- Email: [email protected]
Collision induced absorption spectra of the fundamental band of D2 in binary mixtures D2–Kr at 298 K
Journal of Molecular Spectroscopy 259 (2010) 111–115
Contents lists available at ScienceDirect
Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms
Collision induced absorption spectra of the fundamental band of D2 in binary mixtures D2–Kr at 298 K M. Abu-Kharma a,*, H.Y. Omari b, N. Shawaqfeh a, C. Stamp c a
Department of Applied Sciences, AL-Balqa University, Amman, Jordan Department of Physics, Mu’tah University, Al-Karak, Jordan c Department of Physics, Memorial University, St. John’s, Canada b
a r t i c l e
i n f o
Article history: Received 22 October 2009 In revised form 12 November 2009 Available online 28 December 2009 Keywords: Infrared spectra Fundamental band D2–Kr Collision induced absorption
a b s t r a c t The enhancement spectrum of the collision induced absorption of D2 in its fundamental band region 2600–4000 cm1 in binary mixtures D2–Kr was studied at 298 K for base densities of D2 in the range 9–20 amagat and for partial densities of Kr in the range 7–120 amagat. The binary absorption coefficient of the band has been determined from the measured integrated absorption coefficient and found to be 3.9 103 cm2 amagat2. An analysis of the experimental spectrum was carried out by assuming appropriate line-shape functions and the half-width parameters d1, d2, dd and dc of the long range quadrupole, and of the short range overlap induced transitions have been determined. Good agreement was obtained between the recorded spectrum of the fundamental band and the synthetic profile. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction Isolated homo nuclear diatomic molecules such as H2, D2, N2, and O2, etc. in their lowest (ground) electronic states have no permanent electronic dipole moments because of the symmetry of their charge distribution. Consequently, they have no electric dipole absorption at their translational, rotational, or vibrational frequencies. Collision-induced absorption (ClA) occurs as a result of induced transient electric dipole moments during binary or higher-order collisions. According to the exponential-4 model given by Van Kranendok [1], the induced electric dipole moment, l, of an interacting molecule pair is derived by combining a moment resulting from the overlap forces at short range, lov, with a moment resulting from the interactions of permanent molecular quadrupole moments at long range, lq. The short range moment contributes to the Qoverlap (DJ = 0) lines, whereas the long range moment contributes to the O(DJ = 2), Qquadrupole (DJ = 0) and S(DJ = 2) lines. CIA was first observed in compressed N2 and O2 in the region of their fundamental band by Crawford et al. [2]. The CIA of the fundamental band of H2 was first identified by Welsh et al. [3] in the same year. Reddy and Cho [4] studied the fundamental band of pure D2 for gas pressures up to 250 atm at 298 K. They determined the binary and the ternary absorption coefficients. One year later, Pai et al. [5] investigated the fundamental band of D2 in D2–He, D2–Ar, D2–N2 and D2–D2 at room temperature, * Corresponding author. E-mail address: [email protected] (M. Abu-Kharma). 0022-2852/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2009.11.009
The binary and the ternary absorption coefficients were also determined. Russell et al. [6] studied the collision induced fundamental band of D2 in D2–He, D2–Ne mixtures at different temperatures. Penny et al. [7] obtained and analyzed the collision induced absorption spectra of the fundamental band of D2–D2 at 77, 196 and 298 K. Varghese et al. [8] recorded the enhancement spectra of the collision induced absorption of the fundamental band of D2 in D2–N2 and D2–CO mixtures at room temperature. They analyzed the experimental profiles and compared them with theoretical profiles. Excellent agreement was obtained. In all the previous work, the observed spectra show the usual dip due to intercollisional interference near the band origin Q1(0) of the Qov branch. Welsh [9] has reviewed the experimental work done until 1971 on the translational, rotational and vibrational spectra of H2 and D2. The CIA vibrational spectra of the isotopomers H2, D2 and HD have been reviewed in detail by Reddy [10]. The reader is referred to these reviews for experimental aspects of the CIA and to Van Kranendok [11,12] and Frommhold [13] and the references therein for the theoretical aspects. The H2 molecule and its isotopomers such as D2 and T2 occupy a unique place in molecular physics on account of their simplicity and in particular the abundance of H2 in the universe and the accessibility to both experiment and theoretical studies. Molecules of this class can be considered as benchmarks in the field of CIA. In the present paper we present the absorption spectrum of the infrared fundamental band of deuterium in a D2–Kr mixture at ambient temperature. Enhancement CIA spectra of the fundamental band of D2 in D2–Kr binary mixtures were recorded at 298 K with a 2 m absorption cell. The observed spectra show the usual
112
M. Abu-Kharma et al. / Journal of Molecular Spectroscopy 259 (2010) 111–115
Fig. 1. Profiles of the collision induced enhancement absorption of deuterium in the fundamental band in D2–Kr mixtures at ambient temperature.
characteristic dip near the band origin Q1(0) of the Q branch with two well resolved components Qp and QR as well as the absorption peaks O1(3), O1(2) and S1(J), J = 0–4. The binary absorption coefficient of the band arising from collisions of the type D2–Kr has been determined. The spectra are interpreted in terms of the overlap transitions Qov(J), J = 0–4 and the following quadrupolar transitions of D2–Kr: O1(J = 2–4) (D2), Q1(J = 1–5) (D2); S1(J) (D2);with J = 0–4 for D2. An analysis of the absorption profiles was carried out by assuming appropriate line-shape functions for the short range overlap and the long range quadrupolar contributions. We will not repeat this part, we will follow the procedure of Varghese et al. for more details see [8]. The characteristic half-width parameters dd and dc for the overlap transitions and d1 and d2 for the quadrupole induced transitions were obtained from the analysis of the recorded spectra. 2. Experimental details A transmission absorption cell having a sample path length of 185.4 cm was used to study the fundamental band of deuterium gas in the binary mixtures of deuterium with krypton at 298 K. A general electric FFJ quartzline lamp housed in a water cooled brass jacket was used as a source of continuous infrared radiation. Three base densities were used, the range of D2 was 9–20 amagat while the range of krypton was 7–120 amagat. The spectrometer was a Perkin Elmer model 112 single beam double pass instrument equipped with an LiF prism, an American Time Products 260 Hz tuning fork chopper model L-40 and an infrared N2 cooled PbS detector were used. A slit width maintained at 150 lm gave a spectral resolution of 8 cm1 at 2993 cm1, the origin of the fundamental band of D2. The signal detection and amplification system consisted of SR510 lock-in amplifier. The entire optical path was boxed in a Plexiglas enclosure which was continuously flushed with dry nitrogen gas to decrease and maintain a constant level of water vapor absorption. The wave numbers (in cm1) of the quadrupolar transitions were calculated from the molecular constants of D2 [14]. The isothermal data of D2 were obtained from
Michels and Goudeket [15] and that of Kr were taken from Trappeniers et al. [16]. The enhancement absorption coefficient aen(m) at a given wave number m (in cm1) of an absorbing gas density qKr is given by
aen ðmÞ ¼ ð1=lÞ ln
I1 ðmÞ I2 ðmÞ
ð1Þ
where l is the sample path length of the absorption cell, and I1(m) and I1(m) are the intensities of radiation transmitted by the cell filled with a base density of D2 gas and the cell filled with the binary gas mixture D2–Kr, respectively. The enhancement absorption profiles h i were obtained by plotting ln II12 ððmmÞÞ versus wave number. The enhancement in the integrated absorption coefficient represented R as aen ðmÞdm was determined by calculating the area between the absorption spectrum and the wave number axis and multiplying the area by a factor (1/l). 3. Results and data analysis An example of the enhancement absorption profiles of the D2–Kr at room temperature is shown in Fig. 1. Similar profiles were obtained at different base pressures of deuterium. These profiles show the characteristic broad peaks as compared to the much sharper transitions seen in allowed absorption. The contribution of the overlap induction mechanism is quit strong as illustrated by the sharp dip at 3000 cm1. The observed spectrum peaks have been labeled with corresponding component assignment given in Table 1. The main components of the obtained spectrum are the overlap induced part at the (Qov(J), J = 0–4) region which splits into QP and QR components which are related by a Boltzmann factor [11] and the quadrupole part which cover the whole spectrum. A number of O(Dv = 1, DJ = 2), S(Dv = 1, DJ = 2) lines appear in the spectrum in addition to a Qq (Dv = 1, DJ = 0) component, which do not show any splitting. The splitting is explained by Van Kranendonk as an interference phenomenon occurring between the overlap dipole moments in successive collisions [11].
113
M. Abu-Kharma et al. / Journal of Molecular Spectroscopy 259 (2010) 111–115 Table 1 Assignment for the absorption peaks of the D2 fundamental band enhanced by Kr at 298 K. Peak
Transitions
m(D2) cm1[14]
1 2 3 4 5 6 7 8 9
O3(4) O2(3) O1(2) Q1(J) S1(0) S1(1) S1(2) S1(3) S1(4)
2572.6428 2693.9723 2814.5459 2993–2972 3166.3596 3278.5222 3387.2606 3492.0913 3592.5588
It appears that the splitting is density dependent and results from the negative correlation of the dipoles induced by the over-
Fig. 2. A plot of
1
qD2 qKr
R
lap forces in successive collisions of a D2 molecule with Kr molecules. Hence the dc parameter is density dependent and given by
dc ¼ aq þ bq2
ð2Þ
where a b and dc 1/2pcsc, sc is the time between collisions. R Fig. 2 shows a plot of q 1q aen ðmÞdm against the density of Kr, D2
Kr
qKr for D2–Kr mixture when qD2 = 14.3 amagat at room temperature. The intercept a12 = (3.7 ± 0.1) 103 cm2 amagat2 was obtained from a linear least-square fit of the data. The average of the binary integrated absorption coefficient a12 was obtained and found to be 3.9 103 cm2 amagat2. The influence of the ternary absorption coefficient was not significant, therefore only the binary one is determined.
aen ðmÞdm against qKr for the fundamental band of D2 at 298 K in a binary mixture of D2–Kr.
Fig. 3. Analysis of an enhancement profile of the fundamental band of D2 in a D2–Kr mixture at 298 K. The base density of D2 is 14.3 amagat and the Kr density is 30.4 amagat.
114
M. Abu-Kharma et al. / Journal of Molecular Spectroscopy 259 (2010) 111–115
Fig. 4. Analysis of an enhancement profile of the fundamental band of D2 in a D2–Kr mixture at 298 K. The base density of D2 is 14.3 amagat and the Kr density is 127 amagat.
Two examples of the profile analysis for D2–Kr at different densities of Kr are shown in Figs. 3 and 4, respectively. Fig. 3 shows the synthetic profile (red line) and the experimental profile (cyan line), which agree well, except at peak 3 which results from the O1(2) transition. The synthetic profile is formed from two main components: the overlap profile and the quadrupole profile. The lineshape function for the overlap transitions is represented by the Levine–Birnbaum expression
a~ en ðmÞ ¼
~ X aen:nov
2
2Dm dd
1 K 2 ð2Dm=dd Þ 1 c 1 þ ðDdcm Þ2 ð3Þ
;
1 þ expðhcDm=kTÞ
nov
The line-shape function for the quadrupole transitions is represented by the Birnbaum-Cohen (BC) line-shape function [8]
a~ en ðmÞ ¼
X nq
"
a~ BBC qm
s1 s2 hcDm zK 1 ðzÞ exp exp p s1 2kT 1 þ ð2pcDms1 Þ2
# ð4Þ
where 2 1=2
z ¼ ½1 þ ð2pcDms1 Þ
" 2
s2 s1
h þ 4pkT s1
4. Conclusion The CIA spectra of the fundamental band of D2 enhanced by krypton showed the same general structure for collision induced absorption spectra of D2-Noble Gas, D2–N2 and D2–CO. The observed spectra showed the same broad features characteristic of CIA. The specific dip due to the overlap induction mechanism was found in the spectra of the fundamental band. The average binary integrated absorption coefficient a12 was measured and was found equal to 3.9 103 cm2 amagat2. The profile analysis made it possible to separate the contributions of the quadrupole and overlap induced transitions to the total intensity of the band. The percentage of absorption from quadrupolar and overlap induction mechanisms were calculated to be (30–36)% overlap to (70–64)% quadrupolar with respect to the total band. Appropriate line-shape functions were used to determine the synthetic profiles and the obtained characteristic line-shape parameters are: d1 = 50 ± 5 cm1, d2 = 250 ± 50 cm1, dd = 120 ± 12 cm1 and the parameter dc of the overlap induction line-shape was found to be density dependent. The constant a in Eq. (2) is 9.6 102 cm1 amagat1.
2 #2 :
ð5Þ
For the overlap part only Qov(J) contributes, where the rotational quantum number range from J = 0 to 5 and are represented by the green1 line. The quadrupolar part is formed from the O1(J = 2–4) transitions, the Q1q(J = 1–5) transitions and the S1(J = 0– 4) transitions, and are represented by the dark blue line. The wave number parameters d1 and d2 are related to s1 and s2 by the following expressions: s1 = 1/2pcd1 and s2 = 1/2pcd2. The determined parameters are d1 = 50 ± 5 cm1, d2 = 250 ± 50 cm1 cm1, dd = 120 ± 12 cm1 and the constant a in Eq. (2) is 9.6 102 cm1 amagat1. 1 For interpretation of color in Fig. 3, the reader is referred to the web version of this article.
Acknowledgments We are grateful to S.P. Reddy for his help in obtaining the spectra and to A.R. Sakchel for help in programming some codes.
References [1] [2] [3] [4] [5] [6] [7] [8]
J. Van Kranendonk, Physica 24 (1958) 347. M.F. Crawford, H.L. Welsh, J.L. Locke, Phys. Rev. 75 (1949) 1607. H.L. Welsh, M.F. Crawford, J.L. Locke, Phys. Rev. 76 (1949) 580. S. Paddy Reddy, C.W. Cho, Can. J. Phys. 43 (1965) 793. S.T. Pai, S. Paddy Reddy, C.W. Cho, Can. J. Phys. 44 (1966) 2893. W.E. Russell, S. Paddy Reddy, C.W. Cho, J. Mol. Spectrosc. 52 (1) (1974) 72. R.J. Penney, R.D.G. Prassad, S. Paddy Reddy, J. Chem. Phys. 77 (1) (1982) 131. G. Varghese, C. Stamp, S. Paddy Reddy, JQSRT 87 (2004) 387.
M. Abu-Kharma et al. / Journal of Molecular Spectroscopy 259 (2010) 111–115 [9] H.L. Welsh, Pressure-induced absorption spectra of hydrogen, in: A.D. Buckingham, D.A. Ramsay (Eds.), In MTP International Review of Science – physical chemistry, Series I, vol. III, Butterworth, London, 1972, pp. 33–71. [10] S.P. Reddy, Phenomena induced by intermolecular interactions, in: G. Birnbaum (Ed.), Induced Vibrational Absorption in the Hydrogen, Plenum, New York, 1985, p. 129. [11] J. Van Kranendonk, Can. J. Phys. 46 (1968) 1173.
115
[12] J. Van Kranendonk, Physica 73 (1974) 156. [13] L. Frommhold, Collision-Induced Absorption in Gases, Cambridge Monographs on Atomic, vol. 2, Cambridge University Press, 1993. [14] A.R.W. McKellar, T. Oka, Can. J. Phys. 56 (1978) 1315. [15] A. Michels, M. Goudeket, Physica 8 (1941) 352. [16] N.J. Trappeniers, T. Wassenaar, G.J. Wolkers, Physica 32 (1966) 1503.
Contents lists available at ScienceDirect
Journal of Molecular Spectroscopy journal homepage: www.elsevier.com/locate/jms
Collision induced absorption spectra of the fundamental band of D2 in binary mixtures D2–Kr at 298 K M. Abu-Kharma a,*, H.Y. Omari b, N. Shawaqfeh a, C. Stamp c a
Department of Applied Sciences, AL-Balqa University, Amman, Jordan Department of Physics, Mu’tah University, Al-Karak, Jordan c Department of Physics, Memorial University, St. John’s, Canada b
a r t i c l e
i n f o
Article history: Received 22 October 2009 In revised form 12 November 2009 Available online 28 December 2009 Keywords: Infrared spectra Fundamental band D2–Kr Collision induced absorption
a b s t r a c t The enhancement spectrum of the collision induced absorption of D2 in its fundamental band region 2600–4000 cm1 in binary mixtures D2–Kr was studied at 298 K for base densities of D2 in the range 9–20 amagat and for partial densities of Kr in the range 7–120 amagat. The binary absorption coefficient of the band has been determined from the measured integrated absorption coefficient and found to be 3.9 103 cm2 amagat2. An analysis of the experimental spectrum was carried out by assuming appropriate line-shape functions and the half-width parameters d1, d2, dd and dc of the long range quadrupole, and of the short range overlap induced transitions have been determined. Good agreement was obtained between the recorded spectrum of the fundamental band and the synthetic profile. Ó 2009 Elsevier Inc. All rights reserved.
1. Introduction Isolated homo nuclear diatomic molecules such as H2, D2, N2, and O2, etc. in their lowest (ground) electronic states have no permanent electronic dipole moments because of the symmetry of their charge distribution. Consequently, they have no electric dipole absorption at their translational, rotational, or vibrational frequencies. Collision-induced absorption (ClA) occurs as a result of induced transient electric dipole moments during binary or higher-order collisions. According to the exponential-4 model given by Van Kranendok [1], the induced electric dipole moment, l, of an interacting molecule pair is derived by combining a moment resulting from the overlap forces at short range, lov, with a moment resulting from the interactions of permanent molecular quadrupole moments at long range, lq. The short range moment contributes to the Qoverlap (DJ = 0) lines, whereas the long range moment contributes to the O(DJ = 2), Qquadrupole (DJ = 0) and S(DJ = 2) lines. CIA was first observed in compressed N2 and O2 in the region of their fundamental band by Crawford et al. [2]. The CIA of the fundamental band of H2 was first identified by Welsh et al. [3] in the same year. Reddy and Cho [4] studied the fundamental band of pure D2 for gas pressures up to 250 atm at 298 K. They determined the binary and the ternary absorption coefficients. One year later, Pai et al. [5] investigated the fundamental band of D2 in D2–He, D2–Ar, D2–N2 and D2–D2 at room temperature, * Corresponding author. E-mail address: [email protected] (M. Abu-Kharma). 0022-2852/$ - see front matter Ó 2009 Elsevier Inc. All rights reserved. doi:10.1016/j.jms.2009.11.009
The binary and the ternary absorption coefficients were also determined. Russell et al. [6] studied the collision induced fundamental band of D2 in D2–He, D2–Ne mixtures at different temperatures. Penny et al. [7] obtained and analyzed the collision induced absorption spectra of the fundamental band of D2–D2 at 77, 196 and 298 K. Varghese et al. [8] recorded the enhancement spectra of the collision induced absorption of the fundamental band of D2 in D2–N2 and D2–CO mixtures at room temperature. They analyzed the experimental profiles and compared them with theoretical profiles. Excellent agreement was obtained. In all the previous work, the observed spectra show the usual dip due to intercollisional interference near the band origin Q1(0) of the Qov branch. Welsh [9] has reviewed the experimental work done until 1971 on the translational, rotational and vibrational spectra of H2 and D2. The CIA vibrational spectra of the isotopomers H2, D2 and HD have been reviewed in detail by Reddy [10]. The reader is referred to these reviews for experimental aspects of the CIA and to Van Kranendok [11,12] and Frommhold [13] and the references therein for the theoretical aspects. The H2 molecule and its isotopomers such as D2 and T2 occupy a unique place in molecular physics on account of their simplicity and in particular the abundance of H2 in the universe and the accessibility to both experiment and theoretical studies. Molecules of this class can be considered as benchmarks in the field of CIA. In the present paper we present the absorption spectrum of the infrared fundamental band of deuterium in a D2–Kr mixture at ambient temperature. Enhancement CIA spectra of the fundamental band of D2 in D2–Kr binary mixtures were recorded at 298 K with a 2 m absorption cell. The observed spectra show the usual
112
M. Abu-Kharma et al. / Journal of Molecular Spectroscopy 259 (2010) 111–115
Fig. 1. Profiles of the collision induced enhancement absorption of deuterium in the fundamental band in D2–Kr mixtures at ambient temperature.
characteristic dip near the band origin Q1(0) of the Q branch with two well resolved components Qp and QR as well as the absorption peaks O1(3), O1(2) and S1(J), J = 0–4. The binary absorption coefficient of the band arising from collisions of the type D2–Kr has been determined. The spectra are interpreted in terms of the overlap transitions Qov(J), J = 0–4 and the following quadrupolar transitions of D2–Kr: O1(J = 2–4) (D2), Q1(J = 1–5) (D2); S1(J) (D2);with J = 0–4 for D2. An analysis of the absorption profiles was carried out by assuming appropriate line-shape functions for the short range overlap and the long range quadrupolar contributions. We will not repeat this part, we will follow the procedure of Varghese et al. for more details see [8]. The characteristic half-width parameters dd and dc for the overlap transitions and d1 and d2 for the quadrupole induced transitions were obtained from the analysis of the recorded spectra. 2. Experimental details A transmission absorption cell having a sample path length of 185.4 cm was used to study the fundamental band of deuterium gas in the binary mixtures of deuterium with krypton at 298 K. A general electric FFJ quartzline lamp housed in a water cooled brass jacket was used as a source of continuous infrared radiation. Three base densities were used, the range of D2 was 9–20 amagat while the range of krypton was 7–120 amagat. The spectrometer was a Perkin Elmer model 112 single beam double pass instrument equipped with an LiF prism, an American Time Products 260 Hz tuning fork chopper model L-40 and an infrared N2 cooled PbS detector were used. A slit width maintained at 150 lm gave a spectral resolution of 8 cm1 at 2993 cm1, the origin of the fundamental band of D2. The signal detection and amplification system consisted of SR510 lock-in amplifier. The entire optical path was boxed in a Plexiglas enclosure which was continuously flushed with dry nitrogen gas to decrease and maintain a constant level of water vapor absorption. The wave numbers (in cm1) of the quadrupolar transitions were calculated from the molecular constants of D2 [14]. The isothermal data of D2 were obtained from
Michels and Goudeket [15] and that of Kr were taken from Trappeniers et al. [16]. The enhancement absorption coefficient aen(m) at a given wave number m (in cm1) of an absorbing gas density qKr is given by
aen ðmÞ ¼ ð1=lÞ ln
I1 ðmÞ I2 ðmÞ
ð1Þ
where l is the sample path length of the absorption cell, and I1(m) and I1(m) are the intensities of radiation transmitted by the cell filled with a base density of D2 gas and the cell filled with the binary gas mixture D2–Kr, respectively. The enhancement absorption profiles h i were obtained by plotting ln II12 ððmmÞÞ versus wave number. The enhancement in the integrated absorption coefficient represented R as aen ðmÞdm was determined by calculating the area between the absorption spectrum and the wave number axis and multiplying the area by a factor (1/l). 3. Results and data analysis An example of the enhancement absorption profiles of the D2–Kr at room temperature is shown in Fig. 1. Similar profiles were obtained at different base pressures of deuterium. These profiles show the characteristic broad peaks as compared to the much sharper transitions seen in allowed absorption. The contribution of the overlap induction mechanism is quit strong as illustrated by the sharp dip at 3000 cm1. The observed spectrum peaks have been labeled with corresponding component assignment given in Table 1. The main components of the obtained spectrum are the overlap induced part at the (Qov(J), J = 0–4) region which splits into QP and QR components which are related by a Boltzmann factor [11] and the quadrupole part which cover the whole spectrum. A number of O(Dv = 1, DJ = 2), S(Dv = 1, DJ = 2) lines appear in the spectrum in addition to a Qq (Dv = 1, DJ = 0) component, which do not show any splitting. The splitting is explained by Van Kranendonk as an interference phenomenon occurring between the overlap dipole moments in successive collisions [11].
113
M. Abu-Kharma et al. / Journal of Molecular Spectroscopy 259 (2010) 111–115 Table 1 Assignment for the absorption peaks of the D2 fundamental band enhanced by Kr at 298 K. Peak
Transitions
m(D2) cm1[14]
1 2 3 4 5 6 7 8 9
O3(4) O2(3) O1(2) Q1(J) S1(0) S1(1) S1(2) S1(3) S1(4)
2572.6428 2693.9723 2814.5459 2993–2972 3166.3596 3278.5222 3387.2606 3492.0913 3592.5588
It appears that the splitting is density dependent and results from the negative correlation of the dipoles induced by the over-
Fig. 2. A plot of
1
qD2 qKr
R
lap forces in successive collisions of a D2 molecule with Kr molecules. Hence the dc parameter is density dependent and given by
dc ¼ aq þ bq2
ð2Þ
where a b and dc 1/2pcsc, sc is the time between collisions. R Fig. 2 shows a plot of q 1q aen ðmÞdm against the density of Kr, D2
Kr
qKr for D2–Kr mixture when qD2 = 14.3 amagat at room temperature. The intercept a12 = (3.7 ± 0.1) 103 cm2 amagat2 was obtained from a linear least-square fit of the data. The average of the binary integrated absorption coefficient a12 was obtained and found to be 3.9 103 cm2 amagat2. The influence of the ternary absorption coefficient was not significant, therefore only the binary one is determined.
aen ðmÞdm against qKr for the fundamental band of D2 at 298 K in a binary mixture of D2–Kr.
Fig. 3. Analysis of an enhancement profile of the fundamental band of D2 in a D2–Kr mixture at 298 K. The base density of D2 is 14.3 amagat and the Kr density is 30.4 amagat.
114
M. Abu-Kharma et al. / Journal of Molecular Spectroscopy 259 (2010) 111–115
Fig. 4. Analysis of an enhancement profile of the fundamental band of D2 in a D2–Kr mixture at 298 K. The base density of D2 is 14.3 amagat and the Kr density is 127 amagat.
Two examples of the profile analysis for D2–Kr at different densities of Kr are shown in Figs. 3 and 4, respectively. Fig. 3 shows the synthetic profile (red line) and the experimental profile (cyan line), which agree well, except at peak 3 which results from the O1(2) transition. The synthetic profile is formed from two main components: the overlap profile and the quadrupole profile. The lineshape function for the overlap transitions is represented by the Levine–Birnbaum expression
a~ en ðmÞ ¼
~ X aen:nov
2
2Dm dd
1 K 2 ð2Dm=dd Þ 1 c 1 þ ðDdcm Þ2 ð3Þ
;
1 þ expðhcDm=kTÞ
nov
The line-shape function for the quadrupole transitions is represented by the Birnbaum-Cohen (BC) line-shape function [8]
a~ en ðmÞ ¼
X nq
"
a~ BBC qm
s1 s2 hcDm zK 1 ðzÞ exp exp p s1 2kT 1 þ ð2pcDms1 Þ2
# ð4Þ
where 2 1=2
z ¼ ½1 þ ð2pcDms1 Þ
" 2
s2 s1
h þ 4pkT s1
4. Conclusion The CIA spectra of the fundamental band of D2 enhanced by krypton showed the same general structure for collision induced absorption spectra of D2-Noble Gas, D2–N2 and D2–CO. The observed spectra showed the same broad features characteristic of CIA. The specific dip due to the overlap induction mechanism was found in the spectra of the fundamental band. The average binary integrated absorption coefficient a12 was measured and was found equal to 3.9 103 cm2 amagat2. The profile analysis made it possible to separate the contributions of the quadrupole and overlap induced transitions to the total intensity of the band. The percentage of absorption from quadrupolar and overlap induction mechanisms were calculated to be (30–36)% overlap to (70–64)% quadrupolar with respect to the total band. Appropriate line-shape functions were used to determine the synthetic profiles and the obtained characteristic line-shape parameters are: d1 = 50 ± 5 cm1, d2 = 250 ± 50 cm1, dd = 120 ± 12 cm1 and the parameter dc of the overlap induction line-shape was found to be density dependent. The constant a in Eq. (2) is 9.6 102 cm1 amagat1.
2 #2 :
ð5Þ
For the overlap part only Qov(J) contributes, where the rotational quantum number range from J = 0 to 5 and are represented by the green1 line. The quadrupolar part is formed from the O1(J = 2–4) transitions, the Q1q(J = 1–5) transitions and the S1(J = 0– 4) transitions, and are represented by the dark blue line. The wave number parameters d1 and d2 are related to s1 and s2 by the following expressions: s1 = 1/2pcd1 and s2 = 1/2pcd2. The determined parameters are d1 = 50 ± 5 cm1, d2 = 250 ± 50 cm1 cm1, dd = 120 ± 12 cm1 and the constant a in Eq. (2) is 9.6 102 cm1 amagat1. 1 For interpretation of color in Fig. 3, the reader is referred to the web version of this article.
Acknowledgments We are grateful to S.P. Reddy for his help in obtaining the spectra and to A.R. Sakchel for help in programming some codes.
References [1] [2] [3] [4] [5] [6] [7] [8]
J. Van Kranendonk, Physica 24 (1958) 347. M.F. Crawford, H.L. Welsh, J.L. Locke, Phys. Rev. 75 (1949) 1607. H.L. Welsh, M.F. Crawford, J.L. Locke, Phys. Rev. 76 (1949) 580. S. Paddy Reddy, C.W. Cho, Can. J. Phys. 43 (1965) 793. S.T. Pai, S. Paddy Reddy, C.W. Cho, Can. J. Phys. 44 (1966) 2893. W.E. Russell, S. Paddy Reddy, C.W. Cho, J. Mol. Spectrosc. 52 (1) (1974) 72. R.J. Penney, R.D.G. Prassad, S. Paddy Reddy, J. Chem. Phys. 77 (1) (1982) 131. G. Varghese, C. Stamp, S. Paddy Reddy, JQSRT 87 (2004) 387.
M. Abu-Kharma et al. / Journal of Molecular Spectroscopy 259 (2010) 111–115 [9] H.L. Welsh, Pressure-induced absorption spectra of hydrogen, in: A.D. Buckingham, D.A. Ramsay (Eds.), In MTP International Review of Science – physical chemistry, Series I, vol. III, Butterworth, London, 1972, pp. 33–71. [10] S.P. Reddy, Phenomena induced by intermolecular interactions, in: G. Birnbaum (Ed.), Induced Vibrational Absorption in the Hydrogen, Plenum, New York, 1985, p. 129. [11] J. Van Kranendonk, Can. J. Phys. 46 (1968) 1173.
115
[12] J. Van Kranendonk, Physica 73 (1974) 156. [13] L. Frommhold, Collision-Induced Absorption in Gases, Cambridge Monographs on Atomic, vol. 2, Cambridge University Press, 1993. [14] A.R.W. McKellar, T. Oka, Can. J. Phys. 56 (1978) 1315. [15] A. Michels, M. Goudeket, Physica 8 (1941) 352. [16] N.J. Trappeniers, T. Wassenaar, G.J. Wolkers, Physica 32 (1966) 1503.