Determination of Carbon Monoxide Concentration and Total Pressure

Anal. Chem. 2006, 78, 2382-2387

Determination of Carbon Monoxide Concentration and Total Pressure in Gas Cavities in the Silica Glass Body of Light Bulbs by FT-IR Spectrometry Zolta´n Bacsik,† Andra´s Gyivicsa´n,‡ Krisztia´n Horva´th,‡ and Ja´nos Mink*,†,§,|

Chemical Research Center of the Hungarian Academy of Sciences, Pusztaszeri u´ t 59-67, H-1025 Budapest, Hungary, and Department of Analytical Chemistry, Faculty of Information Technology, Research Institute of Chemical and Process Engineering, and Analytical Chemistry Research Group of the Hungarian Academy of Sciences, University of Veszpre´ m, Egyetem u. 10, H-8200 Veszpre´ m, Hungary

Fourier transform infrared (FT-IR) spectroscopy has been adapted to control the quality of light bulbs made from silica glass. Such light bulbs contain a molybdenum accessory which, if contaminated with carbon, during the melting procedure of bulb fabrication, can cause the production of carbon monoxide. This CO can be trapped in small gas cavities in the silica glass body of the bulb. A method has been developed for the detection of CO and the total pressure within these gas cavities by traditional FT-IR spectrometry using a spectral resolution of 0.5 cm-1. The concentration of CO was determined by using a classical least-squares (CLS) method, and the accuracy of concentration determination is reported for the case with sample and reference spectra recorded at different pressures. The total pressure in the cavities was established by two different methods: either by CLS fitting of reference spectra to sample spectra or fitting a Voigt line shape function to the spectral lines within the CO fundamental stretching band. In the latter method, the width of the lines was determined and pressure-broadening coefficients are given and compared with high-resolution data from the literature. According to the measurements, 0.55-0.80 atm total pressure and 0.8-4.0% (v/v) CO was determined in the gas cavities. This method can also be applied to determine the total pressure in similar enclosed spaces in which an appropriate indicator gas component exists. An infrared spectrum is usually employed as a fingerprint of a material under study. The frequencies and the shapes of absorption bands characterize molecules, while the absorption depends on the quantity of the molecules present in the infrared beam. What is more, since changes in temperature and pressure can affect the fine structure of the spectra of gas-phase molecules significantly, one can also obtain information about the environ* Corresponding author. E-mail: [email protected]. Fax: +36-88-624487. † Chemical Research Center of the Hungarian Academy of Sciences. ‡ Department of Analytical Chemistry, University of Veszpre´m. § Faculty of Information Technology, Research Institute of Chemical and Process Engineering, University of Veszpre´m. | Analytical Chemistry Research Group of the Hungarian Academy of Sciences, University of Veszpre´m.

2382 Analytical Chemistry, Vol. 78, No. 7, April 1, 2006

ment conditions. Although the relationships between infrared spectra and temperature or pressure have been established in detail in the past, they have rarely been utilized for such analytical applications. This relationship has been exploited mainly in combustion and exhaust gas diode-laser measurements.1,2 Gaseous CO, CO2, and H2O concentrations and the gas temperature were measured by diode-laser absorption sensors in the combustion and exhaust regions above a methane-air burner operating at atmospheric pressure.3 A newly developed vertical cavity surface emitting laser was applied to monitor the gas temperature and pressure in a pulse detonation engine (PDE).4 Based on simultaneous measurements of the concentration and temperature in a PDE, a real-time control system (optimal fuel consumption, maximal specific impulse) has been realized.5 Near-infrared diode-laser temperature measurements also have been carried out for water lines in atmospheric pressure flames,6 in high-pressure combustion gases,7 and for steel-making furnace pollution control,8 while oxygen lines are studied in the visible spectral range.9,10 Bak and Clausen11 have used the Fourier transform infrared (FT-IR) emission technique to measure gas concentrations with temperatures established from the thermal radiation at the 2350-cm-1 CO2 fundamental band. In the present work, the possibility of following the minor changes in the CO spectral lines caused by pressure broadening (natural line widths are ∼0.15 cm-1 at atmospheric pressure) has been investigated using a commercial FT-IR spectrometer at a maximum spectral resolution of 0.5 cm-1 (resolution parameter12 (1) Allen, M. G. Meas. Sci. Technol. 1998, 9, 545-562. (2) Silver, J. A.; Kane, D. J. Meas. Sci. Technol. 1999, 10, 845-852. (3) Webber, M. E.; Wang, J.; Sanders, S. T.; Baer, D. S.; Hanson, R. K. Proc. Combust. Inst. 2000, Part 1, 28, 407-413. (4) Sanders, S. T.; Mattison, D. W.; Jeffries, J. B.; Hanson, R. K. Proc. Combust. Inst. 2002, Part 2, 29, 2661-2667. (5) Ma, L.; Sanders, S. T.; Jeffries, J. B.; Hanson, R. K. P. Combust. Inst. 2002, Part 1, 29, 161-166. (6) Zhou, X.; Liu, X.; Jeffries, J. B.; Hanson, R. K. Meas. Sci. Technol. 2003, 14, 1459-1468. (7) Nagali, V.; Hanson, R. K. Appl. Opt. 1997, 36, 9518-9527. (8) Quan, W. U.; Murray, J. T.; Alak, C. Metall. Mater. Trans. B 2005, 36B, 53-57. (9) Sanders, S. T.; Wang, J.; Jeffries, J. B.; Hanson, R. K. Appl. Opt. 2001, 40, 4404-4415. (10) Benedetti, R.; Giulietti, K.; Rosa-Clot, M. Opt. Commun. 1998, 154, 4753. (11) Bak, J.; Clausen, S. Meas. Sci. Technol. 2002, 13, 150-156. 10.1021/ac051843h CCC: $33.50

© 2006 American Chemical Society Published on Web 03/04/2006

is ∼5). A critical aspect was the determination of the pressure from the band shapes that are dominated mainly by the Fourier transform of the apodization function. FT-IR spectrometrysboth extractive and open path methodss has been used to monitor trace gas concentrations in industrial, urban, or indoor environments for approximately two decades (e.g., refs 13-18). The method has already been successfully applied to determine the gas composition in light bulbs19 or discharge chambers.20 The extensive development in lighting technology requires the most sophisticated auxiliary techniques in the course of development, testing, and, in many cases, during the entire process of lamp and light bulb fabrication. Exact knowledge of the contaminants of the materials used is essential for overall quality control. In this study, a method is described for indirect control of the chemical purity of molybdenum foils by detection of CO and measurement of its concentration and also of the total pressure in gas cavities within the light bulb by traditional transmission FT-IR spectrometry. EXPERIMENTAL SECTION The first successful IR spectroscopic measurements on the light bulbs were carried out using a FT-IR microscope. More recently, a less costly and faster method of measurement was developed with good reproducibility. The new system consists of a commercial Bio-Rad (Digilab) FTS-185 FT-IR spectrometer equipped with an InSb detector. This semiconductor detector was chosen as it has very high sensitivity (above 1800 cm-1), and the low-frequency cutoff of silica glass (the material of light bulb) tube is ∼2080 cm-1. Measurements were conducted in the spectral region above this frequency, accumulating 512 scans to collect the spectra. The spectral resolution was 0.5 cm-1, and a triangular apodization function was used. A Specac-type (4×) beam condenser was set up in the sample compartment of the spectrometer, and a special sample holder was constructed and installed at the focus of the infrared beam. With the exception of the part containing a gas cavity, the sample was masked by a special sample holder. Different aluminum foil diaphragms were tailored to different cavity cross sections, and the instrument was adjusted to a maximal throughput before the measurements. To determine the dimensions of the gas cavities, a simple light microscope was used. A 10-cm gas cell was used to calibrate the IR spectrometer. The cell was connected to a vacuum system, evacuated, and 3.03 (12) Griffiths, P. R.; Haseth, J. A. Fourier Transform Infrared Spectrometry; Wiley: New York, 1986; pp 24-25. (13) Hanst, P. L.; Hanst, S. T. In Air Monitoring by Spectroscopic Techniques; Sigrist, M. W., Ed.; Wiley-Interscience: New York, 1994; pp 347-350. (14) Russwurm, G. M.; Childers, J. W. Open-path Fourier Transform Infrared Spectroscopy. In Handbook of Vibrational Spectroscopy; Chalmers, J. M., Griffiths, P. R., Eds.; Wiley: New York, 2002; Vol. 2, pp 1750-1773. (15) Spellicy, R. L.; Webb, J. D. Atmospheric Monitoring Using Extractive Techniques. In Handbook of Vibrational Spectroscopy; Chalmers, J. M., Griffiths, P. R., Eds.; Wiley: New York, 2002; Vol. 2, pp 1721-1749. (16) Bacsik, Z.; Mink, J.; Keresztury, G., Appl. Spectrosc. Rev. 2004, 39, 295-363. (17) Bacsik, Z.; Mink, J.; Keresztury, G. Appl. Spectrosc. Rev. 2005, 40, 327-390. (18) Griffith, D. W. T.; Jamie, I. M. Fourier Transform Infrared Spectrometry in Atmospheric and Trace Gas Analysis. In Encyclopedia of Analytical Chemistry; Meyers, R. A., Ed.; Wiley: Chichester, 2000; pp 1979-2007. (19) Hren, B.; Mink, J.; Balazs, L. Anal. Chem. 2002, 74, 6402-6407. (20) Kurte, R.; Beyer, C.; Heise, H. M.; Klockow, D. Anal. Bioanal. Chem. 2002, 373, 639-646.

Figure 1. FT-IR absorption spectrum of the gas composition in a cavity. The R-branch of CO can be observed in the enlarged part of the spectrum.

× 10-3 atm (1 atm ) 101 325 Pa) carbon monoxide was introduced into it. The cell was then filled with argon to attain the various total pressures keeping the amount of CO constant during each set of experiments. As a result of the calibration procedure, 11 CO spectra were recorded at different total pressures ranging from 0.5 to 1.5 atm using 0.1-atm steps. The pressure was measured by a wide-range vacuum gauge (Kurt Lesker Co, KJL902074). RESULTS AND DISCUSSION The fabrication of the light bulbs examined here uses an argon atmosphere (99.99% purity). In principle, this excludes other gases from being present in the silica glass body of the bulbs. However, if the molybdenum lead-in from the tungsten electrode of the light bulb is contaminated with carbon during the melting procedure of bulb fabrication, CO can be produced that is trapped in small gas cavities (bubbles) in the silica glass body of the bulb, thereby degrading its quality (lifetime). Since silica glass is an IR transparent material above ∼2080 cm-1, FT-IR spectrometry is applicable to detect the CO content of the cavities and, therefore, to control this type of quality degradation of the bulbs. The IR spectrum of a gas cavity is illustrated in Figure 1. The rotational fine structure of the R-branch of the stretching fundamental of CO can be observed only in the enlarged spectrum. Other gaseous compounds in the cavity (argon gas) do not absorb the infrared beam. Qualitative analysis may be made from the spectrum in Figure 1. However, to determine the CO concentration, the optical path length and pressure (to choose the appropriate reference spectrum) must be known. The dimensions of the cavities can be determined by a commercial light microscope. The pressure inside a small-size cavity, however, cannot be measured with a gauge. This pressure was determined instead from the spectra of CO using the pressure-broadening phenomenon. Dimensions of the Cavities. Photographs of light bulbs were taken from different directions by means of a light microscope to determine the dimensions of the gas cavities or gas bubbles (see Figure 2). In most cases, the bubbles had an ellipsoid shape; thus, the volume of the cavity was calculated as

V)

4 π‚rwrdrh 3

(1)

where rw, rd, and rh are the width, depth, and height-half axes Analytical Chemistry, Vol. 78, No. 7, April 1, 2006

2383

Figure 2. (a) Gas cavity in the silica glass body of a light bulb. (b) Same cavity viewed from another direction (along the h axis of the ellipsoid). The dimensions of this cavity are rw ) 300 µm, rd ) 455 µm, and rh ) 195 µm.

Figure 3. Differences (∆, %) between the measured and the real partial pressures of CO in the calibration spectra (3.03 × 10-3 atm CO in Ar at total pressure of 0.5-1.5 atm, path length 10 cm) determined by the CLS method using the CO spectrum measured at 1.0-atm total pressure as a reference (3.03 × 10-3 atm CO in Ar, path length 10 cm).

(radii) of the ellipsoid, respectively. The volumes of the cavities were ∼(0.4-1.4) × 10-10 m3. The path length of the infrared beam inside the gas cavity was determined as an averaged value: the apparent area of the ellipse perpendicular to the propagation of the infrared beam was calculated and then the volume of the ellipsoid was divided by this area. Thus, the path length can be expressed as 4/3r, where r is the radius of the ellipsoid parallel with the beam path. Effect of Pressure on Quantitative Analysis. Initially, the accuracy of the partial pressure determination of CO was investigated when the sample and reference spectra were recorded at different total pressures. Partial pressures of CO in the 11 calibration spectra (3.03 × 10-3 atm CO in Ar atmosphere at different total pressures ranging from 0.5 to 1.5 atm using 0.1atm steps) were determined by the CLS method using the CO spectrum measured at 1.0-atm total pressure as a reference. The differences between the measured and the real (3.03 × 10-3 atm) partial pressures are indicated in Figure 3. In the lower pressure range examined (below 1.0-atm total pressure), the partial pressures were underestimated. For instance, the deviation of partial pressures was close to 20% in the case of the CO spectrum measured at 0.5-atm total pressure. In the upper pressure range investigated (1.1-1.5-atm total pressure), the partial pressures were overestimated, but did not exceed 4% relative error, even in the case of the CO spectrum measured at 1.5-atm total pressure. It can be established that, in general, the more the sample pressure differs from that of the reference spectrum, the greater 2384 Analytical Chemistry, Vol. 78, No. 7, April 1, 2006

the error in quantitative analysis. Thus, the difference between the pressures during the measurements of sample and reference spectra cannot be neglected. Hence, the pressure in the gas cavities must be known to allow use of the appropriate reference spectrum for quantitative analysis. This investigation shows the reasonable steps in pressure necessary during the calibration to obtain an acceptable error in the concentration determination. Determination of Pressure. An individual spectral line within a rotational-vibrational absorption band of a molecule does not occur at one precise frequency; it has a measurable width. A convenient measure of this line width is the full width at halfmaximum (fwhm). Several causes of the finite width of spectral lines are known. These include the following: Doppler broadening and pressure (or collision) broadening in the pressure range investigated.21 In the low-pressure regime, Doppler broadening gives rise to Gaussian line shapes. When the pressure is large enough for pressure broadening to dominate (∼0.5 atm), the line shape is Lorentzian.13,22 There is typically a linear relationship between pressure and line width in the collision-dominated regime, with a coefficient in the range of 0.01-1 cm-1 atm-1. In the pressure regime intermediate between Doppler and collision broadening, the line shapes are represented by the convolution of Gaussian and Lorentzian functions (Voigt profile).23 It is important to note that the pressure-broadened line width depends not only on the total pressure (foreign gas broadening) and the temperature but also on the partial pressure of a certain gas species (self-broadening). Since, in our case, the concentration of the gas of interest in the atmosphere is relatively low, one need not be concerned with self-broadening.24 On the basis of the above-mentioned theoretical considerations and the fact that a relatively low-resolution spectrometer was used for measurements, there are two possible ways to determine the pressure of a gas by FT-IR spectroscopy: the CLS method, which was applied for the total pressure determination in the gas cavities (21) Levine, I. N. Molecular Spectroscopy; John Wiley & Sons: New York, 1975; pp 133-135. (22) Smith, M. A. H.; Rinsland, C. P.; Devi, V. M.; Rothman, L. S.; Rao, K. N. In Spectroscopy of the Earth’s Atmosphere and Interstellar Medium; Rao, K. N., Weber, A., Eds.; Academic Press: New York, 1992; pp 155-156. (23) McDowell, R. S. In Advances in Infrared and Raman Spectroscopy; Clark, R. J. H., Hester, R. E., Eds.; Heyden and Son Ltd.: London, 1980; pp 47-48. (24) Schiff, H. I.; Mackay, G. I.; Bechara, J. In Air Monitoring by Spectroscopic Techniques; Sigrist, M. W., Ed.; Wiley-Interscience: New York, 1994; pp 243-244.

Figure 4. Residual spectra after CLS analysis of 3.03 × 10-3 atm CO in Ar at total pressure of 1 atm (path length 10 cm), using CO spectra measured at total pressure of (a) 0.5, (b) 0.8, (c) 1.3, and (d) 1.5 atm as references.

in this study, and the fwhm method, which can be applied for higher quality spectra. CLS Method. CLS is the simplest multivariate least-squares technique. In our case, a reference spectrum of CO is fitted to the measured sample spectrum such that the sum of the squares of the residuals at each frequency (SSR) is minimized. The smaller the difference between the shapes of the reference and the sample spectra, the smaller the value of SSR. Since increasing total pressure results in an increase in the width and decrease in the height of the lines of the CO spectra, the value of SSR is high when the sample and reference spectra are obtained at different pressures and minimal for those obtained at similar pressures. Using the CLS method, the reference spectra obtained at different pressures are fitted to a sample spectrum obtained at an unknown pressure. In each case, different SSR values are recorded. Plotting the SSR values as a function of the pressure of reference spectra, the pressure of the sample gas can be determined by finding the minimum point of the curve. Typical residual spectra shown in Figure 4 when the sample and the reference spectra are obtained at different pressures. When the reference spectra are obtained at lower pressure than that for the sample spectrum, the residual looks like the (a) or (b) residual spectra in Figure 4, with narrow spikes at the line centers pointing downward (to the direction of negative absorbance). If the reference spectra are obtained at higher pressures than that for the sample spectrum, the narrow spikes of residual are pointing upward [see the (c) and (d) residual spectra in Figure 4]. The SSR values are 11.3 × 10-5, 2.71 × 10-5, 5.98 × 10-5, and 11.0 × 10-5, for the (a-d) residuals, respectively. The reference spectrum obtained at the pressure related to the minimal SSR has to be chosen as the reference for quantitative analysis. If the minimum of the SSR values cannot be determined unambiguously (e.g., the two smallest values are very close to each other), the reference obtained at the higher total pressure has to be used for the CLS quantification, since it can be see in Figure 3 that the relative error of concentration determination is smaller if the reference spectrum is obtained at a higher pressure than that for the sample spectrum. A baseline-corrected sample spectrum from Figure 1 and the residual spectrum after subtraction of the best-fitted reference spectrum (total pressure 0.6 atm) are illustrated in Figure 5. [In the spectral range of the P-branch of the ν(CO) vibration, the noise is larger than at higher

Figure 5. Quantitative determination of CO: (a) Sample spectrum after baseline correction, (b) CO reference spectrum measured at 0.6 atm total pressure (3.03 × 10-3 atm CO in Ar, path length 10 cm), and (c) residual after subtraction of the reference from the sample spectrum.

wavenumbers (R-branch) since the transmittance of the silica glass body of light bulb is very low at the low-frequency end of the region presented in Figure 5.] Considering that the maximum error of pressure determination is 0.05 atm using this set of calibration spectra, CO can be measured with an acceptable relative error (see Figure 3). According to the measurements, the total pressure was in the range of 0.55-0.80 atm and the concentration of CO was found in the range of 0.8-4.0% (v/v) in the cavities. Fwhm Method. The method is based on the investigation of pressure-caused broadening of the lines in the rotational fine structure of the fundamental CO band. The pressure-broadening coefficients for the most common atmospheric gases can be found in the HITRAN25 or GEISA26 databases, and the spectral line parameters of CO, which were measured recently for the fundamental band broadened by air, 27,28 carbon monoxide,29 hydrogen,28,30,31 nitrogen,32,33 helium,34,35 argon,36-39 or more gases.40,41 However, those data cannot be used directly in (25) Rothman, L. S.; Barbe, A.; Benner, D. C.; Brown, L. R.; Camy-Peyret, C.; Carleer, M. R.; Chance, K.; Clerbaux, C.; Dana, V.; Devi, V. M.; Fayt, A.; Flaud, J. M.; Gamache, R. R.; Goldman, A.; Jacquemart, D.; Jucks, K. W.; Lafferty, W. J.; Mandin, J. Y.; Massie, S. T.; Nemtchinov, V.; Newnham, D. A.; Perrin, A.; Rinsland, C. P.; Schroeder, J.; Smith, K. M.; Smith, M. A. H.; Tang, K.; Toth, R. A.; Vander Auwera, J.; Varanasi, P.; Yoshino, K. The HITRAN molecular spectroscopic database: edition of 2000 including updates through 2001. J. Quant. Spectrosc. Radiat. Transfer 2003, 82, 5-44. (26) Jacquinet-Husson, N.; Arie, E.; Ballard, J.; Barbe, A.; Bjoraker, G.; Bonnet, B.; Brown, L. R.; Camy-Peyret, C.; Champion, J. P.; Chedin, A.; Chursin, A.; Clerbaux, C.; Duxbury, G.; Flaud, J. M.; Fourrie, N.; Fayt, A.; Graner, G.; Gamache, R.; Goldman, A.; Golovko, V.; Guelachvili, G.; Hartmann, J. M.; Hilico, J. C.; Hillman, J.; Lefevre, G.; Lellouch, E.; Mikhailenko, S. N.; Naumenko, O. V.; Nemtchinov, V.; Newnham, D. A.; Nikitin, A.; Orphal, J.; Perrin, A.; Reuter, D. C.; Rinsland, C. P.; Rosenmann, L.; Rothman, L. S.; Scott, N. A.; Selby, J.; Sinitsa, L. N.; Sirota, J. M.; Smith, A. M.; Smith, K. M.; Tyuterev, V. G.; Tipping, R. H.; Urban, S.; Varanasi, P.; Weber, M. The 1997 spectroscopic GEISA databank J. Quant. Spectrosc. Radiat. Transfer 1999, 62, 205-254. (27) Zou, Q. J.; Varanasi, P. J. Quant. Spectr. Rad. Transf. 2002, 75, 63-92. (28) Regalia-Jarlot, L.; Thomas, X.; Von der Heyden, P.; Barbe, A. J. Quant. Spectrosc. Radiat. Transfer 2005, 91, 121-131. (29) Sung, K. Y.; Varanasi, P.; J. Quant. Spectrosc. Radiat. Transfer 2005, 91, 319-332. (30) Sung, K.; Varanasi, P. J. Quant. Spectrosc. Radiat. Transfer 2004, 85, 165182. (31) Mengel, M.; Flatin, D. C.; De Lucia, F. C. J. Chem. Phys. 2000, 112, 40694075. (32) Predoi-Cross, A.; Luo, C. Y.; Sinclair, P. M.; Drummond, J. R.; May, A. D. J. Mol. Spectrosc. 1999, 198, 291-303.

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midresolution measurements; it is essential to establish an independent experimental database. This is due to the fact that, with an FT-IR spectrometer, the interferogram cannot be measured to a retardation of infinite length; thus, the recorded spectrum has a finite resolution and the instrumental line shape (ILS) is the convolution of the real spectrum and the FT of a boxcar (which is a sin(x)/x or sinc(x) function). In practice, to eliminate the second minimum of the sinc(x) ILS function, a process known as apodization is used. Thus, the measured line shape is the convolution of the true shape and the FT of the apodization function. Anderson and Griffiths12,42 considered the case of Lorentzian bands convolved with the sinc and sinc2 ILS functions of an FT-IR spectrometer. They demonstrated that the difference between the apparent and true peak absorbance is greater when weakly absorbing bands are measured using triangular apodization than when the interferogram is not apodized. Accordingly, the pressure-broadening coefficients determined by high-resolution measurements cannot be used directly; however, algorithms (see, e.g., refs 43-45) for the retrieval of spectral line parameters can be used to reconstruct real spectra from line parameters even using an apodization function.46 The widths of individual lines in the spectra could not be measured directly in our case since they were obtained with 0.5cm-1 resolution, and therefore, the lines consist of few points (1013). The widths of the R(0)-R(17) lines of the 11 calibration spectra (3.03 × 10-3 atm CO in Ar) obtained at different total pressures (0.5-1.5 atm with 0.1-atm steps) were measured indirectly by fitting Voigt function [K(x,y), eq 2] to each of them and the full width of the fitted function was determined at the half-maximums (fwhm).

K(x, y) ≡

y π

∞

exp(-t2)

-∞

y2 + (x - t)2

∫

dt

(2)

where y ≡ RL/RG xln2 is the ratio of Lorentzian to Gaussian widths and x ≡ vj - vjo/RG xln2 is the frequency scale in units of Gaussian half-width RG. (33) Berman, R.; Sinclair, P. M.; May, A. D.; Drummond, J. R. J. Mol. Spectrosc. 1999, 198, 283-290. (34) Beaky, M. M.; Goyette, T. M.; DeLucia, F. C. J. Chem. Phys. 1996, 105, 3994-4004. (35) Thachuk, M.; Chuaqui, C. E.; LeRoy, R. J. J. Chem. Phys. 1996, 105, 40054014. (36) Mantz, A. W.; Thibault, F.; Cacheiro, J. L.; Fernadez, B.; Pedersen, B.; Koch, H.; Valentin, A.; Claveau, C.; Henry, A.; Hurtmans, D. J. Mol. Spectrosc. 2003, 222, 131-141. (37) Thibault, F.; Martinez, R. Z.; Domenech, J. L.; Bermejo, D.; Bouanich, J. P. J. Chem. Phys. 2002, 117, 2523-2531. (38) Luo, C.; Wehr, R.; Drummond, J. R.; May, A. D.; Thibault, F.; Boissoles, J.; Launay, J. M.; Boulet, C.; Bouanich, J. P.; Hartmann, J. M. J. Chem. Phys. 2001, 115, 2198-2206. (39) Sinclair, P. M.; Duggan, P.; Berman, R.; Drummond, J. R.; May, A. D. J. Mol. Spectrosc. 1998, 191, 258-264. (40) Nissen, N.; Doose, J.; Guarnieri, A.; Mader, H.; Markov, V. N.; Golubyatnikov, G. Y.; Leonov, I. I.; Shanin, V. N.; Krupnov, A. F. Zeits. Naturf. Sect. A-A J. Phys. Sci. 1999, 54, 218-224. (41) Drascher, T.; Giesen, T. F.; Wang, T. Y.; Schmucker. N.; Schieder, R.; Winnewisser, G.; Joubert, P.; Bonamy, J. J. Mol. Spectrosc.1998, 192, 268276. (42) Anderson, R. J.; Griffiths, P. R. Anal. Chem. 1975, 47, 2339-2347. (43) Zou, Q. J.; Nemtchinov, V.; Varanasi, P. J. Quant. Spectrosc. Radiat. Transfer 2002, 75, 53-61. (44) Benner, D. C.; Rinsland, C. P.; Devi, V. M.; Smith, M. A. H.; Atkins, D. J. Quant. Spectrosc. Radiat. Transfer 1995, 53, 705-721. (45) Puzzarini, C.; Dore, L.; Cazzoli, G. J. Mol. Spectrosc. 2002, 216, 428-436.

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Table 1. Regression Coefficients (r2) and 95% Confidence Intervals of the Slopes and Intersections of the Calibration Curves for the Line Widths of R(0)-R(17) Lines of the ν(CO) Band of CO versus Pressure Changes (0.5-1.5 Atm Ar) line

intersection (cm-1)

slope (cm-1 atm-1)

r2

R(0) R(1) R(2) R(3) R(4) R(5) R(6) R(7) R(8) R(9) R(10) R(11) R(12) R(13) R(14) R(15) R(16) R(17)

0.5176 ( 0.0015 0.5213 ( 0.0026 0.5212 ( 0.0015 0.5269 ( 0.0028 0.5273 ( 0.0023 0.5294 ( 0.0018 0.5311 ( 0.0022 0.5337 ( 0.0022 0.5308 ( 0.0014 0.5294 ( 0.0016 0.5323 ( 0.0011 0.5324 ( 0.0019 0.5268 ( 0.0024 0.5282 ( 0.0026 0.5323 ( 0.0016 0.5278 ( 0.0016 0.5229 ( 0.0031 0.5322 ( 0.0028

0.0840 ( 0.0015 0.0745 ( 0.0025 0.0677 ( 0.0015 0.0590 ( 0.0027 0.0556 ( 0.0022 0.0516 ( 0.0017 0.0489 ( 0.0021 0.0458 ( 0.0020 0.0483 ( 0.0013 0.0452 ( 0.0014 0.0462 ( 0.0010 0.0458 ( 0.0018 0.0472 ( 0.0022 0.0467 ( 0.0024 0.0455 ( 0.0015 0.0467 ( 0.0015 0.0460 ( 0.0030 0.0456 ( 0.0027

0.9994 0.9979 0.9991 0.9962 0.9972 0.9981 0.9968 0.9965 0.9986 0.9981 0.9991 0.9973 0.9959 0.9951 0.9980 0.9980 0.9924 0.9936

Figure 6. Fitting of Voigt function to the measured data points of the R(10) CO line (3.03 × 10-3 atm CO in Ar, total pressure 1.0 atm, temperature 23 °C, path length 10 cm). The baseline (narrow solid line) and the residual (dotted line) are also shown.

Eighteen fwhm were recorded for each calibration spectra in this way, and in total, 18 calibration curves were determined by plotting the measured line widths as a function of total pressure. The parameters of calibration equations, such as slopes, y intersects of the curves, and the correlation coefficients (r2), are listed in Table 1. The slopes of the calibration curves show the pressure-broadening coefficients of CO that depend on the line position. Comparing the values of pressure-broadening coefficients with the values determined with high-resolution measurements under an argon atmosphere, a good correlation can be seen. For example, for the R(7) line, values of 0.04653, 0.04666, 0.04618, and 0.0458 ( 0.002 cm-1 atm-1 were measured by Luo,38 Sinclair,39 Mantz36 (13CO) and in this study, respectively. Close examination of Table 1 highlights that the values of r2 are close to unity, which shows that each calibration curve is linear and the relatively small changes of the line widths can be followed with absolute certainty, even in the case of 0.5-cm-1 spectral resolution of the FT-IR spectrometer used. A typical example is given in Figure 6 for illustration of the fitting of Voigt function to the R(10) line of CO. It can be seen (46) The Information System Spectroscopy of Atmospheric Gases. (Web-based software for modeling and visualizing molecular absorption spectra) Institute of Atmospheric Optics of Siberian Branch of the Russian Academy of Science, Tomsk, http://spectra.iao.ru/en.

Table 2. Comparison of Measured Pressures Determined by the Fwhm Method Using the R(10) Line Half-Width of the Fundamental CO Band with the Set Values pressure

difference

set (atm)

measured (atm)

absolute (atm)

relative (%)

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

0.492 0.613 0.705 0.797 0.894 0.995 1.095 1.213 1.295 1.386 1.514

-0.008 0.013 0.005 -0.003 -0.006 -0.005 -0.005 0.013 -0.005 -0.014 0.014

-1.60 2.17 0.71 -0.38 -0.67 -0.50 -0.45 1.08 -0.38 -1.00 0.93

that the Voigt function fits well on the measured data points. The difference between the fitted function and the measured values, namely, that the residual is under 0.003 absorbance unit, is smaller than 2% relative to the intensity of the band. The predictive capability of the method was checked by comparing measured pressures determined by the fwhm method on the basis of the calibration curve obtained from the R(10) line of CO with the set pressures. The results are summarized in Table 2. It can be seen that the absolute difference between the set and measured results remained under 0.015 atm in each case. Therefore, if the signal-to-noise ratio of the measured spectra is above ∼100, then this method can be used safely for pressure determination with good accuracy. The pressure range can most likely be extended to higher and, to a greater extent, to lower pressures. The method is highly sensitive toward the S/N of the spectra. CONCLUSIONS A commercial FT-IR spectrometer has been successfully applied to investigate the small-size gas cavities encountered in

silica glass bodies of modern light bulbs. The gas cavities contain an infrared transparent compound (argon) and the IR-active CO in positions adjacent to the molybdenum foil that are most likely stripped from the metal. The concentration of CO was found to be in the range of 0.8-4.0% (v/v). Since it is necessary to use an appropriate reference spectrum to quantify CO, knowledge of the total pressure is important. The pressure broadening of the CO lines (e.g., 0.0458 ( 0.002 cm-1 atm-1 for the R(7) line of the fundamental CO band according to the measurements in this study) has been successfully followed by means of a spectrometer with 0.5-cm-1 resolution. The total pressure in the cavities was also determined by the CLS method and was found to be between 0.55 and 0.80 atm. A method has been developed to determine the total pressure by the means of FT-IR spectrometry with an acceptable accuracy. This method is also applicable to determine trace concentrations of a gaseous compound showing resolvable rotational fine structure in the vibrational bands, and the total pressure can be established in enclosed spaces within any kind of infrared transparent material using a commercial FT-IR spectrometer with maximum resolution of 0.5 cm-1. ACKNOWLEDGMENT The authors thank to Ga´bor Keresztury (Hungarian Academy of Sciences, Budapest, Hungary), James McGregor (University of Cambridge, UK), and Ian Butler (McGill University, Montreal, Canada) for their assistance in preparation of this paper. The substantial revision and helpful suggestions of the reviewers of the manuscript are also acknowledged.

Received for Review October 14, 2005. Accepted February 8, 2006. AC051843H

Analytical Chemistry, Vol. 78, No. 7, April 1, 2006

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