Vibrational and rotational relaxation of NH3 studied in a molecular jet by infrared-infrared double resonance

-.- : ._- :..171_I

Chemical Physics 100 (1985j 171-191 North-Holland. Amsterdam

-

. -_.:--: VIBRATIONAL AND ROTATiONAL RELAXATION OF NH, STUDIED IN A MOLECULAR JET BY INFRARED-INFRARED K. ViEKEN,

N. DAM and J. REUSS

DOUBLE

IiESONANCE

*, _:.:

..

Received 13 June 1985

infrared-infrared double resonance is applied to an expandingjet .of NH,. Molecules in the ~33) rotational level of the vibrational ground state are excited with a CO&ser into the s(4.3) level of-the cz vibrational stale. zs(4.3). Rotational distributions in the ground and L’2 stale are probed by the infrared absorption cf color-center-laser radiation producing transitionsto the u1 and D, i LF= states. The time delay between pumping and probing is determined by the dir&e betw&. the CO2 laser focus and the color-center-laser focus. along the jet axis. The results indicate an average relaxation time of vibration to rotation/translation of 280(50) ns Torr’ over the temperature range 50-ii0 K_ In that temperature range the population difference between ortho and pm-a species comes in:o equilibrium within 4X(190) ns Torr’. and the relaxation between (3.3) and orher ortho ground state !evels occurs within 56(20) ns Torr’ and between the ls(4.3) and 2s(3.3) lev& uilhin 20(S) ns Torr’. The inversionrelaxationtime between a(3.3) and ~(3.3) is determined 10 7.6(20) ns Torr’. at 50 K (Here 1 Torr’ indicates 3 density. 1 Torr’ = 3.27 x lO= molcculcs/n?_)

1. Introduction Although vibrational and rotational relaxation of NH, have been studied in many ways over the years, our knowledge of these processes is still inc?mplete. The vibrational relaxation of the u, state of NH, has been investigated e.g. by laser excited fluorescence, Hovis and Moore [l]. and by IR UV double resonance. Ambartsumyan et al. [2]. None of these or other methods uses rotationally resolved probing. With the two-laser IRIRDR technique one probes rotational levels and obtains detailed information on the relaxation between well defined vib-rotational levels as demonstrated by Haugen et al. [3] for the HF(u = 1) V-R-T relaxation. The rotational relaxation in NH,, R-R,T, has been the subject of many double-resonance studies; MWMWDR is reviewed by Oka [4]; IRMWDR has been employed by Kano et al. [5] and Dobbs et al. [6]; IRIRDR is reported by * Work supported by Stichting voor FundamexzteelOnderzoek der Materie(FOM).

LMatsushima et al. [7] and Kuze et al_ [8]: rotationally resolved IRUVDR has not yet been applied to NH;. MWMWDR yields information on the R-R relaxation in the ground state; collisional selection rules have been established [4]_ JRMWDR h& the advantage of a higher depopulation, bu: here also V-V and V-R,T relaxation processes contribute [S]. IRIRDR has the advantage that it is sensitive to all population changes. not only to the difference population of inversion states. as in MW probing. In the case that both pumping Bnd probing lead to the uz state, R-R relaxation within the excited vibrational levef may complicate the analysis [S]. Once the IRIRDR method is adopted with a specific pump and probe laser, there is still a choice between various experimental methods. Steady-state measurements yield relative measures of the different relaxation processes [4,5.8]. Absolute values of relaxation rates are obtained by a time-resolved pulsed laser technique [3,5], a timeof-flight technique [7], or a beam-maser scattering experiment [9]. . In the present experiment iRIRDR is applied

0301-0104/85/$03_30 Q Elsevier Science Publishers B-V. (North-Holland Physics Publishing Division)

172

to an expanding NH, jet_ We make use of the variable flight time between pump and probe region in the jet to measure the relaxation time; for an effusive beam of NH, this technique has been applied before by Matsushima et al. [7]. Luijks et al. [lo] used this technique in a jet of SF,, pumping with a CO2 laser and probing by spontaneous Raman effect. In fig. la the energy level scheme is drawn. The rotational levels are characterized by a/s( J, K) in the ground state and Za/s(J.K) in the v2 state, where _! and K arg the rotational quantum numbers and a(s) denotes the upper (lower) inversion level. The levels with K = 312 and K= 3n &-1 (n = 0, 1. 2, ___) belong to ortho and para species, respectively: they correspond to a total nuclear spin I = 3/2 and l/2. Due to the larger inversion splitthe rotational structure of the ting of = 36 cm-‘, vz state is different from the ground state with its inversion splitting of = 0.8 cm-‘_ Therefore the R-R relaxation is different for both states 181. Fig. lb displays the energy transfer processes

I ortho

that occur. The C& laser excites the molecules from a(3J) to 2s(?,3) thus depopulating the a(3,3) and populating the 2s(4,3) level. Consecutively, R-R relaxation repopulates the a(3,3) level and depoptilateg the 2s(4,3) ‘level V-V exchange changes ground and e?tcited St&e populations simultaneously. V-R,T relaxation creates a temperature rise and thus influences the rotational state populations. By varying the distance between excitation and probing region these relaxation processes are followed in time and relaxation rates are extracted. Experimental arrangement and method are described in section 2. Besides the IRIRDR data, absorption measurements are presented &I section 3, necessary to obtain the jet parameters like rotational temperature, molecular density and flow velocity_ In section 4 the experimental method is critically examined: relaxation times are derived in section 5; section 6 contains the discussion of the resuii5_ .

I Dar0

V-RT

Fig 1. In (a) the energy level scheme is drawn for the rotational levels (J.K) in ground and o2 state with -I< 4. The upper. a. and lower. 5. inversion levels are connected by “r_ Also indicated are the (10.0) and (10.3) levels of the ground stale Theenergy transfer processes are shown in (b).

I

Veeken el aL /. Relaxahn

2. Experimental In fig_ 2 the exp@mental arrangement his sketch&d. In a coordinate ‘system $th its origin at the nozzle position, the g& expands, in the r-dire& tion,_ the probe laser is directed along the y-direction and-the pump laser along the x-diiection. 2. I. Gns SJX&PZ The ci&lar stainless steel nozzle has a diameter D = 0.50 m& and a wall thickness of 0.1 mmThe anhydrous NH, has a purity of 99_98% Different stagnation pressures were applied, p. = 95. 190, 380 and 760 Toti. The expansion chamber is pumped by a 775 m3/b booster pump (Edwards EH1200) backed by a 50 rr?/h motor pump. The background gas pressure is 0.017 Torr for-p0 = 95 Torr and 0.16 Ton- for p. = 760 Torr. The pumping speed is reduced by 20% in the latter case. By an air driven piston (frequencies c 5 HZ) the gas

of NH,

in ajct by- IRIRDR

,:

_;

‘-173 -_ I _. ‘c_;_‘;~_: I ,;:~;:

flow can be modulated immediately upstrc:thi_i node_ ,: 1 ::--...:-:_:-:-;: _..... -2.1

2.2. &be-her

: ; __;;_.-,;: ,=;_.

The color-center- probe laser,- CCL (Burle&.._ _. &L-20). is pumped by a Kr’ Jaser.. The .~&ob& beam .is- modulated at @O Hz by an el&ro;optic modulator (EOM) in the Kr’ laser pump; beam! .: The CCL can be tuned continuously. over:. the .. whole rovibrational NH, o, band, centered at3336.2 cm-’ [ll]. The ground state absdrptioti frequencies are identified using the assignment of Benedict et al. [ll]. The excited State frequencies, u, -I- u2 - I.+, are calculated from the u, + u, data’ of Benedict et al. [ll], the o, data of Urban et al. [12] and the inversion splitting data of Townes and Schawlow [13]. The probe laser power is = 2 rnw; its frequency stability remains well within the relevant finewidths and is monitored using the absorption in a reference gas cell. The probe iaser beam is focused

Fig. 2; Experimental arrangement. The gas expands through the cozzle. D = 050 mm. in vertical direction The color-center-laser (CCL) beam travelsalong the y direction. is focused by lens Ll into thejet crosses thejet axis at position zP_ and is collected by lens L2 onto the pyre-electric deteqor. Tbe COz-laser beam t+el~ along tbe x-direction. is focused to an elliptical spot by the cylindrical ‘. reflector M and the spherical lens L. crosses the jet axis at zE and is collected on a thermopile.

by-lens Ll to a diameter of 0.05 mm at x,, =v, = 0 (p for probe)_ It crosses the jet axis at a distance zp from the nozzle and is focused by lens L2 onto a pyro-electric detector (fig. 2). The transmitted laser power is detected phase sensitively and is stabilized by comparing the output to a reference signal with a feedback to the EOM. Two types of absorption measurements are performed_ First. the infrared absorption of the jet is measured. Hereto the gas flow is modulated at OS Hz and the jet absorption, A, is detected. The detection limit yields a 1 x 10-O *minimum absorption_ In the second type the CO,-laser-induced change of the jet absorption, AA, is phase sensitively detected with the pump beam modulated at 85 Hz. A detection limit corresponding to 2 x lo-’ minimum absorption was obtained. The difference in sensitivity for both methods originates from the different modulation frequencies. The infrared jet absorption. A. typically equal to 1%. allows detection of CO,-laser-induced variations of 0.2% of A_ The jet absorption is measured for a number of ground state levels, A( J, K ). yielding the fractional populations of those levels, /(J. K) (we omit the indication a or s where it is not essential)_ This function I( J. K) can be characterized by a rotational temperature, T,. as will be seen in section 3.1. The quantities f(J. K) are proportional to A(J_ K) because the upper states of the probing transitions. u, and ur + u2. are practically unpopulated even after CO,-laser excitation_ and because the transitions are not saturated. In earlier IRIRDR work j7.81 the upper probe state was the u, state. whose population is not negligible after CO, or N,O laser excitation_ This disadvantage is compensated by a larger sensitivity_ because the 0 + u2 transition dipole moment p( u2) = 0.24 D [14], is much larger than the 0 4 u, value, p( u,) = 0.024 D 1151. From the CO,-laser-induced change in absorption aA( J. K) for the ground state. and A-42( J. K) for the u, state, the induced population changes A f(J, K ) and Af 2( J, K) are derived_ In general 4f (J. K) is negative and 4f2( J. K) is positive_ The information on relaxation times is obtained by varying the distance ( z - zp). thereby varying the effective relaxation t&e.

A cw. line tunable CO2 laser has been employed- With a “COz mixture it yields 40 W, with a N,O mixture up to 4 W output-power. In this work the laser has been operated with-- a r’COL mixture_ Sealed off operation on the required 9P8 line was not possible. Therefore, a small flow was introduced. resulting in a consumption of 1 atm C of “CO? per 100 h. With an outcoupling efficiency of% a power of 2.4 W has been obtained on the 9P8 line. The pump beam is focused to an elliptical spot at xE =yE = 0 and a distance zs from the nozzle (fig. 2, E for excitation), and collected on a thermopile. The absorption of CO, radiation by the jet is measured. modulating the gas flow and detccting the power variations. The detection limit corresponds to 1 X 10-s minimum absorption_ The elliptical focus is formed by a combination of a cylindrical mirror. M. and a spherical lens. L. yielding a width 6, = 0.70 mm and a height b, = 0.19 mm. For a line tunable COL/NIO laser a list of coincidences has been published for all possible u, transitions of “NH, by Frank et al. [16]. Only levels with low rotational energy are well popu-1ated and therefore interesting in our jet experiment_ The most suitable coincidence. the ulaR(3,3) transition, has a detuning of 78 MHz with respect to the ‘jC0, 9P8 line at lOlL203 cm-’ and is used in this work. Preliminary measurements were performed based on other coincidences_ The u,sR(S.O) transition is effectively excited by the 30 W “CO, 9R30 line at 1084.635 cm-’ with a detuning of 175 MHz 1161. However, the population of the s(5,O) level is too small to observe R-R transfer to other states. The u?aR(l,l) transition is detuned 1.5 GHz from the “CO1 lOR14 line at 971.931 cm-‘. The 20 W CO, laser beam was then focused to a circular spot with a diameter of 0.09 mm. A CO,-laser-induced change in its absolption has been observed for the a(l,l) and other levels, strongly enhanced by power broadening, which yields a fwhm of = 1.3 GHz. The resulting IRIRDR lineshape was distorted due to the ac-Stark shift f17J.

2.4. Pump-probe

geometry

The pump and probe laser beams are focused~in the z-direction to obtain a maximum time-of-flight resolution. The time delay, t, between pumping

where the absorption strength, a, and. density;? pi Vary ~5th yr,: The Bbsor+tion strength is con&&d io the line strength, S, and the lineshaRe~fun&n, G.

and probing equals_ t = (zp - z&u,.

(1)

where Upis the flow velocity of the jet_ For 4 = 1000 m/s the time resolution is = 100 ns. The positions (Xpr_$Jp) and ( x E: ya,Z~) can be varied with an accuracy of 0.01 mm_ The relevant distance (zP zn) is known within 0.02 mm. i.e. within the spatial laser resolution. in the y-direction the pump beam is focused to a broad spot to ensure that most molecules arriving in the probe reggon have passed through the region pumped by the CO, laser. During the IRIRDR measurements, zP is kept constant while (zP - zn) is varied_ It is important that the excitation probability of the probed ensemble of molecules does not vary too sharply with (rp - I~) to avoid systematical errors in the relaxation data. as will be discussed below. Another important factor is the saturation of the +aR(3,3) transition. which. inferred from the jet absorption of the CO, laser radiation, influences the effective excitation as function of (zP - I~)_

For distances from the nozzle, zP > D, the molecules are assumed to follow straight streamliires originating from the nozzle. At y,, the lineshape function is centered around the Doppler shifted

frequency. Y~(_~~)=Y~[~

sine].

k(uJc)

with tg B = ,.r/zr _

(6)

The function G(v,y,) is determined by the local Doppler and pressure broadening_ If pressure broadening is negligible, G becomes independent of (J-K). The line strength S of the absorption in the level (J. K ) can be written as S(J,K)=K,L,,I~I~~(J,K).

(8)

where g,,- is the degeneracy. E, the rotational energy and Q the partition function Combining (2) to (7). [15], yields

3-I. Probe laser absorption

The determination of a rotational distribution in a jet by CCL infrared absorption has been described by Veeken and Reuss [15]. Here the main ingredients are summarized. The absorption, A, is defined by

A((J,K),~,,z,)=K,L,,liri’p(z,)~, Xf ((J9~)~~,)/~(~,)~ where

(9)

K,

is a constant_ By measuring the distribution is probed in an interval Ay,. around -u,, = 0; AyP is related to the local linewidth, Av, through (5) and (6)

A((J,K),v,,),

A = ln( 1,/r).

(2)

where I, is the intensity without jet excitation and I the attenuated intensity. The jet absorption stems from an integral over the inhomogeneous medium along Y, A =/(1(y.~~Myp)

(7)

where K, is a constant_ L,, the Honl-London factor and p the transition dipole moment. In case of thermal equilibrium

f ( J. K I= a, exd - WkT, l/Q. 3. Results

(5)

dr,.

-

(3)

Ar, = (AY/AY&,

(10)

where AV D=(%/c)%The background gas gives rise to absorption, too. Its contribution is subtracted from- the measured absorption as described in ref. [15]_ The

176 Table ; Transitions probed in jet J

absorption. Transitions indicated uifi

An aster&~ uxr~ used in IRIRDR Band o1 -!- C: - u2 h’

Bandu,

0

1 2 3

K=O

K=l

aR
sR(1.1)’

aR(2.0)’ sR(3,O)’

4

aR(4.0)’

6

aR(6.0) =’

K=2

sQ(2.2)’ sR(3.2)’

aR(Ll )*

a) Used for background gas correction.

” Only used

aQ(4.4)*

rotational

From the slope, T, is determined. Fig. 3 displays double logarithmically the reduced temperature. Tr/To, versus the reduced distance from the nozzle, r,JD. From the E, = 0 intercept of (11). B = K2 ],a 12pzp/u_Q is extracted_ Multiplication by Q (calculated from T,) yields BQ, a quantity independent of 7,.

T, obeys. 1181,

where KS is a constant depending on y = c,/c,._ y = 1.33 and consequently K3 = 0.41; For NH,, the result of (13) yields the straight line drawn in fig. 3. The effect of condensation turns out to be pronounced. The higher p. the more condensation heat is generated. yielding an increase of (rota-

In o(

In zp -10

a0

10

2.0

IC

&I

-CtS

-10

(12)

BQ is called the absorption intensity and reflects the ratio p/q.. Fig. 4 displays double logarithmically BQ versus zr,/D_ The uncertainty of T, amounts to 2-3% and of BQ to 4-6% for zp/D > l- For ‘r/D < 1 the uncertainties are larger. The contribution of the pressure broadening to G, (4). depends on (J,K) and becomes significant here

f1513. I. 1. Rorational 1 emperaf we Without condensation and for

temperature

(13)

J~~‘~~,/~~Q~-(~/x-T,)E,. (11)

BQ = K2 1p I ‘PZ,/D,_

2sQt4.4)’

IRIRDR.

a(6,O) level is probed to obtain the necessary information_ The expressions for A denote the corrected absorption. The absorption A(( J,K ),v,) is measured for p0 A 95, 190, 380 and 760 Torr at eleven distances z,, between 0.14 and 6.63 mm. The probed transitions are indicated in table 1_ The logarithm of A((U’.K),v,)/L,,g,, is plotted versus E,.

=ln(~,

-.

zsQ(3.3)’

sQ(3.3)’ aQ(3.3). sQ(4.3)’

in

-- :

jc=4

K=3

K=4

K=3

i,,,fD > 2, the

-19

-2,

Fig 3. Rotational temperature, Tr/To, vemus distance from the nozzle. +,/D. for p,,- 95 Torr (A). 390 iorr (0). 380 Torr (V) and 760 Tot-r (I)_ The straighhl line is the theoretical dependence from expression(13) (y = 1.33).

_ ,: K,. Veeken eI aL.1 Relaxario~of NH3 in ajei by IRIRDR

._ _,. ~_l .... ~_ _ _. -- ~. ._ ._:-;;;@Jy;. -;’

(I?), observed at zP/D ~13.2: The seci$d-%e&~ that contributes is rotatio~nal free&rig 1 tion from rotation _to. tram&ion, : R-T,- .&¬’. keep in step with translational co&g [email protected]~and Fenn [21] have calculated the: terminal- rotational temperature for different values of y .asa_ function. of Z,, the number of gas kinetic.wllisionsnece&. sary for R-T relaxation_ Assuming a- gas~kin& collision diameter of 3-44-i, applic&ion of--their formulas yields a rotational freezing temperatt& of = 60 K, for Z,.= 5.0, and of =.39 -I( for 2, = l-O_ From fig. 3 we estimate a freezing-t&n- -perature of = 34 K. Including the abovementioned effect of condensation suggests Z,.c 1. The Roltzmarm plots all show a linear r&p&se. Consequently an upper limit to the R-RT relaxation time will be derived in section 5, 7,~ c 150 ns Torr* at 50 K This upper limit corresponds- toZ, c O-6, confirming the presence of clustering assumed above. The relaxation time ~,p will be discussed extensively in section 5; as a first conclusion it appears that R-_R=T relaxation is very efficient for NH,. In the following we assume thermal equilibrium between rotation and transiation and for their temperature we take smoothed values from fig. 3.

~~+-i&&~

_:..

lx’

F

0.1 -_

Fig. 4. Absorptionintensity.BQ. versusdisrance from rhe

for pit= 95 Torr(A). 190 Torr(0). 380 Torr (v) and 760 Torr (I). The strai@t line is the theoretical dependecce from (16) for pO = 95 Torr and O, = Q_ nozzle. z,,/D.

tional) temperature_ For p,, = 95 Tot-r only few clusters are formed and the rotational temperature follows (13) rather closely_ For small z,/D the discrepancy from (13) is caused by the approximative character of (13); the exact expression of T,/T, is far more complicated and will not be discussed here. At z,/D = 0 one has T,/T, = 2/(y + 1) 119]_ With y = 133 and To = 295 K this yields T,(O)= 253 K. For the lowest i,/D = 0.28, we measured T,(O.28)= 254 K, in good agreement with the calculated value. The deviation frcm (13) at large zP/D is due.to two phenomena. First there is condensation, which cannot be excluded even for p0 = 95 Tow, Milne et al_ [20] report a dimer mole fraction of = 2% at our value of p:D. From a comparison of T,/Ta.at different p0 it also appears that the jet at p0 = 95 Toir contains clusters. For NH, the heat of dimerization, AU,, is = 1200 cm-‘, e.g. a 2% dimer fraction creates a temperature rise of = 12 K_ The influence on T,jT,. is substantial but not enough to explain the deviation of 20 K with respect to

3.I.Z. Molecular density and flow- vefociry For zP/D > 2 and under condensation free wnditions of expansion, Hagena 1181 gives as expression for the density, P/P, = J&(=&q

-?

(14)

where K4 depends on y; for y = l-33, K4 =0_068. The exact expression for the flow velocity is u, =

[(Y/Y

-

I)@k/m)(T,

-

T,)]“‘-

(15)

For au ideal expansion the terminal velocity, v,-, corkponds to T, = 0; in our case, T, = 295 K, and r;, = 1078 m/s. Inserting (14) into (12) yields BQ=Kz

]pj’zK,D’p,/u,i,,.

06)

The constant K7 is taken from ref. [15] and~the BP values according to (16) are displayed in fig. 4 for p0 _= 95 Tot-r* and- v, E v,_ For small zp/D, BQ is experimentally found to reach a plateau due. to, the influence of pressure broadening on G; the higher density is. wtmter-

178

K

Veekn

et al. / Rekzxarion of h?H_, in a jet iy ZRIRDR

acted by a lower G value. Even for p. = 95 Torr and for larger zp/D the deviation of BQ from (16) is substantial, up to 40%, although qualitatively BQ follows the (l/z,) dependence reasonably_ There are two reasons for the discrepancy. Firstly. the assumption o, = u, gives too low an e$imate of BQ..25% a: +,/D = 1.1 and 8% at zp/D = 13.2. Secondly. expression (14) is an approximation. In the correct expression, zJD s- 1 should be replaced by (L-,/D) (zJD),_ where (r,/D), denotes the virtual source point [19]_ For y = 1.33. (+/D),. amounts to = O-85. which renders the estimate of BQ 13% too low, at zP,/D = 13.2. The combined effect makes up for the deviation of BQ from (16). For small z,/D the exact expression for p is again complicated and will not be discussed here. At z,/D = 0 one has, p(O)= p0[2/(y + l)]“cr-l’~ sd p(O) = 0_63p,: one infers from fig. 4 that experimentally ~(0.28) = 0_5Op,. reduced by pressure broadening. The discussion above leads to the conclusion that (12) gives a good description of BQ for z,/D > 1.1 at p0 = 95 Torr. The density in the jet is hence determined by (14). where Ka is adjusted to yield the experimental va!ues of BQ in fig. 4 with the help of (16); us is derived from (15). with experimental T, values. This procedure also holds approximately for higher stagation pressures, for zp/D > 1.6. 2.2 and 3.1 at p0 = 190, 380 and 760 Torr. respectively_ The uncertainty is larger in those cases because condensation renders the expression for z,;* (lS), uncertain. The condensation increases the temperature and this increase is transferred into flow energy during the expansion. This enhancement of v, has been observed for an NH, expansion [15]; L: and T, increase with pO_ As an approximation for all p. we take u, equal to its value for p. = 95 Tot-r from (15). This introduces an uncertainty as high as 10% for p,, = 760 Torr. The effect of condensation appears again in fig 4. We calculate the density deficit averaged over the region of interest, which amounts to 7% at p0 = 190 Torr, 21% at p0 = 380 Torr and 30% for p,, = 760 Torr if compared to p0 = 95 Torr. The maximum dimer mole fraction is reported to be = 5% [20] equivalent to a monomer deficit of lo%_

Consequent&, larger clusters are-present at 380 and 760 Torr_ In relaxation measurements the presence of clusters may disturb the results. because its introduces another type of collision partners, with its own particular relaxation characteristics. For the case of V-I/T and R-&T relaxation in NH, the influence will be shown small. section 5; the relaxation by monomer collisions is already v&y efficient; cluster collisions are expected to contribute in proportion to the cluster mole fraction, which is small for p,, = 95 Torr and modest for pt, = 760 Torr. 3-L Fump her

absorprion

The absorption of the CO,-laser beam (‘“CO, 9P8 line. l-2(4) W) by the jet. A,, is measured for p0 = 95. 190. 380 and 760 Torr and values of zE ranging from O-14 to 4.42 mm. In fig. 5 we have Pi’1

Fig 5. Pumpand probe lzser absorption. Ace, and A,,. ver+xs distance from the ncszzlc_~ z/D. for p,, - 95 Ton- (A A). 190 Torr (0 0). 380 Torr (v -v)- and 760 Torr (m Cl): The transitions are +aR(3.3) ( Acol. filled iymbols) and qsQ(3.3) (A,. open symbch). -

-.

._

K &ken e-1al_-/ Relaxa!ion of NW,.in a je: by JRIRDR

(xO(yl) = SG(v,

- z*s)_

PI, a=

a&l

+ E/&r-.

08)

where E denotes the excitation pump rate and Rp equals the relaxation rate repopulating the ground level and depopulating the excited level. From the values of a, pbg and-(18) one calculates E/R = 0.67, 0.63, 0.63 and 0.70 Torr for pbg = 0.017, 0.032, 0.069 and 0.17 Torr, respectively; the average vahte is O-67(4) Torr+ (1 Torr = 1 Torr* at room temperature)_ In fig. 5 saturation causes A,_ to drop faster with ra than AccL with zp_ Without saturation effects both would show approximately the same behaviour; A,,, depends on molecular density. rotational temperature and flow velocity and is found for large zp proportional to z;‘~, whereas A coz appears proportional to ZEN* for large ~a_ Applying (18) to the jet yields .an absorption attenuation factor proportional to dr- for large saturation parameters_ With (14) one obtains an attenuation proportional to z-‘-O_ This describes the observed behaviour reasonably well The remaining J --o-3 dependence is attributed to the variation .of the (Doppler) lineshape function G with decreasing temperature. For p. = 95 Torr,

L-

:

..

._

._:

’ :

-1

.::

.___,

.t’_:.‘_

._ ;~’ _ .; :.79:: i : ..

Aco,/Ac~~ leads to a value of .E/R- of -=~S~To&. -: This value is larger than_. E/e-_ from 1the’.&ck~.. -_ ground measurements, due to the higher- CO,-laser intensity focused on the jet_ For larger p&the saturation becomes important at larger t; because . _ of the increased density (18).-A more quantitative approach to E/R has not been attempted in view of the varying laser beam intensity along xE_ Saturation influences the excited fraction .of molecules, which will be discussed in section 4.2. -:.

3.3. Infrared-infrared

double resonance

The 13C02 9P8 laser beam_ with a power of 2.4 W produces the NH, transition

(17)

Here the line strength S is described by (7) and G is the Doppler broadened lineshape function at 295 K. All parameters are known for the u,aR(3,3) transition and (17) yields n&v,) = 30 m-’ Torr-‘_ Saturation leads to a smaller absorption strength

_

. ..

plotteddouble logarithmically Ac0; .versus zE/D together with Accr(3,3) versus rp/D; A,-c,(3,3) denotes the probe_ beam absorption for the v,sQ(3,3) transition_ The values of A,, are corrected for the large background gas absorption_ The bulk background ‘gas absorption is found to have an absorption strength a equal to 4.6(3), 6.5(Z), 93(2) and 12.7(3) m-t Torr-‘, respectively, for background pressures, pbg = 0.017,0.032,0.069 and 0.16 Torr (corresponding to p,, = 95,190, 380 and 760 Tot-r). The diminishing a for lower background pressure reflects the effect of increasing saturation_ The non-saturated absorption strengtk LYE_ is described by

>::--;_A ,.I:::-.:

I

. .

: .

h,, a(3_3)

+

’ 2~(4.3)

_

(19)

The induced changes of the probe laser absorption, 4A, are measured for the ground and excited state and the rotational levels indicated in table 1. The two hot band -transitions u, --, u1 + U, have been identified from a Fourier transform spectrum. kindly supplied by Johns [23]; u,2sQ(3,3) at 3386.925(5) cm-’ and u,2sQ(4.4) at 3386.815(5) cm-’ are in good agreement with the calculated positions 3386_926(10) and 3386_809(10) cm-r [ll-131. The IRIRDR lineshapes of the 2sQ(3.3) transition are displayed as a function of the CCL frequency in fig. 6a for different combinations of Zn, Z, and po_ The fwhm is estimated from the laser control voltage and discussed in section 4-l_ In fig. 6b the IRIRDR lineshape is displayed as a function of the CO, laser frequency, scanned over the gain profile. The IRIRDR signal is asymmetric with respect to the power curve, due to the detutiing of 78 MHz between uZ transition and C+laser center frequency. The fwhm of the gain profile is estimated from the laser control voltage. The induced change in absorption, 4A. is measured for p. = 95, 190, 380 and 760 Tot-r at z,, = 1_10,2.21,3_31 and 4-42 mm with zn varying from zero to I~_ The relative change of fractional-popu-. lation of a ground state level amounts to : 4I(J,K)/~~J.K)=4A(J,li’)/A(j.i(), The.fractional

population fof

(20) the excited state is

AA(%)

i!~A(a.u)/Pb~.)

.-

Fig_ 6. IRIRDR lineshapes for the o,zSQ(3.3) ~ansition In (a) versus CCL kquency For zp = 1.10 mm. zE = 1.08 mm p0 = 95 Torr 0: sp = 1.10 mm. zE = 1.10 mm. p,, = 190 Torr 0: =,, = 2.21 mm. zE = 2.11 mm. p. = 190Torr 0: and z,, = 3.31 mm. zE = 3.21 mm. p,, = 380 Torr @_ MH; Atso shown in(b)

In (b) versus CO+ser

frequency for z, = 1.10 mm . zE = 1.08 mm. p,, = 95 Tobrr. The values of fwhm are in

is theCO+ser-power curve(- - -)-

negligible without CO,-laser excitation_ We assume that the transition dipole moment of the hot band transition. o, + u2 - v,, is the same as the transition dipole moment of u,, i.e. A12(J,K)/f(J,K)=AAZ(J,K)/A(J,K).

(21)

where A( J, K) denotes the absorption and f (J, K) the population of the corresponding ground state transition [2sQ(3,3) corresponds with sQ(3,3) and 2sQ(4,4) with sQ(4,4)]. The absolirte changes in population are Af (J. K) and Af2( J, K)- In fig. 7a Af( J, K)/f and Af2(J,K)/f are plotted against (:P - zE)- for zp = 2.21 mm and p0 = 190 Ton-. The uncertainty in Af/f is typically = 0.2%. The lower ground state levels show a huge depopulation at larger values of (zP - zn), up to 40% This is due to the temperature rise following V-R,T relaxation. The V-R,T relaxation competes with direct R-R relaxation processes between the ground levels. The temperature rise does not severely influence the 2(3,3) level; therefore

_

Af2(3,3)/f yields direct R-R information in a straightforward fashion. In spite of the thermal effect distinct R-R *processes are observed for the ground levels, too. The a(3.3) level is depopulated by the excitation at zn = zr,, a 16% effect. The depopulation of s(3,3) follows through the inversion relaxation process and is equilibrated with a(3,3) for (zP - zn) > 0.10 mm The other ortho species (K = 0,3) show a more rapid depopulation than the associated para species (K = 1,2,4) for small _(zp - z,); compare. for instance, Af (J, K)/f for the s&O) and s(l,I) levels- Under the assumption that the para speck are only influenced by the thermal effect [El] we determine the associated temperature rise from their AA(J,K). To this end, the jet absorption A( J,K), calculated from (11) with T, and B from section 3.1., is used. The jet absorption after COJaser excitation, A*( J, K ), equals A=(J,K)=A(J,K)+AA(J,ij_

(22)

-iC1 -I

0

A

a(2.0) _.

- 542.2)

-.i;_;;: A

aO,3)

- s(3.3)

. s(3.0) l

r -1cI-

~(3.2)

-1C 0

0 4Ct-

. a(4,Ol . s(4.3) - a(4.41

0

0a Fig. 7-

CO&.iser-indu~

b

population

zp = 2.21 mm and p,, = 190 TOIT_

changes.

4//f.

(Zp’ZE)(mm)

in (a), and the corrected changes

4ffi,/f,

in (b). ..

V~TSIIS (+-+)

for

_ 182

K. Veekeh er 01./ R&xmim

. From the Boltzmann plots of A*( J, K) the excited jet temperatures 7 are calculated. In fig- 8 the relative increase in temperature. (y - T,)/T,. is plotted versus c, a relative measure for the relaxation time between zE and zP_ see section 4. The temperature increase can be more than 50%. From the data of fig. 8 we will determine the V-flT relaxation time in section 5.1. The assumption that the para species are subject only to thermal effects is not entirely true_ This is obvious from the observation of population of the excited para level 2s(4+4), probably due to energy transfer processes where one collision partner (e.g. of ortho species) loses its uz energy to the other collision partner (e.g. of para species), see fig lb_ The influence of this process on y is estimated to be small; the thermal effect of (y T,) > 0 on the para level populations dominates other effects, see fig. 7a. The values of AJ(J.K)/f are corrected for the temperature rise; its contribution is calculated from

c (mm-9

of NH, in.ajet by IRIRDR

(c - T,) and subtracted. -In-fig. 7b the resulting Afdirn-,( J. K)/f are dis&yed against (2; - zn) for zP = 2.21 mm and p0 = 190 Torr, cot-responding to

A f ( Jv K l/f of fig-7a; A_&, 2(33)/f = Af 2(3,3)/f because this excited level population is not very sensitive to a temperature rise (e.g. j(3,3) varies from 5.8% at 50 K to 7.3% at 80 K and to 6.9% at 110 K). Indeed a distinct difference appears- for Afdircut(J, K)/f of ortho and para species- The uncertainty in the thermal correction increases with (z,, - zE). because the relative contribution of the thermal effect increases. The uncertainty is mainly due to changes of CC&-laser power between probing of different (J-K) levels. These changes are magnified through (7 - r,) and are observed for instance as a deviation from zero for ?sJ&.~ (J, K )/f of the para species. From fig. 7b the overall impression is that the depopulation of a(3,3) is transferred, first to ~(3.3) and thereafter to the other ortho levels of the

dmm-1)

Fig 8. The CO,-laser-induced rotational temperature increase. (y.7;)/7,. versus the relaxation parameter. c: for p0 = 95 Torr (A). 190 Torr (0). 380 Torr (0) and 760 Torr (0). for \aIues zP= 1.10 mm (a). 2.21 mm (b). 3.31 mm (c) and 4.42 mm (d). The e..t.rapoIared curves. 7=.-p= 0. are indicated by (- - -)_

ground state. The-Z&(3,3) level is fist populated-by energy transfer from the excited .2s(4,3) level and then depopulated by various .rela.&ion processes. The : CO,-laser-induced absorption of the 2sQ(4,4) transition.has not-been studied in detail; it was only compared qualitatively with 2sQ(3,3). The 2sQ(4.4) .absorption reaches a maximum at values-of ( zP - 2s) for which the 2sQ(3,3) absorption is already clearly ~decreasing; this -gives an indication that-the 2s(4,4) level iS populated slower than the 2s(3,3) level. We have not yet probed the directly excited 2s(4,3) and other uz levels. _

4. The effective excitation of the molecular jet The relaxation results depend critically on the assumption that for constant zp the effective excitation does not vary with (zp - I&_ The factors that influence the effective excitation are the pump-probe geometry and saturation_ 4. I. Pump-probe

geometry

As mentioned in section 3.1. the probed region, A&* is related to the local linewidth, Av, by expression (10). The excited region- can be described by Aye, at jet position ze; Aye equals 0.66,. At position zp the diverging streamlines render the effectively excited region, Ay& larger, AyE = A_+ (z&n)

_

(23)

As a consequence the ratio of excited to probed region, M, becomes M =. ( Av~/Av)(

AyJ+)_

(24)

In this experiment zP is kept constant and M is proportiorial to ( AyE/zn). In fig 6a the IRIRDR lineshapes as a function of VCCLshow a decreasing linewidth, 290(15) MHz at zP = 1.10 mm, 200(X) MHz at 2.21 mm and . lSO(15) MHZ at 3.31. mm. In all cases (zp - is)-< 0_05z,. i-e_ AyE = AyE_ If Ay, B Ay, the IRIRDR lmeshape is .determined by the lozal Doppler width Av, which is 184, 156 and 165 -MHz, respectively -at zP = l-10, 221 and 3.31 mm_ ‘If Ay~s.Ay~ the IRIRDR

influence of Av- and Ays and well within;& jet. absorption linewidth of = 650 MHz,: as i&r-red from ref_.[l5]_ From considering Ayr and Ays it follows that M is = 0.67, 0.49 and 0.25; respectively, at, zp =._. 1.10, 2.21 and 3.31 .mm; only part of the probed : region is excited_ .: In (24) the influence of varying zE is described_ For Mb 1 the complete probe region undergoes. excitation and a decrease of zE would yield no difference_ For M c 1 excitation is incomplete and a decrease of z, would increase the effective. excitation_ In our ease M < 1 and thii geometric effect yields an effective excitation proportional to zEr_

The saturation of the excited transition has two consequences. The first is an increase of Ayn with zu; Ays is the distance between the points where the excitation assumes the half maximum values (for the non-saturated case. AyE = 0_6b,). From saturation line broadening 1221. we infer, Ays = 0_6b,(l

+ E/Rp)“‘,

(25)

where E/Rp denotes the saturation parameter_ For large saturation parameters Ays becomes proportional to zn, see (14) and (25). The increase of AYE enhances the excited fraction (24). In the completely saturated reggme of low pO and large (‘r- I&, the IRIRDR signal is observed to increase with laser power, which reflects the increase of Ays as described by (25). This zE dependence is offset by the’ second consequence of saturation; the larger the saturation, the smaller the excited fraction of molecules. For E x=- Rp the excited fraction is roughly proportional to the relaxation rate Rp and therefore to zf.-‘; if there are few rotaiional levels involved the zE’ proportionality becomes- a_ bad approximation; for small densities -the excited fraction does not approach zero. but is determine&by the

K

184

Veeken e: aL /

Rehxarion of NH,

depopulation of the a(3,3) level. Nevertheless for the estimate in the following paragraph this dependence has been used. The total effect of pump-probe geometry and saturation amounts to an effective excitation that is proportional to zE’ in the case of large saturation and iarge zpr where it4 is much smaller than 1.0. Without saturation, for large zpr the excited fraction becomes proportional to 16’; for smail J where M is of the order of 1.0, the excited f&ion becomes roughly independent of zE_ The effective relaxation between zE and zP depends on the number of collisions, which is characterized by (in the case that the product of the cross section u of the considered inelastic process times the relative velocity u of the colliding partners is approximately z-independent) Q-P=/I$(r) II:

dr = (~u)-~/%--~ *t-

dr.

(26)

where t, and f, are the excitation and probe time_ In the jet. ‘;-p=

=r P(=) I =I..

d=/u,,

(27)

where us equals LJ%(z,)_As expression for p(r) we use (14). but with Ka adjusted to yield the experimental value of ~(2,). Then 7p = K5c,

(28)

where c is in mm-’ c = (zp - ZE)/ZpZE,

(29)

and K, (s Torr* mm) is a constant determined for each combination of p. and zP_ An excited fraction proportional to z;’ causes a 10% higher excitation at c= 0.05/z as compared to c = 0; a proportionality to z~ p creates a 10% higher excitation at I =~.lO/z,_ Note that for these estimates, zP is assumed to stay fixed and zE.
in a jer & IRIRDR

5. Relaxation times 5.1.

V-R,T relaxation

In fig_ 8 the relative change of temperature (I;* - c)/T, is plotted against c; it is influenced by four factors. The first one is the V-RT relaxation, that transforms vibrational into rotationaltranslational energy. The second is the dependence of excitation on tE_ The third neglected one is the cooIing of the expanding jet (v and T, decrease for larger z,/D _values; (r - T,)/T, is a relative measure though and is expected to stay constant). The fourth factor is condensation. If one compares (;r;* - T,)/T, for p,, = 95 Torr at zP = 1.10 and 4.42 mm (see figs. 8a and Sd), the relative temperature change shows quite a different dependence on the time-of-flight parameter c; for constant excitation one would expect that a plateau is reached for larger c values, where all the excitation energy is distributed over the accessible degrees of freedom (see fig. 8a for p. = 95 Torr). In contrast to this expectation, no levelling off is seen for zP = 4.42 mm. Note that the time-of-flight parameter E is proportional to the number of collisions occurring between zE and zP. see (26) and (28). Apparently (fig. 8d) a varying amount of CO,-laser energy is deposited into the jet molecules, for different zE values; this is not in contradiction with the conclusion at the end of section 4_ There the range 0 < CC O-1 mm-’ has been considered whereas in fig. 8 one deals with 0 G c =G 1.0 mm-‘. For higher stagnation pressures, condensation effects play a dominant role; (7 - T,)/T, shows a sharp decrease and even becomes negative. for large c values. This is due to laser-induced inhibition of condensation [24]_ The heat of excitation is more than compensated by the lacking heat of condensation. Despite the fact that (;r;* - T,)/T, does not reach a constant value for large c, -r,.p is estimated by extrapolating (y - T,)/T, from large to small c values, and by comparing the experimental and extrapolated curve, s&e fig 8. This extrapolation disregards relaxation processes. which become unimportant at large c values. This yields qp = 300(60) ns Torr*. With this value corresponds a

. K. Vet-ken er al. / Relax&m

of NH;

in a jet by IRIRDR

-.:‘] &~-f-

am .:

Table 2

-_.__j

Relaxation times determined from IRIRDR measurements together with the effective collision cross sections_,%11relaxation ti&s‘are expressed in s Torr’ and reflect a temperature r+nge 50-110 K. except ‘z~“,.Pat 50 K. Cross sections in A’ Relaxation time

Level

Relaxation PrR-R

ground state

R-R

. -.

W20) 5q20) 75(30)

n2 state

inversion

7rcP %=P ?i,“P(3.3)

%W 120(u)) 20(g) 20(S) 170(30) 7_6(20)

%P

280(50)

~4)

7-P

425(190)

1q7) 37

doublet V-RT cz to ground stare v-v ortho to para gas kinetic

time-of-flight parameter c = 0.18 mm-’ for pa = 95 Torr and c= 0.09 mm-’ for p,, = 190 Torr. Another way to determine r,.p is to consider for a fixed value of zu. (y - T,)/T, as a function of zP (in this method the excited fraction is constant [25]). One finds ~,,.p= 260(50) ns Torr*. The V-R,T relaxation time is estimated from both methods, ~,.p = 280(50) ns Torr* and displayed in table 2. 5.2. R-R and V- V relaxafion Correcting Af( J,K)/f for the V-R,T energy release reveals direct relaxation processes that are sensitive to particular (J. K ) levels. see fig. 7b. For ortho species Afdirccr/f can be described by

Af&a/f

= A[1 - exd--1/7;)]

Comment

45(X).

TiPs(I.0) T;Pa(t.O) ws(3.0) SiPs(4.3) TP %P r&s(3.3)

average R-R

Effective cross wction

ed--h)-

(30)

By (30) two relaxation times are defined; -ri for the direct process, which leads to population transfer between the two laser (de)populated levels a(3,3) and 2s(4,3) and their neighbouring levels, and 7, for e.g. processes leading to equilibrium between ortho and para species and V-R,T relaxation. (Note that for the a(3,3) level of the ground state, depopulated by the CO? laser, different 3 processes cannot be distinguished.) To extract the relaxation. times, Afii_,/f (or - Afdi_,/f if nega-

122(43)

4K=3

_%2(137)

4K=O

1137(296)

4K=O.43-0

tive) is plotted logarithmically versus c for all combinations of p. and zP; see fig. 9 for p. = 190 Torr and zr, = 2.21 mm. For large c values, the Afai,/fdata are calculated as (small) differences relative to a smooth curve which is determined for the para-level responses; the differences can drop below the abcissa [e.g. fig. 7b, s(l,O)J due to the uncertainty of this subtraction procedure_ For the fit of (30) in some cases an eye-fit base line had to be adapted to prevent this. The data of fig. 9 are relative to these base lines. The values of rip and TOPare connected to ci and c,, by (28) %-j&J = KSCi,

(31)

5dp = K5C&

(32)

It follows from (30) that

lnCAf~;,t/f

I = In{A[I- exp(-c/ci>I} - c/cd(33)

The degree of Af,i,,,2(3,3)/f is well described by a relaxation time. asp, fig. 9b; the decrease of Afdirrsl( J, K)/f is influenced by the temperature correction and therefore somewhat uncertain. The slight increase of the excited fraction for smaller zE .values (i.e. for larger c. if z; iS_kept constant) tends to lengthen %p_ In most cases

186

K Veeken PI aL / Relaxation of NH, in a J%I 6-r IRJRDR

Sfdirec!/f (%I

i. I..

0.10

0.00

:

0.20

c (mm-‘) Fig. 9. The correcred population change. Aj-,,,,/f. levels a(3.3) (A) and ~(3.3) (0). in (b) for Zs(3.3) (A) (33). ci = 0. are indicared by (- - -)_

versus relaxation paramefer.

c. for zP = 221 mm and p0 = 95 Torr: in (a) for the

and in (c) for ~(1.0) (A), a(2.0) (0). ~(3.0) (V) and 514.3) (m). The

though we observe a pure exponential decay, which supports us to ignore this effect. At most it can increase rap by 20!%_ The alp values are corrected for the limited spatial resolution_ Note that the excitation is not a delta function at c = 0; it is spread over an interval of c. as can be seen from the instrumental rise time of 4&_8(3.3)/y_ For z,, = 1.10 mm and p. = 760 Torr the decay time gp of 2s(3,3) corresponds to c = 0.017 mm-‘, which makes the c dependence of 412s(3,3)/f due only to the pump-probe geometry_ From the curve In[4j,i,,2s(3.3)/f] versus c it appears that the geometry effects can be translated into an effective decay time. ~-~p, which corresponds to ca = which is used as correction (zp (0.036/z;) mm-’ in mm)_ Unless stated otherwise the obtained relaxation times are the averages over all combinations of p. and zp, which means temperatures ranging from 50 to 110 K_ The spread in results is too large to draw conclusions about the temperature dependence. We observe no systematical dependence on po, indicating that the influence of chtsters is small. For the decay of the excited state, 2s(3,3), we

extrapolations Of

find rJp[2s(3,3)] = 170(30) ns Tot-r*. For the decay of the ortho ground states we obtain an average, r,p( J, K) = 12@(30) ns Torr. The relaxation time 7i is shorter than t; it is determined in two manners: (1) In[4&Jf] as it decays is extrapolated to c = 0. yielding A from

Further

(34)

= In A - C/Cd-

1nTaf,i,//l the

observed

maximum

value

A,

of

Afdire.zJf is given by A,//4

= (1 + or)-“+%“,

(35)

where a = c/cd; combining (34) and (35) yields ci. (2) ci is determined by comparing the extrapolated A&,Jf from (34) with the real observations described by (33). The value of c, where the ratio of these two is 0.68, equals ci. Both methods yield values of ~-rp in agreement with each other. For zr, = 1.10 mm the values of .~~ip must be corrected for the effect of limited spatial resolution. For larger zP this.effect may be ignored. For. the different ortho states the relaxation times 7ip are displayed in table 2, together with the values for rdp; the average ground state value is T;P =

=_ . ._:

._

:

- _._ -~..-.-

k

-Veeken

er d

,/

Rdaxarion

56(20) ns Torr*. the excited.ortho state rise time amounts to_20(8) ns Tot-r*_ ._ 1 .-. :‘. : The fastest rip’ is observed for s(3.3); it corresponds’to the inversion relaxation time ri,,p which describes the speed of achieving equilibrium :between the two :inversion- Ieve&; it. is obtained for about 5.0 K by plotting. ln[Af&,,s(3_3)/fAf&,,a(3,3);/‘] versus c for zp = 4.42 mm. p0 = 95 Torr and p,j = 190.Torr_ The resultant. time. rin,.p T 7.6(20) n& Tot-r*, has been corrected for the limited spatial. resolution. . The decay times, -~,,p, are.shorter than 7.p determined in section 5.X The reason ii that ortho-para vibrational exchange processes. with a relaxation time ~“,p. contribute to TV_

k&P)-‘= bd-’

+(i,&‘9

(36)

+ 2(7,PP)-i-

in aj&

&

IRIIZDR-

-. :

::_.-:_~.;r,-_I_:.~~-~;.;‘

‘~--I z =

: i i-.i,. -.!W

upper.- hmit for.. the rota&o& rr&xati& _time+ total orthorand para. fractions-(both 50%) jdo&ot ; depend significantly on -Tr..for lTr>-4C-K: :th&_qur. Boltzrnann .plots are not senstttve to ortho-&ii_ transitions_ But the-fraction& in‘differentx- st+ks.:~EjX,,f(J.K), depend strongly-on T;_.Fcr-l&ver.-$ the population-of the .K c 3 stack drops;: it _must relax through AK.= 3 . transitions,. to the 1K-L-0. stack. The same holds for. K = 2 and K-i 1; .Forp. = 95 Tot-r, -T, decreases from 47.6-K at -5; = .4_42 mm to 42-4 K at 6.63 mm. For thermal. e+i-~:~ librium this indicates a drop in. K-F-3-populationfrom 11.2%. to 9.4% and an increase -of. K =.O. population from- 38.8% to 40_6%_ Between zr, =. 4.42 and 6.63 mm. the time available for relaxation amounts to i-p = 123 ns Tot-r*. The thermal equilibrium decrease in popula&n of K = 3 is l_S%:. the Boltzmann plot data yield 1.8 f 0.78 for this decrease. Consequently the relaxation time of K =. 3 to K = 0 is smaller than 150 ns-Tot-r*, at T, = 45 K. Besides this estimate for AK = 3 transitions. we can also estimate- the AK = 0. A J f 0 relaxation time. In a single K stack (e.g. for K = 0) f (J;K ) changes with temperature. For the same conditions as before f(3.0) drops from l-8 to 1.4%. The Boltzmann plots yield a decrease of 0.4 + 0.1%.

for the excited state and (7JP) = (WW

g/NH,

._!

1..

(37)

for the ground state; (36) and (37) will be discussed in the following section; (36) yields ‘?l,pp= 430(250) ns Torr* and (37) ~,rp = 420(300) ns Tot-r*. i.e. the average value 70,,p= 425(190) ns Tot-r*. The linearity of the Soltzmann plots yields an Table 3 Maximum PocTo=)

vahes of (de)population

(ia%)

=,bm)

a(3.3)

93-3)

Js(3.3)

(J_K),,,='

1_10

165(10)

llJ(10) S.4(10) 5.4(5) l-9(3)

7.0(20) 7.5(10)

1 l.qlo) 12.0(5) -

55(10) 7.1(5) s.qlo) 73(10)

4.q20) 4.0(S) 5.5(10) 7.0(10)

5_7(10) S-5(5) -

25(10) 4.0(10) 5.1(5) 6.q5)

Zol5) 3.0(10) 35(10)

2x5) 5.6(5) -

-

190 360 760

1.10 l-10 1.10

18.6(10) 16.qlO) -

-95 190 380 760

2.21 221 2.11 221

14.015) 16.q5) 14.0(10) -

95 190 380 760

3.31 3.31 3.31 331

10.5(10) 1x?(5) 16_q5) -

95 190 380 760

4-42 4.42 4.42 4.42

95

=’ (3.K)

-

lLq5) 9-x5) lo.q5)

9.7(10) -

:

denotes the average over ~(1.0). a(Z0). ~(3.0) and ~(4-3).

3_4(5) .3_1(10)

1_5(10)

O-o(5) I-o(5) X0(5) 3-o(5)

.:.

_-.

Therefore.

the relaxation

time of (3.0) to (J-0)

is

smaller than 100 ns Torr*, at = 45 K. The observed values of rip are in agreement with these upper limits. The magnitudes of Afdi,,/f for c > Ci are in agreement with an equilibrium of the (de)population between all ortho levels. i.e. A&,,(J,K)/f assume about the same value and Afdircct2( J, K)/f for all ortho levels. The maximum (de)population values of the levels are displayed for the different combinations of p,, and zP in ta_ble 3. The excited a(3.3) experiences the highest (de)population, followed by ~(3.3) 2s(3.3) and the ortho ground levels, in this order corresponding to increasing values of rip. The maximum depopulation for a(3,3) is highest for zP = 1.10 mm and p. = 95 Torr, = 19%; the overlap of probed and excited region is best here. This overlap diminishes for larger zP; for zP = 4.42 mm and pe = 95 Torr the maximum depopulation is = 11%;. Besides incomplete overlap. M -Z 1. there is a second reason why the maximum depopulation does not reach the attainable 50%. With complete overlap and saturation the excited fraction,

fE. equals I,=‘z{l/[l

+(A/Q)z]).

(38)

where A is the detuning and Q the power broadening. From fig. 6b where the detuning is varied, we estimate D = A: this yields fa = 25%.

6. Discussion of relaxation

x 10-5)

excited fluorescence method [l] detects the decay of the population of .the u, level. It does not distinguish between relaxation to high-lying rotational levels, e.g. as observed by Haugen et al. [3] for HF( D = 1) relaxation, and direct relaxation to translation_ Our IRIRDR method determines ~,.p from the rotational temperature rise obtained from the rotational distribution of. para species- The obtained value of 7,~ yields an upper limit to the real vibration decay time of ref. [l] and the observed increase of a,. (a factor 5 between 295 and 80 K) could thus be larger for the pure decay of vibration_ It is possible that our -r,p observation is the result of significant cascading from higher rotational levels. e.g. from the (10.0) and (10.3) levels (fig. la)_ However. the rotational cascading involves energy gaps of 100-200 cm-‘. These large gaps tend to render R-R relaxation less probable for low temperatures; therefore direct transfer of vibrational excitation into thermal RT energy may dominate at the low jet temperature. Such a direct transfer can occur during orbiting collisions, where the interaction time is large. For the strong dipole-dipole interaction between NH, molecules. orbiting collisions become probable at the low jet temperatures. 6.2 R-R

The relevant relaxation times, 7,~ (x stands for the relaxation in question). are transformed into effective cross sections [26], a; = (r,p)-‘T-‘r-(6-11

regarded as the most reliable one, -r,.p= 770(80) 11s Torr* at 295 K. corrtiponding to uJ295 K)= 4_6(5) g_ The two values of -qp obtained by different methods belong to different. processes_ The laser

2.

(39)

with 7%~in s Tot-P and T in K. The derived cross sections should be compared to the gas kinetic collision cross section, a0 = 37 A’. 6. I. V-R, T relararion Our value 7,~ = 280(50) ns Torr* yield& uJ80 K) = 24(4) g at an average temperature of 80 K (table 2)_ The value of Hovis and Moore [l] is

and V- V relaxation

It is established that the conversion between different nuclear spin species is a very slow process on the time scale of our experiment_ Oka [4] argues the transition between ortho and para species to be strictly forbidden; this point of view is adopted in the following. R-R transitions spread the population deficit of the a(3,3) level to other ortho ground state levels, (uz=O,(J,,K,))+(u,=O.(J’.K’)) “5 (v, = 0, a(3,3))

+ ( uz = 0, (J”,K”)).

(40)

RR transitions also redistribute the population of the 2s(4,3) level to other excited ortho levels.

is equivalent to the &m&nation.

(44) and ($j-i-

_ ’

(uz=1.s(4,3)).+(u,=0,(J’.K’))

For both processes the collision partner is a ground state molecule, the fraction of excitbd tiolecules being smaller ihan 3%. A colli-Zion partner of ortho or para species remains in its nuclear spin state during the collisibn. The result of (41) is again an excited ortho level. We have observed though the excited para level (ul = 1. (4,4)) populated. This is only possible through V-V rela__ation. where the two collision partners of different species exchange a vibrational quantum.

(u~=l,(~~.KO))+((?,=o.(J’.K3) (JI.K,))+(u2=1.

'~(+=O.

(J”.K”)).

(42)

This exchange is of course also possib!e between two ortho collision partners (fig. 1 b). Our assumption that the only influence on the ground state para levels is due to temperature rise mus:

therefore

ortho

ground

be reconsidered. state

populations

The for

correction

of

temperature

rise contains the V-V exchange between ortho and para species, (42). This exchange is characterized by -I-Q_ The replenish& of the ortho ground state population deficit contains the V-V relaxation twice, because we determine the decay of the difference in population of ortho and para levels: this yields (37). The decay of. the Zs(3.3) population origin&s b&h fro& V-ST relaxation and V-V relaxation, resulting in (36)_ The value of ~‘,~p corresponds to an effective collision cross section, %p = 16(7) 2, table 2. The equilibrium between ortho excited state populations is reestablished by (41) and (42). The R-R and V-V processes produce the same effects. e.g.

(u1=0.

'2&;=

(3,O))+J,5.

(3.3))

1, (3.0j)+.(u,=o, (?,3)),

(43)

R-R relaxation requires AK = 3 tr&sitions. V-V relaxation only AK= 0 transitions. In this. experiment no information is obtained concerning the relative contribution of the V-V exchange_ It is a resonant process; its influence may be wnsiderable. Its relaxation time. should be about ~~r,p, which has the same physical origin. Table -2 shows that process (43) is unimportant as compared to the combination (44) and (45). Ortho ground state populations wme to equilibrium within a relaxation time belonging to process (40). From table 2 we conclude that this time does not differ for different rotational levels, within the uncertainties of our experiment. The average relaxation time value is denoted 7,~ and corresponds to an effective cross section. cr== 122(44) A’_ Surprisingly. the AK= 0 relaxation (4,3)-, (3,3) is not faster than the AK= 3 relaxation (J.K = 0) --, (3.31 The AK = 0 transition is dipole-dipole allowed and is expected to have a larger cross section than the AK = 3 transitions. Kuze et al. [S] observe a preference for AK= 0 transitions over AK = 3 transitions (a factor of = 2.5). However, in ref. [8] excitation and relaxation is amongst para levels, which might show different propensities than our ortho levels. In addition atid more important in our case the non-propensity is influenced by the low jet temperatures (80 K wmpared to 295 K [8])_ The fraction of suitable collision partners to render the (4.3) -+ (3,3) transition nearly resonant [e.g. by (3,l) - (4,1)] is not significantly influenced by the low jet temperatures (increase by a factor 1_4), but AK = 3 transitions like (3,O) ---, (3,3) find a more than fivefold increased number of nearly resonant partners (e.g. by (1.1) - (2,l)) at our jet temperatures. The same argument is used by Oka [4] to explain the K dependence of AJ = 1 transitions in MWMWDR

relaxation measurements. The relaxation from particular levels to (3.3) may occur in various steps; e.g. (2,0) - (3,3) may be composed of (2,0) - (3,0) and (3,0) T (3,3). The contribution of orbiting collisions could be important, yielding statistically distributed scattering products. From the Bohzmann plots we obtained that AK = 3 transitions between K = 3 and K = 0 reeStablish equilibrium within IS0 ns Tot-r*, in agreement with the ~=p = 56(20) ns Tot-r* of table 2; A J = 1 transitions were found to be faster than 100 ns Tot-r*_ Klaa$en et al. [9] calculate the cross section for 4 J = 1 transitions; u = 80 A’, which is of the same order of magnitude as our a,, table 2. Matsushima et al. [7] report u = 9 Az for the a(3,2) to a(2.2) transition at 295 K. which appears somewhat low. The 2s(3,3) excited state population appears within the relaxation time, ~,~p_ (41): due to transitions 2s(4,3) - 2s(3,3); drip corresponds to a,, = 342(137) 2, see table 2. This relaxation is probably due to the sequence of two dipole-allowed transitions, 2s(4.3) --, 2a(3.3) and 2a(3,3) - 2s(3,3). This sequence is only possible for the excited state and decreases the exothermicity from the single step value of 79 cm-’ to an exothermicity per sequence of 42 and 37 cm-‘. see fig. la; CJ~ characterizes 4K = 0 transitions in the uz level: relaxa3 relaxation tion is = 3 times as probable as 4K= in the ground level. The inversion relaxation time. ri,,p at 50 K (denoted in literature [27%28] as Tt), is equivalent to an effective cross section, u, = 1137(296) A’. The population difference between s(3,3) and a(3,3) decays due to the inversion transition s(3,3)a(3.3) characterized by uinvrand due to transitions to and from other rotational states, ~(3.3) - (J’. K’) and (J”, K”) - a(3,3), characterized by u,For NH, it is established [27,28] that for the inversion dktblets u, = 2Ui”,. + us

(4)

and U,=Ui,,+",,

(47)

where uZ is equivalent to a relaxation time T2 characterizing the decay of the macroscopic

polarizability with T2 =-1/2-;;.y; y (hwhrn) denotes the p&sure broadening halfkidth.. From (46) and (47) follows Uinv= ui z a2 and 2-r < T2_ For the (3.3) doublet at room temperature; .Arn.tio et al: [28] found u, = 1_40u,,~i.e. uinv= 0.4Ouz or uinv= 0_29u,_ At room temperature y = 24.2 MHz Tot-r-t 1291, which corresponds to a, = 532 Az. This yields uinv(295 K) = 213 AT. The temperature dependence of- ~(3.3) has been determined by Dagg et al 1291; extrapolation to 50 K yields ~~(50 K)= 927 Az. If the same temperature dependence applies to (I;,,., uin,.7 0.4Ouz yields a,,.,,.(50 K) = 366 %. Our value of u, results in a,,.,,.(50 K) = 330(86) Az, assuming *inv = 0_29_u, also at 50 K The two estimates for uinu are in good agreement, but are both critically dependent on the ratio u,/ur which might vary with temperature_ A significant temperature dependence of 7,~. 7ip and asp is absent; this indicates a proportionality of the associated cross sections roughly with T-In, see (39), or q,.,. where orei is the relative velocity_ Anderson’s theory yields approximately the same dependence [9].

7. Conclusions This paper presents data for vibrational and rotational relaxation of NH, at low temperatures obtained by IRIRDR in an expanding jet. The relaxation is defined by the time-of-flight between excited and probed region. The jet parameters crucial to this experiment are rotational temperature, molecular density and flow velocity. The rotational temperature and the molecular density are probed by the CCL absorption_ Deriving quantitative information from the pump-probe experiment is not trivial. The excited fraction of molecules varies with the distance between pump and probe region due to-a variation of geometrical overlap -and saturation_ The vibrational relaxation is determined from the rotational temperature rise in the jet: The vibrational deactivation probability is about five times larger for 80 K than for 295 K The vibiational relaxation is an order of magnitude slower than the rotational relaxation. Vibrational ex-

: _ --: -.

-_

change between ortho and para species.occurs on the same tune scale as vibrational relaxationRotational relaxation. times in the ground and the excited u, state are determined. The time resolution of our method permits to detect and determine the inversion relaxation rate between the a(3,3) and s(3,3) levels. The advantage of this method is the low temperature than can be attained at densities orders of magnitude higher than the vapour density-

Achnowhzdgement The skilful and permanent assistance of Cor S&kens. Frans van Rijn and John Holtkamp is gratefully acknowledged_ We want to thank Rob Smeets for his assistance in the measurements.

References [lj 121 131 [4] [S]

FE Ho+ and C.B. Moore. J. Chem. Phys. 69 (1978) 4947. R.V. Ambansumyan. VS. Letokhcv. G.N. hlakarov and A_A_ Puretskii. Soviet Phys_ Jerk 41 (1976) 871. H-K_ Haugen. W-H. Pence and S_R Leone J_ Chem. Phys. 80 (1984) 1839. T. Oka. Advan. Al. Mol. Phys. 9 (1973) 127. S. Kano. T_ Amano and T. Shimizu. J. Chem. Phys. 64 (1976) 4711.

[6] G.M. Dobbs, RH. hlicheels. J-1. Steinfeld, J.H.S. and J.M. Levy. J. Chem. Phys. 63 (1975) 1904.

.~-- L.. _,._- _I?_1 ::

..

_-

Wang

[7] F_ Matsushima. N. Morita. S. Kane and T_ Shim-w. J_ Chem Phys. 70 (1979) 4225: T. Shimizu. F. Malsushima and Y. Honguh. in: Laser spez~roscopy. Vol. 5. eds. A. McKellar. T. Oka and B.P. Stoicheff (Springer. Berlin. 1981) p_ 212.

[S] H. Kuze.

H. ,Jon&

M;

~suk+xhi.

A.

h&nohi&l.

hi: ‘:

Takami. J.‘Chem. Phys. 80 (1984) 4222. ‘191 D-B-M. Klaassen. J-MM. Reiioders. JJ. ter Meuleo a%..’ A. Dymarms. J_ Chem Phys_ ;6 (1982) 3019: : .: D.B.M. Klaassen. J_J. ter Meden -and A__ Dymanus. i_. Chem. Thys. 77 (1982) 4972, [lo] G. Luijks, J. Timmerman. S. Stolre and J. Reuss_ Chem. Phys. 77 (1983) 169. fll] WS. Benedict. E-K Plyler and ED. Tidwell, J_ Chem. Phys. 32 (1960) 32; J. Res. Nat Bur. Std. 61 (1958) 123_ [i2] S. Urban V. Spirko. D. PaponSek. R.S. hlcDowel1. N-G. Nereson. S.P. Bdov. LI. Gershstein. .A_V: Maslovskij. A-F_ Krupnov. J. Curtis and K_N_ Rae. J. hlol. Spectry_ 79 <1960) 455 1131 CH. Tounes and AL. Schawlou: Microwave spectrosmpy (Dover. New York_ 1975) p_ 311. j14] T_ Shimizu F-0. Shimizu. R. Turner and T_ Oka. J. Chem Phyr 55 (1971) 2X22. 1151 K. Veeken and J. Reuss. Appl. Phys. B34 (1984) 149. (161 E-M. Fraok. CO. Weiss. K. Siemxn M. Grinda and G-D. Willenberg. Opt. Letters 7 (1981) 96. 1171 P. Esherick. AJ. Grimley and A. Chvyoung, Chem. Phys. 73 (1982) 271. [18] 0-F. Hagena. Surface Sci. 106 (1981) 101. [19] H.W_ Beyerinck and N.F_ Verstrr. Physica 1llC (1981) 327. 120) T-A. Miine. J.E Beachcy and F-T. Greene. J. Chem. Phys. 57 (1972) 2221. 1211 C.G.M. Quah and J.B. Fenn. in: 11th inremational Symposium on Rarilied Gas Dynamics (Commissariax a Ilenergie aromique. Paris. 1978) p_ 885_ 1221 W_ Demtraer. Laser spectroscopy (Springer. Berlin. 1982) pp_ 105, 109. [23] J-W_ Johns. private communication. [24] P_ hielinon. R Monet J.M. Zellweger and H. van der Bergh. Chem. Phys. 84 (1984) -345. [25] K. Veeken. N. Dam and J. Reuss. 80 be published. [26] J-D. Lambert. Vibrational and rotational relaxation in gases (Clarendon Press. Oxford. 1977). 1271 W.K. Liu and RA. Ma-. J. Chem. Phys. 63 (1975) 272. 1281 T. Amano. T. Amano and RH. Schwendeman. J. Chem. Phys. 73 (1980) 1238. 1291 1-R. Dagg. P.S. Athenhon and RW. Parsons. J_ MoL Spatry_ 100 (1983) 134.