with LASKIN simulations (broken lines). The experimental proÐles are extracted from the rawdata presented in Fig. 2.

middle : 470 \ t/ps \ 670) and for the fully time-integrated case (bottom). Excitation was in the(1È0) line. For the Ðrst time interval, the spectrum is clearly dominated by the major P-, Q-R1(7)and R-lines originating from the directly populated level. The weak lines visible between 316 and318 nm are due to the small amount of energy transfer present even this close to the exciting laserpulse. Roughly 600 ps later, the Ñuorescence spectrum has changed dramatically. Now, Ñuores-cence stemming from several levels populated by energy transfer can be observed. The majorfeatures are now the band heads of the and branches at 312 and 315 nm, respectively. NoteR1 Q1especially that a signiÐcant amount of Ñuorescence is visible at wavelength shorter than 312 nm.This is due to vibrational energy transfer into the v@\ 0 level. Analysis of the temporal evolutionof the LIF signals (cf. Fig. 2) shows that the Ñuorescence from levels populated by VET reaches itsmaximum at times around 1 ns, which is signiÐcantly later than that from levels populated byRET. Since the population in the v@\ 0 state decays more slowly than that of the initially popu-lated level, the contribution of lines originating from v@\ 0 to the time-integrated Ñuorescence isrelatively high (D15%, cf. Fig. 3, bottom). Implications of this e†ect for broadband measurementswill be discussed in the next section.

For a simulation of energy transfer processes, the composition of the surrounding gas has to beknown. Taking into account the mixing with ambient air always present when using the small-diameter welding torch, the premixed fuel used in the experiments above consists of approximately40% 40% and 20% Using the code of Gordon et al.,32 the following species concen-H2 , N2 O2 .trations have been calculated assuming adiabatic conditions : 47.5% 40.8% 5%N2 , H2O, H2 ,

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2.8% OH, 1.5% 1.3% H and 0.5% O. The adiabatic Ñame temperature is K.O2 , Tadiab\ 2708These values are used as input parameters for a simulation using the LASKIN package. Results ofthe calculation are plotted as broken lines in Fig. 3 ; intensities are normalized to the strongest linein each spectrum. For the fully time-integrated case, comparison of experimental and modeledspectra shows a very good agreement both for lines populated by RET and by VET. Some dis-crepancies still exist for Ñuorescence originating from the directly populated level. This can be seenmost easily in the upper frame of Fig. 3, where the intensity of the P- and R-lines is over-predictedby about 30%. This is mainly due to polarization e†ects that occur since the laser is linearlypolarized and since the spectrometer detection efficiency is also polarization dependent. For thecollision-free case, these e†ects have already been discussed in detail by Doherty and Crosley.21 Incontrast, only a few experiments have been performed to date to study the temporal evolution ofthe anisotropy.19,20,22 Work to include polarization e†ects in the simulation code is currentlyunder way,23 however, it can be seen that even in the current state of development, LASKIN is areliable tool for predicting the shape and temporal evolution of spectra a†ected by energy transfer.

3.2 InÑuence of energy transfer on broadband LIF measurements

In most cases, broadband LIF measurements are used for minor species concentration determi-nation. This means that, in contrast to the measurements described above, Ñuorescence is inte-grated over a wider spectral range (commonly by use of colored-glass or dielectric Ðlters) before itis passed to the detector. The major advantage of this approach is a signiÐcantly better signal-to-noise ratio (SNR) that even allows single-pulse and/or spatially resolved measurements if a suit-able detector is used. Recently, short-pulse lasers and detection systems that allow quench-freeLIF measurements to be performed have become available. The basic idea of these techniques isalways that, at times very close to the exciting laser pulse (that is, at t \ 0), the signal is nota†ected by collisions. Several signal detection techniques have been suggested. The easiest is to usea detector with a gate interval of the order of several hundred picoseconds.15 However, our resultsshow that even for very short gate times, signals are a†ected by energy transfer and quenching (cf.Fig. 3, top). Thus, this technique is quenching-insensitive to some extent, but not truly quench-free. More sophisticated approaches analyze the temporal decay of the LIF signal, either by evalu-ating several gated intervals16 or by observing the full temporal evolution of signals by means of astreak camera.17 Extrapolation of the observed signal intensity backwards to t \ 0 (that is, to thecenter of the exciting laser pulse) then allows one to determine completely quench-free results.This evaluation procedure is described in detail in ref. 17.

Our time- and wavelength-resolved measurements along with the numerical simulations allowus to study in detail how collision-induced processes, in particular VET, might inÑuence eventhese quench-free measurements. For this, we used LASKIN to model a time-integrated Ñuores-cence spectrum after excitation of the OH AÈX (1È0) line in a Ñame at U\ 1.0 andQ1(7) H2/air

K. The results are shown in Fig. 4 (solid line). It can be seen, that besides Ñuores-TadiabB 2400cence from the directly populated level, a multitude of lines populated by RET in the v@\ 1 stateis present. Also, a signiÐcant contribution of Ñuorescence from the v@\ 0 state which is populatedby VET is observed. Since the (0È0) and the (1È1) band partially overlap and transmission curvesof Ðlters are usually not steep enough, discrimination of these bands is generally not possible. In atypical experiment for minor species concentration, only the sum of these signals will be detected.To illustrate this, the transmission curve of a typical Ðlter combination (UG11/WG305) used forbroadband LIF measurements is plotted along with the spectrum in Fig. 4 (dashed line).

Fig. 5 shows the time-integrated, state-resolved population distribution for the spectrum plottedin Fig. 4. The major part of the population (62%) is found in levels populated by RET; only about13% remains in the directly excited level J@\ 7. Quite a notable fraction, i.e. 19% of the popu-lation, is observed in the v@\ 0 state which is populated by VET. Again, this emphasizes thesigniÐcant contribution of VET to the shape and intensity of LIF spectra. The results of thissimulation compare favorably with the observed spectra shown in Fig. 3 (where the directly adja-cent J@\ 8 level has been populated). Since the Einstein A coefficient for spontaneous emission isabout 50% higher in the v@\ 0 level than in the initially populated v@\ 1 level,2 the contributionof VET to the total Ñuorescence is even higher (in this case, more than 25%).

Whereas the contributions of the di†erent vibrational states are readily detected in our

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Fig. 4 LASKIN simulation of the Ñuorescence spectrum after excitation of the OH AÈX (1È0) line in aQ1(7)Ñame, U\ 1.0, K (solid line). The dashed line shows the transmission curve of a typicalH2/air Tadiab B 2400

Ðlter combination (UG11/WG305) used for broadband LIF measurements.

wavelength-resolved measurements, only the integrated Ñuorescence from these states is visiblewhen broadband detection is employed. When performing time-resolved measurements, this hassigniÐcant consequences : Since levels in v@\ 0 are populated by a relatively slow process (VET)and their relative contribution to the total Ñuorescence is higher than that originating from v@\ 1(due to the di†erence in the A coefficient), the total Ñuorescence will no longer be a single expo-nential, but a more complex function of time.

To illustrate this deviation from the single-exponential decay, the following simpliÐed modelcan be used : Consider a two-level system with equal rate coefficients for spontaneous emissionand quenching (combined in in both levels, and allow for energy transfer 0^ 1 between thesekq)levels with a rate Excitation is in the v@\ 1 level. In this case, populations can be describedkVET .by the following di†erential equations :

dN1dt

\ [(kq ] kVET)N1

dN0dt

\ kVETN1[ kq N0

Solutions are :

N1\ N10 e~(kq`kVET)t

N0\ N10 e~kqt [ N10 e~(kq`kVET)t

The LIF intensity can be calculated according to :

ILIF(t)\ g0N0(t)] g1N1(t)Here, the weighting factors of the two Ñuorescence contributions are proportional to the Ein-g

istein A coefficients and/or the detection efficiency. By substituting the expressions for it can beNi,

seen that the solution is a bi-exponential decay. In Fig. 6, time-resolved plots of the LIF intensityare shown for three di†erent cases. For the expected single-exponential function (solidg0 \ g1,line) is observed. For some deviations occur : the intensity is higher for all times, andg0\ 1.5g1,the proÐle is nearly linear at short times (up to t \ 0.5 ns). As mentioned above, this case closelyresembles the excitation of OH in the AÈX (1È0) band with broadband detection of Ñuorescence inthe 0È0 and 1È1 band. The deviations from a single-exponential become even more pronouncedfor Here, the maximum Ñuorescence occurs at t \ 0.3 ns (and not at t \ 0 as in the otherg0 \ 3g1.cases).

It should be pointed out that the methods for quench-free measurements described above willno longer be reliable for spectra signiÐcantly a†ected by VET, since the extrapolation of the

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Fig. 5 Time-integrated, state-resolved population distribution (based on the simulation shown in Fig. 4).Rotational quantum number increases from left to right (J@\ 0 to J@\ 20 is shown) ; for each J@, population inboth Ðne-structure components is shown independently.

observed signal intensity backwards to t \ 0 becomes more complicated. This is most severe forthe detection technique using several gated intervals,16,18 since, here, a single-exponential decaycurve has been explicitly assumed in the data evaluation routine. If the full temporal evolution ofsignals is monitored by means of a streak camera,17 deviations of the LIF intensity from theexpected single-exponential curve can be detected and, in principle, be taken into account.However, reliability of the Ðt, and thus that of the concentration measurement will su†er if theexperimental data have to be Ðtted to a curve with several additional parameters.

In addition to the mechanism described above, there may be further reasons for a deviation ofthe observed temporally-resolved LIF intensity from the expected single exponential. Generally,energy transfer to other levels will lead to a non- or multi-exponential decay if quenching rates orEinstein A coefficients in the populated levels are di†erent, or if the Ðlter efficiency is non-uniform.Additionally, polarization e†ects22,23 or saturation in the excitation step might lead to deviations.

For OH detection there is, however, an easy way to compensate for the e†ects of the higherEinstein A coefficient in the v@\ 0 level. If a Ðlter with a lower transmission at lower wavelengthsis used, Ñuorescence from v@\ 0 will be attenuated and the e†ect of the di†erent Einstein coeffi-

Fig. 6 E†ect of di†erent Einstein coefficients and/or detection efficiency of levels populated by energy transferon wavelength-integrated, time-resolved measurements.

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cients is (at least partially) compensated. In our work, we found that the combination of twoSchott colored glass Ðlters of types WG305 and UG11 is well suited for this purpose (compare thetransmission curve in Fig. 4). In consequence, no deviation from single-exponential behavior wasobserved during our quantitative minor species concentration measurements.17

3.3 Detailed discussion of spectra populated by VET

For a more detailed analysis of the role of vibrational energy transfer for the temporal evolutionof OH LIF spectra, we decided to probe the A 2& v@\ 2 level. This has the advantage, that thetransfer of more than one vibrational quantum can be observed. Fig. 7 shows part of the rotation-ally resolved, time-integrated Ñuorescence spectrum after excitation of AÈX (2È0) Here, theQ1(8).strongest Ñuorescence line is the (2È2) transition at 318.6 nm. Other lines originating fromR1(7)the directly populated level would appear at longer wavelengths and are thus not visible in Fig. 7.Next, a multitude of lines from levels populated by VET are seen : lines belonging to the (1È1)system appear at wavelengths j P 312.5 nm, whereas lines from the (0È0) system appear at wave-lengths j P 306.5 nm. Note, that the spectra partially overlap. Other distinct features are the R1and band heads for the individual vibrational levels ; their position is marked in Fig. 7.R2In order to study the e†ects of the collisional environment on the rotational structure of spectrawhere several vibrational levels are populated by VET, a systematic series of measurements hasbeen performed for di†erent Ñame conditions and excitation lines. Fig. 8 shows a detailed view ofthe (1È1) part of the time-integrated Ñuorescence spectra at two Ñame stoichiometries (U\ 0.5 andU\ 1) in a Ñame. Excitation was in the transition AÈX (2È0) to facilitate compari-H2/air P1(5) ;son, intensities are normalized to the band head. It is clearly seen, that the rotational structureR1in both spectra is very similar. Even for individual rotational lines, deviations are usually wellbelow 10%. Equally, similar spectra are found for other Ñame stoichiometries, indicating that theinÑuence of collision partners and temperature on the rotational structure is small.

Next, we compared spectra obtained with three di†erent excitation lines, namely the P1(5),and line. Even though slightly larger di†erences occur than in Fig. 8 (up to 20% forQ1(8) R1(11)

individual rotational lines), the overall structure changes only insigniÐcantly. Especially, no prefer-ence for the directly populated rotational level was observed, indicating that the rotational popu-lation distribution is scrambled completely during a VET step. Comparison of spectra originatingfrom the v@\ 0 level (that is, after transfer of two vibrational quanta) show an even greater simi-larity. Considering the signal-to-noise ratio in our measurements, the spectra are virtually indistin-guishable.

Fig. 7 Rotationally resolved, time-integrated Ñuorescence spectrum of the (0È0) and (1È1) band populated byVET after excitation of AÈX (2È0) Q1(8).

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Fig. 8 Detailed view of the (1È1) part of the time-integrated Ñuorescence spectra at two Ñame stoichiometriesin Ñames. Excitation in the transition AÈX (2È0) The spectra are normalized to the band head.H2/air P1(5). R1

For further analysis, we compared measured spectra with simulated ones using the LIFBASEcode.33 This is shown in Fig. 9 for an experimental spectrum after excitation of (2È0) (solidQ1(8)line) and a simulation for an apparent temperature of K (broken line) ; covering theTa0 \ 7000spectral interval 306 O j/nm O 312, which corresponds to the (0È0) Ñuorescence band. The overallagreement between both spectra is good. Note, that is not the true Ñame temperature (thatTa0would be K), but it reÑects the rotational distribution in the ““hot ÏÏ band populatedTadiab\ 2400by VET. A similar analysis has been performed for the (1È1) band of the Ñuorescence spectrum.Here, because of the overlap between the vibrational bands originating from v@\ 1 and v@\ 0 (cf.Fig. 7), the spectrum Ðtted for the (0È0) portion has to be subtracted Ðrst. Comparison withspectra generated by LIFBASE showed that the (1È1) band can be described similarly well by thenumerical code. However, the apparent temperature of the rotational distribution in v@\ 1 is

K in this case. This value compares favorably with results by Crosley et al., whoTa1 \ 4000obtained in the (0È0) band populated by VET after excitation of AÈX (1È0) in2250 O Ta/K O 3280a lean methane/air Ñame.34

Fig. 9 Comparison between an experimental spectrum populated by VET after excitation of (2È0) Q1(8)(solid line) and a spectrum simulated by LIFBASE (broken line, K). The spectra are normalized toTa0 \ 7000the band head.R1

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Evaluation of these Ðts allows the determination of the time-averaged population in the vibra-tional states v@\ 2, 1 and 0, respectively. For a stoichiometric Ñame, the ratio of the popu-H2/airlations is 66 : 18 : 16 ; for U\ 0.5 this changes to 51 : 26 : 23. The reason for that is the higherabundance of as an efficient quencher in the former Ñame. The short Ñuorescence lifetime inH2Othis environment allows only a limited amount of energy transfer. In contrast, is the dominantN2collision partner in the lean Ñame; it is much more efficient for VET.35h37 Both results are consis-tent with previous Ðndings.31 Note, that the ratio of the relative time-integrated population inboth levels populated by VET remains constant.

Finally, we have analyzed the temporal evolution of spectra populated by VET. Whereas asmall change in the spectrum with time is observed for v@\ 1, the shape of the rotational structurein v@\ 0 is nearly constant over time. This suggests, that a signiÐcant part of the v@\ 0 level ispopulated by two consecutive VET steps rather than by one step alone with *v\ [2. In conjunc-tion with previous results31,38,39 it seems likely that, for OH, both single- and multiple-quantumvibrational energy transfer contributes to the population in v@\ 0.

4 SummaryTwo-dimensional, time- and wavelength-resolved LIF spectra of OH in atmospheric-pressureÑames have been obtained using a short-pulse laser in conjunction with streak detection. Thisapproach allows the simultaneous observation of time-resolved Ñuorescence from the directlypopulated level as well as from several levels populated by RET and VET and thus facilitates theinvestigation of energy transfer processes. Rotationally resolved spectra after excitation in theAÈX(1È0) band are in good agreement with the results obtained by simulations using the rateequation model LASKIN. Small deviations, especially for Ñuorescence originating from thedirectly populated level, can be attributed to polarization e†ects, which are not yet included in themodel. However, it can be seen that even in the current state of development, LASKIN is areliable tool for prediction of shape and temporal evolution of spectra a†ected by energy transfer.

Measurements and simulations show, that the v@\ 0 level is signiÐcantly populated by VET andthat Ñuorescence from this level may contribute up to 30% of the total Ñuorescence detected bybroad-band techniques. Since Einstein A coefficients are higher in this level, this may seriouslya†ect picosecond-LIF techniques for the time-resolved, quench-free detection of OH. It is shown,that VET may lead to non- or multi-exponential decay in this case. However, these e†ects can betaken into account and compensated for, if suitable Ðlters are used for the Ñuorescence detection.

Additionally, we report the Ðrst rotationally-resolved energy transfer measurements after excita-tion of OH (A, v@\ 2) states in well-deÐned, atmospheric-pressure Ñames. Detailed analysis of LIFfrom levels populated by VET shows that for the and Ñames investigated in thisH2/air H2/O2contribution, the overall shape of the Ñuorescence spectra is insensitive to the collision environ-ment, the temperature and the excitation line. For our Ñames, it can be described by a LIFBASEsimulation with a high apparent temperature (4000 and 7000 K for the v@\ 1 and v@\ 0 levels,respectively). Di†erences in the temporal evolution of Ñuorescence spectra originating from v@\ 1and v@\ 0 suggests, that for OH, both single- and multiple-quantum vibrational energy transfercontribute to the population in v@\ 0.

AcknowledgementContributions of U. Rahmann, U. Lenhard and A. to the work presented in this paper areBu� ltergratefully acknowledged. Financial support was provided by the DFG under contract 1363/9-1.

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