Collision-induced fundamental band of D2 in D2He and D2Ne mixtures at different temperatures

JOURNAL

OP MOLECULAR

SPECTROSCOPY

52, 72-81 (1974)

Collision-Induced Fundamental Band of D, in D,-He Mixtures at Different Temperatures1

and D,-Ne

W. E. RUSSELL, S. PADDI REDDY, AND C. W. CHO Department oj Physics, Memorial University of Newfoundland, St. John’s, N&wjoundland, Ca&a The collision-induced enhancement absorption spectra of deuterium in its fundamental region in DrHe at 77, 195, and 273 K and in DpNe at 77, 195, 273, and 298 K have been recorded with an absorption path length of 26 cm for gas densities up to 670 amagatifor several base densities of deuterium. At each experimental temperature, binary and ternary absorption coefficients for the fundamental band were derived from the measured integrated intensities. The theory of the “exponentiakl” model for the induced dipole moment of the colliding pair of molecules was applied to the binary absorption coefficients. The overlap parts of these coefficients were obtained by subtracting the calculated quadrupolar parts from the experimental values. The magnitude parameter X, and the range p, of the overlap part of the induced dipole moment, were determined for the colliding molecular pairs DrHe and DgNe by obtaining the best fit of the calculated overlap part of the binary absorption coefficients as a function of temperature to the experimental values of the overlap part. Derived parameters X, p, and the overlap induced dipole moment p(u) (at the Lennard-Jones intermolecular diameter U) for D9-He and DpNe are as follows.

Mixture

x

P

DrHe DgNe

4.7 x 10-x 8.5 x 10-a

0.24 i 0.26 Ii

P 64

2.55 X l(r-8 ea0 4.56 X 10--seao

1. INTRODUCTION

The collision-induced infrared fundamental band of gaseous deuterium has been studied in the pure gas at room temperature by Reddy and Cho (1) and at temperatures in the range 24 to 77 R by Watanabe and Welsh (2) and in D2-He, D,-Ar, and D2-N2 mixtures at room temperature by Pai, Reddy, and Cho (3). There have also been studies of the fundamental band of solid Dz (4) and of Ds dissolved in liquid argon (5) and in liquid neon (6). In addition, there have been studies of the collision-induced 1st overtone band of gaseous DZ in pure Dz and in D2-Ar and Dz-N~ mixtures at room temperature by Ready and Kuo (7) and of Dz dissolved in liquid nitrogen by Monson, Chen, and Ewing (8). The studies on the collision-induced spectra of Hz have been more extensive than those on the corresponding spectra of Ds. A detailed review of the work on the collision-induced spectra of Hz has recently been given by Welsh (9). According to the “exponential-4” model of Van Kranendonk (IO), the dipole moment induced in a colliding pair of molecules consists of two additive parts: a short-range 1This research was supported in part by the National Research Council of Canada. 72 Copyright

All rights

0

1974 by Academic

of reproduction

Press, Inc.

in any form reserved.

FUNDAMENTAL

BAND OF Dz

73

overlap-induced part which arises from the overlap of the electron clouds of the molecules, and a long-range quadrupole-induced part which results from the polarization of one molecule by the quadrupole moment of the other. The short-range moment mainly contributes to the Q lines (i.e., Qoverlsp ; AJ = 0), whereas the long-range moment contributes to the S (AJ = + 2), Q (i.e., QQ; AJ = 0) and 0 (AJ = - 2) lines. Recently in our laboratory Reddy and Chang (II) have measured the integrated absorption coefficients of the collision-induced fundamental band of Hz in binary mixtures H.r--He and HZ-Ne at 77,195,273, and 298 K and determined the binary and ternary absorption coefficients. They have obtained the overlap parts of the binary absorption coefficients by subtracting from the experimental binary coefficients the quadrupolar parts, calculated from the matrix elements of the quadrupole moment of Hz and other molecular constants of the colliding pairs of molecules. For each of the molecular pairs HZ-He and H2-Ne, the overlap parameters X and p which represent the magnitude and range of the overlap induced moment and ~(a) the induced dipole moment at the Lennard-Jones intermolecular diameter u have been determined by these authors by obtaining the best fit of the calculated overlap part of the binary absorption coefficients as a function of temperature to the experimental values of the overlap part. The present communication reports the results of our work on the collisioninduced fundamental band of Dz in binary mixtures D2-He and D2-Ne at temperatures 77, 195, 273, and 298 K. It also gives the overlap parameters of the molecular pairs D2-He and Dr-Ne obtained by adopting a procedure similar to the one used by Reddy and Chang (II) for H2-He and HZ-Ne. 2. EXPERIMENTAL

PROCEDURE

A transmission-type absorption cell having a sample path length of 26 cm at room temperature was used to study the fundamental band of Dz in binary mixtures of deuterium with helium and neon at temperatures in the range 77 to 298 K. Details of the cell and the cooling arrangement have been described previously by Reddy and Chang (11). The coolants were ice (273 K), dry ice-alcohol mixture (195 K), and liquid nitrogen (77 K). The source of infrared radiation was a water-cooled globar operated at about 150 W by means of a stabilized power supply from an electronic source radiation controller, supplied by Warner and Swansey Co. A Perkin-Elmer Model 112 single-pass doublebeam spectrometer equipped with a LiF prism and a Golay detector was used to record the spectra. An instrumental slit width of 500 pm gave a spectral resolution of - 13 cm-l at the position of Q(0) (2994 cm-l) of the fundamental band of Dz. Absorption peaks of atmospheric water vapor and liquid indene were used for frequency calibration. The method of obtaining profiles of enhancement of absorption of the binary mixtures Dz-He and D2-Ne was similar to the one described by Pai, Reddy, and Cho (3). Commercial grade deuterium and research grade neon, both supplied by Matheson of Canada, and commercial grade helium, supplied by Canadian Liquid Air, were purified by passing them through a liquid nitrogen trap before they were admitted into the absorption cell. In a given experiment the base density of deuterium was maintained constant and the profiles of enhancement of absorption of the band were obtained for a series of partial densities of the perturbing gas, helium or neon. A mercury-column gas compressor was used to obtain the required pressures of helium or neon.

74

RUSSELL, REDDY AND CHO

The densities of deuterium at 298 and 273 K were obtained directly from the data given by Michels and Goudeket (12) and those at 19.5 K were calculated from the data given by Michels et d. (13). Its densities at 77 K were derived, by the procedure described by Woolley et al. (14), from the isothermal data of hydrogen at 77 K which were obtained as described in Ref. (II). The isothermal data of helium and neon at all the four experimental temperatures were also obtained as described in Ref. (11). For a given experiment the base density p. of deuterium was obtained from its isothermal data directly while the method described by Reddy and Cho (15) was used to obtain the partial density pb of helium or neon in a binary mixture with deuterium. The enhancement absorption coefficient c+(v) corresponding to the addition of the perturbing gas helium or neon at a density ~6 into the cell of sample path length 1 (in cm) containing deuterium at a fixed base density pa is expressed as a,,(v)

= (l/Z) ln

where Y is the wave number in cm+, cell filled with deuterium and with the ment of absorption were obtained by the region of the band. The integrated (in crne2) were derived from the areas

[II(v)II~(~)I,

(1)

11 and 12 are the intensities tra~mitted by the gas mixture, respectively. Profiles of the enhanceplotting log10 (IJ12) at intervals of 10 cm-l in absorption coefficients of the band fff~=(u)~v under the experimental profiles. 3. RESULTS

3.1. Proses of Evtlzamemmt of Absorption The experimental conditions under which the profiles of enhancement of absorption were recorded are summarized in Table I. The base densities of Dz were in the range 29 to 75 amagat. Representative profiles of the enhancement of absorption of the DS fundamental band obtained in H&e mixtures at 273, 195, and 77 I(: are presented in Fig. 1. Values of log&ll/lJ are plotted against wave number (cm-‘). The positions of O(3), O(2), vJ=Q(O)] and S(J) for J = 0 to 4, derived from the constants of the free DS molecule (16), are shown on the wave number axis. When the perturbing molecule is monatomic the enhancement absorption profiles consist of only single transitions. For the proties in

D2-He

273

25.8

393

14

D*-Re

19s

25.7

509

16

D2-A'

77

23.7

598

12

D2-'J'

298

23.8

367

13

n2--Ne

273

25.8

400

lb

Dpe

195

25.7

480

13

77

25.7

416

13

D2-Ne

FUNDAMENTAL

2600

2800

BAND OF Dz

3200

3000

WAVE

NUMBER

7.5

3400

3600

hi’)

FIG. 1. Profiles of the enhancement of absorption of the collision-induced fundamental band of DI in DrHe mixtures:

A

1

PDz

(cm)

(amagat)

(amagat)

273 195 77

25.8 25.7 25.1

53 5.5 59

380 49.5 556

PHa

Fig. 1 the dip in the Q branch occurs at the position of yo. This dip is similar to the one observed in Hz, which was explained by Van Kranendonk (17) as an interference phenomenon occurring between the overlap dipole moments in successive collisions. The separations AVPRm* between the peaks of the components Qp and QE in the profiles at a given temperature increase with increasing density of the mixtures. For the contours in Fig. 1, AvpPr’ are 11.5, 130, and 100 cm-l at temperatures 273, 195, and 77 K, respectively. As the temperature is lowered, the intensity of the Qp peak falls off more rapidly than that of QR. For the profiles of Dz-He at 77 K, the SR(O) peak occurs at about 30 to 40 cm-l toward high frequency side of the S(0) transition of the free Dz molecule. Typical profiles of the enhancement of absorption of the DS fundamental band in D2-He mixtures at 298,273,195, and 77 K are shown in Fig. 2. The separations AVPJ~~ of the Q branch for the profiies in Fig. 2. at 298, 273,195, and 77 K are 105, 100, 110, and 70 cm-l, respectively. For the profiles of Dz--Ne at 77 K the peaks of the S(0) and S(1) lines occur at 10 and 20 cm-’ higher than the S(0) and S(1) positions of the free Dz molecule. These peaks are interpreted as SR(O) and 5’~(1). 3.2. Absorption Coeficients In Figs. 3 and 4 are plotted (1/~~~)Jcz~,,(v)dv against pb for the Dz fundamental band in Dz-He and Dz-Ne mixtures, respectively. The intercepts and slopes of the

76

RUSSELL,

REDDY

AND

,200

MOO

WAVE

FIG. 2. Profiles of the enhancement in DrNe mixtures:

CHO

NUMBER

of absorption

hi’)

of the collision-induced

1

(c) (d)

25.8 25.8 25.7 25.7

band

PNe

PC2 (amagat)

h-4

298 273 19.5 77

fundamental

(amagat)

36 29 56 52

367 316 396 368

&-He

5 0.6e e>

?? K

!!I = : 3;:

Qmagol n

0.2

e_L+-*-.e_)~ 0

100

200 DENSITY

FIG. 3. Plots of (l/p,pb)J~,(v)d~

against

. 300 pb

400

500

i

0 I 600

lomogatl

pbfor DrHe

mixtures

at 273, 195, and 77 K.

of DP

77

FUNDAN’EMTAL BAND OF Dz Dz-Ne P rr @:36.2 omngat .:40.2 I

298

1.6c.'_ %. ,,2__&-*+m-+'-@g

*o-o-8-0

s *-to-r a 0.8L 5 2 0.877 e _ 2 o,4 -a3-.o-.-Q-~-e-~-o0

100

r:::", : . -'

l

P 2

aImgot *

gag::.

200 300 400 DENSITY Pb hmagall

FIG. 4. Plots of (l/pop~)J~,,Cv)dv against pb for DrNe

500

600

mixtures at 298, 273, 195, and 77 K.

lines obtained in these figures represent the binary and ternary absorption coefficients &lb (cmW2 amagatW2) and Q2b (cmm2 amagatm3), respectively [cf. Eq. (4) of (U)]. The values of these coefficients as determined from the least-squares fit, together with the binary coefficients &lb in units of cm6 set-‘, are summarized in Table II. The new coefficients &lb are related to alb by the IdatiOn &b= (c/no2)alb/~, which represent the transition probabilities; here c is the speed of light, no is Loschmidt’s number, and 8 is the effective band center [cf. Eq. (7) of (II)]. Also included in Table II are the absorption coefficients of the D2 fundamental band in D2-He at 298 K as obtained by Pai, Reddy, and Cho (3).

straight

AFBORPTION COEFFICIENTS OF ME

Sitmy

INDUCED PUNDAHENTAL SAND OF D2 IA D2-He AND D2-Ne MIXTURESa

Absorption Coefficient

Mixture

Temperature

( K)

Ternary Absorption Coefficient

'lb

'lb

'Zb

(lo-3 cm2emagat-2)(1o-35 d s-5

Ipe

298

0.82* o.oP

1.08

O.Olb

0.27* 0.03b

D2-He

273

0.71f 0.01

0.96f

0.01

0.36f 0.04

D,p

195

0.52f 0.01

0.69

0.01

0.24t 0.03

77

0.22t 0.02

0.29f 0.03

0.15f 0.03

1.24* 0.02

1.66+ 0.03

0.25

1.06t 0.01

1.42* 0.01

0.53* 0.04

IJ2-“FA

i:

f

f 0.09

0.86* 0.01

1.15* 0.01

0.19* 0.03

0.47* 0.01

0.63 t 0.01

-0.01f 0.03

78

RUSSELL, REDDY AND CHO

3.3. The Qu&upolar Coeficients

and Overlap Parts (iiw, auadand

&lb

overtap)

of

the Birtary Absorptiort

The binary absorption coeflicient &lb of the fundamental band of a symmetric atomic gas in a binary mixture with a monatomic gas can be expressed as &lb

=

X2&

(Qlh2/ed)2 J+,

f

di-

(2)

where X21? is the contribution from the overlap interaction and (Ql’ols/ed1)2Jf is the contribution from the quadrupolar induction (10). Here 4 = &W/~~OVO where m. and vo are the reduced mass and the frequency (in se&> of the absorbing molecule. The dime~io~ess overlap integral I(T*), where T* = &T/e, represents the average R (intermolecular distance) dependence of the square of the overlap part of the induced dipole moment and depends on the factor a/p [cf. (u)], where p, as defined previously, is the range of the oscillating overlap moment whose amplitude is represented by Xe (e being the electronic charge) when the distance between the molecules is CT.The parameter Q1’ is the derivative of the quadruple moment of the absorbing molecule, and ~2 is the polar&ability of the perturbing molecule. The dimensionless quadrupolar integral J(T*) represents the average R dependence of the square of the quadrupoleinduced moment [cf. (II)]. In the evaluation of the integrals I and J, the LennardJones 12-6 intermolecular potential with parameters E and u has been assumed (10). Birnbaum and Poll (18) have calculated the matrix elements of the quadrupole moment of Da, (vii Q/ et’J’). For the fundamental band [cf. (u)] of D2, Q1’ is approximately given by the relation Q1’ = [l/r,(B,,~/w)~](OJ~ QI 1J’). The individual quadrupolar components of a branch B of the fundamental band are given by

$1(OJIQ I lJ’>

{ We(&d~) &bquadtB(.f)l

=

,4

[

where

1 2

a2

P(J)L2(J,

J’>JT

(3)

gT exp (--EJ/kT) P(J)

=

$

gTgJ

exp

C--EJ/kTl

are the notched Bol~m~n factors, defined in terms of the Racah coefficients L&J,J’) so that &(2J+ l)P(J) = 1. Here gT = 6 and 3 for the even and odd rotational states of D2 and gJ( = 2J + 1) is the degeneracy of a rotational state J. The quantities L2(J, .7’) are &(J, J - 2), &(J, J) and &(J, J+ 2) for O(J), Q&J), and S(J), respectively. The quadrupolar binary absorption coefficient &la puad is given by the sum c J.B(J) &b[B(J)]. The molecular constants used in the calculation of &a aaad for the Dz f~d~ent~ band in Dz-He and Da-Ne are summarized in Table III. In Eq. (3), ra = 0.74143 X W8 cm, B,,, = 30.46 cm-‘, and w = 2993.6 cm-l for Dz (16). The matrix elements (OJlQjlJ’) of D 2 were obtained from Bimbaum and Poll (18). Values of e and u of the Lennard-Jones intermolecular potential for the binary mixtures were obtained, respectively, from the geometric mean of the values of et and the a~thmetic mean of the values of (r, of the component gases, which were taken from Hirschfelder, Curtiss, and Bird (19). The polarizability (Y~of He or Ne was also obtained from Ref. (19). The values of the integral J(T*) for temperatures up to T* = 10 were taken from Van

FUNDA~~~~

79

BAND OF Ds

TASLE III HXSCZJLAR CONSTANTSFUR D2-Ife AND D2-pu? %EXT”KSS

D2-Re

298

19.45 2.742 15.3

3.443

1.4

1.606

Is.28

Q2-&

273

19.45

3.443

1.4

1.606

14.91

2.742

lb.0

r12-lIe 195

19.45 2.742 10.03

3.443

1.4

1.606

13.62

D2-W

19.45 2.742

3.96

3.443

1.4

1.606

IX.42

71

D2-Ne

298

36.29 2.839

8.21

3.822

2.7

0.988

13.26

92-a"

273

36.29 2.839

7.52

3.622

2.7

0,966

13.01

D2-!?e

195

36.29 2.839

5.37

3.622

2.7

0.988

12.29

D2-Nt?

77

36.29 2.839

2.12

3.622

2.7

0.968

11.63

Kranendonk and Kiss (20). For T* > 10, J values were obtained in a manner described by Reddy and Chang (U), Table III also includes the values of the mean de Broglie wavelengths A* for D2-He and D2--Ne, which were used in the estimation of corrections to be applied to the classical values of J, i.e., Jo1[cf. (II)]. Finally the calculated quadrupolar binary absorption coefficients &lb sum and the overlap binary coefficients &lb oWrlap (=A*&), obtained by subtracting~~b pu~ from the corresponding experimental values of the binary absorption coefficients &b, are presented in Table IV. The percentage contributions of the quadrupolar and overlap parts of the binary absorption coefficients are also included in the same table. In the temperature range 77-298 H the overlap part contributes 90 to 95% for Dz--He and 82 to 92% for Dz-Ne. 3.4. Overlap Parameters for &-He

artd D2-Ne Pairs

The quantities X21for Ds-He and Dt-Ne, obtained from the values of the overlap parts (Table IV) and of Y (Table III), were plotted against temperature T in Fig. 5 TABLE IV ADZE

UfxNre

AND LWEFZAPPARBS OF i%E BINARY ABSOWTION COEFFICIiZ?T3

Binary absorption Temperature coefficient cD (lo-35cm6 s4

cu1eulated gusdrupolsr part (lo-35cm6 e-1,

Percentage ovsr1appart (lo-35,,6 s-11 Quad. Overlap

Q2-Ice

298

1.08

0.05

1.03

4.6

95.4

D2-He

273

0.94

0.05

0.89

3.3

94.7

D2-He

195

0.69

0.04

0.65

5.6

94.2

77

0.29

0.03

0.26

lJ,-lle

10.3

89.7

D2-Ne

29s

1.66

0.13

1.53

7.8

92.2

D2-Ne

273

1.42

0.13

1.29

9.2

90.8

D2-Ne

195

1.15

0.12

1.03

10.4

89.6

D2-tG

77

0.63

0.11

0.52

17.5

82.5

80

RUSSELL, REDDY AND GHO

Oi 0

200

100

300

J

T tK1

FIG. 5. Variation of PI with temperaturefor DrHe mixtures.

In the expression for the integral I [cf. Eq. (10) in (II)], the factor U/P occurs in the exponential. The most probable value of r/p for each of the molecular pairs Dz-He and Dz-Ne was obtained by adopting the procedure described by Reddy and Chang (II). The classical overlap integrals I,r(T*) were calculated for a series of values for p/u by means of a computer program. The quantum corrections to be applied to these classical overlap integrals were either directly obtained or extrapolated from the data given by Van Kranendonk and Kiss (20). Assuming X to be independent of temperature, the values of X21 calculated for a series of p/u values were fitted to the corresponding experimental values. The criterion used for the best fit of the curves X21 vs. T was that the sum XI &i2be a minimum, where & are the deviations of the calculated

and 6, respectively.

values of PI from the corr~~n~ng e~e~mental values. The calculated values of ha1 of D2-He and D2-Ne for the best fit are shown in Figs. 5 and 6, respectively. The values of p/u, p, A, and ~(a) (=Xeu) thus obtained for Dt-He and IA_-Ne are given in Table V. It is necessary to comment at least briefly on the errors involved in the calculated values of bib sUsdwhich are expected to be sensitive to the molecular parameters in Eq. (3). However, the absolute errors of most of these parameters, taken from the literature, are not available. It is believed that the principal error in the calculated values of &b quadlies in the uncertainty of the values of d of the pairs D2-He and D2-Ne because it occurs in the fifth power in Eq. (3). It is seen from Table IV that the quadrupolar

0

FIG.

100

T IKI

200

300

6. Variation of PI with temperaturefor DrNe mixtures.

F~NDAME~~

BAND OF Do

D2-N”

0.086

4.7

x 10-3

‘ib2-Ne

0.090

8.5

x

1O-3

2.742

0.24

2.55

2.839

0.26

4.56

of tJt.e binary abs~~t~on coe@icient varies from 5yo for Ds_& at 298 K to 18% for DrNe at 77 K. Even if one assumes an error as large as 25oJ, (which is probably the upper knit> in the calculated v&es of &lb clusdtthe percentage error in &lbover~aawill be very much less, this is about 1% for Ds-He at 298 R and about 5% for DrNe at 77 K. It is then expected that errors in the derived values of h and p will be less than 5%.

part

ACKNOWLEDGMENTS The authors are thaukfui to Professor S. W. Breckon for his interest iu this research, to Dr. B, B. P. Sinha for his assistauce in the initial design of the absorption ceil, and to Mr. K. S. Chaug for some C&&tiOZlS.

RECEIVEI):

1. 2. 3. 4. 5. 6. 7. 8. 9.

December 3, t%‘3

s. P. REDDY Mm c. w. CHO, can. J. P&s. 43,793 (1%5). A. WATANABEmu H. L. WELSH, Cm. J. Pkys. 433,818 (1965). S. T. PAI, S. P. REDDY,AND C. W. CHO, Cm. J. Phys. 44,2893 (1966). A. CIMNE AND HE.P. ‘%SH, Con. J. Phys. 44,373 (1966). G. E. EWING AND S. TRAJNAR,J. Chem. Phys. 41, 814 (1964). G. E. EWING AND S. TRAJMAB,J. Ckem. Phys. 42,4038 (IMS). S. P. REDDY AND C. Z. Kuo, J. MOE.Spectrosc. 37,327 (1971). P. R. MONSON,JR,, H. CHEN, ANDG. E. EWING, J. hfd. Spectmc. 25,501 (1943). H. L. Wm.sq “Xnternational Reviews of Science, Physical Chemistry, Vol. 3, SpeCtroscapy,’ Ruttemorths, London, 197.2

(19.59). R. B. SCOTT,ANDF. G. BRICII~DE, J. Res. Nat. Bw. Standards 41,396 (19&i). S. P. REDDVm C. W. CHO, Can. J. Phys. 43, 2331 (1965). B. P. ST~ICBERP,Can. J. Pkys. 35, 730 (1957). J. VAN KBANENDQNK, Can. J. Pbys. 46, 1173 (1968). A. BIF.NBAUMAND J. D. Pow, J. Atmospheric Sci. 26,943 (1969). J. 0. HIXSCWF~JI~, C. F. CUETISS,AND R. B. Bm, “Molecular Theory of Gases and Liquids,” 2nd ed., Wiley, New York, 1957. 20. J. Vm KBANENWNK AND Z. J. KISS, Cm. 3. Pkys, 3’7, 1187 <1959).

14. H. W. Woomm, 15. 16. 17. 18. 19.