- Email: [email protected]
Comparison of CRDS to ICL-PAS and phase-shift CRDS spectroscopies for the absolute intensities of C–H (ΔvCH=6) overtone absorptions
Chemical Physics Letters 366 (2002) 383–389 www.elsevier.com/locate/cplett
Comparison of CRDS to ICL-PAS and phase-shift CRDS spectroscopies for the absolute intensities of C–H (DvCH ¼ 6) overtone absorptions S. DeMille a, R.H. deLaat b, R.M. Tanner b, R.L. Brooks b
a,*
, N.P.C. Westwood
b
a Guelph-Waterloo Physics Institute, University of Guelph, Guelph, Ont., Canada N1G 2W1 Department of Chemistry and Biochemistry, Guelph-Waterloo Centre for Graduate Work in Chemistry and Biochemistry, University of Guelph, Guelph, Ont., Canada N1G 2W1
Received 29 August 2002; in final form 30 September 2002
Abstract Cavity ring-down spectroscopy (CRDS) has been used to obtain the visible overtone spectra (DvCH ¼ 6) of neopentane, CðCH3 Þ4 , propane, C3 H8 , and n-butane, C4 H10 , yielding absolute f-values for the transitions to better than 3%. For the neo-pentane overtone intensity, comparison with a recent measurement using intra-cavity laser photoacoustic spectroscopy (ICL-PAS) provides favourable agreement, with improved precision. Being absolute this value may be used as a standard for relative intensity measurements obtained by ICL-PAS. The measured propane and n-butane overtone intensities, when compared to recent work using phase-shift CRDS, indicate a lack of agreement to quoted uncertainties. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Cavity ring-down spectroscopy (CRDS) [1,2], has been shown to be a highly sensitive technique for measuring weak absorption spectra of gaseous samples. The method is ideally suited either to very weak absorbers or to very dilute samples of strong absorbers. The present work applies this technique, in its conventional (pulsed) ring-down variant [3], to an investigation of overtone intensities
*
Corresponding author. Fax: +519-836-9967. E-mail address: [email protected] (R.L. Brooks).
in saturated hydrocarbons, viz. neo-pentane, CðCH3 Þ4 , propane, C3 H8 , and n-butane, C4 H10 at a selection of pressures at room temperature. The high overtone spectra of C–H oscillators in hydrocarbons are of interest in intramolecular vibrational redistribution (IVR), and are important as sensitive probes of C–H bonding [4]. In addition, there is a need for absolute intensities of weak absorptions relevant to the atmospheric and astrophysical sciences. Hitherto, laser-based methods such as intra-cavity laser photoacoustic spectroscopy (ICL-PAS) have been used for the higher overtones, e.g., DvCH ¼ 5; 6; 7; 8; . . ., where methods based on transmittance measurements
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 1 6 1 6 - 0
384
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389
lack sensitivity. Neo-pentane has been investigated previously using ICL-PAS [5–7] with emphasis on both IVR and the absolute overtone intensities. In the determination of such intensities the method requires an internal calibrant added to the sample (see, for example [7]) and as a result large uncertainties (ca. 30%) are common. Overtone intensities for both propane [8–10] and n-butane [8,10,11] in the DvCH ¼ 6 region have been investigated previously by ICL-PAS and by phase-shift CRDS [10]. The motivation for the present work is to compare the accuracy and precision of f-values obtained using the conventional ring-down method with those from state-of-the-art ICL-PAS measurements and to determine whether or not these results can be used to calibrate ICL-PAS measurements. In addition, the reliability and uncertainties associated with absolute intensities obtained using phase-shift CRDS are evaluated.
2. Experiment The experimental arrangement has been described previously [12] and will only be briefly described here. The gases, neo-pentane, propane, and n-butane were Matheson Gas Products with stated purity better than 99.5%. Pressures were measured with an Omega, Model PX302-015AV, pressure transducer accurate to 0.25%, and temperatures were monitored to 0.5°. The apparatus consists of a one meter confocal cavity with offthe-shelf Newport mirrors (0.9997 reflectivity at 620 nm) for an empty cavity ring-down time in excess of 10 ls. A 10-Hz Nd:YAG pumped dye laser (TDL 60), using a DCM dye in the region of interest, was employed. The wavelength axis was calibrated using the known atomic transitions of iodine obtained by multiphoton ionization [13] and from the known transitions in discharged (and excited) Ar gas within the ring-down apparatus. Typically 20 pulses per point are collected using a silicon photodiode (in preference to a PMT) as the leak-out detector, together with a specially designed, fast, linear preamplifier. Two DSP units, a transient digitizer model 2030 (8 bits, 33 ns) and signal averaging memory unit, model 4001, are used to collect the data. A PC performs real-time
non-linear regression (single exponential plus background constant) to extract the decay constant, s, which is then used to obtain the absorption coefficient, a (more properly extinction coefficient since it includes scattering contributions but we shall abide by common terminology) 1 1 1 a¼ : ð1Þ c s s0 Here c is the speed of light in the medium and s0 is the ring-down time of the empty cavity. A minimum of 30 points per decay curve is ensured by adjusting the sampling rate to a maximum of 30 MHz, but usually there are many more. As discussed in [12], the accuracy of the integrated intensity is strongly influenced by the systemÕs ability to measure the short decay time of a relatively strong absorption feature. Spectra were taken at a selection of pressures to provide a check that the integrated intensities scale linearly with density, and that the observed line widths are independent of pressure. This also confirms that the cavity, because of its design, is mechanically stable under pressure changes, thus providing reproduceable ring-down times. Care was also taken to ensure that replicate measurements at each pressure were made with descending pressure adjustments. Averaging the results provides statistical uncertainties that scale as N 1=2 , where N is the number of sample spectra acquired. We have found that systematic uncertainties are significantly larger than statistical ones and shall subsequently indicate how the error estimates were made. The background is fit to a straight line whose slope is calculated to satisfy the Rayleigh scattering criterion. Hence only one of the two background fitting parameters (which incorporate Rayleigh scattering and its wavelength dependence) is free and the background slope can be rigorously justified. The overall background level can also be influenced by slight mirror contamination occurring when the sample is admitted to the chamber. The value of s0 can be different from the value used in the analysis but this has no effect but to shift the background slightly from its correct position. Mirrors require cleaning after only a few experimental days. Oscillator strengths (f-values) were calculated using the number densities obtained from the van
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389
der Waals equation of state (for neo-pentane the npentane values were used; see [14]), although ideal gas densities would have sufficed, and by integrating over the absorption profile Z 4 104 0 mc2 f ¼ aðmÞ dm: ð2Þ N e2 Here 0 is the permittivity of free space, m and e are the mass and charge of the electron, c is the speed of light and N is the number density in m3 . All constants are in SI units while the integralÕs dimensions are cm2 because all frequencies in this Letter are in wavenumbers (cm1 ). The integrated cross-sections are obtained using a different integral in order to make comparisons to the phase-shift CRDS work on propane and nbutane [10]. If the number density is expressed in cm3 , and the integral in cm1 , the result is in 1026 cm2 or fm2 per molecule. Z 1 aðmÞ dm: ð3Þ r¼ N m Specifically, we used our fitted Lorentzians for aðmÞ and numerically generated aðmÞ=m which was integrated over a sufficiently wide interval to include the contribution from the wings of the lines 1.
3. Results The results given in Table 1 for all three molecules are averages taken over nine or 10 data sets per molecule at five different gas pressures (2, 5, 10, 12 and 15 psi to gauge accuracy (1 psi ¼ 6.895 kPa or 51.7 Torr)). Fig. 1 shows the variation of absorption coefficient with gas density for each of the three molecules considered. It should be noted that the data points shown are actually superimpositions of replicate data, demonstrating the reproducibility of the experimental procedures. No deviation from linearity (though some scatter) can
385
be observed justifying the use of the average for both the quoted f-values and cross-sections given in Table 1. The statistical uncertainties obtained from the fitting procedures are much smaller than those quoted in Table 1. For example, the statistical error for the 3-peak f-value of neo-pentane is 0:013 1010 whereas our quoted value is 0:05 1010 . The quoted uncertainties are our best estimates of the systematic errors arising principally from the fitting methods employed. This includes issues such as the use of Lorentzians, the number of peaks employed, the removal of the background and consideration of the wings of the peaks that extend beyond the range of the acquired spectrum. 3.1. Neo-pentane Fig. 2 shows the absorption spectra of neopentane for the DvCH ¼ 6 transition at the highest (15 psi) and lowest pressures (2 psi) obtained. The absorption coefficient, given by Eq. (1), is displayed on the vertical axis. In principle all C–H oscillators are equivalent in such a symmetric molecule, but in practice, other effects, including through-space coupling and Fermi resonance [15], lead to more complicated structure in this region. The absorption features have been fitted using Lorentzians, either to the three main peaks, or to five peaks, the three which predominate, plus two smaller ones in the high frequency wings. This is shown in Fig. 2, with the sum shown as a continuous line overlapping the experimental data. The smaller bumps are apparent in the spectra obtained in earlier work [5,7] but were not previously included when calculating the integrated absorption intensity. Table 1 lists the values for both the 3- and 5-peak fits, but comparison to previous results should be made with the 3-peak value. 3.2. Propane and n-butane
1
Of course there is no numerical conversion between f-value and cross-section as defined in Eq. (3). However, if the band is narrow compared to its frequency then an approximate expression is given by f ¼ 1:1296 1012 cm1 m0 r, where m0 is the band centroid in cm1 and r is the cross-section in cm2 .
The peak identifications for propane and nbutane given in Table 1 have been made using the previous notation [8,10], where Hm refers to the methylene C–H oscillators (which are to lower
386
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389
Table 1 Peak assignments and fitting resultsa Molecule
Assignment
C3 H8
n-C4 H10
CðCH3 Þ4
Centroid (cm1 )
FWHM (cm1 )
f-value (1010 )
Total band Hm Ha Hs
0.70 (3)b
0.50 (1)c
140 96.0 131
1.26 (5)b 0.35 0.43 0.48
–
15 563 15 746 15 843
Total band Hm1 Hm2 Ha Hs
0.83 (3)b
0.62 (2)c
135 175 129 106
1.47 (4)b 0.35 0.23 0.51 0.38
–
15 468 15 542 15 753 15 854
1.6 (5)d –
0.92 (3)b 0.97 (3)b
– –
111 99.1 52.4 72.6 118
1.65 (5)b 1.73 (5)b 0.28 1.17 0.20 0.03 0.05
Total band (3 peaks) Total band (5 peaks) – 15 641 – 15 757 – 15 811 – 15 995 – 16 075
Cross-section (fm2 =molecule)
a
Uncertainties in parentheses are estimated errors (see text). This experiment. c Ref. [10]. d Ref. [7]. b
Fig. 1. Variation of integrated absorption intensity with sample density. Top, CðCH3 Þ4 ; middle, C4 H10 ; bottom, C3 H8 .
frequency) and Ha and Hs refer to the out-of-plane and in-plane methyl hydrogen atoms, respectively. The quoted centroids and widths are those of the
fitting Lorentzian peaks which may not be the ÔcorrectÕ line shape to use, but are commonly used in overtone intensity measurements. The absorption spectra for propane and n-butane at the highest pressures (15 psi) are shown in Fig. 3 with the vertical axis the same as Fig. 2. Three Lorentzians have been used to fit the propane data, and four for n-butane which yield acceptably good fits, as can be seen on the figure, perhaps somewhat better for n-butane than for propane. The quality of both the data and the fits permits and supports the inclusion of the fourth fitting peak for n-butane, and concurs with recent unpublished data [11]. The phase-shift CRDS approach [10] uses three Lorentzians, but this cannot account for the differences from the present work (vide infra). Propane can also be fit to four peaks, but the fourth has a small amplitude and cannot be justified spectroscopically as there are only three different C–H oscillators with no evidence [9,11] for Fermi resonances or other effects. We have, however, taken half the difference between the 3- and 4-peak results for the total band intensities as one indicator for our error bars.
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389
Fig. 2. Top: absorption, am , vs frequency of neo-pentane DvCH ¼ 6 at 2 psi. Bottom: same at 15 psi.
387
Fig. 3. Top: absorption, am , vs frequency of propane DvCH ¼ 6 at 15 psi. Bottom: spectrum of n-butane DvCH ¼ 6 at 15 psi.
4. Discussion 4.2. Propane and n-butane 4.1. Neo-pentane A recent ICL-PAS study of higher overtones in neo-pentane [7] provided an experimental f-value of 1:6 1010 for DvCH ¼ 6 and a theoretical value (from ab initio calculations) of 1:70 1010 . Both are in excellent agreement with the present value of 1:65 1010 . As mentioned previously, the ICLPAS technique relies on the addition of a known amount of a (carefully chosen) gas to calibrate the f-value whereas the CRDS technique produces an absolute f-value. Consequently, the present measurement can be taken as a confirmation and calibration of the ICL-PAS results, albeit with a significantly improved precision.
The present results are only the second CRDS measurements for the DvCH ¼ 6 transitions in propane and n-butane, with the determined absolute intensities for the transitions in both of these molecules higher than those obtained by the earlier study using phase-shift CRDS [10]. As shown in Fig. 3 and in Table 1, the n-butane overtone spectrum is fit to four Lorentzians giving an f-value of 1:47 1010 . The 3-peak fit gives a value of 1:53 1010 . Chi-squared considerations argue convincingly that the methylene group feature to low frequency is composed of two features (Hm1 and Hm2 ). Recent ICL-PAS measurements [11], on the basis of the observed split of this band
388
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389
at DvCH ¼ 4 and the trend up through the DvCH ¼ 5; 6, and 7 regions, conclude that the origin of the asymmetry at DvCH ¼ 6 is most likely a Fermi resonance, although contributions from small amounts of another (gauche) isomer cannot be entirely ruled out. Irrespective of the origin of this effect, the small difference for the absolute intensities using either a 3- or 4-peak fit cannot account for the differences observed upon comparison with the intensities obtained by the phaseshift CRDS method. The present results for the overall cross-sections of both propane and n-butane are markedly higher (about 35%) than those obtained earlier using phase-shift CRDS [10]. Interestingly, and in agreement with the present findings, ICL-PAS DvCH ¼ 6 intensities for other hydrocarbons, viz. C2 H4 and C2 H6 [16], are also higher (by 30% and 27%, respectively) than those obtained by the phase-shift CRDS method. These discrepancies clearly point to some difficulty, possibly associated with the phase-shift method itself. Although the phase-shift CRDS measurements are specified as being very precise it is not evident that systematic errors are well understood. While it is true that phase-shift CRDS is very sensitive, it is not at all clear that linearity of the absorption scale is maintained. The use of the phase-shift method in CRDS was first described by Engelin et al. [17], but they did not attempt to extract absolute f-values. For the phase shift to maintain linearity against the possibly rapid intensity changes, and hence the lifetime changes, one must rely on the internal electronics of the lock-in amplifier to exclude those harmonic frequency components that are present because the intensity modulated light source is not modulated with a pure sine wave. The intensity and phase of the signal are both dependent on the lifetime, and extracting the two values cleanly as the lifetime changes is more prone to error using this technique than using the classic lifetime measurement technique employed herein. Nonetheless, the reason for this discrepancy between the present values and the phase-shift results is not immediately apparent, but caution against using the phase-shift technique for absolute f-values or cross-sections until this issue is clarified.
5. Conclusion Cavity ring-down spectroscopy has been used to measure the spectra arising from the v ¼ 0 ! v ¼ 6 overtone transitions in propane, C3 H8 , n-butane, C4 H10 , and neo-pentane, CðCH3 Þ4 . Absolute f-values and integrated cross-sections were obtained and compared to values from previous workers. The value for neo-pentane compared favourably with that obtained using ICL-PAS but was ten times more precise. The values obtained for propane and n-butane were about 35% higher than those obtained using phase-shift CRDS. This difference cannot be attributed to fitting and may indicate a problem with that technique. CRDS can precisely yield absorption coefficients for weak transitions. Furthermore, the absorption coefficients are absolute, this being a significant advantage over ICL-PAS measurements. Both methods have their strengths and limitations. In the region of DvCH ¼ 6, studied here, the sensitivities appear comparable. The higher (and weaker) overtones would provide a more severe test for CRDS as well as requiring a selection of (expensive) mirrors. ICL-PAS does not have this limitation.
Acknowledgements We would like to thank Bryan Henry for helpful discussions, and to acknowledge the Natural Sciences and Engineering Research Council (NSERC) of Canada for research and equipment grants in support of this work. Special acknowledgment to the memory of Tom Riddolls (1945– 2002), machinist and technical consultant to the PIÕs for over 20 years, seems appropriate.
References [1] M.D. Wheeler, S.M. Newman, A.J. Orr-Ewing, M.N.R. Ashfold, J. Chem. Soc. Faraday Trans. 94 (1998) 337, and references therein. [2] G. Berden, R. Peeters, G. Meijer, Int. Rev. Phys. Chem. 18 (2000) 565. [3] A. OÕKeefe, D.A.G. Deacon, Rev. Sci. Instrum. 59 (1988) 2544.
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389 [4] B.R. Henry, Acc. Chem. Res. 20 (1987) 429. [5] C. Manzanares, N.L.S. Yamasaki, E. Weitz, J.T. Knudtson, Chem. Phys. Lett. 117 (1985) 477. [6] A.W. Tarr, B.R. Henry, J. Chem. Phys. 84 (1985) 1355. [7] M.W.P. Petryk, B.R. Henry, Can. J. Chem. 79 (2001) 279. [8] J.S. Wong, C.B. Moore, J. Chem. Phys. 77 (1982) 603. [9] H.J. Kjaergaard, H. Yu, B.J. Schattka, B.R. Henry, J. Chem. Phys. 93 (1990) 6239. [10] E.K. Lewis, D. Reynolds, X. Li, G. de Villele, C. Leduc, D.L. Cede~ no, C. Manzanares I, Chem. Phys. Lett. 334 (2001) 357. [11] B.R. Henry, D.M. Turnbull, D.P. Schofield, H.G. Kjaergaard, J. Phys. Chem. A, submitted.
389
[12] H.F. Tiedje, S. DeMille, L. MacArthur, R.L. Brooks, Can. J. Phys. 79 (2001) 773. [13] C.E. Moore, Atomic Energy Levels, Natl. Bur. Stand. Ref. Data Ser., Natl. Bur. Stand. (US), Circ. No. 35, US GPO, Washington, DC, 1971. [14] R.C. Weast (Ed.), Handbook of Chemistry and Physics, 49th ed., Chemical Rubber Co., Cleveland, 1968. [15] M.W.P. Petryk, B.R. Henry, J. Phys. Chem. A 106 (2002) 8599. [16] J.H. Gutow, J. Davidsson, R.N. Zare, Chem. Phys. Lett. 185 (1991) 120. [17] R. Engelin, G. von Helden, G. Berden, G. Meijer, Chem. Phys. Lett. 262 (1996) 105.
Comparison of CRDS to ICL-PAS and phase-shift CRDS spectroscopies for the absolute intensities of C–H (DvCH ¼ 6) overtone absorptions S. DeMille a, R.H. deLaat b, R.M. Tanner b, R.L. Brooks b
a,*
, N.P.C. Westwood
b
a Guelph-Waterloo Physics Institute, University of Guelph, Guelph, Ont., Canada N1G 2W1 Department of Chemistry and Biochemistry, Guelph-Waterloo Centre for Graduate Work in Chemistry and Biochemistry, University of Guelph, Guelph, Ont., Canada N1G 2W1
Received 29 August 2002; in final form 30 September 2002
Abstract Cavity ring-down spectroscopy (CRDS) has been used to obtain the visible overtone spectra (DvCH ¼ 6) of neopentane, CðCH3 Þ4 , propane, C3 H8 , and n-butane, C4 H10 , yielding absolute f-values for the transitions to better than 3%. For the neo-pentane overtone intensity, comparison with a recent measurement using intra-cavity laser photoacoustic spectroscopy (ICL-PAS) provides favourable agreement, with improved precision. Being absolute this value may be used as a standard for relative intensity measurements obtained by ICL-PAS. The measured propane and n-butane overtone intensities, when compared to recent work using phase-shift CRDS, indicate a lack of agreement to quoted uncertainties. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Cavity ring-down spectroscopy (CRDS) [1,2], has been shown to be a highly sensitive technique for measuring weak absorption spectra of gaseous samples. The method is ideally suited either to very weak absorbers or to very dilute samples of strong absorbers. The present work applies this technique, in its conventional (pulsed) ring-down variant [3], to an investigation of overtone intensities
*
Corresponding author. Fax: +519-836-9967. E-mail address: [email protected] (R.L. Brooks).
in saturated hydrocarbons, viz. neo-pentane, CðCH3 Þ4 , propane, C3 H8 , and n-butane, C4 H10 at a selection of pressures at room temperature. The high overtone spectra of C–H oscillators in hydrocarbons are of interest in intramolecular vibrational redistribution (IVR), and are important as sensitive probes of C–H bonding [4]. In addition, there is a need for absolute intensities of weak absorptions relevant to the atmospheric and astrophysical sciences. Hitherto, laser-based methods such as intra-cavity laser photoacoustic spectroscopy (ICL-PAS) have been used for the higher overtones, e.g., DvCH ¼ 5; 6; 7; 8; . . ., where methods based on transmittance measurements
0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 ( 0 2 ) 0 1 6 1 6 - 0
384
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389
lack sensitivity. Neo-pentane has been investigated previously using ICL-PAS [5–7] with emphasis on both IVR and the absolute overtone intensities. In the determination of such intensities the method requires an internal calibrant added to the sample (see, for example [7]) and as a result large uncertainties (ca. 30%) are common. Overtone intensities for both propane [8–10] and n-butane [8,10,11] in the DvCH ¼ 6 region have been investigated previously by ICL-PAS and by phase-shift CRDS [10]. The motivation for the present work is to compare the accuracy and precision of f-values obtained using the conventional ring-down method with those from state-of-the-art ICL-PAS measurements and to determine whether or not these results can be used to calibrate ICL-PAS measurements. In addition, the reliability and uncertainties associated with absolute intensities obtained using phase-shift CRDS are evaluated.
2. Experiment The experimental arrangement has been described previously [12] and will only be briefly described here. The gases, neo-pentane, propane, and n-butane were Matheson Gas Products with stated purity better than 99.5%. Pressures were measured with an Omega, Model PX302-015AV, pressure transducer accurate to 0.25%, and temperatures were monitored to 0.5°. The apparatus consists of a one meter confocal cavity with offthe-shelf Newport mirrors (0.9997 reflectivity at 620 nm) for an empty cavity ring-down time in excess of 10 ls. A 10-Hz Nd:YAG pumped dye laser (TDL 60), using a DCM dye in the region of interest, was employed. The wavelength axis was calibrated using the known atomic transitions of iodine obtained by multiphoton ionization [13] and from the known transitions in discharged (and excited) Ar gas within the ring-down apparatus. Typically 20 pulses per point are collected using a silicon photodiode (in preference to a PMT) as the leak-out detector, together with a specially designed, fast, linear preamplifier. Two DSP units, a transient digitizer model 2030 (8 bits, 33 ns) and signal averaging memory unit, model 4001, are used to collect the data. A PC performs real-time
non-linear regression (single exponential plus background constant) to extract the decay constant, s, which is then used to obtain the absorption coefficient, a (more properly extinction coefficient since it includes scattering contributions but we shall abide by common terminology) 1 1 1 a¼ : ð1Þ c s s0 Here c is the speed of light in the medium and s0 is the ring-down time of the empty cavity. A minimum of 30 points per decay curve is ensured by adjusting the sampling rate to a maximum of 30 MHz, but usually there are many more. As discussed in [12], the accuracy of the integrated intensity is strongly influenced by the systemÕs ability to measure the short decay time of a relatively strong absorption feature. Spectra were taken at a selection of pressures to provide a check that the integrated intensities scale linearly with density, and that the observed line widths are independent of pressure. This also confirms that the cavity, because of its design, is mechanically stable under pressure changes, thus providing reproduceable ring-down times. Care was also taken to ensure that replicate measurements at each pressure were made with descending pressure adjustments. Averaging the results provides statistical uncertainties that scale as N 1=2 , where N is the number of sample spectra acquired. We have found that systematic uncertainties are significantly larger than statistical ones and shall subsequently indicate how the error estimates were made. The background is fit to a straight line whose slope is calculated to satisfy the Rayleigh scattering criterion. Hence only one of the two background fitting parameters (which incorporate Rayleigh scattering and its wavelength dependence) is free and the background slope can be rigorously justified. The overall background level can also be influenced by slight mirror contamination occurring when the sample is admitted to the chamber. The value of s0 can be different from the value used in the analysis but this has no effect but to shift the background slightly from its correct position. Mirrors require cleaning after only a few experimental days. Oscillator strengths (f-values) were calculated using the number densities obtained from the van
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389
der Waals equation of state (for neo-pentane the npentane values were used; see [14]), although ideal gas densities would have sufficed, and by integrating over the absorption profile Z 4 104 0 mc2 f ¼ aðmÞ dm: ð2Þ N e2 Here 0 is the permittivity of free space, m and e are the mass and charge of the electron, c is the speed of light and N is the number density in m3 . All constants are in SI units while the integralÕs dimensions are cm2 because all frequencies in this Letter are in wavenumbers (cm1 ). The integrated cross-sections are obtained using a different integral in order to make comparisons to the phase-shift CRDS work on propane and nbutane [10]. If the number density is expressed in cm3 , and the integral in cm1 , the result is in 1026 cm2 or fm2 per molecule. Z 1 aðmÞ dm: ð3Þ r¼ N m Specifically, we used our fitted Lorentzians for aðmÞ and numerically generated aðmÞ=m which was integrated over a sufficiently wide interval to include the contribution from the wings of the lines 1.
3. Results The results given in Table 1 for all three molecules are averages taken over nine or 10 data sets per molecule at five different gas pressures (2, 5, 10, 12 and 15 psi to gauge accuracy (1 psi ¼ 6.895 kPa or 51.7 Torr)). Fig. 1 shows the variation of absorption coefficient with gas density for each of the three molecules considered. It should be noted that the data points shown are actually superimpositions of replicate data, demonstrating the reproducibility of the experimental procedures. No deviation from linearity (though some scatter) can
385
be observed justifying the use of the average for both the quoted f-values and cross-sections given in Table 1. The statistical uncertainties obtained from the fitting procedures are much smaller than those quoted in Table 1. For example, the statistical error for the 3-peak f-value of neo-pentane is 0:013 1010 whereas our quoted value is 0:05 1010 . The quoted uncertainties are our best estimates of the systematic errors arising principally from the fitting methods employed. This includes issues such as the use of Lorentzians, the number of peaks employed, the removal of the background and consideration of the wings of the peaks that extend beyond the range of the acquired spectrum. 3.1. Neo-pentane Fig. 2 shows the absorption spectra of neopentane for the DvCH ¼ 6 transition at the highest (15 psi) and lowest pressures (2 psi) obtained. The absorption coefficient, given by Eq. (1), is displayed on the vertical axis. In principle all C–H oscillators are equivalent in such a symmetric molecule, but in practice, other effects, including through-space coupling and Fermi resonance [15], lead to more complicated structure in this region. The absorption features have been fitted using Lorentzians, either to the three main peaks, or to five peaks, the three which predominate, plus two smaller ones in the high frequency wings. This is shown in Fig. 2, with the sum shown as a continuous line overlapping the experimental data. The smaller bumps are apparent in the spectra obtained in earlier work [5,7] but were not previously included when calculating the integrated absorption intensity. Table 1 lists the values for both the 3- and 5-peak fits, but comparison to previous results should be made with the 3-peak value. 3.2. Propane and n-butane
1
Of course there is no numerical conversion between f-value and cross-section as defined in Eq. (3). However, if the band is narrow compared to its frequency then an approximate expression is given by f ¼ 1:1296 1012 cm1 m0 r, where m0 is the band centroid in cm1 and r is the cross-section in cm2 .
The peak identifications for propane and nbutane given in Table 1 have been made using the previous notation [8,10], where Hm refers to the methylene C–H oscillators (which are to lower
386
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389
Table 1 Peak assignments and fitting resultsa Molecule
Assignment
C3 H8
n-C4 H10
CðCH3 Þ4
Centroid (cm1 )
FWHM (cm1 )
f-value (1010 )
Total band Hm Ha Hs
0.70 (3)b
0.50 (1)c
140 96.0 131
1.26 (5)b 0.35 0.43 0.48
–
15 563 15 746 15 843
Total band Hm1 Hm2 Ha Hs
0.83 (3)b
0.62 (2)c
135 175 129 106
1.47 (4)b 0.35 0.23 0.51 0.38
–
15 468 15 542 15 753 15 854
1.6 (5)d –
0.92 (3)b 0.97 (3)b
– –
111 99.1 52.4 72.6 118
1.65 (5)b 1.73 (5)b 0.28 1.17 0.20 0.03 0.05
Total band (3 peaks) Total band (5 peaks) – 15 641 – 15 757 – 15 811 – 15 995 – 16 075
Cross-section (fm2 =molecule)
a
Uncertainties in parentheses are estimated errors (see text). This experiment. c Ref. [10]. d Ref. [7]. b
Fig. 1. Variation of integrated absorption intensity with sample density. Top, CðCH3 Þ4 ; middle, C4 H10 ; bottom, C3 H8 .
frequency) and Ha and Hs refer to the out-of-plane and in-plane methyl hydrogen atoms, respectively. The quoted centroids and widths are those of the
fitting Lorentzian peaks which may not be the ÔcorrectÕ line shape to use, but are commonly used in overtone intensity measurements. The absorption spectra for propane and n-butane at the highest pressures (15 psi) are shown in Fig. 3 with the vertical axis the same as Fig. 2. Three Lorentzians have been used to fit the propane data, and four for n-butane which yield acceptably good fits, as can be seen on the figure, perhaps somewhat better for n-butane than for propane. The quality of both the data and the fits permits and supports the inclusion of the fourth fitting peak for n-butane, and concurs with recent unpublished data [11]. The phase-shift CRDS approach [10] uses three Lorentzians, but this cannot account for the differences from the present work (vide infra). Propane can also be fit to four peaks, but the fourth has a small amplitude and cannot be justified spectroscopically as there are only three different C–H oscillators with no evidence [9,11] for Fermi resonances or other effects. We have, however, taken half the difference between the 3- and 4-peak results for the total band intensities as one indicator for our error bars.
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389
Fig. 2. Top: absorption, am , vs frequency of neo-pentane DvCH ¼ 6 at 2 psi. Bottom: same at 15 psi.
387
Fig. 3. Top: absorption, am , vs frequency of propane DvCH ¼ 6 at 15 psi. Bottom: spectrum of n-butane DvCH ¼ 6 at 15 psi.
4. Discussion 4.2. Propane and n-butane 4.1. Neo-pentane A recent ICL-PAS study of higher overtones in neo-pentane [7] provided an experimental f-value of 1:6 1010 for DvCH ¼ 6 and a theoretical value (from ab initio calculations) of 1:70 1010 . Both are in excellent agreement with the present value of 1:65 1010 . As mentioned previously, the ICLPAS technique relies on the addition of a known amount of a (carefully chosen) gas to calibrate the f-value whereas the CRDS technique produces an absolute f-value. Consequently, the present measurement can be taken as a confirmation and calibration of the ICL-PAS results, albeit with a significantly improved precision.
The present results are only the second CRDS measurements for the DvCH ¼ 6 transitions in propane and n-butane, with the determined absolute intensities for the transitions in both of these molecules higher than those obtained by the earlier study using phase-shift CRDS [10]. As shown in Fig. 3 and in Table 1, the n-butane overtone spectrum is fit to four Lorentzians giving an f-value of 1:47 1010 . The 3-peak fit gives a value of 1:53 1010 . Chi-squared considerations argue convincingly that the methylene group feature to low frequency is composed of two features (Hm1 and Hm2 ). Recent ICL-PAS measurements [11], on the basis of the observed split of this band
388
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389
at DvCH ¼ 4 and the trend up through the DvCH ¼ 5; 6, and 7 regions, conclude that the origin of the asymmetry at DvCH ¼ 6 is most likely a Fermi resonance, although contributions from small amounts of another (gauche) isomer cannot be entirely ruled out. Irrespective of the origin of this effect, the small difference for the absolute intensities using either a 3- or 4-peak fit cannot account for the differences observed upon comparison with the intensities obtained by the phaseshift CRDS method. The present results for the overall cross-sections of both propane and n-butane are markedly higher (about 35%) than those obtained earlier using phase-shift CRDS [10]. Interestingly, and in agreement with the present findings, ICL-PAS DvCH ¼ 6 intensities for other hydrocarbons, viz. C2 H4 and C2 H6 [16], are also higher (by 30% and 27%, respectively) than those obtained by the phase-shift CRDS method. These discrepancies clearly point to some difficulty, possibly associated with the phase-shift method itself. Although the phase-shift CRDS measurements are specified as being very precise it is not evident that systematic errors are well understood. While it is true that phase-shift CRDS is very sensitive, it is not at all clear that linearity of the absorption scale is maintained. The use of the phase-shift method in CRDS was first described by Engelin et al. [17], but they did not attempt to extract absolute f-values. For the phase shift to maintain linearity against the possibly rapid intensity changes, and hence the lifetime changes, one must rely on the internal electronics of the lock-in amplifier to exclude those harmonic frequency components that are present because the intensity modulated light source is not modulated with a pure sine wave. The intensity and phase of the signal are both dependent on the lifetime, and extracting the two values cleanly as the lifetime changes is more prone to error using this technique than using the classic lifetime measurement technique employed herein. Nonetheless, the reason for this discrepancy between the present values and the phase-shift results is not immediately apparent, but caution against using the phase-shift technique for absolute f-values or cross-sections until this issue is clarified.
5. Conclusion Cavity ring-down spectroscopy has been used to measure the spectra arising from the v ¼ 0 ! v ¼ 6 overtone transitions in propane, C3 H8 , n-butane, C4 H10 , and neo-pentane, CðCH3 Þ4 . Absolute f-values and integrated cross-sections were obtained and compared to values from previous workers. The value for neo-pentane compared favourably with that obtained using ICL-PAS but was ten times more precise. The values obtained for propane and n-butane were about 35% higher than those obtained using phase-shift CRDS. This difference cannot be attributed to fitting and may indicate a problem with that technique. CRDS can precisely yield absorption coefficients for weak transitions. Furthermore, the absorption coefficients are absolute, this being a significant advantage over ICL-PAS measurements. Both methods have their strengths and limitations. In the region of DvCH ¼ 6, studied here, the sensitivities appear comparable. The higher (and weaker) overtones would provide a more severe test for CRDS as well as requiring a selection of (expensive) mirrors. ICL-PAS does not have this limitation.
Acknowledgements We would like to thank Bryan Henry for helpful discussions, and to acknowledge the Natural Sciences and Engineering Research Council (NSERC) of Canada for research and equipment grants in support of this work. Special acknowledgment to the memory of Tom Riddolls (1945– 2002), machinist and technical consultant to the PIÕs for over 20 years, seems appropriate.
References [1] M.D. Wheeler, S.M. Newman, A.J. Orr-Ewing, M.N.R. Ashfold, J. Chem. Soc. Faraday Trans. 94 (1998) 337, and references therein. [2] G. Berden, R. Peeters, G. Meijer, Int. Rev. Phys. Chem. 18 (2000) 565. [3] A. OÕKeefe, D.A.G. Deacon, Rev. Sci. Instrum. 59 (1988) 2544.
S. DeMille et al. / Chemical Physics Letters 366 (2002) 383–389 [4] B.R. Henry, Acc. Chem. Res. 20 (1987) 429. [5] C. Manzanares, N.L.S. Yamasaki, E. Weitz, J.T. Knudtson, Chem. Phys. Lett. 117 (1985) 477. [6] A.W. Tarr, B.R. Henry, J. Chem. Phys. 84 (1985) 1355. [7] M.W.P. Petryk, B.R. Henry, Can. J. Chem. 79 (2001) 279. [8] J.S. Wong, C.B. Moore, J. Chem. Phys. 77 (1982) 603. [9] H.J. Kjaergaard, H. Yu, B.J. Schattka, B.R. Henry, J. Chem. Phys. 93 (1990) 6239. [10] E.K. Lewis, D. Reynolds, X. Li, G. de Villele, C. Leduc, D.L. Cede~ no, C. Manzanares I, Chem. Phys. Lett. 334 (2001) 357. [11] B.R. Henry, D.M. Turnbull, D.P. Schofield, H.G. Kjaergaard, J. Phys. Chem. A, submitted.
389
[12] H.F. Tiedje, S. DeMille, L. MacArthur, R.L. Brooks, Can. J. Phys. 79 (2001) 773. [13] C.E. Moore, Atomic Energy Levels, Natl. Bur. Stand. Ref. Data Ser., Natl. Bur. Stand. (US), Circ. No. 35, US GPO, Washington, DC, 1971. [14] R.C. Weast (Ed.), Handbook of Chemistry and Physics, 49th ed., Chemical Rubber Co., Cleveland, 1968. [15] M.W.P. Petryk, B.R. Henry, J. Phys. Chem. A 106 (2002) 8599. [16] J.H. Gutow, J. Davidsson, R.N. Zare, Chem. Phys. Lett. 185 (1991) 120. [17] R. Engelin, G. von Helden, G. Berden, G. Meijer, Chem. Phys. Lett. 262 (1996) 105.