M-dependence of collisional transfer of rotational energy in methanol

Volume 41, number 3

cHEhfK!AL

FHYSKS

I August 1976

LETTERS

M-DEPENDENCE OF COLLISI(ONAL TRANSFER QF ROTATIONAL ENERGY IN METHANOL” RM. LEES and L.J. RETALLACK of Physics, Universiv of New Brunswick. Fredericton, New tinswick,

Department

Gmada

Received 17 March 1976

An M-resolved microwave doubIe resonance experiment on methanol is described. Relative s&-ml intensities and Mselection rules in pure CH30H are consistent with a dipole-dipole collisional interaction, while those for CHSOH-He and CHsOH-Hz mixtures indicate more complex titeractions.

1. Introduction Four-level microwave double resonance experiments, recently reviewed by Oka [l] 5 have in the last few years been employed to investigate collision-induced transitions between rotational levels of a number of gases. In most cases;measurements were made only for unsplit zero-field transitions, in which the components of the transition corresponding to particular values of the space-fwed component M of the rotational angular momentum were not separated. In the analyses of these experiments, it was then generally implicitly assumed that the collisional transfer was independent of M. However, as pointed out recently [2], the fact that the miclawave radiation is linearly polarized introduces directionality into the problem, and can lead to significant M-dependence OEthe collisional transfer. In order to analyze the transfer in detail, it is necessary to know the collisional rates for particular M-values, yet so far very few experiments involving individual M-components have been reported [l, 31. In selecting a molecule to give maximum information in an experiment on M-dependence, one would seek a first-order Stark effect, so that +i%iand -M signal components would be separated. This immediately suggests a symmetric top, or perhaps less obviously, the E torsional species of an asymmetric molecule, such as CHsOH with very fast internal rota* Finanti support of this research by the National Research Counci? of Canada is gratefully acknowledged.

tion of a three-fold internal top. In this Iatter case, the fast internal rotation effectively averages out the molecular asymmetry, so that the spectrum has a number of the features of symmetric top spectra, including a first-order Stark effect for levels with k # 0 of thz degenerate E torsional species, where k is the molecule-fixed component of the rotational angular momentum J. The asymmetric molecule still has a perpendicular component of the dipole moment, however, which means that transitions with Ak = C-1are aliowed, permitting one to avoid the near degeneracy with k characteristic of the M = 0 R-branch transitions of a symmetric top. Thus, as in many other situations, methyl alcohol presents itself as the ideal test molecule, and in this letter, we present initial results of an M-resolved experiment on one four-level system, the (4* + 3,),-(2, + 3& system 141, for pure CH30H, and for dilute mixtures of CH30H in excess He and HZ. We find that such an experiment, even for a singIe four-level system, provides a great deal of information, with significant implications for the form of the collisional interaction.

2. Experimental The experiment is performed by applying a sufficient amplitude of Stark square wave modulation to resolve clearly the&f-components of the pump and signal transitions, then phase-locking the signal klystron at the peak of a particular MS component of the signal line. The pumping klystron is then slowly swept 583

CHENICAL PHYSICS LETTERS

Volume 41, number 3

1 August 1976

Table 1 Observed collisional transfer s&n& for the (40 + 31)p-<21 c 30)~ system in purz CH30H

4O

Mp=-3

.

34

‘I

1

E=O

E>C

f ;

’ ‘:

i :

1 2 0

-i

1;

2

~~~~~

1 2 3 -1 -2 -3

-2 c

Fig. 1. (40 + 3~J,-(2~ + 3& system of CHaOH, showing fist order Stark splittings (exaggerated) in field E. The Mp

= 1 component C pumped (bold arrow) ard the ?M,= 2 component is the sign11(thin arrow). Pashed arrows denote allowed dipolar collision-induced transitions between pumped and s&al levels. through the frequencies

of the various M, components of the pumped transition, and the values measured for Ai(Al,; Mp), the change in intensity I@&) of the I&-component of the signal when the Mp-component is pumped. Fig. 1 illustrates the four-level system for a typical arragement of signal and pumping, with only dipole-type collision-induced transitions shown. The double resonance spectrometer was identical to that described previously ;C43,except that an eightfoot X-band Stark cell was used instead of the previous K-band cell, and that the Stark modulation was at 33 kHz, as supplied by a Hewlett-Packard 8421C Stark Modulator and 84286 Modulator Control. Pumping power at the pump frequency of 28316 MHz was obtained from an Oki 3OV12 klystron, and at the signal frequency of 19967 MHz from an Oki ZOVI 0. The sample pressure was about SO mtorr for the pure CH,OH experiments, and about 20 mtorr of CH,OH to about 60 mtorr of He or 100 mtorr of Hz for the foreign-gas experiments.

3. Results and analysis In table 1, we report the observed AI(M,; Mp)/ ratios for the various combina tiers of MS and

I(M$

584

Or4 3414 21.c 4 054

0

23

allall

28*4-F4 43 -3-1-3 7*3 IS”-3 -6.5 c 3 115 3 19 Y 3 131i 5

1400 f 20 1535 I20 485 f 10 670 + 10

0 2.4 1.5 0

f * f f

G.3 0.3 0.3 0.3

2.8 1.8 *f 0.3 -0.6 2 0.6 1.4 + 0.6 3.1* 0.6 -1.0 i 0.5 1.6 f 0.5 2.8 c 0.5

2810 * 25

4.7 -F0.2 b)

a) In arbitrary units. b, Value at zero Stark field, corresponding to the N/I of ref. 141.

Mp in pure CH,OH, along with N/., the ratio for the central unsplit line..Table 2 gives thd ratios for the foreigngas mixtures, with ilkf values averaged. Here, a low signal-to-noise ratio permitted meaningful measurements only for MS = il. Some typical experimental traces are shown in figs. 2 and 3. As can be seen, orrly the effects of AM = 0,51 collision-induced transitions are observed for the pure gas, consistent with a dipolar collisional interaction, while for the foreign-gas mixtures there is definite evidence for collisional transitions with 1AiI4l > 1, indicating a higher-order interaction.

that the relative values of for the pure gas are quaiitatively quite consistent with a simplified dipolar interaction model outlined earlier 121. In this model, all parameters other than the dipolar transition matrix elements It is

AI(M,;

interesting MJI(M~

are considered

constants,

to be identical for the collisional rate when averaged over the distributions of col-

lision impact parameters and molecular velocities, so that the rate constant /??&%ii + Mj) for a collisional transition between sublevels Mi arrd Mi of rotational levels i and j is simpIy given by

Volume 41, number

3

1 August 1976

CHEMICAL PHYSLCS LSTIXRS

Table 2 Observed collisional transfer signals for the (40 + 31)p-(21 + 3& system in CHsOH-He and CHsOH-Hs mixtures

Heb)

Hz d)

-3 -2 -1 0 1 2 3 allc) -3 -2 -1 0

0.7 + 1.9 f 2.4 * 3.5 * 6.5 * 5.32 3.0 * 42*2 3.0 i 2.7 -t 2.5 2 4.0 f

1 1 1 1 1 1 1 2 2 2 2

190 + 10

0.4 f 0.5 1.o f 0.5 1.3 f 0.5 1.8 + 0.5 3.4 f 0.5 2.8 f 0.5 1.6 i 0.5 375* 10 11.2*0.6 310 f 10 1.0 f 0.5 0.9 r 0.6

:

,‘:;r;

0.8 1.3 2.9 2.7

3 all

2.6 f 2 ss i 2

0.8 * 0.6 7.9 * 0.4

700 I 10

if 5 *

Mp=

0 L---2L-_f_J

3

(b)

B

0.6 0.6 0.6 0.6

I -;

I 0

a) Same arbitrary units as in tabIe 1. b, Values are averages of MS = i-1, Mp (three traces) with M’s = -1, -Mp (two traces). c, Value at zero Stark field, corresponding to the AI/I of ref.

I

I

-3

-2

=Mp

Fig. 2. Colliiional transfer signals for components of the (40 6 31)~-(2r + 30)s system in pure CHsOH for (a) MS = 1, and (b) MS = -2. Stark splitting between the pumped comgonents is about 10 MHz.

[41d, Values are averages of MS = +l , Mp and Ms = - 1, --Mp (five traces each).

where I? is a constant, Pa is a component of the dipole moment, the 9’s are the factors of the dipole matrix element [S] , and denotes a torsional overlap matrix element [6]. The space-fixed axes are denoted by G, and the molecule-fixed axes by g. For methanol, =0.885Dandpb=1.G4D [7]. g=a orb,with& For the Ieve: system of fig. 1, the energy differences are all small compared to kT, so the exponential Eoltzmann factors in the rate constants [2] can be set to unity. Then, in the usual first-order treatment of the collisional transfer by linear rate equations [I ,2,8], the collisional transfer signal for the present four-level system follows the proportionality NM,

; Mp)/I(M,)

a4,,

3. 053, + 4) (2)

+~3r+2r(Mp

+Ms)

-k31+30(Mp

+U

where it is assumed that the total transition rates for a molecuie out of a level are identical for both signal levels and are independent of M, and further that the + fifs) are small compared to those rates&,.+3,(M,

I Mp= 3

I

I

2

1

I

0

I

-1

+-

-3

Fig. 3. Cohisional transfer signals for the MS = -1 component of the (40 f- 3r)9-(2r +- 30)~ system for a CHaOH-He mixture. Stark splitting between pumped components is about 10 MHZ

total rates. In table 3, we present the relative values of the rate constants, with I? set to unity in eq. (1) and the resulting relative AI(lUs; Mp)/I(Ms) ratios from eq. (2), normalized to a value of 1 for the MS =Mp = 1 ratio. The calculated ratios are to be compared with the observed ratios, normalized in the same way with the fMs and -MS values averaged, as shown in the last column of table 3. It can be seen that the qualitative behaviour of the ratios, which was a bit unexpected when first observed, in fact follows the predicted pattern quite well.

1 Au,~ust1976

CHFMICAL PHYSICS LETTIZRS

Volume 41. number 3

Table 3 Rare constantsand AI/. valuesfrom sim>Ie dipolar model Normalized Ar(Ms; Mp)/I(&fs) b, J%

L40 + 30 a’

AF31-fZl

a)

Al+30

calculated

observed

1

2 1 0

0.1865 0.1865 0.0746

0.1989 0.1591 0.0597

0.1867 0.0373 0.2241

0.645 1.000 -0.291

0.635 1.000 0.000

2

3 2 1

0.2611 0.1492 0.0373

0.2984 G.0995 0.0199

0.1120 0.1494 0.1867

1.452 0.322 -0.420

1.134 0.589 -0.304

a) Calculatedfrom eq. (1) with r set to 1. b, Normalized with respect to the MS = Mp = 1 value, which is taken as 1.0.

The limited accuracy of the data for the foreign-gas mixtures precludes a detailed analysis at this stage. It does appear that the collisional rate constants are decreasing relativeIy slowly with IAMI, analogous to behaviour with INI [29].

4. Discussion It is evident that the M-resolved experiment described here provides much more information than the single value of AI/I derived from previous zerofield studies [2,9] _ Unfortunately, this is obtained at the expense of a greatly degraded signal-to-noise ratio, because the total collisional transfer signal, which is already rather small, is further subdivided into many weak components. Thus, the present results, particularly for the foreign-gas mixtures, are principally qualitative in character, but serve to establish the Mselection rules and to demonstrate the potential of the technique. There are several instrumental problems which remain to be solved before the AI(_Ms;Mp)/I(Ms) ratios can be considered to be quantitatively reiiable. For example, at the sample pressures necessary here for a reasonable signal-to-noise ratio, the AI/I values for the unsplit lines are considerably smaller than those originally observed [4] , indicating a mean pumping efficiency well below 100%. Also, the AI(M,; Mp) values do not sum properly to give AI, indicating a variation of system performance over the frequency ranges covering the signal and pump M-components. These problems 586

may Iargely be due to poor transmission in the oversize X-band absorption cell, as we observed fluctuations of the order of 50% in transmitted pump power over the pumping frequency range. Similarly, there were marked asymmetries between the intensities of the +Ms and -MS signal components, as seen in table 1, indicating s large standing wave ratio ‘for the signal power as well. A return to a K-band absorption cell should improve the quality of the results, hence in future we hope to obtain more reliable data, and to extend the measurements to other four-level systems. An important implication of the present low mean pumping efficiency is that the degree of pumping for different X, components will vary significantly, and, in particular, the Mp = 13 components will be underpumped relative to the others. Thus, the low value for the observed AI(Ms; Mp)/I(Ms) ratio for MS = 2, Mp = 3, in table 3 con,yY,red to the calculated value may be ascribed in large part to this. Two main conclusions can be drawn from the present results. First, the case for the collisional mteraction being predominantly dipole-dipole for pure CH,OH is greatly strengthened. Second, transitions with large I AMI occur in CH3 OH-He and CHs OH--HZ collisions. paralleling the occurrence of transitions with large I AJI deduced previously from zero-field studies [2,9]. This implies the existence of high-order tensor terms in the collisional interaction, either as direct highorder multipole--muitipole interactions, or indirectly through higher-order effects of lower-order multipole terms. Quantitative measurements of the variation of collisiond transition rates with [AM]

Volume 41, number 3

CK-BMICAL PEWSECS LEJXXS

should clarify the picture of the interaction. Such measurements may also assume importance for astrophysical work on &tersteflar mole&es, because a&otfopy of the radiation distribution in ttre intesstebr medium or the presence of weak electric OKmagnetic fiekls, might lead to partid alignment of the molecules, and could haye significant effects on their collisional excitation.

[l]

T. Oka,

Advan. At. Mol. Phys. 9 {X973)

1 August 8976

t21 K.M.Lees.Can. J. 3~s. 53 (1475) 2593. [3] J.B. Cohen and E.B. Wixm.Jr., J. C&m. Pltys. 456.

58 (1973)

[et K.M.Lees end S.S. Haque,CZUI. 3.

fhys. 52 f1974)

ISI C.H. Tow=es and AL. Schawfow,

M~CEOWW

2250.

~pe~tr~sc~py

(McGrav+HiU, New York. 1955). 161 I&. Lees and 3-G. Bak&, I. &em. Phys. 48 (1968) 5299. [7] E-V.Iva.&and D.M.Dennison,J. Chem. Phys. 21(1953) 1804. t81 T. Oka, J- Ckm. P&s. 47 (1967) 13. 191 P.M. Lees and T. Oka, J. Chem. Fhys. 49 f1968) 4234.

127.

587