Collisional line broadening and line shifting in N2-CO2 mixture studied by inverse Raman spectroscopy

Chemical Physics 148 ( 1990) 417-428 Nosh-Holland

Cullisional line broadening and line shifting in &-CO2 mixture studied by inverse Rarnan spectroscopy M.L. Gonze, R. Saint-Loup, J. Santos, B. Lavorel, R. Chaux, G. Millot, H. Berger Laboratoirede SpectronomieMolhculaire,UA CNRS No. 777, Universitc! de Bourgogne, 6, Bd. Gabriel,2llOOD@onCedexsFrance

L. Bonamy, J. Bonamy and D. Robert Laboratoirede PhysiqueMokulaire, VA CNRS No. 772, UniversitP de Franche-ComtP,25030 Besancon Cedex, France Received 5 June 1989; in final form 6 August 1990

Collisional effects in the Raman Q-branch of Ns perturbed by Co, have been studied by high-resolution stimulated Raman spectroscopy. The Raman spectra recorded in the 0.3- 1.Oatm and 295-1000 K pressure and temperature ranges arc fitted with a theoretical profile taking into account line broadening, frequency shift and line mixing due to rotational energy transfers. The data at low density are used as basic data for the modeling of rotationally inelastic rates through sets of adjustable parameters. We have used in this study the two main models developed in the last decade and known as modified exponential gap(MEG) and energy corrected sudden (ECS) laws. Experimental spectra recorded at density up to 32 ama8at are compared with simulated spectra derived from both models. This constitutes a test for these models which give similar results at low density.

1. Introduction Raman spectroscopy is an important diagnostic technique for the determination of temperature and concentration of gases in combusting media [ l-3 1. The vibrational and rotational spectra of Nz are often used for this purpose. Numerous studies on Nz have already been realized, particularly on the Q-branch of the v1 isotropic band [4-l 01. Nowever, in reactive media, collision partners such as COt and HZ0 [ 6 ] play a significant role, as shown in a recent study of the mixture N2-Hz0 [ 111. The aim of this research is to determine the contribution of N2-CO2 collisions in the N2 Q-branch profile recorded for the diagnostic of ~mbustion media. The spectra are recorded (section 2) by inverse Raman spectroscopy (IRS). The interest of this technique, beyond its high instrumental resolution (about 10d3 cm-’ ), is that the IRS signal is proportional to the imaginary part of the third-order nonlinear susceptib~ity, and not to the square of it as in other nonlinear techniques such as CARS. Thus line profiles are not complicated by interference effects between

non-resonant and real parts of the susceptibility and the extraction of widths from the profile is considerably more strai~tfo~ard. Linewidth data as a fimo tion of temperature (2951000 K) were obtained (section 3) in the 30-100 kPa pressure range. In order to have a good signal-to-noise ratio it was necessary to work with mixtures containing at least 30% of N2. Data concerning the contribution of N2-Nz collisional line broadening were taken from refs. [ IO,12 1. After this first step, the y(J, I’) coefficients were inverted to obtain state-to-state relaxation constants by using fitting or scaling laws, as described in numerous papers devoted to this field [ 6- 111. The determination of the collisional frequency shift is also important because the collisional mechanisms contributing to the line shift are different from those responsible for the line broadening. From the experimental point of view, line shift measurements (section 4) are difftcult in comparison with the line broadening measurements because there is one order of magnitude between these coefficients. Often, the results present a large scatter. This problem has been overcome in this study by using a differential method

0301-0104/90/S 03.50 0 1990 - Elsevier Science Publishers B.V. (North-Holland)

418

h4.L. Gonze et al. / Collisionalline broadeningin N.&O2 mixture

recently developed by Millot et al. in an O2 study [ 131. In this manner, the line shift due to N2-CO2 collisions was obtained accurately for one line and the N2-N2 shift has been also reinvestigated leading to a value lower than found in an earlier study [ 14 1. The accurate set of line broadening coefftcients measured as a function of density has allowed the modeling of the rotational relaxation matrix (section 5). The final step of this research (section 6 ) consists of the prediction of Q-branch profiles at higher densities, as required for combustion diagnostics; that is to say under conditions where the line coupling resulting from rotational inelastic transfers becomes significant and produces the blending of the lines and band narrowing. As a consequence it is necessary to test the behaviour of the fitting laws in the high-density range. For that, experimental spectra recorded from 1 to 32 amagat are compared with calculated profiles derived from modified exponential gap (MEG) and energy corrected sudden polynomial (ECS-P) models. This comparison reveals weak differences between these fitting laws, concerning the simulation of the band profile. More important is the dispersion of results obtained for the line shifting derived from these laws. Furthermore, these values significantly differ from low-density measurements, probably due to the models themselves. A discussion of these results is in section 7.

2. Experimental The inverse Raman spectrometer (fig. 1) has been described previously [ IO, 141. The probe laser which must have a very stable amplitude is a single mode argon ion laser actively stabilized with a Fabry-Perot interferometer reducing the linewidth to z 1 MHz. Moreover, the frequency is locked to a Doppler free saturated absorption line of Iz. The pump beam is obtained by amplifying a tunable single mode dye laser in a four-stage dye amplifier system pumped by a pulsed frequency-doubled Nd3+ : YAG laser (pulse duration 12 ns ) . This gives us an intense, tunable and single mode pump beam. The probe laser is modulated by an acousto-optic system generating 50 us pulses coinciding with the pulses of the pump laser. The two beams are focused in the gas sample placed

in an oven in a crossed configuration. to avoid the generation of a Raman signal in atmospheric Nz outside the cell. They are then separated by an optical filter. The inverse Raman signal is detected by a fast photodiode, amplified and stored in the data acquisition system. A reference signal is also recorded to take into account the pump laser fluctuations. Calibration of the wavelengths is achieved by using a wavemeter of Michelson type [ 15 ] in which the travelling mirror has been replaced by a comer cube moving vertically in an evacuated cylinder at a distance of x 1 m. The accuracy in the Raman frequencies is = 10-l 5 MHz. Linewidth data have been recorded as a function of temperature (295-1000 K) by using a low-pressure silica cell located in a furnace, whereas a highpressure cell with sapphire windows was used for recording spectra at high densities. This cell is able to work up to 500 K at pressures of up to 2 x 10’ Pa (200 bar). In order to increase the accuracy of line shift measurements, we have used a differential technique, which consists of using a reference cell working at low pressure. Two spectra are simultaneously recorded, the first one in the main cell at high pressure, the second one in the reference cell at lower pressure. The details of this experimental device are given elsewhere [ 13 1. In this manner, we directly obtain the frequency shift, eliminating problems of calibration or Stark shift. In these investigations on line shifting, the two laser beams were mixed in a collinear way by a dichroic mirror and sent on the focusing lens, before being separated by a beam splitter to enter the two cells.

2. LinewIdth analysis The IRS spectra of the Nz fundamental (v= 04 v= 1) Q-branch have been recorded for each temperature and pressure condition from J= 0 to J= 16. We have used two mixtures, the first with 30% of N2 and the second with 50% of N1, in order to have a good signal-to-noise ratio. The total pressure was less than 1.5x lo5 Pa. Three processes can contribute to the observed line broadening: experimental apparatus function, Doppler effect and collisions. The experimental apparatus function can be approximated by a Gaussian pro-

419

ML. Gonze et al. / Collisionalline broadeningin N&O2 mixture

PROBE SOlRCE

PUnP SOURCE Al-+Lamer

Modulator anelitirr

Fig. 1. Inverse Raman spectrometer at Dijon.

tile, the width of which, estimated to be = 10m3cm-’ (hwhm) has been neglected. The Doppler width at room temperature is ~2.7~ 10m3 cm-‘. The collisional shape arising from the impact approximation is a Lorentzian profile. At low pressure a Voigt profile [ 16 ] is an adequate description when line mixing and Dicke narrowing [ 17,lS ] are negligible. By increasing the pressure, the non-additivity of individual line contributions and collisional narrowing can be observed [ 19,201. Then the approximation of an additive superposition of Lorentzian or Voigt shapes is not valid. The observed Raman intensity for the isotropic fundamental Q-branch (u=O+ u= 1) is proportional to the following expression [ 2 1 ] :

(1)

where the G matrix is defined by:

[G(w)l~,=i(o-w,,.,,.)6,.,+nW~,,

+ccoz

W,.,(N,-COz)

(2)

(Yis the isotropic polarizability operator, n the perturber density, o,~,,,., =wJ. the unperturbed transition frequency for the Q(J’ ) line. W,, denotes the off-diagonal elements of the relaxation matrix accounting for rotational population transfer rates from J to J’ in the vibrational state u= 0 or u= 1, assumed u-independent, in the limit of small vibrational dephasing. The effect of the imaginary part of W,.,

(3)

,

where C,, and C,, are the respective mole fractions of N2 and CO2 gases, and WJ J(&-N2) and W, J(N2CO*) denote the relaxation matrices for the N2-N2 and N2-CO2 binary systems. The offdiagonal elements of the relaxation matrix represent the line mixing and lead to the non additivity of individual shapes. The diagonal elements W:J are related to the halfwidths y; and shifts A; through: y;=Re

Z(W)=X-‘I(Yi=OI(YIVf=l)1* x Re~&~[G-‘(w)l~~,

(J’ # J) is assumed to be negligible [ 12 1. Notice that for the presently considered mixture the WyJ term in eq. (2) becomes

WJ_,,

A;=-Im

WJJ,

(4)

where WJJ must include the vibrational dephasing contribution since it plays the dominant role for the Q(J) line shifting [ 221. An approximation to this profile (eq. ( 1) ) has been developed in the case of small overlapping by Rosenkranz [ 23 ] and used for Raman profile by Rosasco [ 71 and our group [ 10,111. From a perturbation expansion in powers of the density, Rosenkranz has obtained the following relation:

J

(a-OJ-nd;)*+

(nr;)*

’

(5)

ML. Gonze et al. / Collisionalline broadeningin N_AX& mixture

420

pJ is the rotational population, Y, is a line coupling coefficient given by

(6) It is obvious from eqs. ( 5) and (6) that equations similar to (3 ) hold for v;, d; and Y,. This simplified model being valid in the pressure range of our experimental study, we have fitted our data with this profile and extracted the collisional broadening due to the N2-CO2 collisions. In the least-squares procedure for obtaining the line broadening y; x y., and line coupling Y,, the shifted frequencies mJ+nAj were also adjusted and compared to unperturbed frequencies oJ for N1. The spectroscopic constants used were those of ref. [ 14 ] : IT,,= 1.989707 cm-‘, v0=2329.91165 cm-’ and Bi -B,=-O.l73714cm-*.Thetotalintensityisadjusted by using a scale factor. The baseline is measured for each record, its origin is essentially electronic but in this experiment with CO2 as perturber, a non resonant signal produced by the COZ gas was observed. The Nz-CO2 contribution to the total line broadening was deduced through the linear mixture rule deduced from eq. (3). This requires the knowledge of the self-broadening coefficients resulting from the tit of experimental data given in refs. [ 10,223 using MEG and ECS-P models. The N2-N2 line broadening coefficients deduced from these models are very close. Moreover, as the proportion of N2 is small in the mixture, that induces a difference less than 10e3 cm-‘/atm depending on the model chosen. We have verified that the N2-CO2 collisional broadening exhibits, as expected, a linear behaviour as a function of the partial pressure of CO2 molecules in the range 0.2-0.7 atm. Table 1 gives the line broadening coefficients of N2-CO2 at various temperatures. A detailed calculation of the line broadening coefficients for N2 perturbed by CO* has been performed within the frame of the semiclassical model proposed by two of the authors [ 241. The molecular parameters used in this calculation are the same as those of ref. [25] for the study of CO2 infrared lines broadened by Nz perturbers. They are given in table 2. The so-calculated Q line broadening coefficients are gathered in fig. 2 and compared with IRS data. In conyJ

trast with the pure Nz case [ 121, the J dependence is not well reproduced at the lowest temperatures considered. This is particularly true in the quadrupolequadrupole resonance region (i.e. Jg4) at room temperature. When the tempemture increases this discrepancy decreases and the agreement becomes satisfactory at high temperature. A similar behavior has been obtained by Margottin-Maclou et al. [ 27 ] for the infrared lines in the v3 and Y,+ v3 bands of CO;?perturbed by N2 and O2 while the agreement was more satisfactorily for pure COZ. Note that in this case, the resonance region is shifted to JS 40 at room temperature. This discrepancy was interpreted [ 271 in terms of the trajectory model [ 24 ] which does not account for energy or momentum transfers from or to rotation. A slight modification of the apparent velocity leads to a rather good agreement. The same type of behavior was also recently observed in CO*-Ar [ 28 1. A more justified physical explanation could be obtained for such simpler molecular system. In spite of this discrepancy at low tempemtu~, the good agreement obtained at 900 K between theory and experiment and the fact that accuracy of semiclassical calculations increases with temperature, would allow us to extend with confidency these calculations of line broadening to flame temperatures.

4. Line shift anaiysis Up to now, the line shift measurements were obtained by measuring with high accuracy the Raman line positions and assuming a linear dependence as a function of density. Unfortunately this technique leads to a large scatter of results if absolute frequency measurements are not very accurate. That is why we developed the differential method described in section 2. Moreover the line profile used for the extraction of line positions also plays a significant role. In our earlier work on Nz [ 141 we have noted a non negligible deviation of the frequency measurements between the fits with a Voigt profile and those with a Rosenkranz profile, leading to a smaller value of the shift when measured with a Rosenkranz profile. This is not mainly due to a correction of non-additivity effects, because in our investigations we have chosen the Q ( 14) line which can be considered as a quasiisolated line in the pressure range below 1 atm. In

421

hf. L. Gonze et al. / Collisional line broadening in N.&O2 mixture Table 1 Collisional

broadening

Y, of the N2 Q-lines perturbed

T=296 K

i

0 1 2 3 4 5 6 7 8 9 10 I1 12 13 14 15 16

Table 2 Parameters

coefftcients

by C02. SY, is one standard

T=427 K

deviation T=9OOK

T=6OOK

h

&Jf

YJt

6YJ,

YJI

hJ,

Yr,

6Y_li

83.4 71.5 62.6 64.1 64.3 64.1 59.9 59.6 58.4 53.2

3.3 4.8 4.2 3.0 3.9 1.8 3.6 3.0 1.8 2.1

55.8 59.8 56.6 55.5 53.3 51.7 48.0 48.1 47.1 42.9

6.0 3.0 2.4 3.3 3.0 2.4 4.2 3.0 2.4 2.1

43.3 46.1 44.6 43.1 41.8 41.1 41.2 39.5 40.4 35.8

3.6 1.5 2.4 1.2 1.5 0.9 0.9 1.5 1.5 1.2

35.6 35.5 34.4 35.3 32.7 31.8 31.0 29.9 29.7 28.8

3.0 2.4 1.8 2.4 1.5 1.5 1.8 1.2 1.2 1.8

49.5

2.7

41.1

2.4

34.1

1.5

27.3

1.8

45.3

2.4

37.4

1.8

32.4

1.5

26.4

1.8

40.2

1.2

35.8

3.0

28.9

1.5

25.0

0.8

for the N2-CO2 interaction

Atom-atom,parametem

potential

a)

‘)

d,(10-‘4JA’2)

-.

e#(lO-“JA6)

T - 285 K T = 427 K

-+

doN 0.307 da 0.117 Molecular t (K) 0 (A) &, (DA) &oz (DA)

eoN 0.302 enr 0.143

‘--

#$

T = 600

K

.----

X

T = 800

K

parameters 140 3.89 -1.3 -3.6

‘s il

a) Ref. [26].

‘0 40

such physical situation, the apparent shift due to line mixing is easily deduced [ 291 from daPP = - lYJYJnCoO. For J= 14, this apparent shift is -0.53x 100~ cm:*/amagat, significantly lower than the observed decrease. The observed phenomenon is due to a small asymmetry on the shape, whose origin is experimental. This small distorsion is taken into account with a Rosenkranz profile through an effective parameter Y.,.This explains why the frequency is determined with a better accuracy with a Rosenkranz profile, which can also be considered as a ju-

Fig. 2. Calculated N&Or line broadening coefftcients (in 10m3 cm-‘/atm) for various temperatures; measured values are also given with error bar.

422

M.L. Gonze et al. / Collisionalline broadeningin NrCOz mixture

dicious profile in case of asymmetry having an experimental origin. Consequently, the effective Y, coefficients deduced from such a profile cannot be directly compared with the expected Y, of eq. (6) corresponding to line mixing, since additional experimental contributions take place. Our experience on the shift measurements resulting from works on Nz [ 141 and O2 [ 13 ] learns us that it is difficult experimentally to measure the dependence of the lineshift as a function of the J rotational quantum number. So we have only repeated our measurements on the same Q( 14) line of N2 which has a good intensity and is sufftciently isolated. The shift linearity with respect to the perturber density is shown in fig. 3. By using this differential technique we have re-investigated the N2 line shift and measured the effects of collisions N2-CO2 on the line shift of the Q( 14) line at 295 K. We obtained: %I,-,, = - (3.5f0.5)X10-3cm-‘/amagat

The line shifting coefficients may also be calculated by using the same semiclassical model as for line broadening (cf. section 3). A detailed analysis for such calculation has been reported in ref. [22] for pure Nz. The model only depends on one adjustable parameter y which characterizes the ratio of repulsive and attractive parts of the vibrationally dependent isotropic intermolecular potential (cf. eq. ( 18 ) of ref. [ 22 ] ) . This parameter was fitted at room temperature to obtain the overall better consistency with experimental data. The previous calculations allowed us to explain the weak .I dependence and also gave a good prediction of the T dependence. However, for N2-CO*, since a single value of the shift has been determined for Q( 14), it was not reasonable to assert a theoretical variation in J and T for this molecular system, depending on an adjustable parameter y. More experimental work should have to be done first.

and 5. Theoretical models

&,_coz=-(4.1f0.6)x10-3cm-‘/amagat. This new value for the Nz-N2 shift is smaller than the value found ( - 5.5 x lo-’ cm-‘/amagat) in earlier measurements by fitting the data to a Voigt protile. These earlier data have been also fitted to a Rosenkranz profile and the extracted value of the shift is - 3.6 + 0.4, -4.7f1.4 and -(3.3+1.7)x10-3 cm-‘/amagat at respectively 295, 768 and 1057 K. The value at 295 K is in a good agreement with the recent result obtained with the differential method. 7

NZ-CO2

Sh i f t

0 0 /

0 8 *

0

i 0 0

/-

_-__---___---__----__~---_~----.

0.0

Pressure

(

atm )

‘A5

Fig. 3. Shift ( -6) linearity versus partial pressure of CO*.

As the pressure increases, line couplings play a significant role, especially in the bandhead, and the rotational structure disappears. Then, the Rosenkranz profile is not valid anymore; knowledge of each offdiagonal element of the W matrix is needed. Unfortunately, ab initio calculations of state-to-state rate constants W,., are not available and a direct determination from experimental data is not realistic. A modeling of the off-diagonal elements of the relaxation matrix is thus required. This explains the increasing interest given in the last decade to model this matrix through a simple representation using a few adjustable parameters. We can distinguish two classes of representation of the rotational energy transfer rates: scaling and fitting laws. scaling laws express~any rate constant in terms of a subset of the matrix, typically a column or a row. On the other hand, the fitting laws express the entire matrix in terms of a set of parameters. These laws can also be classified in two categories: those based on the energy variation AE named statistical laws and those based on the rotational angular momentum variation AJ named dynamical laws.

M.L. Gonze et al. /Collisional line broadening in N&O,

The principal assumption of statistical laws is that for a given temperature, the rotational energy transfer rates depend on the energy gap AEJc, = IET EJ I and that the dependence on the quantum numbers J and J’ can be expressed through the statistical factor for the angular momentum iV(J’ , J) . They lead to: .

5.2. Dynamically based scaling law The so-called energy corrected sudden .(ECS) law is based on the infinite order sudden (10s) approximation [ 341. In the case of atom-diatom collisions, the assumption that the molecules do not rotate during the collisions (10s) leads to important simplifications of the numerous coupled quantum equations for the scattering of the molecule; in particular, all the off-diagonal elements of the W matrix are connected to the first row of the matrix. Nevertheless, this law is only applicable to atomdiatom systems for which the atom is much lighter than the diatom [ 34,35 ] and when the reduced duration of the collision r, is very short compared to the rotation period of the diatom. DePristo et al. [36 ] have proposed an adiabatic correction (ECS) for this law through the Q term:

(7)

The choice of the functionfand the factor N(J’, J) will determine the model. Among several models introduced in previous studies [ 301 the modified exponential law (MEG model) has led to very consistent results [ 3 l-33 1. For J’ +J transitions with J’ > J, the rate law is given by: -Re W,.,(T)

x exp( -BAE,,/kT)

.

(8)

Detailed balance is applied to generate the remainder of the matrix. The model has been successfully applied to the N2 case [ 121 and seems to be also accurate for the N2-CO2 collisional system without varying the semi-empirical constant 1.5 which, in fact, depends on the nature of the perturber but has no significant effect on the fitting law itself. The parameters (Y,N, 8, J?deduced from the experimental set yJ by using the equation y,(T)=

- &

423

good overall fit of the experimental yJ values (fig. 4a). Nevertheless, at room temperature, the presence of a local maximum near Jx; 4-6, due to quadrupolar resonance effects, is not reproduced by this model.

5. I. Statistically basedjitting law

-Re W,,,(T) =A( T)N(J’, J)f(A&,)

mixture

WJJ( T)

Re WTsss= (25’ + 1) exp (“;TE”)R:, (2L+ 1)s~~ Re W,,,

where J, is the maximum of J and J’ and where the adiabatic factor for an homonuclear molecule as N2 is given by .n,= (1 +CJ&_~T,~/%)with

(9)

(10)

TV= b,/ij .

(11)

17 is the thermal average relative velocity, z7= ( 8kT/nm ) ‘f2, m is the reduced mass of the N2-CO2

are summarized in table 3. The MEG model allows a

Table 3 MEG and ECSP adjustable parameters determined from experimental collisional broadening coeffkients measured at low density a(295 K) ( 10e3 cm-’ atm-‘) MEG

ECS-P

N

6

B

36.3 (0.1)

1.36(0.02)

1.47(0.06)

1.75(0.06)

A(295 K) (lo-‘cm-‘atm-I)

(Y

N

b, (A)

72(6)

1.07(0.03)

0.97(0.?2)

1.2(0.1)

424

ML. Gonze et al / Collisional line broadening in Nz-CO2 mixture

Rotational OuantumNumber [J)

ECS-P

MODEL

20 10 -

b

0 0

I

I

I

I

I

I

2

4

6

2

10

i2

I

14

I

I

16

10

20

Rotational Quantum Number (J) Fig.4. Collisional bxwhhg MEG, (b) E&P.

c&licients

of the N&O2

Q-lines fitted with two models for the rotational energy transfer rates. (a)

ML. Gonzeet al. / Collisional line broadening in N.&O> mixture

collisional pair and b, is the characteristic length. This model is already being applied to atom-diatom collisions but also to other collisional systems [ 37,38 1. For instance, it has not been possible to determine the elements W,, from experimental data because of the great number of parameters. So, it is necessary to find a simple analytical representation for the elements Re W,,. Brunner et al. [38] have proposed a polynomial law which leads to an ECS-P law: Re WOr.=-

A(T) [ (L+ 1 )L]” ’

(12)

with A(T)=A(295K)

(13)

which is characterized by only four adjustable factors, A( 295 K), cy,and N. The parameters of the ECS-P law for the mixture Nz-CO2 are summarized in table 3. The calculated line broadening coefficients derived from the ECS-P law are reproduced in fig. 4b; they are in good agreement with the experimental ones, with the same restriction at 295 K as the MEG model.

6. High-density

spectra

The two above models give a consistent representation of the experimental yJ set (cf. fig. 4). The accuracy of these models is more stringent at high density when the collisional shift A; and collisional narrowing must be accounted for. High-density spectra allow us to test the complete relaxation matrix (diagonal part with and AJ on one hand and offdiagonal part corresponding to relaxation rates on the other hand). To this aim, we have recorded the Q-branch of the mixture N2-CO2 at room temperature, varying the density between 4.9 and 32.6 amagat. The corresponding spectra have been calculated with the two models described in section 5 (fig. 5 ) . Remark that the MEG and ECS-P models give ap proximately similar Q-branch shapes, but neither model gives the absolute frequency, each of them leading to a different shift. So, in order to point out this difference we have adjusted the global shift for yJ

425

each model at different densities. Table 4 gives the values of the total shift due to both Nz-N2 and NzCO2 collisions for various densities. These values are much higher than the expected value of - 3.9 x 1Om3 cm- ‘/amagat corresponding to a mixture containing 29.8% Nz and 70.2% of CO* and assuming no dependence of the shift on the rotational quantum number. The MEG and EC!+P models give similar results, the discrepancy lies between a factor four and two. As the pressure increases, the discrepancy decreases. It is also expected from calculations [ 22 ] that, as temperature increases, the discrepancy also decreases. Let us mention that this observed discrepancy is probably due to the insufficient accuracy of the relaxation models at this level of preciseness for comparison with experimental data. Indeed, the collisionally induced intensity transfers inside the Q-branch lead to an apparent shift of the maximum for the coalesced branch. So, the accuracy of the relaxation rates has a direct consequence on that of the maximum frequency. This is the plausible origin of the discrepancy observed in ref. [22] between low- and high-density measurements of frequency shift (cf. fig. 7 of ref. [ 22 ] ; the discrepancy is in fact even more pronounced, accounting for the presently observed decrease of the measured shift value at low density). This high sensitivity of the relaxation models to reproduce the absolute frequency of the Q-branch maximum could be used to perform more severe tests of these models. Notice that in the present case, the discrepancy is higher for the ECS-P than the MEG model (cf. table 4). The aim of this paper was to provide information on the contribution of N,-CO2 collisions on the shape of the N2 Q-branch, from which the temperature is deduced in CARS thetinometry. Moreover, this work was motivated to complete recent investigations on the Nz-H20 mixture; data on the N2-CO2 collision pairs appeared necessary to calculate the rotationally inelastic relaxation rates of N2 in presence of both CO* and Hz0 perturbers. For the users of CARS thermometry it seems evident that a unique model is required. This model must be able to well reproduce the contributions of the three major partners: It has been recently shown that the ECS-P law was not suitable for the N2-Hz0 collisional system { 111. Accounting for the present results andthose for pure N2 [ 31,32,12,22], we believe.the MEG law is the most

ML. Gonze et al. / Collisionalline broudeningin N&O2 mixture

426

P= 32.60 Amagat T= 295.0 K

N2-CO2 MEG MODEL

WAVENUMBER (CM-11

2324:701

P= 32.60 Amagat T- 295.0 K

N2-CO2 EC!+P

2324l701

MODEL

WAVENUMBEA (CM-I)

2331:561

Fig. 5. Simulated spectra fitted to the experimental data with the global shift adjusted for (a) the MEG model and (b) ECS-P model at 32.6 amagat.

adapted to model the relaxation rates in a ternary mixture corresponding to a combustion in air. Let us mention that a more precise analysis of the shifts which would be of particular interest for a deep physical understanding of the collisional effects, is of no use for practical CARS thermometry purpose, since the fit between calculated and experimental

profiles is made in relative frequency scale [ 39 1. The present experimental study provides a complete set of data on individual line broadening for the Q-branch of N2 in the presence of CO,. These data complete those already determined on N2 in the presence of Hz0 [ 111. We have shown that the’ N2-CO2 broadening coeffkients and their dependences on J

M.L. Gonzeet al. /Collisional line broadening in N&O2 Table 4 Total shift d for the mixture Nr-CO2 expressed in lo-’ cm-‘/ amagat at 295 K derived from the two models, the density varying from 4.93 to 32.6 amagat. The total shift d is related to the N2-N2 and N&G2 contributions through the relation d= 6Ais one standard deviation C,, AN>N~+ C, &-. Model

Amagat 4.93

MEG

-A 6A

ECS-P -A 6A

13.7

23.3

32.6

10.68 0.25

9.29 0.10

8.98 0.07

8.34 0.06

16.80 0.30

13.08 0.12

11.37 0.07

9.98 0.04

Fig. 6. Effect of the perturbernature on the Ns Q-line broadening coeffkients (semiclassical calculated values).

and T are very different from those for N2-N2. For instance at the temperature of the methane-air post flame gas [ 6 ] the yNz_cozvalues are x 60% greater than those of pure N2 for low and mid J (tig. 6).

7. Discussion and conclusion A detailed study of the MEG model [ 12 ] for pure

mixture

427

Nz has shown good consistency with IRS Q-branch profiles. For the mixture N2-C02, the accuracy is significantly poorer at room temperature. This is probably due to the nature of the two considered models which are rotation-translation effective models. They are basically unable to take into account strong specific rotational resonance processes which play a significant role for couples like N2-CO2 at room temperature. The present work clearly evidences the need of new relaxation models accounting, for fundamental physical understanding for both rotation-translation and rotation-rotation energy exchanges. Nevertheless, it is to be pointed out, in spite of the discrepancy discussed above concerning the global shift of the coalesced Q-branch (which stays within a few lo-’ cm-‘/amagat ), the ability of the two considered models to reproduce the Q-branch shapes as pressure increases is fairly good at room temperature (cf. fig. 5). It is expected that at higher temperature, due to the basic approximations inherent to MEG and ECSP models, the agreement will be even improved. This would be true for the global shift. This contributes to explain the relatively important differences observed on yNzmeasurements realized in flame [ 6 ] where CO1 and Hz0 perturbers are present in a proportion of about 10% to 20% respectively [ 40 1. The present data and those derived from a similar study on N2-Hz0 constitute new basic data to accurately determine the temperature in combustion media from Raman diagnostic methods.

Acknowledgement

This research was supported by DRET grant No. 87-066 and by the Conseil Regional de Bourgogne. We thank J.M. Hartmann for helpful discussions during this work. The skillful technical assistance of P. Michaux is acknowledged.

References [ I ] W. Riefer and D.A. Long, Nato AS1 Ser. Vol. 93 (Reidel, Dordrecht, 1982).

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