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Far infrared absorption in compressed nitrous oxide
Volume 9; number ,6
‘.
‘.
:
_. : ABSORPTI-tiN
INFRARED.,
Edward Davies
15 June 1971
.:
_ .;-
.
FAR
. . ._
CREMICAL-PHYSICS LETTERS
._ NIT&S
IN dOMPRESSED
QXrDE
‘A. L BAISE Chemical Labonztwy. U&ersit,u Aberystwyth:,UK
College
ofWaZes,
Received 5 April 197l
The far IIt spectra (6: I.00 cm-l) of gaseous N2C from 34 to 64 bars are reported. The absorpttoa due to the (small) permanent dipole is +cdmpahied by contributionsdue to dipole- and quadrupoleinduced momenta, the latter being the larger. An acceptable value,’ Q(N20) x 8 x 10-26 esu is estimated from the observed imensities. -. There have been several recent studies inthe far infrared of absorption in compressed nonpolar gases [l-S], and of the effect of inert. gases on pure rotational lines [4,5]. However, very little work has been done on dense polar gases in this region [S]. Despite the- complexity of the molecular interactions in these systems, such studies should yield valuable information on molecular motion and intermolecular forces in the dense gaseous and liquid states. lVe report here the far infrared absorption of compressed nitrous oxide; the spectrumof -liquid N20 has also been measured; and will be published elsewhere. The spectra from 20 to 100 cm-1 have been obtained by.Fourier spectroscopy- using an NPL - Grubb Parsons interferometer, and the region 8 - 20 cm-l was covered by using an RDCClamellar grating interferometer with a He-cooled InSb (Putfe+y) detector*. The sample was cohtained in a high pressure cell with,? mm
z-cut crystalline quartz windows,- and the reso-’ lution used was -1cm’1 in the. 8-2dcm;l region, and 4 cm:l-in the high frequency range. Spectra were obtained at 34.5 and 41.4 bars at room ternperature (296’K), fig. 1, and the-spectra of the gas in equilibrium Gith liquid N20 were’ recorded at 298°K-(56.5 bars) a.nd-304°E-(64.1- bars), fig. 2. The.gas was dried by using type 4A Union .Carbide molecular sieve, which- was contained in the
1
.6-
-I
. =
-
0
.
I
1
-
20
of
Fig. 1. Far infrared spectrum, gaseous N20 at 34.5 bars and 296oK. The vertical tines give the frequencies and relative idtegrsted intensities for some of the pure rotational (J + J + 1) transitions. The dipole-induced transitions have the same frequencies sod relative intenaities as the pure rotationat Knee.
.
Volume 9, number 6
CHEMICAL
We assume that the absorption intensity arises from the pure rotational contribution,
and
from dipoles
induced in the mqlecules during These induced dipoles result Zrom both the dipole and qwxdrupole fields of the N@ molecule. While the pure rotational absorption is proportion31 to the number density of polar collisions.
molecuIes, the induced effects are expected to be proportional to the square of the d6nsity Thus we write jcz(G)ddir)=AN +A”N2 ,
PHYSICS
LETTERS
15 June 1971
(O.l7D), the induced absorption becomes larger than the pure rotational absorption at high densities. From the observed sfope in fig. 3, we can estimate 8, the molecular quadrupole moment iIf N20, by using the equations for collision-induced absorption derived by Colpa and Ketelaar [lo]. These authors considered the quadrupote-induced intensity, AQ; their equations have been used by Rothschild [li j to derive the dipole-induced intensity, AP. These integrated intensities are:
(la)
01
Here A and A’ are constants (at constant temperature), a(v) is the absorption coefficient in neper cm-l, and N is the number of molecules per cm3. The value of A can be obtained from a theoretical expression given by Gordon 171: A = 2ng2/(3c21) ,
AQ=cAQ J-em J
for linear molecules.
For N30, A = 0.97 X 10W20 cm. A plot of the left-hand side of (lb) - the ‘ex-
cess’ absorption - agaikst N sho;lld give a straight line through the origin with slope A'; this is confirmed in fig. 3. The uncertainties shown by the error bars have been estimated from the temperature and pressure fluctuations during the runs, and from the extrapolation of the curves at the low and high frequency ends. As A represents
the contribution
of the pure ro-
tational mode, it can be seen from the ordinates of fig. 3 that N2C?is a particularlY suitable moiecule to study: since Me dipole moment is small
Here ETis the rotational constant in cm-l, cr the dipole mom&t, and ap the mean polarizability. The molecular quadrupole moment Q is defined bY
where the symbols have their usual meaning 1141.
The integrals were evaluated using tinetables given by Buckingham and Pople [12], with Lennard-Sones Brameters e/k = 193% and Rg = 4.54 x 10’ B cm’ [X31. The value of ap used was 3.0 x 10-34 cm3 f13j. These intensities were evaluated on a computer for each temperature used. Since the variation with temperature was OII$ F 18, the average values were used to estimate 8. The dipole and quadrupole intensities . were then: A@ = 1.23 x lo-44 N2 cm-2 , AQ = 6-33 x 106 Q2A@ cm-2 . Numbwdensity N (10z’cm-5~ Ffg. 3. The excoaa abaorptfon aa a Eunctton of deneity. 1:34.5 bare. 296%; 2 ;41.4 bars, 296%; 3:56.5 bara, 293%;4 : 64.1 bara, 304%
628
The vahe of A’ from fig, 3 is 5.7 x lo-42 cm4. Hence, usingA’IV2 =A& + AQ, a value of Q = 8 x 10-26 esu ;Jvasobtained. The magnitude of Q the induced birefringence technique measured is 3.5 X IO-b%6 esu f14f The analysis presented
Volume 9, number 6 here
haa therefore
CHEMICAL PHYSICS LETTERS led to the correct
order
of
magnitude for Q, which justifies the treatment in terms of dipole- and quadrupole-induced absorption mechanisms. While no great accuracy can be claimed for our value of Q, it is intcresting to note that Q values which are too large by a faktor of -2 have been obtained when the quadrupole-quadrupole interaction energy is neglected [15], as has been done here. Other possible contributions to the integrated intensity have been neglected, such as translational absorption [l], and transitions associated with the anisotropic poIarizabiIity [lo]. The former is expected to contribute mainly below 10 cm-l; in CO2 [16], the calculated translational contribution at 10 cm-l is approximately the same as that due to the induced rotational absorption. Furthermore, the rigid dipole-quadrupole model has distinct limitations for close collisional interactions, and some contribution to the excess absorption may arise from the distortion of the molecule by the translational energy term kT. This factor might well be of increased significance in the liquid state. I wish to th.ank Professor Manse1 Davies for his advice and interest, and for helpful suggestions for improving the manuscript.
15 June 1971
REFERENCES (11 D. R.Bosomworth arxi H. P.Gush, Can.J. Phye. 43 (1965) 751. [2] A. Rosenberg and G.Birnbaum. S.Chem.Phys. 52 (II)?@) 683. (3) J. E. Harries, J. Phys. B.: Atom. Molec. Phys. 3 (19701 704. [4] k. E.‘van Kreveld. R.M. van Aalst and J. van der Elsken. Chem. Phvs. Letters 4 (1970) 580. [5] H.A.G&bbio and C.W.B. Sane, ‘Pro& Phys. Sac. (London) 62 (1963) 309. [6] LDPrmon, A.Gerschet nnd C.Brot, Chem. Phys. Lettcl% 6 (1971) 454. [ 7)’ R. G. Gordon, J. Chem. Phys. 38 (2963) 1724. [8] D. Cook, Trans. Faraday Sac. 49 (1953) 716. [S] 0. A. Hougen, K. M. Watson and R.A. Ragatz,
Chemical process York, 1964). [lo]
J.P.Colpa
snd
principles
charts
J.A.A.Ketelaar,
(Wiley.
Mo[.Phys.
New 1
(1958) 343.
Ill] W. G. Rothschild, J. Chem. Phye. 49 (1968) 2250. [L2] A. D. Buckingham and J.A. Pople, Trans. Fa:adsy Sot. 51 (1955) 1173. 1131 J.O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular theory of gases atxi Liquids (Wi(ey, New ” York. 1954). [14] A.D.Buckinghom, R. L.Disch and D.A.Dunmur. J.Am. Chem. Sot. 90 (1968) 3104.
[lS] J. E. Harries. J. Phys:B.: ktam.Molcc. Phys. 3 (1970) L150. [16] W. Ho. LA. KaKfrnsn 3nd P.Thaddcus. J. Chem. Phys. 45 (1966) 877.
629
‘.
‘.
:
_. : ABSORPTI-tiN
INFRARED.,
Edward Davies
15 June 1971
.:
_ .;-
.
FAR
. . ._
CREMICAL-PHYSICS LETTERS
._ NIT&S
IN dOMPRESSED
QXrDE
‘A. L BAISE Chemical Labonztwy. U&ersit,u Aberystwyth:,UK
College
ofWaZes,
Received 5 April 197l
The far IIt spectra (6: I.00 cm-l) of gaseous N2C from 34 to 64 bars are reported. The absorpttoa due to the (small) permanent dipole is +cdmpahied by contributionsdue to dipole- and quadrupoleinduced momenta, the latter being the larger. An acceptable value,’ Q(N20) x 8 x 10-26 esu is estimated from the observed imensities. -. There have been several recent studies inthe far infrared of absorption in compressed nonpolar gases [l-S], and of the effect of inert. gases on pure rotational lines [4,5]. However, very little work has been done on dense polar gases in this region [S]. Despite the- complexity of the molecular interactions in these systems, such studies should yield valuable information on molecular motion and intermolecular forces in the dense gaseous and liquid states. lVe report here the far infrared absorption of compressed nitrous oxide; the spectrumof -liquid N20 has also been measured; and will be published elsewhere. The spectra from 20 to 100 cm-1 have been obtained by.Fourier spectroscopy- using an NPL - Grubb Parsons interferometer, and the region 8 - 20 cm-l was covered by using an RDCClamellar grating interferometer with a He-cooled InSb (Putfe+y) detector*. The sample was cohtained in a high pressure cell with,? mm
z-cut crystalline quartz windows,- and the reso-’ lution used was -1cm’1 in the. 8-2dcm;l region, and 4 cm:l-in the high frequency range. Spectra were obtained at 34.5 and 41.4 bars at room ternperature (296’K), fig. 1, and the-spectra of the gas in equilibrium Gith liquid N20 were’ recorded at 298°K-(56.5 bars) a.nd-304°E-(64.1- bars), fig. 2. The.gas was dried by using type 4A Union .Carbide molecular sieve, which- was contained in the
1
.6-
-I
. =
-
0
.
I
1
-
20
of
Fig. 1. Far infrared spectrum, gaseous N20 at 34.5 bars and 296oK. The vertical tines give the frequencies and relative idtegrsted intensities for some of the pure rotational (J + J + 1) transitions. The dipole-induced transitions have the same frequencies sod relative intenaities as the pure rotationat Knee.
.
Volume 9, number 6
CHEMICAL
We assume that the absorption intensity arises from the pure rotational contribution,
and
from dipoles
induced in the mqlecules during These induced dipoles result Zrom both the dipole and qwxdrupole fields of the N@ molecule. While the pure rotational absorption is proportion31 to the number density of polar collisions.
molecuIes, the induced effects are expected to be proportional to the square of the d6nsity Thus we write jcz(G)ddir)=AN +A”N2 ,
PHYSICS
LETTERS
15 June 1971
(O.l7D), the induced absorption becomes larger than the pure rotational absorption at high densities. From the observed sfope in fig. 3, we can estimate 8, the molecular quadrupole moment iIf N20, by using the equations for collision-induced absorption derived by Colpa and Ketelaar [lo]. These authors considered the quadrupote-induced intensity, AQ; their equations have been used by Rothschild [li j to derive the dipole-induced intensity, AP. These integrated intensities are:
(la)
01
Here A and A’ are constants (at constant temperature), a(v) is the absorption coefficient in neper cm-l, and N is the number of molecules per cm3. The value of A can be obtained from a theoretical expression given by Gordon 171: A = 2ng2/(3c21) ,
AQ=cAQ J-em J
for linear molecules.
For N30, A = 0.97 X 10W20 cm. A plot of the left-hand side of (lb) - the ‘ex-
cess’ absorption - agaikst N sho;lld give a straight line through the origin with slope A'; this is confirmed in fig. 3. The uncertainties shown by the error bars have been estimated from the temperature and pressure fluctuations during the runs, and from the extrapolation of the curves at the low and high frequency ends. As A represents
the contribution
of the pure ro-
tational mode, it can be seen from the ordinates of fig. 3 that N2C?is a particularlY suitable moiecule to study: since Me dipole moment is small
Here ETis the rotational constant in cm-l, cr the dipole mom&t, and ap the mean polarizability. The molecular quadrupole moment Q is defined bY
where the symbols have their usual meaning 1141.
The integrals were evaluated using tinetables given by Buckingham and Pople [12], with Lennard-Sones Brameters e/k = 193% and Rg = 4.54 x 10’ B cm’ [X31. The value of ap used was 3.0 x 10-34 cm3 f13j. These intensities were evaluated on a computer for each temperature used. Since the variation with temperature was OII$ F 18, the average values were used to estimate 8. The dipole and quadrupole intensities . were then: A@ = 1.23 x lo-44 N2 cm-2 , AQ = 6-33 x 106 Q2A@ cm-2 . Numbwdensity N (10z’cm-5~ Ffg. 3. The excoaa abaorptfon aa a Eunctton of deneity. 1:34.5 bare. 296%; 2 ;41.4 bars, 296%; 3:56.5 bara, 293%;4 : 64.1 bara, 304%
628
The vahe of A’ from fig, 3 is 5.7 x lo-42 cm4. Hence, usingA’IV2 =A& + AQ, a value of Q = 8 x 10-26 esu ;Jvasobtained. The magnitude of Q the induced birefringence technique measured is 3.5 X IO-b%6 esu f14f The analysis presented
Volume 9, number 6 here
haa therefore
CHEMICAL PHYSICS LETTERS led to the correct
order
of
magnitude for Q, which justifies the treatment in terms of dipole- and quadrupole-induced absorption mechanisms. While no great accuracy can be claimed for our value of Q, it is intcresting to note that Q values which are too large by a faktor of -2 have been obtained when the quadrupole-quadrupole interaction energy is neglected [15], as has been done here. Other possible contributions to the integrated intensity have been neglected, such as translational absorption [l], and transitions associated with the anisotropic poIarizabiIity [lo]. The former is expected to contribute mainly below 10 cm-l; in CO2 [16], the calculated translational contribution at 10 cm-l is approximately the same as that due to the induced rotational absorption. Furthermore, the rigid dipole-quadrupole model has distinct limitations for close collisional interactions, and some contribution to the excess absorption may arise from the distortion of the molecule by the translational energy term kT. This factor might well be of increased significance in the liquid state. I wish to th.ank Professor Manse1 Davies for his advice and interest, and for helpful suggestions for improving the manuscript.
15 June 1971
REFERENCES (11 D. R.Bosomworth arxi H. P.Gush, Can.J. Phye. 43 (1965) 751. [2] A. Rosenberg and G.Birnbaum. S.Chem.Phys. 52 (II)?@) 683. (3) J. E. Harries, J. Phys. B.: Atom. Molec. Phys. 3 (19701 704. [4] k. E.‘van Kreveld. R.M. van Aalst and J. van der Elsken. Chem. Phvs. Letters 4 (1970) 580. [5] H.A.G&bbio and C.W.B. Sane, ‘Pro& Phys. Sac. (London) 62 (1963) 309. [6] LDPrmon, A.Gerschet nnd C.Brot, Chem. Phys. Lettcl% 6 (1971) 454. [ 7)’ R. G. Gordon, J. Chem. Phys. 38 (2963) 1724. [8] D. Cook, Trans. Faraday Sac. 49 (1953) 716. [S] 0. A. Hougen, K. M. Watson and R.A. Ragatz,
Chemical process York, 1964). [lo]
J.P.Colpa
snd
principles
charts
J.A.A.Ketelaar,
(Wiley.
Mo[.Phys.
New 1
(1958) 343.
Ill] W. G. Rothschild, J. Chem. Phye. 49 (1968) 2250. [L2] A. D. Buckingham and J.A. Pople, Trans. Fa:adsy Sot. 51 (1955) 1173. 1131 J.O. Hirschfelder, C. F. Curtiss and R. B. Bird, Molecular theory of gases atxi Liquids (Wi(ey, New ” York. 1954). [14] A.D.Buckinghom, R. L.Disch and D.A.Dunmur. J.Am. Chem. Sot. 90 (1968) 3104.
[lS] J. E. Harries. J. Phys:B.: ktam.Molcc. Phys. 3 (1970) L150. [16] W. Ho. LA. KaKfrnsn 3nd P.Thaddcus. J. Chem. Phys. 45 (1966) 877.
629