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Phase shift cavity ring down and FT-VIS measurements of C–H (Δv = 5) vibrational overtone absorptions
Chemical Physics Letters 394 (2004) 25–31 www.elsevier.com/locate/cplett
Phase shift cavity ring down and FT-VIS measurements of C–H (Dv = 5) vibrational overtone absorptions Ernest K. Lewis, Craig J. Moehnke, Carlos E. Manzanares
*
Department of Chemistry and Biochemistry, 2nd floor, Office E-216, Sciences Building, Baylor University, 101 Bagby Ave., Waco, TX 76798, USA Received 12 May 2004; in final form 15 June 2004 Available online 20 July 2004
Abstract The integrated absorption bands for the C–H stretching overtones (Dv = 5) of C2H4, C2H6, C3H8, C4H10, HC(CH3)3, and C(CH3)4 have been measured at 295 K between 13 000 and 14 300 cm1, using the phase shift cavity ring down (PS-CRD) technique. Similar absorption bands have been obtained using a White cell with an optical path length of 6.0 m and a Fourier transform spectrophotometer operating in the visible (FT-VIS) region. The integrated intensity and the linearity of the absorption with the density of the gas are independent of the form of modulation of the laser (square or sine wave) using the PS-CRD technique. The oscillator strengths calculated with the two techniques are in excellent agreement. 2004 Elsevier B.V. All rights reserved.
1. Introduction The phase shift cavity ring down (PS-CRD) technique was originally used by Herbelin et al. [1] to measure mirror reflectivities. In 1996, Engeln et al. [2] used for the first time the same method to obtain an electronic transition of O2 in the visible region. In 2001, we used this technique [3] to measure the fifth (Dv = 6) C–H overtone spectra of hydrocarbons. The conventional cavity ring down technique (CRD) has its origin in the work of Anderson et al. [4] to measure mirror reflectivities and the work of OÕKeefe and Deacon [5] which used the CRD technique as a spectroscopic method for absorption measurements. Since then, the CRD technique and its variations like cavity enhanced absorption, have been used in many spectroscopic and kinetic measurements [6,7]. The CRD technique has been used to measure absolute cross sections and high vibrational overtone absorptions of HCN [8], HCCH [9,10], CHF3 [11], N2O *
Corresponding author. Fax: +1-254-710-2403. E-mail address: [email protected] (C.E. Manzanares). 0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.06.102
[12,13], H2O [14], OH [15], and C6H6 [16] and hydrocarbons [17]. In [17] the authors used the CRD technique to measure the Dv = 6, C–H overtone spectra of propane, butane, and 2,2-dimethylpropane and calculated the integrated intensities, oscillator strengths, and cross sections of the transitions. For propane and butane the cross sections in [17] were 25–30% higher in magnitude than our measurements [3]. The authors [17] recognized the high sensitivity of the PS-CRD technique and also pointed out two important questions related to the use of the technique; mainly, the form of modulation (square vs sine wave) of the laser and the linearity of the integrated bands with pressure. In this Letter, we investigate the two questions presented in [17] in relation to the PS-CRD technique. The absorption coefficients and integrated absorptions were measured for the (Dv = 5) C–H stretching overtones of C2H4, C2H6, C3H8, C4H10, HC(CH3)3 and C(CH3)4. The bands obtained with the PS-CRD technique are compared with absorption bands of the same molecules obtained using a White cell with an optical path length of 6.0 m and a Fourier transform spectrophotometer in the visible region.
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2. Experimental The pump laser is a solid state, frequency doubled Nd:YVO4 laser (Coherent-Verdi) providing single wavelength (532 nm) at a power level of 5 W. This laser is used to pump a continuous wave (Coherent 899-01) Ti:Sapphire ring laser. The output of the Ti:Sapphire laser (between 13 000 and 14 300 cm1) is passed through an electro-optic modulator (EOM). The modulated output (square or sine wave) of the laser is coupled into an optical cavity (43 cm) which consists of two highly reflective mirrors. The mirrors of quoted reflectivity 99.995% have a diameter of 20.32 mm and a radius of curvature r = 6 m. With the vacuum system that we had at the time of the experiments, the highest measured reflectivity of the mirrors was 99.977%. The signal is detected by a photomultiplier which is located behind the cavity. The signal is amplified and connected to a lock-in amplifier (Stanford SR 830). The zero phase shift is obtained by bypassing the cavity. The lock-in amplifier measures the amplitude and the phase difference between the signal passing through the cavity and the signal obtained by bypassing the cavity. The phase shift of the empty cavity is around 45 with an angular modulation frequency, X = (2p · 25) kHz. The reference signal for the lock-in amplifier is obtained from a function generator which also supplies the modulation signal to the driver input of the EOM. We use LabVIEW programs to control the data acquisition. Absolute calibration of the laser lines was achieved obtaining the optogalvanic spectrum of a hollow cathode lamp filled with neon [18]. A Thermo Nicolet Fourier Transform Spectrometer (Nexus 670) was used to observe the Dv = 5 vibrational transitions in the visible region at (22 ± 2) C. The spectra were recorded at 2 cm1 resolution in the range of 12 800–14 400 cm1, using a 6.0-m optical path length cell with quartz windows. An average of 100 scans was taken. Samples of C2H6 (99%), C3H8 (98%), and HC(CH3)3 (99%) were obtained from Aldrich, C2H4 (99.9%) and n-C4H10 (99.98%) were from Matheson, and C(CH3)4 (99%) was from AGA specialty gases.
Fig. 1. (Top) Phase shift cavity ring down absorption spectra of the Dv = 5 (C–H) overtone of gaseous C(CH3)4 as a function of the wavenumber (cm1) and the pressure (Torr) at 295 K. (Bottom) Variation of the integrated absorption (S) as a function of the density (q) of C(CH3)4. High density points (j) are from FT-VIS spectra. Low density points (inset) are from PS-CRD spectra. For low density points (h) indicates square wave modulation and (d) indicates sine wave modulation.
3. Results The spectra of the Dv = 5 (C–H) absorption of C(CH3)4 are shown in Fig. 1. The spectra (top) show the absorption (cm1) on the vertical axis as a function of the wavenumber (cm1) and the pressure of the gas (Torr). The variation of the integrated absorption intensity (S) as a function of the density (q) is shown in the bottom part of Fig. 1. The dark square (j) points with density above 20 · 1018 molecules cm3 are from FTVIS measurements. For densities below 5 · 1018 molecules cm3 the points are from PS-CRD measurements. Details for points at low densities are shown in the inset.
The open squares (h) are from bands obtained using square wave modulation of the laser and the dark circles (d) are from bands obtained using sine wave modulation of the laser. The PS-CRD spectra of the Dv = 5 (C–H) absorption of C2H4, C2H6, and C3H8 (deconvoluted) are shown in Fig. 2 and the deconvoluted spectra of C4H10 and HC(CH3)3 are shown in Fig. 3. The (Dv = 5) C–H bands have been assigned previously [19–22]. The single bands on Fig. 2 (top) correspond to C2H6 and C2H4 centered at 13 490 and 14 080 cm1, respectively. Fig. 2 (bottom) shows the spectrum of propane (CH3–CH2–CH3) deconvoluted into three main
E.K. Lewis et al. / Chemical Physics Letters 394 (2004) 25–31
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Fig. 3. Phase shift cavity ring down absorption spectra of the Dv = 5 (C–H) vibrational overtone of gaseous n-C4H10 (105 Torr), and HC(CH3)3 (100 Torr) at 295 K. Fig. 2. Phase shift cavity ring down absorption spectra of the Dv = 5 (C–H) vibrational overtone of gaseous C2H6 (50 Torr), C2H4 (50 Torr) and C3H8 (100 Torr) at 295 K.
bands. The lowest energy band corresponds to the –CH2 absorption (Hm). The band in the middle corresponds to methyl out-of-plane CH bonds (Ha) and the highest energy band corresponds to the in-plane C–H bonds (Hs). The deconvoluted spectrum of n-butane is shown Fig. 3 (top). The spectrum of methyl propane (HC(CH3)3) shown in Fig. 3 (bottom) was deconvoluted into three main bands in which the lowest energy band corresponds to the single H–C bond (Ht), the intermediate energy band corresponds to the C–H bonds (Hs) trans to C–H and the highest energy C–H bonds (Ha) trans to C–C following the rule [21,22] that C–H bonds trans to C–C bonds are higher in energy than those trans to C–H bonds.
4. Discussion The phase shift (/) of the modulated beam that emerges from the optical cavity relative to the modulated input beam is related to the time that the light spends in the cavity or ring-down time (s) by the equation: tan/ = xs, where x is the angular modulation frequency.
For a cavity filled with an absorbing gas under conditions where the Beer–Lambert law is valid, the ringdown time is: sðmÞ ¼
‘ : c½ð1 RÞ þ aðmÞ‘
ð1Þ
The lifetime is related to the reflectivity of the mirrors (R), the speed of light (c), the absorption coefficient (a) of the sample and the length (‘) of the optical cavity. The absorption spectrum of the background or empty cavity; [s0(m)c]1 = [(1R)/‘], is subtracted from the absorption spectrum of the sample plus the background [s(m)c]1 in order to obtain the absorption of the sample. The integrated absorption (S), the band strength (S0), and the oscillator strength (f) of the vibrational overtones were obtained using the following relations: The integrated absorption (S) in units of (cm2) is S = a(m) dm. The band strength (S0) in units of (cm2 cm1 moleecule1) was obtained from the slope of a plot of the integrated absorption S versus the density of the gas (q) in units of molecules cm3. Linear plots of integrated absorptions S versus the density of the gas (q) for C2H6, C3H8, C4H10, C2H4, and HC(CH3)3 are shown in Fig. 4. The dimensionless oscillator strength (f) is defined as
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E.K. Lewis et al. / Chemical Physics Letters 394 (2004) 25–31
Fig. 4. Variation of the integrated absorption (S) as a function of the density (q) of n-C4H10, C3H8, C2H6, HC(CH3)3 and C2H4.
f ¼
4 102 e0 mc2 S 0 ¼ 1:1296 1012 S 0 ; e2
ð2Þ
where e0 is the permittivity of free space, m and e are the mass and charge of the electron, and c is the speed of light. All constants are in SI units. The results of these calculations were compared with similar results obtained using FT-VIS absorption measurements from our laboratory. In this case the band strength (S0) was obtained from a plot of the integrated absorbance (A(v) dv) multiplied by 2.303 and divided by the optical path length of the cell (d = 600 cm) as a function of the density of molecules. For each molecule, the band centers, assignments, full width at half maximum (fwhm) and oscillator strengths are summarized in Table 1. The calculated oscillator strengths from PS-CRD and FT-VIS measurements for the same bands are within 1–3% of each other as shown in Table 1. Note that the (PS-CRD) integrated bands that are reported in this Letter, were obtained with square wave modulation of the laser. The results presented in Fig. 1 (bottom) show the maximum dispersion between the points (open squares and dark circles) that we were able to obtain by doing the experiments in different weeks. For a given week we used square modulation only and the alignment
of the system, the laser power, and the sample pressures were different from the week where sine modulation was used. It is clear that no appreciable difference was observed between results using square or sine modulation. Figs. 1 and 4 show that the integrated absorption is linear over the range of densities covered. In fact, Fig. 1 (bottom) shows that the linearity is extended to results obtained with a different technique (FT-VIS) at high densities. In Table 1, the oscillator strengths are also compared with literature values using FT-VIS with a White cell from Quack and co-workers and Laser Photoacoustic (LPA) from Zare and co-workers, both reported in [23]. Visible absorption (VIS) with a White cell and LPA oscillator strengths reported by Henry and co-workers are shown for C(CH3)4 [24] and for C3H8 and C4H10 [20]. The largest disagreement (10– 12%) with our measurements was with two LPA measurements (C2H6, C3H8) of [23] but this was expected because the LPA values were already around 8% higher than the FT-VIS results of the same Letter. It has been shown that the integrated absorption values obtained with the PS-CRD technique are linear as a function of the density of the gas. In addition, the form of modulation has no influence on the shape and magnitude of the absorption bands. It is now possible for us to discuss the oscillator strengths that were observed but not reported for C–H stretching overtones (Dv = 6) of C2H4, C2H6, C3H8, and n-C4H10 in a previous publication [3]. Table 2 presents the (Dv = 6) C–H oscillator strengths obtained with our PS-CRD technique and compares them with literature results. The PS-CRD [3] technique was tested first using CH4. The previously reported oscillator strength [26] was within 2% of our result. We also tested the technique against two published results of C2H4. The oscillator strength of C2H4 can be calculated from the S0 values reported previously [21,23]. Using the LPA technique, Wong and Moore obtained the S0 value of C2H4 with CH4 as the reference and Zare and co-workers [23] used H-D as the reference. The overlap between the C2H4 with CH4 bands around Dv = 6 is very small. Wong and Moore [21] reported uncertainties that are less than 15% of the calculated value and our direct measurement is within their experimental error. The reported LPA oscillator strength for C2H4 using HD as the reference gas [23] is 34% and 25% higher than the values reported by Wong and Moore and our measurements, respectively. In addition, the LPA oscillator strength of C2H4 [23] is 18% higher than the oscillator strength of CH4. In the past, we have compared the Dv = 5 and 6 absorptions of CH4 and C2H4 using the LPA method and we have found that at the same pressure, the peak absorption of C2H4 is higher than CH4 but the full width at half maximum is smaller making their integrated bands comparable in magnitude with CH4 slightly higher. Fig. 5 illustrates the degree of overlap of the C2H4 and CH4
E.K. Lewis et al. / Chemical Physics Letters 394 (2004) 25–31
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Table 1 Assignment, band maximum, full width at half maximum (fwhm), and oscillator strength (f) for the Dv = 5 (C–H) bands obtained from PS-CRD and FT-VIS spectra Molecule
Assignment
CH4 C2H4 C2H6
CH (band) CH (band)
HC(CH3)3
Total band
Oscillator strength (f/1010)
Band max. (cm1)
fwhm (cm1)
PS-CRDa
FT-VISa
Literature values
Ref.
13 755 14 080 13 490
180 106 138
3.22 ± 0.08 5.49 ± 0.27
3.20 ± 0.06 5.67 ± 0.21
3.5 ± 0.1 (VIS); 3.2 (VIS) 3.24 ± 0.23 (LPA) 5.82 (FT-VIS); 6.21 ± 0.43 (LPA)
[25] [23] [23]
6.99 ± 0.32
6.90 ± 0.11
C–Ht C–Hs C–Ha Side band
13 221 13 328 13 444 13 675
131 57 123 123
C(CH3)4
CH (band)
13 432
62
7.07 ± 0.07
7.09 ± 0.15
6.8 ± 1.4 (VIS); 7.1 ± 2.2 (LPA)
[24]
C3H8
Total band C–Hm C–Ha C–Hs Side band
7.34 (FT-VIS); 8.0 ± 0.3 (LPA); 7.5 (VIS)
[20,23]
181 107 110 95
7.22 ± 0.34 2.54 2.58 1.94 0.16
7.39 ± 0.34
13 284 13 424 13 513 13 648
Total band C–Hm C–Ha C–Hs Side band
8.6 (VIS)
[20]
167 149 84 107
8.92 ± 0.41 2.98 3.90 1.83 0.21
8.86 ± 0.30
13 204 13 422 13 513 13 644
C4H10
0.54 0.51 5.78 0.16
The error bars represent 95% confidence limits based on the statistical scatter in the measurements. a Present work; LPA, laser intracavity photoacoustic.
Table 2 Band maximum, full width at half maximum (fwhm), and oscillator strength (f) for the Dv = 6 (C–H) bands Molecule
Band max. (cm1)
fwhm (cm1)
Oscillator strength (f/1010) PS-CRDa
CH4 C2H4
16 150 16 551
200 132
0.59 ± 0.05 0.55 ± 0.02
C2H6 HC(CH3)3 C3H8 C4H10 C(CH3)4
15 823 15 804 15 741 15 750 15 757
131
0.79 ± 0.08 0.92 ± 0.05 1.09 ± 0.03
CRD
LPA
VIS
Ref.
0.60 ± 0.02
[25] [21] [23] [23] [21] [17] [17] [17,24]
0.48 ± 0.05 0.73 ± 0.07 1.16 ± 0.14 0.89 ± 0.15 1.26 ± 0.05 1.47 ± 0.04 1.65 ± 0.05
1.6 ± 0.5
1.2 ± 0.4
The PS-CRD error bars represent 95% confidence limits based on the statistical scatter in the measurements. a Present work; LPA, laser intracavity photoacoustic.
bands. The CRD Letter [17] states that the acoustic method using CH4 as a reference gives a good value of oscillator strength for C(CH3)4. It is reasonable to think that the reported oscillator strength for C2H4 given by Wong and Moore is a good determination because the band overlap between C2H4 and CH4 is smaller than the band overlap between CH4 and C(CH3)4. The calculated oscillator strength for C(CH3)4 using the pulsed CRD method [17] is in good agreement (3% higher) with the reported LPA result [24] and the authors of the CRD technique use this agreement as indicator of the validity
of their measured value. The oscillator strength for C(CH3)4 of the CRD Letter [17] is also 27% larger than the result of the direct absorption method using a visible spectrophotometer (VIS) and a White cell [24]. Henry and co-workers allow for large uncertainties in their measurements based on the fact that the LPA method is not very reliable when the sample and reference gases have large band overlap. Once we tested the PS-CRD technique using CH4 and C2H4 and were satisfied that the results were in agreement with results of two different techniques (VIS [25]
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E.K. Lewis et al. / Chemical Physics Letters 394 (2004) 25–31
densities as low as 5 · 1017 molecules cm3. The CRD work was done mainly at densities around 1019 molecules cm3. Their baseline was a function of the reflectivity of the mirrors and the pressure of the sample. Because of this, they had to make background and scattering corrections to each band in order to get the absorption coefficients. We believe that the scattering correction is probably the source of the differences between results and we do not think that the techniques employed are at fault. We are still convinced that our measured oscillator strengths are the correct ones. 5. Conclusion
Fig. 5. PS-CRD spectra of CH4 (200 Torr) and C2H4 (200 Torr) around the Dv = 6 (C–H) absorption at 295 K. The degree of overlap between the bands is shown.
and LPA [21]) we continued with the other molecules C2H6, C3H8, n-C4H10, and n-C5H10. The calculated oscillator strength of C2H6 using LPA with H-D as the reference gas [23] was 30% larger than the oscillator strength calculated using PS-CRD [3]. Our oscillator strength values for C3H8, n-C4H10 are also 27% lower than the ones reported using the CRD technique [17]. The authors using the CRD technique [17] attribute the difference in results to possible problems associated with the PS-CRD technique. As we have shown before, the PS-CRD technique has been tested by obtaining the oscillator strengths (Dv = 5) of seven different molecules and making comparisons with absorption techniques such as FT-VIS and VIS absorption with a White cell. The only explanation that we can provide for the difference between the PS-CRD [3] and the CRD [17] results is in relation to the magnitude of the gas densities studied. There is approximately one order of magnitude difference between the gas densities studied using the two techniques. The highest density studied using the PS-CRD technique produced a maximum of 2 variation (<2 · 107 cm1 approximately) in the baseline (outside the absorption band region) with respect to the baseline of the empty cell (3.2 · 106 cm1). Under this self imposed restriction, we did not have to worry about large corrections due to scattering that occur at higher densities. The mirrors used in the CRD [17] and PSCRD [3] techniques were from the same company and had the same reflectivity. The optical resonators were 1 m [17] and 0.81 m [3]. The sensitivity of the PS-CRD technique was such that we could study samples at
The phase-shift cavity ring down technique was used to measure the absorption spectrum of the C–H (Dv = 5) overtone transition of several hydrocarbons. The absorption scale and the integrated absorption are linear over a wide range of densities. In addition, the oscillator strengths calculated from absorption bands using a White cell and a FT-VIS spectrophotometer are in excellent agreement with the results of the PS-CRD technique. One of the advantages of using the PS-CRD technique with phase sensitive detection is that there is no need to average the signals; in addition, the technique is very sensitive. With the PS-CRD technique, it is possible to detect high C–H overtone levels (Dv = 6) at pressures as low as 10 Torr. This is advantageous to obtain the spectra of low vapor pressure samples at temperatures around 100 K. Currently we are doing experiments using the PS-CRD technique in combination with a low temperature static gas cell. With this new technique we have measured the (Dv = 5) C–H absorption bands of CH4 at temperatures between 100 and 298 K. These results will be presented in a future publication.
Acknowledgements This work was supported by the Robert A. Welch Foundation under Grant No. AA-1173. This study was supported in part by funds from the Quantum Optics Initiative funded by the ONR, Texas A&M, and the Vice Provost for Research at Baylor University. Partial support from the Baylor University Research Committee is also acknowledged. The authors thank K.W. Busch and M.A. Busch for providing the lock-in amplifier used in this study.
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E.K. Lewis et al. / Chemical Physics Letters 394 (2004) 25–31 [3] E.K. Lewis, D. Reynolds, X. Li, G. deVillele, C. Leduc, D.L. Ceden˜o, C.E. Manzanares I, Chem. Phys. Lett. 334 (2001) 357. [4] D.Z. Anderson, J.C. Frisch, C.S. Masser, Appl. Opt. 23 (1984) 1238. [5] A. OÕKeefe, D.A.G. Deacon, Rev. Sci. Instrum. 59 (1988) 2544. [6] G. Berden, R. Peeters, G. Meijer, Int. Rev. Phys. Chem. 19 (2000) 565. [7] K.W. Busch, M.A. Busch, Cavity-Ringdown Spectroscopy, American Chemical Society, Washington, DC, 1999. [8] D. Romanini, K.K. Lehmann, J. Chem. Phys. 99 (1993) 6287. [9] D. Romanini, A.A. Kachanov, N. Sadeghi, F. Stoeckel, Chem. Phys. Lett. 264 (1997) 316. [10] J.J. Scherer, D. Voelkel, D.J. Rakestraw, J.B. Paul, C.P. Collier, R.J. Saykally, A. OÕKeefe, Appl. Chem. Phys. Lett. 245 (1995) 273. [11] D. Romanini, A.A. Kachanov, F. Stoeckel, Chem. Phys. Lett. 270 (1997) 546. [12] D. Romanini, A.A. Kachanov, F. Stoeckel, Chem. Phys. Lett. 270 (1997) 538.
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Phase shift cavity ring down and FT-VIS measurements of C–H (Dv = 5) vibrational overtone absorptions Ernest K. Lewis, Craig J. Moehnke, Carlos E. Manzanares
*
Department of Chemistry and Biochemistry, 2nd floor, Office E-216, Sciences Building, Baylor University, 101 Bagby Ave., Waco, TX 76798, USA Received 12 May 2004; in final form 15 June 2004 Available online 20 July 2004
Abstract The integrated absorption bands for the C–H stretching overtones (Dv = 5) of C2H4, C2H6, C3H8, C4H10, HC(CH3)3, and C(CH3)4 have been measured at 295 K between 13 000 and 14 300 cm1, using the phase shift cavity ring down (PS-CRD) technique. Similar absorption bands have been obtained using a White cell with an optical path length of 6.0 m and a Fourier transform spectrophotometer operating in the visible (FT-VIS) region. The integrated intensity and the linearity of the absorption with the density of the gas are independent of the form of modulation of the laser (square or sine wave) using the PS-CRD technique. The oscillator strengths calculated with the two techniques are in excellent agreement. 2004 Elsevier B.V. All rights reserved.
1. Introduction The phase shift cavity ring down (PS-CRD) technique was originally used by Herbelin et al. [1] to measure mirror reflectivities. In 1996, Engeln et al. [2] used for the first time the same method to obtain an electronic transition of O2 in the visible region. In 2001, we used this technique [3] to measure the fifth (Dv = 6) C–H overtone spectra of hydrocarbons. The conventional cavity ring down technique (CRD) has its origin in the work of Anderson et al. [4] to measure mirror reflectivities and the work of OÕKeefe and Deacon [5] which used the CRD technique as a spectroscopic method for absorption measurements. Since then, the CRD technique and its variations like cavity enhanced absorption, have been used in many spectroscopic and kinetic measurements [6,7]. The CRD technique has been used to measure absolute cross sections and high vibrational overtone absorptions of HCN [8], HCCH [9,10], CHF3 [11], N2O *
Corresponding author. Fax: +1-254-710-2403. E-mail address: [email protected] (C.E. Manzanares). 0009-2614/$ - see front matter 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.06.102
[12,13], H2O [14], OH [15], and C6H6 [16] and hydrocarbons [17]. In [17] the authors used the CRD technique to measure the Dv = 6, C–H overtone spectra of propane, butane, and 2,2-dimethylpropane and calculated the integrated intensities, oscillator strengths, and cross sections of the transitions. For propane and butane the cross sections in [17] were 25–30% higher in magnitude than our measurements [3]. The authors [17] recognized the high sensitivity of the PS-CRD technique and also pointed out two important questions related to the use of the technique; mainly, the form of modulation (square vs sine wave) of the laser and the linearity of the integrated bands with pressure. In this Letter, we investigate the two questions presented in [17] in relation to the PS-CRD technique. The absorption coefficients and integrated absorptions were measured for the (Dv = 5) C–H stretching overtones of C2H4, C2H6, C3H8, C4H10, HC(CH3)3 and C(CH3)4. The bands obtained with the PS-CRD technique are compared with absorption bands of the same molecules obtained using a White cell with an optical path length of 6.0 m and a Fourier transform spectrophotometer in the visible region.
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2. Experimental The pump laser is a solid state, frequency doubled Nd:YVO4 laser (Coherent-Verdi) providing single wavelength (532 nm) at a power level of 5 W. This laser is used to pump a continuous wave (Coherent 899-01) Ti:Sapphire ring laser. The output of the Ti:Sapphire laser (between 13 000 and 14 300 cm1) is passed through an electro-optic modulator (EOM). The modulated output (square or sine wave) of the laser is coupled into an optical cavity (43 cm) which consists of two highly reflective mirrors. The mirrors of quoted reflectivity 99.995% have a diameter of 20.32 mm and a radius of curvature r = 6 m. With the vacuum system that we had at the time of the experiments, the highest measured reflectivity of the mirrors was 99.977%. The signal is detected by a photomultiplier which is located behind the cavity. The signal is amplified and connected to a lock-in amplifier (Stanford SR 830). The zero phase shift is obtained by bypassing the cavity. The lock-in amplifier measures the amplitude and the phase difference between the signal passing through the cavity and the signal obtained by bypassing the cavity. The phase shift of the empty cavity is around 45 with an angular modulation frequency, X = (2p · 25) kHz. The reference signal for the lock-in amplifier is obtained from a function generator which also supplies the modulation signal to the driver input of the EOM. We use LabVIEW programs to control the data acquisition. Absolute calibration of the laser lines was achieved obtaining the optogalvanic spectrum of a hollow cathode lamp filled with neon [18]. A Thermo Nicolet Fourier Transform Spectrometer (Nexus 670) was used to observe the Dv = 5 vibrational transitions in the visible region at (22 ± 2) C. The spectra were recorded at 2 cm1 resolution in the range of 12 800–14 400 cm1, using a 6.0-m optical path length cell with quartz windows. An average of 100 scans was taken. Samples of C2H6 (99%), C3H8 (98%), and HC(CH3)3 (99%) were obtained from Aldrich, C2H4 (99.9%) and n-C4H10 (99.98%) were from Matheson, and C(CH3)4 (99%) was from AGA specialty gases.
Fig. 1. (Top) Phase shift cavity ring down absorption spectra of the Dv = 5 (C–H) overtone of gaseous C(CH3)4 as a function of the wavenumber (cm1) and the pressure (Torr) at 295 K. (Bottom) Variation of the integrated absorption (S) as a function of the density (q) of C(CH3)4. High density points (j) are from FT-VIS spectra. Low density points (inset) are from PS-CRD spectra. For low density points (h) indicates square wave modulation and (d) indicates sine wave modulation.
3. Results The spectra of the Dv = 5 (C–H) absorption of C(CH3)4 are shown in Fig. 1. The spectra (top) show the absorption (cm1) on the vertical axis as a function of the wavenumber (cm1) and the pressure of the gas (Torr). The variation of the integrated absorption intensity (S) as a function of the density (q) is shown in the bottom part of Fig. 1. The dark square (j) points with density above 20 · 1018 molecules cm3 are from FTVIS measurements. For densities below 5 · 1018 molecules cm3 the points are from PS-CRD measurements. Details for points at low densities are shown in the inset.
The open squares (h) are from bands obtained using square wave modulation of the laser and the dark circles (d) are from bands obtained using sine wave modulation of the laser. The PS-CRD spectra of the Dv = 5 (C–H) absorption of C2H4, C2H6, and C3H8 (deconvoluted) are shown in Fig. 2 and the deconvoluted spectra of C4H10 and HC(CH3)3 are shown in Fig. 3. The (Dv = 5) C–H bands have been assigned previously [19–22]. The single bands on Fig. 2 (top) correspond to C2H6 and C2H4 centered at 13 490 and 14 080 cm1, respectively. Fig. 2 (bottom) shows the spectrum of propane (CH3–CH2–CH3) deconvoluted into three main
E.K. Lewis et al. / Chemical Physics Letters 394 (2004) 25–31
27
Fig. 3. Phase shift cavity ring down absorption spectra of the Dv = 5 (C–H) vibrational overtone of gaseous n-C4H10 (105 Torr), and HC(CH3)3 (100 Torr) at 295 K. Fig. 2. Phase shift cavity ring down absorption spectra of the Dv = 5 (C–H) vibrational overtone of gaseous C2H6 (50 Torr), C2H4 (50 Torr) and C3H8 (100 Torr) at 295 K.
bands. The lowest energy band corresponds to the –CH2 absorption (Hm). The band in the middle corresponds to methyl out-of-plane CH bonds (Ha) and the highest energy band corresponds to the in-plane C–H bonds (Hs). The deconvoluted spectrum of n-butane is shown Fig. 3 (top). The spectrum of methyl propane (HC(CH3)3) shown in Fig. 3 (bottom) was deconvoluted into three main bands in which the lowest energy band corresponds to the single H–C bond (Ht), the intermediate energy band corresponds to the C–H bonds (Hs) trans to C–H and the highest energy C–H bonds (Ha) trans to C–C following the rule [21,22] that C–H bonds trans to C–C bonds are higher in energy than those trans to C–H bonds.
4. Discussion The phase shift (/) of the modulated beam that emerges from the optical cavity relative to the modulated input beam is related to the time that the light spends in the cavity or ring-down time (s) by the equation: tan/ = xs, where x is the angular modulation frequency.
For a cavity filled with an absorbing gas under conditions where the Beer–Lambert law is valid, the ringdown time is: sðmÞ ¼
‘ : c½ð1 RÞ þ aðmÞ‘
ð1Þ
The lifetime is related to the reflectivity of the mirrors (R), the speed of light (c), the absorption coefficient (a) of the sample and the length (‘) of the optical cavity. The absorption spectrum of the background or empty cavity; [s0(m)c]1 = [(1R)/‘], is subtracted from the absorption spectrum of the sample plus the background [s(m)c]1 in order to obtain the absorption of the sample. The integrated absorption (S), the band strength (S0), and the oscillator strength (f) of the vibrational overtones were obtained using the following relations: The integrated absorption (S) in units of (cm2) is S = a(m) dm. The band strength (S0) in units of (cm2 cm1 moleecule1) was obtained from the slope of a plot of the integrated absorption S versus the density of the gas (q) in units of molecules cm3. Linear plots of integrated absorptions S versus the density of the gas (q) for C2H6, C3H8, C4H10, C2H4, and HC(CH3)3 are shown in Fig. 4. The dimensionless oscillator strength (f) is defined as
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E.K. Lewis et al. / Chemical Physics Letters 394 (2004) 25–31
Fig. 4. Variation of the integrated absorption (S) as a function of the density (q) of n-C4H10, C3H8, C2H6, HC(CH3)3 and C2H4.
f ¼
4 102 e0 mc2 S 0 ¼ 1:1296 1012 S 0 ; e2
ð2Þ
where e0 is the permittivity of free space, m and e are the mass and charge of the electron, and c is the speed of light. All constants are in SI units. The results of these calculations were compared with similar results obtained using FT-VIS absorption measurements from our laboratory. In this case the band strength (S0) was obtained from a plot of the integrated absorbance (A(v) dv) multiplied by 2.303 and divided by the optical path length of the cell (d = 600 cm) as a function of the density of molecules. For each molecule, the band centers, assignments, full width at half maximum (fwhm) and oscillator strengths are summarized in Table 1. The calculated oscillator strengths from PS-CRD and FT-VIS measurements for the same bands are within 1–3% of each other as shown in Table 1. Note that the (PS-CRD) integrated bands that are reported in this Letter, were obtained with square wave modulation of the laser. The results presented in Fig. 1 (bottom) show the maximum dispersion between the points (open squares and dark circles) that we were able to obtain by doing the experiments in different weeks. For a given week we used square modulation only and the alignment
of the system, the laser power, and the sample pressures were different from the week where sine modulation was used. It is clear that no appreciable difference was observed between results using square or sine modulation. Figs. 1 and 4 show that the integrated absorption is linear over the range of densities covered. In fact, Fig. 1 (bottom) shows that the linearity is extended to results obtained with a different technique (FT-VIS) at high densities. In Table 1, the oscillator strengths are also compared with literature values using FT-VIS with a White cell from Quack and co-workers and Laser Photoacoustic (LPA) from Zare and co-workers, both reported in [23]. Visible absorption (VIS) with a White cell and LPA oscillator strengths reported by Henry and co-workers are shown for C(CH3)4 [24] and for C3H8 and C4H10 [20]. The largest disagreement (10– 12%) with our measurements was with two LPA measurements (C2H6, C3H8) of [23] but this was expected because the LPA values were already around 8% higher than the FT-VIS results of the same Letter. It has been shown that the integrated absorption values obtained with the PS-CRD technique are linear as a function of the density of the gas. In addition, the form of modulation has no influence on the shape and magnitude of the absorption bands. It is now possible for us to discuss the oscillator strengths that were observed but not reported for C–H stretching overtones (Dv = 6) of C2H4, C2H6, C3H8, and n-C4H10 in a previous publication [3]. Table 2 presents the (Dv = 6) C–H oscillator strengths obtained with our PS-CRD technique and compares them with literature results. The PS-CRD [3] technique was tested first using CH4. The previously reported oscillator strength [26] was within 2% of our result. We also tested the technique against two published results of C2H4. The oscillator strength of C2H4 can be calculated from the S0 values reported previously [21,23]. Using the LPA technique, Wong and Moore obtained the S0 value of C2H4 with CH4 as the reference and Zare and co-workers [23] used H-D as the reference. The overlap between the C2H4 with CH4 bands around Dv = 6 is very small. Wong and Moore [21] reported uncertainties that are less than 15% of the calculated value and our direct measurement is within their experimental error. The reported LPA oscillator strength for C2H4 using HD as the reference gas [23] is 34% and 25% higher than the values reported by Wong and Moore and our measurements, respectively. In addition, the LPA oscillator strength of C2H4 [23] is 18% higher than the oscillator strength of CH4. In the past, we have compared the Dv = 5 and 6 absorptions of CH4 and C2H4 using the LPA method and we have found that at the same pressure, the peak absorption of C2H4 is higher than CH4 but the full width at half maximum is smaller making their integrated bands comparable in magnitude with CH4 slightly higher. Fig. 5 illustrates the degree of overlap of the C2H4 and CH4
E.K. Lewis et al. / Chemical Physics Letters 394 (2004) 25–31
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Table 1 Assignment, band maximum, full width at half maximum (fwhm), and oscillator strength (f) for the Dv = 5 (C–H) bands obtained from PS-CRD and FT-VIS spectra Molecule
Assignment
CH4 C2H4 C2H6
CH (band) CH (band)
HC(CH3)3
Total band
Oscillator strength (f/1010)
Band max. (cm1)
fwhm (cm1)
PS-CRDa
FT-VISa
Literature values
Ref.
13 755 14 080 13 490
180 106 138
3.22 ± 0.08 5.49 ± 0.27
3.20 ± 0.06 5.67 ± 0.21
3.5 ± 0.1 (VIS); 3.2 (VIS) 3.24 ± 0.23 (LPA) 5.82 (FT-VIS); 6.21 ± 0.43 (LPA)
[25] [23] [23]
6.99 ± 0.32
6.90 ± 0.11
C–Ht C–Hs C–Ha Side band
13 221 13 328 13 444 13 675
131 57 123 123
C(CH3)4
CH (band)
13 432
62
7.07 ± 0.07
7.09 ± 0.15
6.8 ± 1.4 (VIS); 7.1 ± 2.2 (LPA)
[24]
C3H8
Total band C–Hm C–Ha C–Hs Side band
7.34 (FT-VIS); 8.0 ± 0.3 (LPA); 7.5 (VIS)
[20,23]
181 107 110 95
7.22 ± 0.34 2.54 2.58 1.94 0.16
7.39 ± 0.34
13 284 13 424 13 513 13 648
Total band C–Hm C–Ha C–Hs Side band
8.6 (VIS)
[20]
167 149 84 107
8.92 ± 0.41 2.98 3.90 1.83 0.21
8.86 ± 0.30
13 204 13 422 13 513 13 644
C4H10
0.54 0.51 5.78 0.16
The error bars represent 95% confidence limits based on the statistical scatter in the measurements. a Present work; LPA, laser intracavity photoacoustic.
Table 2 Band maximum, full width at half maximum (fwhm), and oscillator strength (f) for the Dv = 6 (C–H) bands Molecule
Band max. (cm1)
fwhm (cm1)
Oscillator strength (f/1010) PS-CRDa
CH4 C2H4
16 150 16 551
200 132
0.59 ± 0.05 0.55 ± 0.02
C2H6 HC(CH3)3 C3H8 C4H10 C(CH3)4
15 823 15 804 15 741 15 750 15 757
131
0.79 ± 0.08 0.92 ± 0.05 1.09 ± 0.03
CRD
LPA
VIS
Ref.
0.60 ± 0.02
[25] [21] [23] [23] [21] [17] [17] [17,24]
0.48 ± 0.05 0.73 ± 0.07 1.16 ± 0.14 0.89 ± 0.15 1.26 ± 0.05 1.47 ± 0.04 1.65 ± 0.05
1.6 ± 0.5
1.2 ± 0.4
The PS-CRD error bars represent 95% confidence limits based on the statistical scatter in the measurements. a Present work; LPA, laser intracavity photoacoustic.
bands. The CRD Letter [17] states that the acoustic method using CH4 as a reference gives a good value of oscillator strength for C(CH3)4. It is reasonable to think that the reported oscillator strength for C2H4 given by Wong and Moore is a good determination because the band overlap between C2H4 and CH4 is smaller than the band overlap between CH4 and C(CH3)4. The calculated oscillator strength for C(CH3)4 using the pulsed CRD method [17] is in good agreement (3% higher) with the reported LPA result [24] and the authors of the CRD technique use this agreement as indicator of the validity
of their measured value. The oscillator strength for C(CH3)4 of the CRD Letter [17] is also 27% larger than the result of the direct absorption method using a visible spectrophotometer (VIS) and a White cell [24]. Henry and co-workers allow for large uncertainties in their measurements based on the fact that the LPA method is not very reliable when the sample and reference gases have large band overlap. Once we tested the PS-CRD technique using CH4 and C2H4 and were satisfied that the results were in agreement with results of two different techniques (VIS [25]
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E.K. Lewis et al. / Chemical Physics Letters 394 (2004) 25–31
densities as low as 5 · 1017 molecules cm3. The CRD work was done mainly at densities around 1019 molecules cm3. Their baseline was a function of the reflectivity of the mirrors and the pressure of the sample. Because of this, they had to make background and scattering corrections to each band in order to get the absorption coefficients. We believe that the scattering correction is probably the source of the differences between results and we do not think that the techniques employed are at fault. We are still convinced that our measured oscillator strengths are the correct ones. 5. Conclusion
Fig. 5. PS-CRD spectra of CH4 (200 Torr) and C2H4 (200 Torr) around the Dv = 6 (C–H) absorption at 295 K. The degree of overlap between the bands is shown.
and LPA [21]) we continued with the other molecules C2H6, C3H8, n-C4H10, and n-C5H10. The calculated oscillator strength of C2H6 using LPA with H-D as the reference gas [23] was 30% larger than the oscillator strength calculated using PS-CRD [3]. Our oscillator strength values for C3H8, n-C4H10 are also 27% lower than the ones reported using the CRD technique [17]. The authors using the CRD technique [17] attribute the difference in results to possible problems associated with the PS-CRD technique. As we have shown before, the PS-CRD technique has been tested by obtaining the oscillator strengths (Dv = 5) of seven different molecules and making comparisons with absorption techniques such as FT-VIS and VIS absorption with a White cell. The only explanation that we can provide for the difference between the PS-CRD [3] and the CRD [17] results is in relation to the magnitude of the gas densities studied. There is approximately one order of magnitude difference between the gas densities studied using the two techniques. The highest density studied using the PS-CRD technique produced a maximum of 2 variation (<2 · 107 cm1 approximately) in the baseline (outside the absorption band region) with respect to the baseline of the empty cell (3.2 · 106 cm1). Under this self imposed restriction, we did not have to worry about large corrections due to scattering that occur at higher densities. The mirrors used in the CRD [17] and PSCRD [3] techniques were from the same company and had the same reflectivity. The optical resonators were 1 m [17] and 0.81 m [3]. The sensitivity of the PS-CRD technique was such that we could study samples at
The phase-shift cavity ring down technique was used to measure the absorption spectrum of the C–H (Dv = 5) overtone transition of several hydrocarbons. The absorption scale and the integrated absorption are linear over a wide range of densities. In addition, the oscillator strengths calculated from absorption bands using a White cell and a FT-VIS spectrophotometer are in excellent agreement with the results of the PS-CRD technique. One of the advantages of using the PS-CRD technique with phase sensitive detection is that there is no need to average the signals; in addition, the technique is very sensitive. With the PS-CRD technique, it is possible to detect high C–H overtone levels (Dv = 6) at pressures as low as 10 Torr. This is advantageous to obtain the spectra of low vapor pressure samples at temperatures around 100 K. Currently we are doing experiments using the PS-CRD technique in combination with a low temperature static gas cell. With this new technique we have measured the (Dv = 5) C–H absorption bands of CH4 at temperatures between 100 and 298 K. These results will be presented in a future publication.
Acknowledgements This work was supported by the Robert A. Welch Foundation under Grant No. AA-1173. This study was supported in part by funds from the Quantum Optics Initiative funded by the ONR, Texas A&M, and the Vice Provost for Research at Baylor University. Partial support from the Baylor University Research Committee is also acknowledged. The authors thank K.W. Busch and M.A. Busch for providing the lock-in amplifier used in this study.
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