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Temperature Dependence of the Spectral Intensity of the Fermi Resonant 1943cm−1 Band of Carbonyl FluorideTerry N. Adams, David M. Weston, and Richard A. Matula Citation: The Journal of Chemical Physics 55, 5674 (1971); doi: 10.1063/1.1675738 View online: http://dx.doi.org/10.1063/1.1675738 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/55/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Nomograph of the Temperature Dependence of the Fermi Level in a Degenerate Parabolic Band J. Appl. Phys. 36, 3948 (1965); 10.1063/1.1713981 Anomalous Band Intensity in Fermi Resonance J. Chem. Phys. 31, 258 (1959); 10.1063/1.1730304 Absolute Intensities of the 721 and 742 cm—1 Bands of CO2 J. Chem. Phys. 26, 1252 (1957); 10.1063/1.1743501 Conjugation and the Intensity of the Infrared Carbonyl Band J. Chem. Phys. 21, 2008 (1953); 10.1063/1.1698732 Intensities of Vibration Bands of Carbonyl Sulfide and Carbon Disulfide J. Chem. Phys. 20, 520 (1952); 10.1063/1.1700453
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5674 J. P. LARKINDALE AND D. J. SIMKIN
18 P. J. Stephens, Chern. Phys. Letters. 2,241 (1968). 19 C. H. Henry, S. E. Schnatterly, and C. P. Slichter, Phys.
Rev. 137, A583 (1965). 20 P. J. Stephens, W. Suetaka, and P. N. Schatz, J. Chern. Phys.
44, 4592 (1966). 21 B. Briat, D. A. Schooley, R. Records, E. Bunnenberg, C.
Djerassi, and E. Vogel, J. Am. Chern. Soc. 90, 4691 (1968). 2\l J. A. Pople and D. L. Beveridge, Approximate Molecular
Orbital Theory (McGraw-Hill, New York, 1970).
23 Y. H. Pao and D. P. Santry., J. Am. Chern. Soc. 88, 4157 (1966) .
24 J. A. Pople, D. P. Santry, and G. A. Segal, J. Chern. Phys. 43, S129 (1965).
2. J. A. Pople and G. A. Segal, J. Chern. Phys. 43, S136 (1965). 26 J. A. Pople and G. A. Segal, J. Chern. Phys. 44, 3289 (1966). 27 H. W. Kroto and D. P. Santry, J. Chern. Phys. 47, 792
(1967) .
THE JOURNAL OF CHEMICAL PHYSICS VOLUME 55, NUMBER 12 15 DECEMBER 1971
Temperature Dependence of the Spectral Intensity of the Fermi Resonant 1943 cm- 1
Band of Carbonyl Fluoride
TERRY N. AoAMS,* DAVID M. WESTON,t AND RICHARD A. MATULA
Combustion Kinetics Laboratory, Thermal and Fluid Sciences, Drexel University, Philadelphia, Pennsylvania 19104
(Received 8 February 1971)
The temperature dependence of the spectral and integrated intensity of the 1943 cm-1 infrared band of carbonyl fluoride was experimentally determined in the temperature range 30Q--600°K. The total integrated intensity, "'1943, is independent of temperature and has a value of 4.04±0.08X 107 cm-2• (moles/cc)-I. An expression for the temperature dependence of the theoretical band shape of the V2 fundamental vibration of carbonyl fluoride is presented, and numerical results based on this model are compared to the experimental data. Since the first overtone of the VI vibration is in Fermi resonance with the V2 vibration, the temperature dependence of the Fermi resonant contribution was evaluated. The Fermi resonance effects were combined with the theoretical band shape to predict the spectral intensity of the 1943 cm-1 band at temperatures above 600oK.
INTRODUCTION
One of the most important species in fluorocarbonoxygen systems is carbonyl fluoride, COF2. This compound is of considerable interest due to its role in the kinetics and radiant heat transfer from high temperature fluorocarbon-combustion systems.I- 4 The infrared absorption spectrum of COF2 consists of a number of vibrational-rotational bands between 2 and 38 fJ.. 5 The highest frequency fundamental band is centered at 1943 cm-I, and it is the strongest absorber in the infrared. Therefore this band is dominant in heat transfer considerations, and due to its strength and spectral position it has been used by a number of investigators6.7 to monitor concentration changes of COF2 in reacting systems.
To date, little work has been done on the spectral emissivity of carbonyl fluoride. Hopper and co-workers8
measured the room temperature oscillator strengths of the six fundamental bands of COF2. The temperature dependence of the integrated intensity of the 1943 cm- l band of COF2 has been studied by Modica,9 using a shock tube in conjunction with a fast scanning spectrometer. His experiments were carried out with COF2 concentrations between 6XlO-6 and 4.2XlO-5
moles/cc, and the temperatures and total pressure were varied from 1300 to 24000 K and 3 to 10 atm, respectively. He estimated the error in his measurements to be ±30%. Although the experimentally determined temperature variation of the integrated intensity was
essentially in agreement with theory, little knowledge of the shape of the band was obtained. He also reported a value for the room temperature integrated intensity of the 1943 cm-1 band.
The 1943 cm-1 band of COF2 is composed of two vibrational contributions, the V2 fundamental and the first overtone of the VI fundamental which are in Fermi resonance. The purpose of the present investigation was to determine the effect of Fermi resonance on the shape and intensity of the band and to determine the temperature dependence of both its spectral and integrated intensity.
EXPERIMENTAL APPARATUS AND PROCEDURES
The experimental facility utilized for these studies is shown schematically in Fig. 1. The radiation source, similar to the one described by Simmons et al.,w has been modified for continuous operation up to 3000oK. The 23.S-cm long test cell was constructed from aluminum and fitted with CaF2 optical windows. A Hilger-Engis model 600 scanning monochromater was employed using a 150 line/mm grating which was blazed at 6 fJ.. The slit function of this device is approximately triangular, and, at the mechanical slit widths used during the present work, the system's spectral slit width was 0.9 cm-l . A Philco GPC 216 gold-doped germanium detector was used to transduce the chopped optical signal into an ac electrical signal.
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TEMPERATURE DEPENDENCE OF SPECTRAL INTENSITY 5675
~------------(0 .::~;~;~?~~~~__ .-_F_u_r_n_a_c_e--,
BB Radiation Source
Loc k-In Amplifiers
~-----.:::=-------- Grating
~ ~ §~~ ~ ~ ~~:-:~ _ly--M_O _n o_c_h_r_o_m_a_t_e_r ....
Flushing Cover
Dial Monometer
Backfill Gas
Mechanical Vacuum Diffusion
Pump
~============================~========~ __ ~ P~mp FIG. 1. Schematic diagram of infrared absorption spectroscopy facility.
The electrical signal was processed by a Princeton Applied Research Model 120 lock-in amplifier and recorded on a Moseley 7100B strip chart recorder.
The vessel was installed in a resistance type furnace capable of operation to 1200oK. The temperature was controlled with a Thermac MPRY Temperature Controller, and isothermal conditions were insured by the use of guard heaters at both ends of the furnace. The temperature gradient along the vessel was monitored with five Chromel-Alumel thermocouples, and a maximum gradient of 1 KO at 6000 K was allowed.
The gas handling system was of stainless steel construction and pressures were measured with a Wallace and Tiernan Model FA 145 precision dial monometer. In order to minimize decomposition of COF2, it was necessary to eliminate water vapor from the system. This was accomplished by heating while pumping to a pressure less than 1 X 10-6 torr and to subsequently passivate the walls of both the gas handling system and the optical cell system with COF2 for a day. After such a procedure, there was an insignificant change in the concentration of COF2 during any of the experimental runs.
Two cylinders of COF2 were purchased from Peninsular ChemResearch, Gainesville, Florida. The supplier stated that the purity of the COF2 was 99%. Subsequent mass spectroscopic, gas chromatographic, and infrared analysis of these two cylinders, however, indicated that their purity upon receipt was 97%. In addition, it was found necessary to regularly check the purity of the test gases, since COF2 was observed
to undergo a slow decomposition in the cylinder at room temperature. During the course of this investigation, the purity levels were 90.1 and 91.8% respectively. Matheson ultrapure argon and helium were used as diluent gases in the COF2 test gas mixtures.
Since these experiments were conducted in the single beam mode, it was necessary to accurately determine the positions of both the 0% and 100% transmission lines. The 0% line was set by scanning a 760 torr sample of COF2. The 1943 cm-1 band of COF2 is a strong absorber and, at this optical density, is essentially black. Thus the scan of the 760 torr sample defined the 0% transmission line. The 100% transmission line was determined from background scans of the test vessel, evacuated to less than 1XIQ-a torr, taken before and after each set of runs.
The general experimental technique used in these integrated intensity measurements is based on the pressure broadening methods developed by Wilson and Wells,ll as stated by Penner.'2 In order to apply this technique, the 1943 cm-1 band of COF2 must be sufficiently pressure broadened to eliminate variations of the transmitted signal over the spectral band passed by the spectrometer. The total pressure required to sufficiently pressure broaden the band was determined at room temperature, the most extreme case, by running successive spectra of a single sample of COF2 at increasing total pressures. At a spectral slit width of 0.9 cm-I, the 1943 cm-1 band of COF2 was sufficiently broadened at a total pressure of approximately 400 torr. All subsequent data were measured at a total pressure
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S676 ADAMS, WESTON, AND MATULA
.. E 0
;:; -0
;:; !:: c: ...J ....... ;:,.
<l
200
160
120
80
40
0- 300"K DATA
8- 400"K DATA 0- 500"K DATA A- 600"K DATA
2 4 5 6 XIO'
OPTICAL DENSITY, nl, em - moles/ee
FIG. 2. Optical density dependence of the integral of the logarithmic transmission for the temperatures 300, 400, 500, 6OOoK.
of 800 torr to insure that the pressure broadening criteria were satisfied.
EXPERIMENTAL RESULTS
The apparent spectral transmission of the 1943 cm-l
band of COF2 was experimentally determined as a function of both temperature and optical density. These data were obtained for optical densities and temperatures in the range 0.SXlO-LS.OXlO-7 cm· moles/cc and 300-600oK, respectively. In order to determine the integrated intensity of this band, the integral of the natural log of the apparent spectral transmission was determined numerically from the raw data. These results are plotted as a function of optical density in Fig. 2.
Wilson and Wellsll have shown that the limiting slope of such a plot yields the true value of the integrated intensity. It can be seen in Fig. 2 that all of the experimental data lie on a straight line. A least-meansquares fit of the data yields a value for the integrated intensity of the 1943 cm-l band of
0!1943 = 4.04± (0.08) X 107 cm-2 " (moles/cc)-l. (1)
Since the data shown in Fig. 2 are linear with respect to optical density, the experimentally determined transmission is identical to the actual transmission for the optical densities used in the present experiments.u This result was also verified by plotting the natural log of the measured transmission versus optical density at several points in the spectrum and obtaining a linear dependence of these two variables. Based on these results, Beer's law was invoked for the remainder of the data analysis.
The experimental data were reduced to spectral absorption coefficients by employing Beer's law. The experimentally determined band shapes for 300, 400, SOO, and 6000 K are shown in Fig. 3. The room temperature experimental data show three maxima of ap-
proximately equal magnitude. The effects of population broadening are evidenced by the spreading of the band at higher temperatures.
THEORETICAL CONSIDERATIONS
In order to extend the results of the present investigation to temperatures above those studied here, it is necessary to determine the temperature dependence of the contributions to the spectral absorption coefficient from both the V2 fundamental and the 1'1 overtone. Since Fermi resonance plays an important role in determining the temperature dependence of the spectral absorption coefficients of both of these bands, this effect must be investigated before the temperature dependence of the 1943 cm-l band of COF2 can be accurately determined. In a subsequent section, the theoretical band shape of the 112 fundamental will be developed. This result will be used, in conjunction with an empirical expression for the III overtone, to calculate the temperature dependence of the 1943 cm-l band shape. The effects of Fermi resonance on the transition moments of the two vibrations will be taken into account.
The COF2 molecule is planar and of C2V symmetry. The moments of inertia, as reported in the JANAF Tables,13 indicate that COF2 is very nearly an oblate, symmetric top molecule with the symmetry axis along the carbonyl bond and bisecting the F-C-F angle. The figure axis is perpendicular to the plane of the molecule.
The 1943 cm-l band of COF2 is made up of three vibrational contributions. The most intense contribution is due to the 1943 cm-l V2 fundamental vibration which is the carbonyl group stretching.5 Overlapping this on the low wavenumber side is the 1907 cm-1 II}
overtone, which is the C-F in-phase vibration. On the high wavenumber side of the band is the (2113+116) combination band. This last band has a parallel en-
0 0 ~~Io E 10
" E ()
0.. .. 8
~ 6 in z ILl r- 4 z
...J ct 2 a: ru ~'lo5L-~~~=-__ ~ __________ -L ______ ~~~ __
II) 1850 1950 1900
WAVENUMBER ,11, em-'
FIG. 3. Experimental spectral intensity for temperatures 300, 400, 500, 6OOoK.
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T E M PER AT U RED E PEN DEN CEO F S P E C T R A LIN TEN SIT Y 5677
velope due to the V6 out of plane vibration. At high optical densities the sharp Q branch associated with this combination is discernable in the spectrum at 2010 cm-1• However, at the low optical densities of these experiments, no Q branch was found. Based on this observation it was concluded that the (2V3+V6) combination is a very weak absorber, and it was not included during the course of subsequent analysis.
If the Vl overtone is neglected for a moment, it is possible to obtain the theoretical band shape and spectral absorption coefficient for the V2 fundamental vibration. The band shape of a rotation-vibration band is dependent on both the type of vibration, i.e., parallel or perpendicular, and on the distribution of molecules in the various rotational levels. The envelope of a band (which corresponds to the laboratory situation of a completely pressure broadened band) can be determined from the ratios of the rotational line
intensities to the rotational line spacings. The spacing can be calculated from the equation for the energy levels, and the intensity is proportional to the product of the rotational transition moment and the popUlation of the initial state.
Expressions for the energy levels, population distribution, matrix elements, and line position are available for a symmetric top molecule.14 •15 A single expression for the spectral intensity can be obtained by combining these quantities. This expression initially is a function of both the temperature and the two quantum numbers which define the energy levels and transition wavenumbers. It is convenient to remove the quantum number dependence by utilizing the wavenumber expression. The final expression for the spectral intensity of the high wavenumber side of the band, given below, is a function of wavenumber and temperature only:
P '8reI [( J=2(cv/H/2) [3J - (2ev/~) +tJ[3J - (2cp/~) +!] ) P/'= -" __ a 2 L e-!l(J·v.T) Plr h J-(c"/~)-7/2 2(J+l)
+(1 f31-1 Ji:"" [J+(cp/~)+!][J-(2cv/~)+!](2J+l) e-I2<J .•. T»] (2) J-(2c./t>+1/2 2J(J+1) ,
with
j1= (h2/8rIakT)[J(J+1)+f3[2J+(2ev/~)+!]2], (3)
12= (h2/81r2IakT)[J(J+1)+f3[(2ep/~)+!]2], (4)
where ~ = h/41r2I a , p." = pseudo absorption coefficient, P.'=normalization factor, e=speed of light, Ia= symmetry axis moment of inertia, h = Planck's constant, J=quantum number, v=wavenumber, T= temperature, f3=l-Ia/Ic, k=Boltzmann's constant, Ic= figure axis moment of inertia. The above expression was programmed for an IBM 360/65 computer system and the value of Pv" was determined, for a wide variety
0
;Iu OU E_ o E ~ 8 .. 0-
>- 6 .... 00 z
4 UJ .... ~
.J
'" 2
a:
t; .,00 UJ
1850 Q. 2000 <f)
WAVENUMBER ,11, em-'
FIG. 4. Comparison of the theoretical and experimental band shape at 300oK.
of temperatures, over the entire wavenumber region of interest. The normalization factor, P/, was taken such that
1 P."dv= 1. (5) <I..
This procedure yields knowledge of the band shape as a function of temperature. The value of the spectral absorption coefficient at a particular wavenumber can be readily obtained by multiplying the appropriate value of Po" by the integrated absorption coefficient a. In order to initially compare the experimental and theoretical spectral band shapes, a value of the integrated intensity for the fundamental band was chosen such that the spectral absorption coefficient of both the theoretical and experimental curves were equal at the band center. A comparison of the theoretical and experimental band shapes at room temperatures are shown in Fig. 4.
The theoretical and experimental band shapes would be identical if the V2 fundamental was the only contribution to the total band. However, the V2 fundamental and the overlapping V1 overtone are in Fermi resonance,s and hence the experimental band is distorted on the low wavenumber side of the band. Fermi resonance has the effect of not only slightly shifting the position of each band but also of amplifying the intensity of the weaker overtone at the expsense of the fundamental. Comparison of the experimental and theoretical results shows that the high wavenumber side of the band is not affected by the overtone. Based on these observa-
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5678 ADAMS, WESTON, AND MATULA
0
t:I ..... ~
t:I . 0 i= <l 4 a:: )0-
f-Cii 3 z W f-~ 2
0 W 1.11 up(351/T) f-<l a:: (!) w f-~ 400 500 600 700 800
TEMPERATURE. T. oK
FIG. S. Temperature dependence of the apparent integrated intensity ratio.
tions, it is possible to separate the apparent contributions to the band by both the fundamental and the overtone.
The total integrated intensity of the band, a1943, is composed of contributions from both the fundamental af, and the overtone, ao. The total integrated intensity for the 1943 cm-l band has been shown to be independent of temperature and is given by Eq. (1). The apparent contribution of af can be determined as twice the value of the integrated intensity of the high wavenumber half of the experimental band. The contribution of the overtone is the difference between the total intensity and the contribution from the fundamental. The experimentally determined ratio of the fundamental contribution to the overtone contribution, aj/ao, is shown as a function of temperature in Fig. 5. The ratio of the apparent contributions was fitted to an expression of the following form:
aj/ao=A exp(+d/T). (6)
A least-me an-squares fit of the experimental data yielded
A = 1.11± (0.002),
d=351±(4) .
(7)
(8)
The relative temperature dependences of the V2
fundamental and of the VI overtone is represented by Eq. (6), but the temperature dependence of the total integrated intensity is as yet unexplained. Lisitsa and Strizhevskil6 have proposed that the temperature dependence of the integrated intensity of a band composed of two components in Fermi resonance should correspond to that of the most intense component. Therefore, since the V2 is most intense and its integrated intensity would be independent of temperature,I7 the total integrated intensity of the 1943 cm-I band should be independent of temperature.
Briefly, the reason the temperature dependence of
the whole band corresponds to that of its most intense component is that the apparent strength of the weaker component comes from the mixing of wavefunctions. The weaker component's absolute strength is usually quite small. Thus, although its real contribution to the band increases with temperature,t7 its absolute strength is never large enough to appreciably change the total intensity.
EFFECTS OF FERMI RESONANCE
Breese, Ferriso, Ludwig, and MalkmusI7 have developed expressions for the temperature dependence of integrated intensity of infrared bands. Their expressions indicate that the integrated intensity is proportional to the product of the centerline wavenumber and the average transition moment of all contributing transitions. Under normal circumstances the ratio of the integrated intensity of a fundamental to that of an overtone is a very large number because the average transition moment of a fundamental is much larger than that of an overtone. However, their expression does not take into account the Fermi resonance of the two vibrations. Fermi resonance causes mixing of the wavefunctions of the two vibrations. The perturbed wavefunctions for the two modes are linear combinations of the unperturbed wavefunctions. Thus, when the transition moment integral is evaluated for each transition, the result will be a linear combination of the transition moments of the unperturbed modes. The transition moment for the fundamental is usually much larger than that for the overtone, with the result that the moment for both the fundamental and the overtone is some fraction of the unperturbed moment of the fundamental. Substitution of the moments thus obtained into the expressions developed by Breese and co-workersl6 yields the following result for the ratio ad ao for the case of Fermi resonance:
(9)
where af = integrated intensity of V2 fundamental, ao = integrated intensity of VI overtone, V2 = centerline wavenumber of V2 fundamental, VI = centerline wavenumber of VI overtone, a2 = average of unperturbed fundamental transition moment retained by perturbed fundamental,62 = average of unperturbed fundamental transition moment contained in perturbed overtone.
Comparison of this result with the experimental results, given by Eqs. (6)-(8), indicates that the mixing ratio, a,2/b2, has its highest values at low temperatures and decays to an asymptote of approximately 1.1. Considering the origin of the quantity a,? /b2 from the transition moments, this is a reasonable result.
The lowest value a,2/b2 could take on would be 1, which correspond to complete 50-50 mixing of all the pairs of wavefunctions. Whereas the highest transitions
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T E M PER A T U RED E PEN DEN CEO F S PEe T R A LIN TEN SIT Y 5679
are between two mixed levels, the amount of mixing should decrease in the higher levels. Thus the average ii,2fb2 should never reach 1 but should decrease to an asymptote greater than one as the higher levels become populated at higher temperatures.
Hertzberg15 and Dennison18 have reported that the amount of mixing of wavefunctions of two states in Fermi resonance depends on both the separation in energies of the two states as they exist in nature and on the separation which could have occurred without resonance. At low temperatures where all transitions are from the ground state, a comparison can be made between their theoretical predictions and the experimental results at 300oK.
Neilson5 has studied the infrared spectrum of COF2 and determined the values of the observed positions of the two transitions and made estimates of the unperturbed positions. When Hertzberg's equations are applied to these results the values of the mixing coefficients are:
a2=0.66 with a range of O.S8~a2~0.74, (10)
b2=O.34 with a range of O.26~b2~0.42. (11)
Since at room temperature the integrated intensity of the 1943 cm-1 band is due primarily to transitions. from the ground state, it is possible to compare the theoretical predictions of a2 and b2 given by Eqs. (10) and (11) to the experimentally determined values of a2
and b2• Equation (9) can be used in conjunction with the experimentally determined values of af=3.14X 107 cm-2 • (moles/cc)-1 and 0'0= 9.0X 106 crri-2 • (moles/ CC)-1 to calculate the numerical values of a2 and b2
at 300oK: a300'K2= 0.777,
b300 'K2 = 0.223.
(12)
(13)
Considering the lack of precise knowledge of the energy
>Iiii z UJ I~
o W I-«
4
3
2
~ _____________ «f_A_P_P_AR_E_NT_~~_
«. APPARENT J
ffi .,O'L-.--L--L. __ ..I-__ l..-_-L. __ ..I-__ l..-_
UJ I;
300500 1000 1500 2000 2500 3000
TEMPERATURE,T,OK
FIG. 6. Apparent contribution of the V2 fundamental and the VI
overtone to the total integrated intensity.
3
I 2
'0 0 0 E
" E 0 0 -
rt 1800 1900 2000
>-I-iii 6 600· K EXPERIMENTAL Z UJ I-~ 5 .J « Q: 4 l-e..> UJ (l. Ul 3
2
.,OS L-._.J........:::;..~ __ --L-______ =~ __ _ 1800 1900 2000
WAVENUMBER ,v,em-' FIG. 7. Predicted spectral intensity for 1000, 1500, 2000, 2500,
3500oK.
levels of COF2, the experimental and theoretical values are in good agreement.
PREDICTION OF THE BAND SHAPE AS A FUNCTION OF TEMPERATURE
Based on the results presented in previous sections of this paper, it is possible to predict the temperature dependence of the spectral intensity of the 1943 cm-1
band of COF2• The total integrated intensity, 0'1943,
of the band is equal to the sum of the apparent contributions from the fundamental band, at. and the overtone band, 0'0. The total integrated intensity is independent of temperature and its numerical value is given by Eq. (1). The ratio of af/ao has also been experimentally determined, and its temperature dependence is shown in Fig~. (5) and is given by Eqs. (6)-(8). These two results can be combined to calculate the temperature dependence of the apparent contributions af and 0'0; these results are shown in Fig. 6.
The temperature dependence of the spectral intensity of the 1943 cm-1 band has been calculated by summing the contributions from both the fundamental and the overtone. The contribution from the fundamental at any temperature was obtained as previously described by multiplying the computer results for the fundamental band shape by the appropriate numerical value of the apparent intensity af. The contribution from the
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5680 ADAMS, WESTON, AND MATULA
overtone at any temperature was obtained by combining its apparent intensity ao with an empirical fit of the overtone band shape. The results of these calculations are shown in Fig. 7.
DISCUSSION OF RESULTS
Both the spectral intensity and total integrated intensity of the 1943 cm-I band of COF2 , which is composed of a fundamental and first overtone band in Fermi resonance, have been experimentally determined in the temperature range 300-600oK. It has been found that the total integrated intensity of this band is independent of temperature and has a numerical value of 4.04±0.08X107 cm-2• (moles/cc)-I. Hopper, Russel, and Overend8 have also studied the 1943 cm-I band of COF2 at room temperatures. Their results are reported in a slightly different form than the present results:
r= - (lInt)! In(Tv)d(lnv), (14) normally
a= - (llnt)J In(Tv)dv, (15)
where r=Hopper's integrated intensity, a=Present integrated intensity n=concentration moleslcc, l= path length, cm, T.=spectral transmission, v=wavenumber, cm-I.
A corresponding value of aHopper can be obtained by multiplying r by the average wavenumber 1943 cm-I. When this is done, aHopper is given as 3.91X107 cm-2 •
(moles/cc)-I. This value is in good agreement with the integrated intensity, reported in the present study. Modica and Brochu9 have reported a room temperature value of a for the 1943 cm-1 band of COF2 which is somewhat higher at 4.8X 107 cm-2• (mole/cc)-I. The present results have shown that even for this Fermi resonant band, that the total integrated intensity is constant in the temperature range 300-600oK.
These experimental results were utilized in conjunction with theoretically determined band shapes,
taking into account the effects of Fermi resonance, to calculate the intensity of this band at higher temperatures.
ACKNOWLEDGMENT
This research was supported by the Air Force Office of Scientific Research under Grant Number AFAFOSR -68-1606.
* Department of Health, Education and Welfare, Air Pollution, Special Fellow (Predoctoral).
t Present Address: Scott Research Laboratories, San Ber-nardino, Calif. 92404.
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(1946). 12 S. S. Penner, Quantitative Molecular Spectroscopy and Gas
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