J . Phys. Chem. 1992, 96,4282-4288
4282
Pressure and Temperature Study of the Isotropic Raman Spectra for the Symmetric A, Vibrational Modes of Liquid Furan Y. T. Lee, S. L. Wallen, and J. Jonas* Department of Chemistry, School of Chemical Sciences, University of Illinois, Urbana, Illinois 61801 (Received: November 18, 1991; In Final Form: January 28, 1992)
The Raman bands of the symmetric AI modes of liquid furan have been measured as a function of temperature (-42.0 to 80.8 "C) and pressure (1 bar to 5 kbar). Line widths and peak frequencies of the isotropic spectra are determined for two C-H bending modes, three ring stretching modes, and two C-H stretching modes. More conclusive evidence concerning these assignments are offered since the three types of vibrational modes have distinctive bandwidth and frequency shift trends in response to increasing temperature and pressure. Although a nonmonotonic temperature dependence of line width is passible according to a model proposed by Strekalov and Burshtein, it is observed that the line widths and frequency shifts of all the modes analyzed show, both under isothermal and isochoric conditions, either definite monotonic trends or no dependence. Furthermore, the experimental line widths are fit very well by the Schweizer-Chandler (SC) model using a parametric fit justified by the soft-core/hard-sphere assumption as suggested by Chesnoy.
I. Introduction In view of the fact that furan is an important and commonly used precursor in many chemical reactions, it has been extensively studied during the last 60 years by various techniques such as IR,Is2 Raman,3 and microwave ~pectroscopy.4~~ These and other earlier studies concentrated on properties such as molecular structure,6 force constant^,^ phase transitions,8 dipole moments9J0 and the assignment of vibrational modes" rather than the molecular dynamics. A comprehensive review covering the vibrational spectroscopy of furan is given by Dollish et a1.I2and the references therein. In our group, one of the goals of high-pressure Raman scattering experiments is to characterize the various vibrational relaxation mechanisms and molecular interactions in the liquid state. In general, this can be achieved by comparing the experimentally determined temperature and density dependences of the Raman line shapes, line widths, and peak shifts to the existing theoretical models such as Kubo stochastic line-shape theory,I3 the isolated binary collision (IBC) model of Fischer and LaubereauI4and the Schweizer-Chandler (SC) m0del.l5 The importance of separating the density and temperature effects on molecular interactions has been proven to be essential to any comprehensive understanding of fluid dynamics.16 In the present work, we analyze the isotropic spectra of seven vibrational modes of liquid furan in the temperature range from -42.0 to 80.8 "C and at pressures up to 5 kbar. This study was motivated by the observation of Oehme et that the line widths of some of the symmetric vibrational modes in liquid furan show
a nonmonotonic temperature dependence which appears to agree with the vibrational dephasing model proposed by Strekalov and Burshtein.ls However, since the work in ref 17 was not performed at constant density, it is necessary to carry out both isothermal and isochoric experiments to demonstrate whether there is any nonmonotonic temperature dependence for the dephasing rate. Although both the original IBC and SC models have been used successfully in explaining the results of some earlier high-pressure Raman work,I5J9 they were later modified to introduce more general assumptions and/or to match other experimental results. For the IBC model, Oxtoby introduced anharmonic effects,20 whereas, for the SC model, Chesnoy2' suggested the model of the soft core/hard sphere rather than making the assumption of a hard core/hard sphere. The results presented here indicate the usefulness of these corrections in applying the SC model. Unfortunately, the IBC and S C models were originally developed for diatomic molecules, and its application to a polyatomic molecule is very difficult due to the necessity of implementing a normalmode analysis. Schweizer and Chandleris performed the normal-mode analysis by neglecting all interbond coupling, which is an acceptable approximation for some molecular fluids. However, due to the ring structure of furan this is not possible. Therefore, a normal-mode analysis was not carried out in simplifying the vibrational modes of furan as a "quasi-diatomic" oscillator. Since the uncertainty arising from this approximation is smaller for the symmetric breathing modes than for the other modes, only the analyzed results of the 1140-cm-I ring breathing mode and 3159-cm-I C-H breathing mode were compared with the theoretical models.
Pickett, L. W. J . Chem. Phys. 1942, 10, 660. Thompson, H. W.; Temple, R. B. Trans. Faraday Soc. 1945, 41, 27. Sidorov, N. K.; Kalashnikova, L. P. Opt. Spectrosc. 1967, 24, 469. Bak, B.; Christensen, D.; Dixon, W. B.; Hansen-Nygaard, L.; Andersen, J. R.; Schottlander, M. J . Mol. Specrrosc. 1962, 9, 124. ( 5 ) Mata, F.; Martin, M. C.; Sorensen, G. 0. J . Mol. Sfruct. 1978, 48,
11. Experimental Section
(1) (2) (3) (4)
157. (6) Liescheski, P. B.; Rankin, D. W. H. J . Mol. Struct. 1989, 196, 1. (7) Scott, D. W. J. Mol. Spectrosc. 1971, 37, 77. (8) Figuiere, P. High Temp.-High Press. 1975, 7 , 395. (9) Marino, G. J . Heterocycl. Chem. 1972, 9, 817. (10) Oh, J. J.; Hillig 11, K. W.; Kuczkowski, R. L.; Bohn, R. K. J . Phys. Chem. 1990, 94,4453. (1 1) Rico, M.; Barrachina, M.; Orza, J. M. J . Mol. Spectrosc. 1967, 24, 133. (12) Dollish, F. R.; Fateley, W. G.; Bentley, F. F. Chorocterisfic Raman Frequencies of Organic Compounds; John Wiley & Sons: New York, 1974; p 217. (13) Kubo, R. Flucfuation, Relaxation, and Resononce in Magnetic Systems; ter Haar, D., Ed.; Plenum Press: New York, 1962. (14) Fischer, S.F.; Laubereau, A. Chem. Phys. Lett. 1975, 35, 6. (15) Schweizer, K. S.; Chandler, D. J . Chem. Phys. 1982, 76, 2296. (16) Jonas, J. Acc. Chem. Res. 1984, 17, 74. (17) Rzanny, V. R.; Oehme, K.-L.; Rudakoff, G.; Holzer, W.; Carius, W.; Schroter, 0. 2. Phys. Chem., (Leipzig) 1988, 269, 496.
The liquid furan sample, used for both density and Raman measurements, was purchased from Fluka Chemical Corp. and according to the manufacturer the purity was greater than 99%. Before the sample cell was loaded, the furan was purified and dried by distillation over N a with benzophenone under a dried nitrogen atmosphere.22 After distillation the sample was stored in a refrigerator to inhibit peroxide formation. The sample was degassed using four freezepumpthaw cycles and then loaded into a small glass insert fitted with a syringe tolerance glass piston. This glass sample cell was then placed into a high-pressure cell and surrounded with n-hexane which acts as a pressurizing med i ~ m The . ~ ~complete details of the high-pressure apparatus are Strekalov, M. L.; Burshtein, A. I. Chem. Phys. Lert. 1982, 86, 295. Schroeder, J.; Schiemann, V. H.; Jonas, J. Mol. Phys. 1977.34, 1501. Oxtoby, D. W. Adu. Chem. Phys. 1979, 40, 1. Chesnoy, J. Chem. Phys. 1984.83, 283. Perrin, D. D.; Armarego, W. L. F. Purification of Laboratory Chemicals, 3rd ed.; Pergamon Press: Oxford, 1988. (18) (19) (20) (21) (22)
0022-365419212096-4282SO3.0010 , 0 1992 American Chemical Society I
,
The Journal of Physical Chemistry, Vol. 96, No. 11, 1992 4283
Raman Spectra of Liquid Furan described in a previous paper by Perry et aLZ4 The spectral region between 2800 and 3000 cm-I was scanned at each pressure to ensure that there was no leakage of hexane back into the insert as the pressure was increased. In the density measurements, the degassed sample was loaded into a bellows which was inserted into a high-pressure densitometer which uses a linear variable differential transformer as a detector. This apparatus has been described in detail elsewhere.25 The excitation was provided by the 488-nm line of a SpectraPhysics Model 2020-05 argon ion laser. The power of the incident beam was 0.6 or 0.9 W depending on the intensity of the signal. The slits of the double monochromator were set to values of 60-120-120-60 pm which correspond to a fwhm of the measurement function of 0.4 cm-'. Each spectra was recorded twice with intervals of 0.2 cm-I and an integration time of 1 s. Temperature and pressure uncertainties for both the Raman and density experiments were k0.2 OC and f5 bar, respectively. For the density measurements, a calibration of the bellows' constant was performed by measuring the length changes of the bellows for methanol at ambient temperature as pressure was increased and fitting the data to the experimental data obtained earlier in our laboratory.z6 The changes of the bellows' length for furan were measured as a function of temperature and pressure. A Tait equation was fitted for each temperature so that densities could be interpolated for use in the interpretation of the Raman results as a function of density. The Raman bands were analyzed using PEAKFIT peak analysis software from Jandel Scientific and all modes were fitted by a Lorentzian band shape. Although the typical Raman spectrum is described by a Voigt profile, the peak position and the full width at half-maximum (fwhm) determined by Lorentzian line shapes result in negligible errors. For those modes which showed some asymmetry, only the half of the line not influenced by overtones, combination bands, or hot bands was used to perform the fitting (Figure 1, A and B). It was not possible to eliminate these effects by a multiple peak fitting since the origins of the side bands were not definitely known. In this paper we are only concerned with the isotropic component of the Raman scattering spectrum and, therefore, we used the standard definition ZISO(4
= Ivv(v)
- 4/J"H(V)
(1)
HI. Results The typical polarized and depolarized Raman spectra of furan a t ambient pressure and room temperature are shown in Figure 1 for the two spectral regions studied. The furan molecule has a planar structure of C, symmetry and 21 fundamental vibrational modes. According to earlier assignments for the furan molecule,1-3J1,27*z* 13 fundamental vibrations belonging to either Al or BI species are located in the regions investigated. In this study, seven modes of the AI t p are analyzed since they have sufficient S/N and minimal overlap. The modes investigated are the inplane deformation modes 6 (CH) at 992 and 1060 cm-'; the ring modes Y (ring) at 1140, 1381, and 1486 cm-I; the symmetric breathing mode v (CH) at 3159 cm-l; and a mode at 3092 cm-I. The 3092-cm-' peak was assigned by Rico et al." as the first overtone of the Y (ring)-B1 fundamental at 1556 cm-l. However, Sidorov et al.3 assigned it to the v (CH)-AI fundamental stretching mode. We prefer the latter assignment based on the discussions in the next section. A. Density. The densities of furan were measured at pressures up to 5 kbar over temperatures ranging from -45 to 100 O C . These equation of state curves are fitted by the Tait equation and the parameters (Table I) are used to calculate the densities for the high-pressure Raman experiments. Since the boiling temperature 23) 24) 25) 26) 27)
Schindler, W.; Zerda, T. W.; Jonas, J. J. Chem. Phys. 1984,81,4306. Perry, S.; Zerda, T. W.; Jonas, J. J . Chem. Phys. 1981, 75, 4214. Akai, J. A., Ph.D. Thesis, University of Illinois, 1977. Jonas, J.; Akai, J. A. J . Chem. Phys. 1973, 58, 4030. Bak, B.; Brodersen, S.; Hansen, L. Acta Chem. Scand. 1955, 9,749. 28) Svcrdlov, L. M.;Kovner, M.A.; Krainov, E. P. Vibrational Spectra 'olyatomic Molecules; John Wiley & Sons: New York, 1974; p 506.
6000
I
5000
-i
4000
I
1
1400
1600
1
h
5
3000 i
2000
1 I
0 1000
1200
Frequency ( c m - ' )
3000
2500
1
1
1
x
e) .d
1500 e)
1000
3100
3000
3200
Frequency
3300
(cm-l)
Figure 1. (A, top) Raman spectra of furan in the region from 900 to 1600 cm-' at room temperature and ambient pressure. Curves I and I1 are the spectra of VV and VH polarizations, respectively. For clarity, curve I has been offset by 1000 counts and curve I1 has been multiplied by 10. (B, bottom) Same as Figure l A , except the spectral region from 3000 to 3300 cm-I is shown. TABLE I: Tait Equation, V = Yo - A * In [l + (P-L / B ) I , Parameters A , B. and L for Furan as a Function of Temwratureo VO, A, T, "C cm3g-' cm3 g-l B, bar L, bar -45.6 -28.2 -10.0 5.2 19.8 27.8 44.4 65.5 85.8 100.2
0.980 1.ooo 1.024 1.046 1.066 1.078 1.075 1.07 1 1.079 1.091
0.013 0.049 0.101 0.111 0.112 0.108 0.1 10 0.1 14 0.110 0.114
128 557 1217 1194 1065 910 1011 1202 1114 1116
0 0 0
0 0 0 215 495 630 690
L is the pressure necessary to liquify furan. of furan is 31.4 OC, the initial pressures for all measurements above this temperature were at least 215 bar. The freezing point of furan is -85.6 OC at 1 bar and is expected to increase at higher pressures. Hence, to avoid freezing the sample which could damage the expensive bellows used, the upper limits of pressure for the lower temperature measurements are 2160 bar for -28.2 OC and 690 bar for -45.6 O C . B. Frequency Shift. The frequency shifts of the peak maxima as a function of density and temperature are shown in Figure 2 for one C-H bending mode (A, 1060 cm-I), one ring stretching mode (B, 1486 cm-I), a mode whose assignment is unsure (C, 3092
4284
The Journal of Physical Chemistry, Vol. 96, No. 11, 1992
Lee et al.
0 6 1
1058 I
1 -
1
I
,
I
1488 I
1486
1484
1
4
1
B '
Bi
1
1
1
1
I
1
1
3092
L
1
3164,
3158 092
I
I
I
,
,
108
112
116
1
096
100
104
-
I
I
6
]
Density (g/cm3)
Figure 2. Isotropic peak frequencies of furan as a function of density and temperature for the (A) 1060-~m-~ mode, (B) 1485-cm-l mode, (C) 3092-cm-l mode, and (D) 3159-cm-' mode. The y-axis is in units of cm-l for each plot. The isothermal curves are for temperatures of 80.8 'C ( O ) , 3.8 'C (0)and -42.0 'C (A).
cm-I), and a symmetric breathing mode (D, 3159 cm-I). In order to clearly illustrate the general trends, we have chosen to show only the highest, the lowest, and an intermediate isothermal curve for each plot. AU curves are fitted by using a linear or second-order polynomial least-squares method. In general, the frequencies increase with increasing density and temperature for all seven modes studied. The pressure effect on frequency shift is determined by the interplay of attractive and repulsive forces exerted on the observed molecule by the surrounding medium. For stretching vibrations, the enhanced repulsive interactions due to the increasing pressure cause a blue shift whereas the increased attractive interactions result in a red shift. The peak frequency of the symmetric breathing mode at 3 159 cm-'(Figure 2D) shows the greatest response to both temperature and pressure. The dv/dp is approximately 20 cm-'/(g cm-') and the peak frequency changes about 2.5 cm-I between -42.0 and 80.8 OC. This is expected for the C-H stretching bonds which experience stronger perturbations due to intermolecular forces than do the internal ring modes. The three ring modes all show similar behavior as the temperature and pressure are increased (Figure 2B). For these modes, the dvldp is only 50% of that in the C-H breathing mode and the peak frequency changes by about 1 cm-I over the temperature range of our experiment. For the two C-H bending modes at 992 and 1060 cm-' (Figure 2A), the responses are similar to the ring modes except that the IMO-cm-' peak has larger frequency changes over the temperature range studied. It is interesting to note that the peak frequency of the 3092-cm-I mode shown in Figure 2C has behavior much closer to that of the C-H breathing mode than to that of either the ring or bending modes. This indicates that the 3092-cm-I peak is possibly due to a C-H stretching mode rather than the first overtone of the fundamental ring mode at 1556 cm-l.ll However, it should be noted that we do not observe sufficient S/Nof the 1556-cm-' Bl fundamental to determine its pressure dependence. Similar ev-
092
096
100
104
108
112
116
Density ( g / c m 3 )
Figure 3. Density and temperature dependence of the isotropic bandwidths for the (A) lMO-cm-' mode, (B) 1485-cm-l mode, (C) 3092-cm-' mode, and (D) 3159-cm-' mode. The isothermal curves are for temperatures of 80.8 OC ( O ) , 44.8 'C (0),3.8 OC (0),and -42.0 'C (A). The y-axis for each plot is the fwhm in units of cm-'.
idence can also be observed in the line-width data as discussed below. C. Isotropic Line Width. The density and temperature dependences of the fwhm are given in Figure 3 in the same order as the representative plots for the frequency shifts (A-D). The solid lines in each plot are the results of first-order least-squares fits. The general trend, for all seven modes analyzed, is that the bandwidths are broadened as temperature and pressure are increased. As discussed above for the frequency shifts, the bandwidth data can be grouped according to the type of vibration the mode belongs to, namely, the symmetric C-H breathing mode, the ring stretching modes and the C-H bending modes (Table 11). The symmetric breathing mode at 3159 cm-' (Figure 3D) is the mode whose bandwidth is most affected by both temperature and pressure. The dI'/dp for this mode is 27 cm-'/(g cm-') while the slopes for the bending modes are about 15 cm-'/(g cm-') (Figure 3A). The slopes of the ring modes are approximately 11 cm-'/(g cm-') for the 1486-cm-I band, 9 cm-'/(g cm-') for the 1140-cm-l band, and 4 cm-l/(g ~ m - for ~ ) the 1381-cm-' band (Figure 3B). The slope of the peak at 3092 cm-' is 13 cm-l/(g ~ m - (Figure ~) 3C) which is larger than the values obtained for all the ring modes. It is of interest to note that the temperature-induced band broadening for the different types of modes also distinguishes between them (Table 11). At constant density two of the ring modes (1 140 and 1381 cm-l) are broadened by only about 0.6 cm-I over the temperature range studied, while the bandwidth of the 1486-cm-I band is temperature independent within the experimental uncertainty (Figure 3B). For the two bending modes, it is observed that significant line-width broadening occurs with increasing temperature, above furan's boiling temperature, which is about 0.8 and 1.5 cm-I, from 44.8 to 80.8 OC, for the 992- and 1060-cm-' peaks, respectively. At the boiling temperature and below, the line broadening due to the temperature is negligible for these bands. The strongest temperature line broadening effect
The Journal of Physical Chemistry, Vol. 96, No. 11, 1992 4285
Raman Spectra of Liquid Furan
1 0 ,
TABLE II: Line Widths of All Modes Studied, at 44.4 O C , and the Approximate Values for the Slopes of the Line Width versus Density, dr/dp, and the Isoharic Line-Width Changes over the Whole Temperature Range Studied at a Density of 1.04 g/cm3, A P modes dr/dp Ar'
bending
ring
C-H stretch
15 0.8-1.5
511 50.6
13 2.5
p,
992
1060
1140
1381
1486
3092
3159
cm-'
cm-l
cm-l
cm-'
cm-l
cm-l
cm-l
4.1
5.5 5.8
1.9 2.0 2.2
1.7 1.9
5.7
8.1
5.0
6.5
6.:
3.8 2.1 2.1
-0.6
10.1
4.0 -0
2.7 3.0
7.5 7.6 7.9 8.1
6.6 7.2
8.2 8.4
2.4 2.4 2.2 2.6
3.1 3.1 3.6
2.4 2.5
3.3
2.7
a
, 096
7.0
6.4
i
attractive
6.5
6.9 7.1
I
i
h
3.6 6.9
5.5
I
3.3
2.3 5.3
,
27 3
g/cm3 0.942 0.951 0.968 0.990 0.992 1.016 1.018 1.020 1.041 1.042 1.060 1.063 1.078 1.080 1.082 1.093 1.111 1,120 1.122
,
100
104
108
112
Density (g/cm3)
4.3 4.6 7.5
10.9
7.6
11.6
5.1 5.1
12.0 12.7 8.1
12.9
"dI'/dp and A r are in the units of cm-l/(g ~ m - and ~ ) cm-I, respectively.
is seen for the 3 159-cm-l band, which broadens by about 3 cm-I over the temperature range studied. The fwhm of the 3092-cm-I mode is broadened by 2.5 cm-I between 4 2 . 0 and 80.8 "C, which is much larger than the temperature broadening for all three ring modes. This also indicates that the 3092-cm-l peak should probably be assigned to a C-H stretching mode rather than to the first overtone of the fundamental ring mode at 1556 cm-l.
IV. Discussion For two of the seven modes investigated (1 140 and 3 159 cm-l), we performed a thorough analysis to compare the experimental data with the existing theoretical models. The theoretical models proposed thus far are developed for hard-core/hard-sphere diatomic molecules. Therefore, a major problem in applying the theoretical models is how to describe the modes of a polyatomic molecule as the mode of a quasi-diatomic. We chose to analyze the 1140-cm-' ring breathing mode and the 3159-cm-l C-H stretching mode of furan since the totally symmetric ring breathing modes of aromatic molecules such as benzene, pyridine and toluene have been approximated by the quasi-diatomic formula29and the symmetric C-H stretching mode can be treated as a heteronuclear diatomic.30 In calculating either the frequency shifts or the line widths, it is necessary to know the effective hard-sphere diameter, uf, of the furan molecule. This quantity is estimated by fitting the measured equation of state to the modified Carnahan-Starling formula.31 In liquids, the effective hard-sphere diameter generally decreases with increasing temperature due to the fact that as the temperature is increased, the molecules have higher kinetic energies which allow them to approach each other more closely. For furan, at temperatures higher than 0 "C, duf/dT z -2 X lo4 A/K and uf 4.828 A at 3.8 OC which are the same order of magnitude as those of other organic l i q ~ i d s . ~The ' effective diameter of the quasidiatomic oscillator is not readily available for the furan molecule. Therefore, we use the value of similar quasi-diatomics for aromatic compounds (3.3 A for the 1140-cm-l mode and 3.0 A for the 3159-cm-I mode) as given by Zakin and H e r ~ c h b a c h . ~ ~ " ~
Figure 4. Experimentally observed (Au/u0), repulsive (AvR/vo), and attractive (AvA/uo) frequency shifts of the 1140-cm-l band as a function of density and temperature. AuR/v0 data and AvA/vo data are fitted by second- and first-order polynomials, respectively.
A. Frequency Shifts. In the SC model, the pressure-induced frequency shifts and line-width broadening are considered simultaneously. According to this model, the measured frequency shift (Av)is composed of the frequency shifts due to the repulsive (AvR) and attractive (AYA) forces and given by AV = AvR + AuA
(2)
The interplay between the attractive and repulsive forces determines whether Av is positive or negative. The repulsive frequency shift was derived15 as
where the anharmonic force constant, g, can be estimated by Badger's rule,33w is the reduced mass of the oscillator with frequency v, L is the characteristic range parameter for the repulsive interaction and can be estimated by ~/23.3,~O where u is the average hard-sphere diameter of furan and the quasi-diatomic oscil1at0r.l~The force induced along the bond axis by surrounding molecules, FR, is determined by the derivative of the two-pint cavity distribution function, yb, at the equilibrium bond length r with FR = -kT(6 In yhs/6r)and (4) The coefficients, a,,, which have been calculated by Pratt et al.,34 are functions of the reduced density, pr = p p f ' . The shift due to the attractive forces, AvA, can then be calculated by subtracting AvR from the experimentally observed shift, Av. On the basis of the SC model, Zakin and H e r ~ c h b a c hproposed ~~ a more readily computable formula for AuR as a function of the reduced density, PI:
AYR/AVO= CI ~ x P ( ~ I P+, )c2 exp(m2pr) - c3 exp(m3pr)
(5)
where the coefficients, c, and m, are defined in the original paper and can be determined from the molecular properties of the interacting molecules. The density dependence of Au, AvR, and AvA for the ring breathing mode and C-H breathing mode are shown in Figures 4 and 5 , respectively. It is found that frequency shifts due to the attractive forces are as important as those due to the repulsive
~
(29) Zakin,
M.R.; Herschbach, D. R. J . Chem. Phys. 1986, 85, 2376.
(30) Zerda, T. W.; Thomas, H. D.; Bradley, M.; Jonas, J. J. Chem. Phys.
1987, 86, 3219.
(31) Ben-Amotz, D.; Herschbach, D. R. J . Chem. Phys. 1990, 94, 1038.
(32) Zakin, M. R.; Herschbach, D. R. J . Chem. Phys. 1988, 89, 2380. (33) Herschbach, D. R.;Laurie, V. W. J . Chem. Phys. 1961, 35, 458. (34) Pratt, L. R.; Hsu, C. S.;Chandler, D. J . Chem. Phys. 1978,68,4202.
4286 The Journal of Physical Chemistry, Vol. 96, No. 11, 1992
4
I:
4
x
00
23
-051
h h
i: bp
attractive
-10
Lee et al.
where T ~ is C the time between collisions and is approximately related to the Enskog collision time by T~~ = ( 2 / 3 ) ~ $ and ~~~ yo are in units of cm-I. A is a function of the reduced mass of the oscillator ( p ) , the reduced mass of the two colliding molecules (p') and the mass ratios (yA and yB),whereas B is also a function of these four quantities as well as the harmonic and anharmonic force constants and the interaction length. For more detail we refer the reader to the original reference since it contains succinct definitions of all the terms in the above equations.20 Although the repulsive interactions are usually the dominant forces in liquids, the interactions due to attractive forces and the vibration-rotation coupling can play an important role as demonstrated by Schweizer and Chandler.15 Consequently, in the S C model, the line width has three components, the repulsive (rR), the coupling (rVR), and the attractive (FA)terms, which have the following forms:
9
-1.5
096
100
104
108
112
116
Density (g/cm3)
Figure 5. Experimentally observed (Av/uo), repulsive (AvR/vO),and attractive (AuJvo) frequency shifts of the 3159-cm-l band as a function of density and temperature. A a / v o data and AVJIJOdata are again fitted by second- and first-order polynomials, respectively.
808C
0
where line widths and frequencies are in units of cm-l. The harmonic force constant,f, has been calculated for furan by Soott,' r is the diatomic bond length, X = [l - ( r / 2 ~ ) ~ ] / 2 [ 1 (r/2u)],l5 K is the isothermal compressibility which can be calculated from the measured equation of state and N is the average number of nearest neighbors. It should be noted that, when comparing the above equations with those from earlier references, different symbols are used for the anharmonic force constant. We chose the convention used by Zakin and Herschbach (Le., g),29whereas in ref 20 it is represented byfand refs 30 and 15 it is represented by K. These different symbols are related to each other by the equation, K =f/6 = g/2. The angular momentum relaxation time, TJ, is approximated by ~ T Ewhere , y is an adjustable parameter. The hard-sphere Enskog collision rate T ~ - I is given by
+
I
-2 2 1 -004
I
1
-002
000
002
,
1
1
004
006
008
Log(reduced density)
Figure 6. Relative attractive frequency shifts of the 3159-cm-l band (-AvA/vo) versus the reduced density (p,) in a logarithmic scale illustrating the temperature dependence and the nonlinear density dependence. The straight lines are the results of linear least-squares fits.
where g(u) is the contact value of the radial distribution function for two interacting molecules.ls In the present study of furan, the theoretical line widths according to eqs 7-9 show weaker pressure dependence compared forces and, for both modes, IAvR/uO~ and IAvA/vO~ increase with to the observed line widths. Oksengorn et al.35 have noted in increasing temperature density. In the SC model, PYA is assumed to be linearly proportional to the density. Zakh and H e r s c h b a ~ h ~ ~ Raman studies of compressed liquid nitrogen that the density dependence of the repulsive term in the SC model is too weak to have investigated 10 different molecular liquids and found that fit the isotherms of line width measured and, hence, they applied for quasi-diatomic C-H or 0-H stretching vibrations deviations a modified model which was introduced by Chesnoy.21 Chesnoy from a linear dependence occur. They demonstrate that a powgeneralized the contact value of the radial distribution function, er-law dependence, of the form AuA/uO = with exponents g(u), from the hard-core/hard-sphere model to a soft-core/ SA = 2.1 f 0.3, represents the experiment data quite well. Our hard-sphere model and found that g(u) can have a much stronger results for liquid furan indicate that AUA/UOof the C-H breathing density dependence in the soft-core model than in the hard-core mode also follows this exponential dependence with SA = 2.22, model. The degree of deviation depends on the ratio R*/u, where 2.09, and 1.89 at T = 80.8,3.8, and -42.0 OC, repectively (Figure the critical distance, R*, is generally smaller than the effective 6). diameter, u. The larger the ratio, R*/u, the smaller the deviation. B. Line Width. Two of the most frequently used models to In applying Chesnoy's modification, it is necessary to know the describe mechanisms of liquid dephasing are the isolated binary values of the intermolecular interaction parameters in both the collision model (IBC) of Fischer and Laubereau and the liquid and gas phases. Without knowing g(u) for furan in the Schweim-chandler (SC) model. The original IBC model treated gas phase, we prefer to compare our line-width data to the SC the diatomic molecule as a harmonic oscillator and assumed that model by introducing a parameter, S,, into the fitting equation: vibrational dephasing arises exclusively from the harsh repulsive r = (SJR+ rVR) @ (FA). The parameter, S,,corresponds to interactions between molecules. This model was later generalized a strengthening of the density dependence for the repulsive term by Oxtoby20 to include effects due to anharmonicity. As shown in the S C model and is justified in light of Chesnoy's correction. by Oxtoby, the dephasing rate of nitrogen in a 'harmonic" model can be 30 times smaller than that in an 'anharmonic" model. In the anharmonic IBC model, the line width due to the vibrational (35) Oksengorn, B.; Fabre, D.; Lavorel, B.; Saint-Loup, R.; Berger, H. J . Chem. Phys. 1991, 94, 1114. dephasing is given by
The Journal of Physical Chemistry, Vol. 96, No. 11, 1992 4231
Raman Spectra of Liquid Furan 4 1
I
1
I
m
.
I
1
I
a
TABLE IIk (A) Fwhm of the 3 1 5 9 - c d Mode Calculated by the IBC Model (rIac) a d the SC Model (rRK.) (B)Fwhm of the 1140-cm-I Mode with the Same Description as (A)
T, -42.0 3.8
- 1O
0.96
1.00
1.04
1.08
1 312
80.8
Density (g/cm3)
Figure 7. Observed line width ( 0 ) and the line widths due to the recontripulsive (0),attractive (A)and vibration-rotation coupling (0) butions of the 1140-cm-l band as a function of density at 80.8 'C. The fitted data of the modified SC model are shown (0). The straight lines are the results of linear fits and are included to illustrate the density dependences of the different contributions.
dcm' rlsc rRSC* roes s, (A) Fwhm of the 3159-cm-' Mode 1.035 18.9 7.6 7.8 2.10 1.046 19.6 7.9 8.3 1.052 20.0 8.1 8.4 0.958 18.6 6.3 7.5 1.76 0.996 21.3 7.2 8.9 1.024 23.4 7.9 9.2 8.0 9.3 1.026 23.6 1.048 25.6 8.6 9.5 1.068 27.5 9.3 10.3 1.100 31.0 10.5 11.2 1.122 33.8 11.4 12.1 1.134 35.3 11.9 13.1 1.145 36.9 12.5 13.0 1.158 38.9 13.1 13.4 0.943 25.1 6.9 9.0 1.45 0.978 28.3 7.8 9.6 1.003 30.9 8.5 10.2 1.026 33.4 9.3 11.0 1.042 35.4 9.8 11.2 1.076 40.1 11.1 12.5 1.088 41.9 11.6 15.5
A
,
I
I
-42.0
24.8
i
4 1
80.8
-2
1.016 1.019 1.021 1.032 1.036 1.046 0.932 0.960 0.982 1.004 1.012 1.056 1.122 1.124 0.943 0.947 0.982 1.009 1.055 1.074 1.088 1.105
1 096
100
1 a4
io8
112
Density (g/cm3)
F i p e 8. Observed line width (0)and the line widths due to the repulsive (0),attractive (A)and vibration-rotation coupling ( 0 )contributions of the 3159-cm-' band as a function of density at 80.8 'C. The fitted data of the modified SC model are also shown (0).The straight lines are the results of linear fits and are included to illustrate the density dependences of the different contributions.
The symbol @ indicates the convolution of the Lorentzian term (SJR r V R )with the Gaussian term (FA). The analytical approximations used here in computing the line width of the Voigt function, €', were developed by KielkopP6 and N e ~ m a n . ~ ' The line-width fitting results for the 1140-cm-' ring and 3159-cm-' C-H breathing modes at a temperature of 80.8 OC are shown in Figures 7 and 8, respectively. The fitting results for three different temperatures are listed in Table 111. Also shown in Table I11 are the line widths calculated by the IBC model, rIBc, and the experimentally observed line widths, rOBS. First of all, it is not surprising that rIac for the 3159-cm-' mode is larger than the roes.The IBC model usually overestimates the dephasing rate due to its basic assumptionsm and this overestimation becomes even larger when one includes the soft-core modification. The decreasing contribution from the coupling term ( P R ) with decreasing temperatures is also expected, since at lower temperatures the time scale of rotational motions become longer than that of
+
(36) Kielkopf, J. F. J. Opt. Soc. Am. 1973, 63, 987. (37) Neuman, M.N. Speclrochim. Acta A 1985, 41, 1163.
-0 0.93
1.26
(B) Fwhm of the 1140-cm-l Mode ~
I
Y
2.5 2.6 2.6 2.7 2.7 2.8 2.7 3.0 3.2 3.5 3.6 4.2 5.4 5.5 3.6 3.8 4.1 4.6 5.4 5.8 6.1 6.5
2.1 2.1 2.1 2.2 2.2 2.3 1.7 1.8 2.0 2.1 2.2 2.6 3.3 3.3 1.9 2.0 2.2 2.4 2.8 3.1 3.2 3.4
2.1 2.1 2.1 2.2 2.3 2.4 1.8 1.9 2.1 2.2 2.3 2.8 3.3 3.3 2.1 2.3 2.4 2.5 3.0 3.1 3.3 3.6
~~
4.17
-0
3.12
0.41
2.72
1.97
OrRSC. is the repulsive part of the bandwidth modified by the softcore correction factor, S,. roes is the observed experimental bandwidth. y is the adjustable parameter for the band broadening due to the vibration-rotation coupling. All line widths are in the units of cm-I.
the vibrational motions which means that less coupling will o a r . In fact, at lower temperatures the vibration-rotation coupling should be insignificant, in agreement with the results obtained here. The values of S,indicate that the ring mode requires a larger soft-core correction than the C-H breathing mode does; however, it is not clear whether this is due to intrinsic properties of the modes or to the uncertainties arising from the 'quasi-diatomic" a p proximation. The values of S,appear to imply that Chesnoy's correction is more important at lower temperatures than at higher temperatures and the ratio R * / u becomes smaller at the lower temperatures. Although both R* and u will increase with decreasing temperature, it seems that u, which is more related to the external environment should be more sensitive to the temperature variation than R*, which is, on the other hand, more related to the hard inner core and, consequently, R * / u decreases with decreasing temperature. Oksengom et also found that the ratio R*/u increases strongly with increasing temperature for compressed liquid nitrogen between its boiling and critical temperatures. Strekalov and Burshtein have developed a model predicting a nonmonotonic temperature dependence of line width in the
J. Phys. Chem. 1992, 96, 4288-4294
4288
framework of a two-body collision picture.'* Aechtner et al.38 observed a nonmonotonic temperature dependence of the dephasing time for the v 1 mode of CS2 in the pressure range from 1 bar to 4 kbar and a temperature range of 160-450 K. Oehme et ala" observed a nonmonotonic temperature dependence of the line width for furan over a large temperature range and we were able to reproduce their data at ambient pressure up to the boiling temperature. However, it is not clear from their experimental description whether the line widths were recorded at constant pressure or even exclusively in the liquid phase. In our pressure experiments, a nonmonotonic temperature dependence at constant pressure is not observed for any of the modes in the temperature range studied except for the 3092-an-' peak. At constant pressure, the 3092-cm-l band first narrows and then begins to broaden a t the end of the density range studied. However, at constant density which is required in the Strekalov and Burshtein theory,I8 all of the modes studied showed monotonic temperature dependencies within the experimental error. Furthermore, our data indicate that the linewidth narrowing observed by Oehme et al.I7 as the temperature was increased to room temperature is caused mainly by density changes rather than being attributable solely to temperature effects.
V. Conclusions In this work, our discussions included three basic topics concerning liquid furan, namely, the temperature and pressure responses of various vibrational modes in terms of their line widths and peak maxima, the temperature dependence of isotropic line widths and the vibrational dephasing mechanisms interpreted by the modified Schweizer-Chandler model. It was found that the line widths and frequency shifts of all the modes analyzed show definite monotonic trends along either isotherms or iscchores, but (38) Aechtner, P.; Fickenscher, M.; Laubereau, A. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 399.
with varying degrees. Among the three different types of vibrational modes studied we observe that the C-H stretching modes have the strongest temperature and pressure responses, followed by the bending modes and the ring modes. On the basis of these phenomenologicalobservations, we expect that the 3092-an-' peak, which was previously assigned as an overtone of the 1556-cm-l ring vibration, is instead a fundamental C-H stretching vibration. From the density dependence of the frequency shifts for the C-H breathing mode at 3159 cm-l, our results showed that the behavior of this mode in furan is similar to those of other organic liquids.32 This implies that, in liquid furan, the repulsive and attractive frequency shifts are also dominated by packing effects rather than by the intermolecular potential. The IBC model modified by anharmonic effects overestimates the line width due to vibrational dephasing. The original Schweizer-Chandler model also failed to describe the density and temperature dependences of our measured line widths. However, the SC model with a parametric correction can be used to fit our data quite well and resulted in two main qualitative results. First, the vibration-rotation coupling contribution to the line-width broadening decreases with decreasing temperature. Second, the necessity of including the soft-core correction is more important at the lower temperatures due to the different temperature responses of the critical diameter and the effective diameter of the furan molecule. In addition to the vibrational dephasing, the temperature and pressure dependences of the depolarized Rayleigh and Raman spectra would also be useful in providing information about the molecular interactions, such as the reorientational and collision-induced effects, in liquid furan. This will be discussed elsewhere in the near future.
Acknowledgment. This work was supported in part by the National Science Foundation under grant N S F C H E 90- 17649. We express our thanks to Professor K.-L. Oehme for suggesting the high-pressure study of liquid furan. Registry No. Furan, 110-00-9.
Matrix Isolation Study of the Reaction of B,H, with CH,OH: Spectroscopic Characterizatlon of Methoxyborane, H,B =OCH, John D. Carpenter and Bruce S. Ault* Department of Chemistry, University of Cincinnati, Cincinnati, Ohio 45221 (Received: November 18, 1991; I n Final Form: February 4, 1992)
Merged jet copyrolysis of mixtures of Ar/B2H6and Ar/CH30H followed by trapping into a cryogenic matrix has led to the formation, isolation, and characterization of methoxyborane, H2B--VCH3. The same product was observed in lesser yield following merged jet copyrolysis of B2H6 and (CH3)20;ethoxyborane was detected following copyrolysis of mixtures of B2H6and CzHSOHin argon. Of the 18 fundamentals of methoxyborane, 17 were observed, including the boron-oxygen stretch at 1358 cm-l ("B). The position of this mode, compared to a range of known compounds, suggests considerable double bond character in methoxyborane. Additional products were detected at higher pyrolysis temperature and higher relative methanol concentration, including methane, boroxin, and dimethyl ether. These observations collectively lead to an overall mechanism for the reaction of B2H6with CH30H.
(1) Stock, A.; Massenez, C. Chem. Ber. 1912, 45, 3539.
(2)
Muetterties, E. Boron Hydride Chemistry; Academic Press: New
York, 1975. (3) Lane, C. F. Chem. Rev. 1976, 76, 773.
(4) Hirayama, M.; Shohno, K. J . Electrochem. SOC. 1975, 122, 1671. ( 5 ) Hyder, S. B.; Yep, T. 0. J . Electrochem. SOC.1976, 123, 1721. (6) A d a m , A. C.; Capio, C. D. J . Electrochem. SOC.1980, 127, 399. (7) Carpenter, J. D.; Ault, B. S. J . Phys. Chem. 1991, 95, 3502.
0022-365419212096-4288%03.00/0 0 1992 American Chemical Society
