OODR-LIF direct measurement of N2(C 3Πu, v = 0–4) electronic quenching and vibrational relaxation rate coefficients by N2 collision

Chemical Physics Letters 431 (2006) 241–246 www.elsevier.com/locate/cplett

OODR-LIF direct measurement of N2(C 3Pu, v = 0–4) electronic quenching and vibrational relaxation rate coefficients by N2 collision G. Dilecce *, P.F. Ambrico, S. De Benedictis Istituto di Metodologie Inorganiche e dei Plasmi-CNR, sede di Bari, Via Orabona, 4 – 70126 Bari, Italy Received 2 August 2006; in final form 18 September 2006 Available online 30 September 2006

Abstract We report measurements of electronic quenching and vibrational relaxation rate constants by collision with N2 of the whole N2(C3Pu, v = 0–4) vibrational manifold. These results are obtained by selective excitation of single vibrational levels by Optical–Optical Double Resonance laser pumping from the triplet metastable N2 ðA3 Rþ u Þ, and observation of the fluorescence (LIF) emitted by both directly pumped and collision populated vibrational levels. A pulsed dielectric barrier discharge is used as N2 ðA3 Rþ u Þ source.  2006 Elsevier B.V. All rights reserved.

1. Introduction Collision phenomena relevant to the C3Pu state vibrational manifold are:  0 N2 ðC3 Pu ; vÞ þ N2 ðX1 Rþ g ; v Þ ! N2 þ N2 1

3

N2 ðC Pu ; vÞ þ N2 ðX þ N2 ðX

1

0 Rþ g ;w Þ

0 Rþ g ;v Þ

ð1Þ

3

! N2 ðC Pu ; wÞ

þ trasl þ rot

ð2Þ

The electronic quenching (1) moves species outside the C3Pu state, while the vibrational relaxation (2) redistributes species inside the C3Pu state. In our previous work [1] we used Optical–Optical Double-Resonance Laser Induced Fluorescence (OODR-LIF) for the measurement of level v = 2 quenching. That was the first such measurement obtained by a vibrational level-selective excitation of Cstate. All previous experiments had been carried out by non-selective excitation techniques: fission fragments [2], a particles [3], proton [4], pulsed electron beam [5] and discharge [6–8]. The experiment in [2] revealed a vibrational relaxation component of the quenching, claiming, *

Corresponding author. Fax: +39 0805442024. E-mail address: [email protected] (G. Dilecce).

0009-2614/$ - see front matter  2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2006.09.094

for the coulple v = 1, w = 0, a relaxation cross section comparable to the electronic quenching one. On excitation of (C3Pu, v) by two resonant photons absorption from N2 ðA3 Rþ u Þ, fluorescence is observed from level v (‘direct’ fluorescence) and from all levels w < v (‘collision’ fluorescence). Direct fluorescence observation allows the measurement of the total quenching rate coefficient of level v, while collision fluorescence observation from levels w allows the measurement of both vibrational relaxation v ! w and w total quenching rate coefficients. The apparatus of [1] was not suited to a complete characterization of all the collision phenomena. The laser system allowed pumping level v = 2 only, while the discharge used as a N2 ðA3 Rþ uÞ source showed problems of stability and reproducibility. Collision fluorescence was observable, but at such a low signal level that a correct data analysis was very difficult. We have improved the experimental apparatus by using two tunable lasers for OODR-LIF and a dielectric barrier discharge as a N2 ðA3 Rþ u Þ source. In this Letter, we present the first measurements of collision rate constants of the N2(C3Pu, v = 0–4) manifold, i.e. both electronic quenching and vibrational relaxation, after selective vibrational state excitation and fluorescence observation, achieved by the new OODR-LIF plus DBD discharge apparatus.

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2. Experimental details 80

The OODR- LIF measurement is based on the following scheme for the two resonant photons excitation:

ð3Þ

The photons are produced by two pulsed Nd-YAG pumped dye lasers. The FPS (3, 0) band, with band head at 687.7 nm is pumped by the fundamental of one laser with LDS698 dye (bandwidth 0.04 cm1). The second laser with a selection of dyes and second harmonica generation by BBO crystal (bandwidth 0.4 cm1), produces the photons for the (1, 3), (2, 3), (3, 3) and (4, 3) bands of the SPS system. Level v = 0 is not directly pumped due to difficulties in generating the proper wavelength. Both lasers are tuned close to the band-heads, such that the maximum signal is achieved. In this way we pump the low J rotational levels, even if we cannot state exactly which levels are pumped. The two lasers are synchronized by means of a timing card that drives all the flash lamps and Pockels cells. The relative time position of the two laser shots is finely adjusted with sub-ns resolution by an additional delay generator in the trigger line of one of the two Pockels cells drive. The two laser beams are recombined into a dichroic plate and sent collinearly into the discharge gap. The energy/pulse fed into the discharge chamber is about 20 mJ for the red laser and 3–5 mJ for the UV photons. The duration of the laser pulses, as measured by a 350 MHz bandwidth oscilloscope, is about 10 ns FWHM. The discharge (more details in [9]) is a dielectric barrier one, with 8 · 10 mm2 parallel plate electrodes made of a silver–palladium enamel on alumina plates. The discharge setup is mounted inside a vacuum chamber. The N2 gas is fed into the discharge gap through a slit aperture close to the gap and parallel to the electrodes. The power supply is a chain of a gateable sine-wave generator, a wideband amplifier and a HV transformer (max 10 kVpp, 50 Hz to 5 kHz operation frequency). Along the experiments the discharge is operated at pressures in the range 2–35 Torr, gas flux 100–1000 sccm, voltage around 1 kVpp 5 kHz, pulsed at TON = 5 ms and TOFF = 10 ms, and at a fixed gap of 5 mm. The DBD produces a sufficiently large triplet metastable density at room temperature. The pulsed discharge and a large flow rate help maintaining low the gas and alumina electrodes temperature. SPS emission spectroscopy, in the hypothesis that Tgas = Trot, showed that the gas temperature is Tgas = (290 ± 10) K in the whole range of experimental conditions. Fluorescence signals from levels v and w are detected simultaneously. The fluorescence light, after the collection optics, is split by a 50% beam splitter into two paths that reach two monochromators equipped with two identical photomultipliers (Hamamatsu R2949). The bandwidth of the monochromators is adjusted such as

Signal (mV)

! N2 ðC3 Pu ; vÞ

60 50 40 30 20 10 0 -10

-200

-100

0

100 Time (ns)

200

300

400

(1,2) band - direct (0,1) band - collision

20 Torr

70

Signal (mV)

00 3 0 N2 ðA3 Rþ u ; v ¼ 0Þ þ hmL1 ! N2 ðB Pg ; v ¼ 3Þ þ hmL2

(1,2) band (0,1) band

5 Torr

70

50

30

10

-10

-200

-100

0

100

200

300

Time (ns)

Fig. 1. Fluorescence signals in the case of level (C, v = 1) laser excitation. Solid line is the ‘direct’ fluorescence [observed through (1, 2) band]. Dotted line is the ‘collision’ fluorescence from level w = 0. In the 20 Torr figure, the light from (1, 2) is attenuated by a factor 8.5 by means of a calibrated metallic filter.

to collect one whole fluorescence band without superposition with adjacent bands. The signal is then measured by a digitizing oscilloscope (Le Croy waveRunner 6030A). In Fig. 1 we report an example of such signals. Since the direct fluorescence signal can be very high, reaching peak values of the order of 20 mA, it is attenuated by means of calibrated metallic filters down to values lower than 2 mA, that is the pulse saturation limit of the photomultiplier. 3. Results The analysis of fluorescence curves as those shown in Fig. 1 provides three rates. Simple fit of the exponential decay of level v fluorescence gives the total (electronic + vibrational relaxation) quenching rate of level v. Analysis of level w fluorescence gives both the v ! w relaxation rate and the w quenching rate. Measurements at many pressures and Stern–Volmer plot analysis give the relevant rate coefficients.

G. Dilecce et al. / Chemical Physics Letters 431 (2006) 241–246 16 v=4 v=3 v=2 v=1 v=0

14

10

7

-1

KvQ (10 s )

12

8 6 4 2 0 0

10

20

30

40

Pressure (Torr)

Fig. 2. Stern–Volmer plots of (C, v = 0–4) quenching rates in the pressure range 2–35 Torr.

3.1. Total quenching The criteria for the exponential fit of the decay of the direct fluorescence are the same as those discussed in [1]. Only note that the duration of the laser pulse is much shorter than that of the fluorescence pulse, so that a long single exponential decay region is available. Stern–Volmer plots relevant to all levels v = 0–4 are reported in Fig. 2. Level v = 0 is not directly excited, and the relevant plot is made of the quenching rates obtained by collision fluorescence analysis after v = 1 excitation (see Section 3.2.1). The rate coefficients of the total collision quenching, k Qv , calculated at Tgas = 290 K are reported in Table 1 and compared to literature data. Errors of the rate coefficients are the sum of fitting errors plus the error caused by the Tgas incertitude. The values of radiative probability deduced from the Stern–Volmer plots are in good agreement with the values of [11,12], confirming the validity of the measurements. The rate constants values of levels v = 0, 1, 2 agree well with those of [4,7,8], while they are markedly larger than literature data for levels v = 3, 4. Measurements based on emission

243

spectroscopy can infact suffer large errors on high v-levels, since the emission from v = 3, 4 is very low. For level v = 4 the rotational levels J P 28 are above the dissociation threshold [11]. Direct pumping of such levels might artificially increase the measured quenching rates. This is not the case for the present measurements. We pump only low-J levels, certainly with J < 28. If we were pumping J P 28 levels, the contribution of dissociation to the quenching would be pressure-independent, resulting in a constant shift towards higher values of the measured quenching rates. The Stern–Volmer fit would then give the same rate constant and a larger radiative rate, that is not observed in our measurements. On pumping J < 28, on the other hand, rotational collisions can push molecules above the dissociation threshold, leading to a pressuredependent contribution of the dissociation to the quenching. This is what happens with any excitation process, (and might be one of the reasons for such a high v = 4 quenching rate coefficient), so our measurements correctly represent real situations. The ‘pure’ electronic quenching rate coefficients, k Qel v , must be calculated by subtracting the vibrational relaxation from the total quenching ones. We report k Qel values v in Table 2 after the discussion on vibrational relaxation. 3.2. Vibrational relaxation 3.2.1. Collision fluorescence analysis We have calculated the vibrational relaxation rate coefficients from the simultaneous direct and collision fluorescence measurements by means of the following analysis. Let us define the quantities: Sx(t) = measured x = v, w-level fluorescence signal Nx(t) = x = v, w-level population Ax = x = v, w-level total radiative rate Axf = radiative rate of the x = v, w-level observed fluorescence band KQ = collison quenching rate of level x = v, w x Kv, w = v ! w collision transfer rate

Table 1 Quenching rate constants of the N2(C3Pu) state vibrational levels by collision with N2 (in 1011 cm3 s1) kQ v

A

v=0

v=1

v=2

v=3

v=4

Reference

1.14 ± 0.12

3.14 ± 0.21

6.34 ± 0.27

9.86 ± 0.46

1.09a 1.09a 1.09 ± 0.1 1.30 ± 0.2 1b – 1 2.77 ± 0.05 2.73 2.697

2.9 ± 0.4 2.7 2.53 ± 0.3 2.90 ± 0.3 3.30 ± 0.4 – 2.6 2.67 ± 0.02 2.75 2.668

4.28 ± 0.21 4.19 ± 0.13 4.3 ± 0.6 3.8 4.13 ± 0.4 4.60 ± 0.6 6.30 ± 0.8 8.1 – 2.72 ± 0.03 2.735 2.625

4.8 ± 0.8 4.2 4.28 ± 0.4 4.30 ± 0.6 8.00 ± 2.0 – – 2.62 ± 0.03 2.67 2.565

4.9 ± 0.9 3.9 – – – – – 2.36 ± 0.07 2.498 2.478

This work [1] Time-dependent model, [8] Steady-state model, [8] [4] [7] [6] [10] [3] This work [11] [12]

The radiative rate A is in 107 s1. a Level v = 0 value fixed to that of [4]. b Level v = 0 value fixed to that of [3].

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G. Dilecce et al. / Chemical Physics Letters 431 (2006) 241–246

Table 2 Vibrational relaxation rate constants of the N2(C3Pu) state vibrational levels by collision with N2 (in 1011 cm3 s1) wnv

0

0 1 2 3 P

w k v;w

k Qel v

1.14 ± 0.12

1

2

3

4

1.19 ± 0.13

0.528 ± 0.043 0.763 ± 0.094

0.734 ± 0.72 0.464 ± 0.59 0.360 ± 0.34

1.19 ± 0.13 1.95 ± 0.34

1.291 ± 0.137 2.989 ± 0.347

1.558 ± 0.165 4.782 ± 0.435

0.736 ± 0.067 1.02 ± 0.093 0.285 ± 0.036 0.105 ± 0.037 2.146 ± 0.233 7.714 ± 0.693

In the last row the value of the electronic quenching rate is reported.

C A

= spectral + geometrical light collection constant = attenuation factor on the v-level fluorescence band observation

The measured signals are proportional to the populations of excited states through the relation: S v ðtÞ ¼ CAN v ðtÞAvf ;

S w ðtÞ ¼ CN w ðtÞAwf

ð4Þ

The constant C is chosen to be the same for the two collection apparatuses, by including differences of the two light collection-detection paths in the attenuation factor A only. C will then be omitted from now on. The factor A is calibrated by measuring Sv(t) by both apparatuses tuned at the same wavelength. The factor A includes the beamsplitting ratio, alignment imperfections and different response of the monochromator/photomultiplier. In addition it includes the attenuation factor of the metallic filters used to attenuate Sv(t). When one of the monochromators is tuned to Sw(t), the factor A should also include a spectral response factor of this monochromator due to the different wavelength of the observed w-band and the calibration v-band. Such spectral factor can be discarded by choosing close bands (in the same sequence) for the v and w fluorescence measurements, since the spectral response of our apparatus is quite smooth in the spectral region of interest. This imperfection is anyway included in the allowed error of the factor A. Let us start from the simplest case: v  w = 1. The analysis combines a time-dependent description of the fluorescence signals and a correlation between the integrals of the fluorescence pulses. The population of the collision excited w state is described by the following equation: dN w ðtÞ ¼ N v ðtÞK v;w  N w ðtÞðAw þ K Q wÞ dt

ð5Þ

This equation is solved numerically with two parameters Kv,w and K Q w , with Nv(t) calculated by (4) from the measured Sv(t) signal, and the result fitted to the measured Nw(t). Furthermore, if we take the integrals of the measured fluorescence pulses: Z 1 Ix ¼ S x ðtÞ dt ð6Þ 0

Using (4) we obtain:

I v ¼ AAvf

Z

1

N v ðtÞ dt

and

I w ¼ Awf

0

Z

1

N w ðtÞ dt

ð7Þ

0

We integrate (5) as Z 1 dN w ðtÞ dt ¼ N w ð1Þ  N w ð0Þ ¼ 0  0 ¼ 0 0 Z 1 Z N v ðtÞ dt  ðAw þ K Q Þ ¼ K v;w w 0

1

N w ðtÞ dt

0

ð8Þ Combining (8) with (7) we obtain:   Aw þ K Q K v;w w 0 ¼ Iv  Iw Awf AAvf

ð9Þ

or: K v;w ¼

I w AAvf ðAw þ K Q wÞ I v Awf

ð10Þ

In (10) Kv, w depends linearly on K Q w . This is a stronger dependence than in the case of the time-dependent fit, so that the combination of the time-dependent analysis (5) and formula (10) provides a convergent algorithm for the determination of both Kv,w and K Q w. The procedure is as follows. From the measured fluorescence pulses the integrals Ix and the maximum of the collision fluorescence signal, S Max w , are calculated. Then: 1. S Max is put in the algorithm. This is the only parameter w external to the algorithm. 2. Kv, w and K Q w are varied in such a way that the value of the maximum of the fitting curve coincides with S Max w , until the value of Kv,w used in the fit and that calculated using (10) are equal. The calculated Nw(t) is in most cases perfectly superimposed to the measured one. In the practical application, the total quenching ðAw þ K Q w Þ is used. Analysis of measurements at various pressures allows constructing Stern–Volmer plots for both Kv, w and ðAw þ K Q w Þ. The comparison of the rate K Q measured in this way with that measured w from the fluorescence of the same level directly excited by the laser gives a control on the correctness of the analysis. The total quenching rate coefficient of level v = 0 is calculated only by this analysis, together with the 1 ! 0 vibrational relaxation rate coefficient, when v = 1 is excited.

G. Dilecce et al. / Chemical Physics Letters 431 (2006) 241–246

The general 1 6 v  w 6 4 case is an extension of this method including multi-step collision contribution to the w-level population. It is described in detail in the Appendix. 3.2.2. Rate constants The measured vibrational relaxation rate constants are reported in Table 2, and two examples of Stern–Volmer plots are shown in Fig. 3a and b. The errors are a sum of many components, caused by both statistical and systematic sources. Apart from the normal fit error, statistical error sources include the error in the determination of the maximum of the fluorescence signal and of the baseline subtraction. These errors are included in the error of individual data points. Systematic errors are two. The first one is the error of the attenuation factor, that is the same for all points of the Stern–Volmer plot. Dashed fits in Fig. 3 are the fits calculated using all maximum and all minimum values of Kv, w values, that, in turn, are determined using the extreme values of the attenuation factor. The fit parameters relevant to the dashed fits are used to calculate the error corresponding to the attenuation factor error.

245

The second systematic error is caused by the fact that there are two transition probability data sets in the literature for the SPS bands [11,12]. The Kv, w values are then calculated two times, one for each data set, and two independent Stern–Volmer plots are produced for each v, w couple. The rate constant values in the Table 2 are the average of the two values calculated by the two transition probability data sets, while the scattering of the two values is added to the error. The final contribution to the error is due to the Tgas error. All measurements are limited to a single excitationdetection bands couple, except for the case of k4,3, for which the measurements has been done two times with two different bands couples. One such measurement is reported in Fig. 3b. Due to the low value of k4,3 this measurement is the less precise one, so we checked it with a different bands couple. The error of k4,3 contains then the scattering between these two measurements. The ‘pure’ electronic quenching rate coefficients, k Qel v , must be calculated by subtracting the vibrational relaxation from the total quenching ones: X k Qel ¼ kQ k v;w ð11Þ v v  w

we report

k Qel v

values in Table 2.

14

Appendix. Collision fluorescence analysis in the general 1 < v  w < 4 case

12

K1,0 (10 6 s-1 )

10

We write in the following a set of equations that extend Eqs. (5) and (10) to the general case, retaining the idea of solving for Kv, w and K Q w with the same algorithm as for the simplest case already described. The time-dependent analysis is obtained by the following system of rate equations:

8 6 4 2 0 0

9

18

26

35

vw1 X dN w ðtÞ ¼ N v ðtÞK v;w þ N vi K vi;w  N w ðtÞðAw þ K Q wÞ dt i¼1

Pressure (Torr)

ð12aÞ dN v1 ðtÞ ¼ N v ðtÞK v;v1  N v1 ðtÞðAv1 þ K Q v1 Þ dt 1 dN v2 ðtÞ X ¼ N vi K vi;v2  N v2 ðtÞðAv2 þ K Q v2 Þ dt i¼0

11 10

K4,3 (10 5 s -1 )

9 8

2 dN v3 ðtÞ X ¼ N vi K vi;v3  N v3 ðtÞðAv3 þ K Q v3 Þ dt i¼0

7 6 5 4 3 2 10

15

20

25

30

35

Pressure (Torr)

Fig. 3. Stern–Volmer plots of vibrational relaxation rates in the cases: (a) K1, 0 with transition probabilities of [12] and (b) K4, 3 with transition probabilities of [11].

ð12bÞ ð12cÞ ð12dÞ

In the case v  w = 4 the complete system of four equations must be solved; in the cases v  w = 3 the system to be solved is made of the first three equations; in the cases v  w = 2 Eqs. (12a) and (12b) only must be solved. Eq. (12a) differs from (5) in the second term of the right-hand-side (RHS), that contains the contributions to the w-level population not coming from direct collision with the laser excited vlevel. In other words the more-than-one step collision transfer processes with all the levels of the manifold other than v. Eq. (10) is generalized as follows:

246

K v;w ¼

G. Dilecce et al. / Chemical Physics Letters 431 (2006) 241–246

X K v;vi K vi;w  vw1 I w AAvf  Aw þ K Q w  Q I v Awf i¼1 Avi þ K vi ( vw2 X K v;vi K vi;vi1 K vi1;w  Q ðAvi þ K Q vi ÞðAvi1 þ K vi1 Þ i¼1 ) K v;vi K vi;vi2 K vi2;w þ Q ðAvi þ K Q vi ÞðAvi2 þ K vi2 Þ K v;vi K vi;vi1 K vi1;vi2 K vi2;w  Q Q ðAvi þ K Q vi ÞðAvi1 þ K vi1 ÞðAvi2 þ K vi2 Þ

We emphasise the usefulness of this algorithm as a control on the correctness of the analysis results. Receiving the correct K Q w value at the end of the Stern–Volmer plot analysis for any v-w case is a strong check on the consistency of the whole set of rate constants employed. Finally, since the Kv, w values are quite lower than the radiative plus collision quenching, three-step and four-step collision processes are practically negligible. References ð13Þ

where the terms Kij with i = j are equal to zero. The extraterms of the RHS of Eq. (13) with respect to (10) contain two-step, three-step and four-step collision contribution to w-level population. These are the second, third and fourth terms and are non-zero for v  w P 2, v  w P 3 and v  w = 4, respectively. The algorithm described for Eqs. (5) and (10) is maintained by calculating extra-terms in Eqs. (12) and (13) using known values of the collision rates. First, the quenching of levels v and the collision rate constants of the cases v  w = 1 are analysed for v = 0–4. Then the cases v  w = 2 are analysed using the known quenching and v  w = 1 collision transfer rate constants. Then, similarly, the cases v  w = 3 and the case v  w = 4 are analysed in this order. The second term of the RHS of (12a) is calculated solving numerically and sequentially Eqs. (12b), (12c) and (12d).

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