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Time-Resolved Broadband Cavity-Enhanced Absorption Spectroscopy behind Shock Waves Akira Matsugi,*,† Hiroumi Shiina,† Tatsuo Oguchi,‡ and Kazuo Takahashi§ †

National Institute of Advanced Industrial Science and Technology (AIST), 16-1 Onogawa, Tsukuba, Ibaraki 305-8569, Japan Department of Environmental and Life Sciences, Toyohashi University of Technology, 1-1 Hibarigaoka, Tenpaku-cho, Toyohashi 441-8580, Japan § Department of Materials and Life Sciences, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan ‡

S Supporting Information *

ABSTRACT: A fast and sensitive broadband absorption technique for measurements of high-temperature chemical kinetics and spectroscopy has been developed by applying broadband cavity-enhanced absorption spectroscopy (BBCEAS) in a shock tube. The developed method has effective absorption path lengths of 60−200 cm, or cavity enhancement factors of 12−40, over a wavelength range of 280−420 nm, and is capable of simultaneously recording absorption time profiles over an ∼32 nm spectral bandpass in a single experiment with temporal and spectral resolutions of 5 μs and 2 nm, respectively. The accuracy of the kinetic and spectroscopic measurements was examined by investigating high-temperature reactions and absorption spectra of formaldehyde behind reflected shock waves using 1,3,5-trioxane as a precursor. The rate constants obtained for the thermal decomposition reactions of 1,3,5-trioxane (to three formaldehyde molecules) and formaldehyde (to HCO + H) agreed well with the literature data. High-temperature absorption cross sections of formaldehyde between 280 and 410 nm have been determined at the post-reflected-shock temperatures of 955, 1265, and 1708 K. The results demonstrate the applicability of the BBCEAS technique to time- and wavelength-resolved sensitive absorption measurements at high temperatures.

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problem, multipass9,10 or cavity-enhanced11−13 absorption spectroscopies have been successfully incorporated to extend the effective absorption path length. A series of studies on reactions of OH radicals using the multipass resonant absorption spectroscopy (e.g., ref 14) has demonstrated the applicability of the technique to high temperature kinetic measurements for reactions important in combustion modeling. Krasnoperov and Michael11 developed a similar resonant absorption method using a Fabry−Perot cavity as a multipass cell, which was a kind of cavity-enhanced absorption spectroscopy (CEAS).15,16 Recently, laser-based CEAS methods have also been developed and utilized to monitor species time histories behind shock waves.12,13 These multipass and cavity-enhanced techniques have many potential applications in shock tube kinetics studies. The previously developed methods are effective especially for detecting species that have distinct sharp absorption peaks, or under conditions where interference absorption is negligible or can be corrected. Nonetheless, there are a number of molecules and radicals of combustion interest that have broad and/or predissociative electronic transition bands in the ultraviolet (UV)−visible region and, therefore, are often difficult to identify without obtaining their broadband absorption spectra. In such cases, a method that is capable of simultaneously recording

INTRODUCTION Shock tubes are one of the most effective and reliable reactors for studying high-temperature gas phase chemical kinetics. They are capable of almost instantaneously creating uniform reaction conditions with well-defined temperatures and pressures.1,2 A shock tube experiment is essentially a single-shot measurement for a rapid transient phenomenon. Although the use of diaphragmless shock tubes enables some signal averaging with well reproducible postshock conditions,3−5 the time required to evacuate the driven section of the reactor tube between experiments limits the cycle time for data acquisition. (A recently developed miniature high-repetition rate shock tube6 enables extensive signal averaging and is anticipated to be a promising alternative in this regard.) Due to these characteristics, a fast and sensitive diagnostic method should be employed to accurately monitor the temporal behavior of the species of interest. For chemical kinetic applications, improved detection sensitivity is always desirable to reduce complexity caused by a number of secondary reactions. Absorption spectroscopy is a widely used technique to directly obtain species time profiles behind shock waves.2,7,8 Direct resonant or nonresonant absorption methods have been adopted in a number of shock-tube kinetics studies by sensitively monitoring the absorption of some atoms or small molecules having strong electronic absorption lines. A crucial limitation in applying absorption spectroscopy in a shock tube is its limited optical path length, which is typically 5−15 cm. To overcome the © 2016 American Chemical Society

Received: February 1, 2016 Revised: March 14, 2016 Published: March 18, 2016 2070

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Figure 1. Schematic diagram of the optical setup used in this study: A, aperture; CM, cavity mirror; L, lens.

using method (a) in ref 24. The driven section was evacuated with a 180 L/s turbomolecular pump down to pressures on the order of 10−3 Pa prior to each experiment. Although the tube can be evacuated down to an ultimate pressure of 10−5 Pa by pumping for a long period, such high vacuum was found to not be necessary in the present application. The operation for generating the shock wave is automated using pneumatic and solenoid valves controlled by a microcontroller. The cycle time between the experiments can be as low as several minutes. The postshock conditions are highly reproducible; the standard deviation of the incident shock velocities was typically 0.3% when the shock waves were generated from the same preshock conditions. The uncertainty in the measured velocity translates into ±1 and ±2% uncertainties in T5 and p5, respectively. Time-Resolved BBCEAS. A schematic of the optical setup is shown in Figure 1. The shock tube was equipped with two UVgrade fused silica windows with broadband dielectric antireflection coatings (Edmund Optics) at a distance of 30 mm from the end wall. A pair of plano-concave mirrors with a 20 cm radius of curvature was placed outside the tube with a separation of 14 cm, forming an optically stable cavity. The mirrors were held in adjustable gimbal mounts. The concave surface of the mirror was dielectric coated (OptoSigma) with a reflectivity of 95−98% over a wavelength range of 280−420 nm. The probe light was emitted from a Xe short-arc lamp (USHIO UXL-500SX2), which generates broadband radiation in the UV−visible region. The lamp output was collimated by using lenses, an off-axis parabolic mirror, and iris apertures. A set of band-pass filters restricted the spectral range (USHIO IRC240UV and Semrock FF01-300/80-25 for 280−348 nm; USHIO IRC240-UV, Semrock FF01-424/SP-25, and Asahi Spectra LUX325 for 348−420 nm). A lens with a 250 mm focal length was mounted before the cavity to focus the light into the cavity. The beam width in the cavity was less than 5 mm. The light transmitted from the cavity was collected and focused on the entrance slit (200 μm width) of a spectrograph (Andor SR-163) equipped with a 2400 line/mm grating. The dispersed light was focused on the photocathode of a 16channel, linear-array, multianode photomultiplier tube (MAPMT) module (Hamamatsu Photonics H11459-04). Photoelectrons emitted from the photocathode were spatially discriminated and directed into metal channel dynodes using a focusing electrode mesh, multiplied, and collected on 16-channel anodes. The channel pitch of the MAPMT was 1 mm with the widths of active photocathode areas being 0.8 mm per channel. The wavelength and spectral resolution were calibrated using a low pressure mercury lamp. The wavelength dispersion was typically 2 nm per channel. Since the width of the entrance slit of the spectrograph was 5 times narrower than the channel pitch,

absorption time profiles over a wide spectral region is desirable. Several studies employed broadband absorption techniques, utilizing an incoherent light source and a spectrograph equipped with a frame transfer charge coupled device (CCD) chip, to achieve temporally and spectrally resolved absorption measurements behind shock waves.17−19 However, the method has been limited to single-pass detection and only a few chemical kinetics applications have been reported. Presented in this Article is a time-resolved broadband absorption spectroscopy in the UV−visible region combined with the cavity-enhanced method, namely, time-resolved broadband cavity-enhanced absorption spectroscopy (BBCEAS), behind shock waves. The BBCEAS method itself was originally developed for static absorption measurements,20,21 and was recently extended to time-resolved measurements in a flow reactor.22 Herein, the technique has been utilized in shock-tube experiments by incorporating a fast and sensitive light-detection system. Potential applications of the present method include kinetic and spectroscopic studies on unsaturated and aromatic radicals and molecules that are considered to be important precursors for the soot formation in combustion, on oxygenated compound formed during oxidation of hydrocarbon fuels, and on fluorocarbon radicals that play critical roles in the combustion and explosion of hydrofluorocarbons. Descriptions of the shocktube apparatus, optical setup, and data acquisition are given in the next section. The subsequent section presents the performance of the developed method and its application to high-temperature kinetic and spectroscopic studies of formaldehyde.

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EXPERIMENTAL APPARATUS AND METHOD Shock Tube. A double-piston-actuated diaphragmless shock tube3,4 with a 4.2 m long and 5.0 cm i.d. stainless-steel driven section23 was employed. The shock waves were generated by pneumatically removing the piston.3 Shock wave velocities were measured with four miniature pressure transducers placed at 30, 205, 405, and 605 mm upstream from the end wall of the tube. For the experimental conditions presented in this study, variations in the incident shock velocities measured at the three intervals are less than the uncertainty in each velocity; this uncertainty was estimated to be 0.5% on the basis of the transducers’ response time and uncertainty in the spatial intervals. Also, there were decelerations of a few percent in the reflected shock velocities. These observations indicate that the incident shock wave is well developed, and that corrections for boundary layer perturbations24,25 can be applied assuming that the boundary layer has developed to its steady state at least near the shock front. The temperature T5 and pressure p5 behind the reflected shock wave were calculated from preshock conditions and the measured incident shock velocity with corrections made 2071

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due to Rayleigh scattering was more than 50 times smaller than the detection limit presented in the next section.

the spectral resolution was predominantly limited by the spatial width of the active areas and was determined to be 2 nm. The MAPMT module has a built-in preamplifier that converts the anode currents to voltages with a bandwidth of 1 MHz. The total and per-channel time-averaged anode currents were kept at less than 100 and 10 μA, respectively, to avoid saturation. The voltage signals were recorded by digital oscilloscopes with sampling rates larger than 10 MS/s and vertical resolutions of at least 12 bit. The recorded signals were then convolved with a Gaussian temporal distribution function with a standard deviation of 1.2 μs to eliminate small but detectable high-frequency (>4 MHz) electrical noises caused by the arc discharge. The total bandwidth of the processed signals was 0.35 MHz. A small portion (∼3%) of the light was sampled by a beam sampler before entering the cavity, and its intensity was monitored using a GaP photodiode (Thorlabs PDA25K-EC). This reference signal was used to normalize the transmitted light intensities to reduce intensity fluctuations originating from the light source. Most BBCEAS applications have employed CCDs to detect dispersed light from spectrographs,16,21 which generally have finer spectral resolution and/or a wider spectral range than the present setup using a MAPMT as the array detector. However, the use of CCDs necessitates a relatively long exposure time to obtain a signal-to-noise ratio that is appropriate for a kinetic analysis. Time-resolved measurement was recently facilitated by introducing a phase-locked rotating mirror to sweep the output spectrum across the CCD chip in the direction perpendicular to the spectral axis.22 Thereby, the temporal as well as spectral information can be accumulated on the two-dimensional chip over multiple kinetic events synchronized with the mirrorrotation frequency. This technique, however, requires a high and constant measurement duty cycle, which is impractical in ordinary shock-tube experiments. A drawback of using the 16-channel MAPMT, that is, a limited number of detection channels compared to a CCD, can be partially compensated for by using a fine-pitch grating to increase the spectral resolution. Although the present 2 nm resolution is not capable of resolving fine spectral structures, it is still suitable for detection of relatively broad absorptions, as noted in the previous section. A spectral range (∼32 nm bandpass for a single measurement) can be readily extended, if necessary, by combining the data taken at different center wavelengths, owing to the high reproducibility and short cycle time of the diaphragmless shock tube. These advantages also enable signal averaging over several experiments. In the present study, the data were recorded at least three times to ensure reproducibility of the BBCEAS measurements. For a small absorption, the absorption coefficient (α) can be calculated using the following equation16

α=

(I0/I − 1) leff

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RESULTS AND DISCUSSION Effective Path Length and Performance. Determination of the effective path length is essential for quantitative

Figure 2. (a) Absorption cross section of NO2 at 296 K and (b) effective absorption path length of the cavity. The literature absorption cross section (at 293 K) was taken from ref 27 and convolved with a rectangular window of 2 nm width.

measurement of species concentration. For broadband measurements, the effective path length must be calibrated as a function of the wavelength over the entire spectral range of interest. Here, leff has been obtained by measuring the absorption of a known concentration of a calibration gas, NO2, at room temperature (295 ± 3 K). First, the absorption cross sections of NO2 were determined from single-pass broadband absorption spectroscopy using the standard Beer−Lambert law, after introducing 10−100 kPa of a known composition of the calibration gas (0.966% NO2 diluted with Ar; Takachiho Chemical Industrial) into the shock tube. This measurement was performed using the optical setup shown in Figure 1 but without placing the cavity mirrors (the absorption path length is 5.0 cm) and with attenuated light intensity to avoid saturation of the MAPMT signals. The results are shown in Figure 2a, which were in close agreement with the literature absorption cross section27 convolved with a 2 nm wide rectangular window, shown as a dashed line. Uncertainties in the derived absorption cross sections are ±1.5, ±3.1, and ±10.1% for wavelength ranges of 350−420, 300−350, and 280−300 nm, respectively, at 95% confidence intervals on the basis of the statistical uncertainty and uncertainty in the sample concentration (0.5%). The large uncertainty below 300 nm is due to the low light intensity from the light source and the small absorption cross section in this region. The transmitted light intensities were then measured with the BBCEAS setup for 1−12 kPa of 0.966% NO2/Ar, and the effective path lengths were calculated from eq 1. Typical values of leff are plotted in Figure 2b as a function of the wavelength. Due

(1)

where I0 and I are the transmitted light intensities in the absence and presence of the absorbing medium, respectively, and leff represents an effective absorption path length, which can also be expressed as a product of the single-pass absorption path length and the cavity enhancement (or gain) factor. The effect of Rayleigh scattering on the transmitted light intensities was negligible under the conditions investigated in this study; on the basis of the Rayleigh scattering cross section of Ar (calculated using the expression given in ref 26), the extinction coefficient 2072

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several times during each set of measurements (typically 3−8 shots) and was found to be stable within ±3%. Therefore, the total uncertainties in the absorption path lengths are ±3.4, ±4.3, and ±10.6% for wavelength ranges 350−420, 300−350, and 280−300 nm, respectively, at 95% confidence intervals. The performance of the time-resolved BBCEAS method is characterized by its temporal resolution and detection sensitivity. The temporal resolution for the shock experiments is influenced by the bandwidth of the light detection system, the shock wave velocity, and the effective beam width inside the cavity. Since this last quantity is difficult to estimate owing to the imperfect coupling of the light, the resolution was evaluated as the full width at half-maximum of the schlieren spike due to density deflection caused by the passage of shock waves, which was found to be less than 5 μs for the reflected shock conditions T5 > 950 K and p5 = 100 kPa. The noise-equivalent per-channel detection limit of the absorption coefficient behind the reflected shock wave significantly depends on the wavelength; it was approximately 2 × 10−5 cm−1 around 400 nm, and increased by a factor of 2 around 350 nm and by more than a factor of 10 at wavelengths below 300 nm when the signals were averaged over three shock experiments. These values correspond to single-pass absorbance of 0.01, 0.02, and 0.1%, respectively, which are significant improvements over the detection limit for the single-pass setup, which was 0.3−0.7%. A severe reduction in the sensitivity at the shorter wavelengths was caused not only by the short effective path length in this region but also by the low light intensity from the lamp and the light absorption by the surface coatings of the mirrors and windows. Further improvement of the sensitivity can be achieved by employing a light source with high brightness at deep UV wavelengths, such as a laser-driven plasma light source.28,29 Additionally, the effective path length can be elongated using mirrors with higher reflectivity. In such cases, it is desirable to mount the mirrors directly on the shock tube in the place of the windows, because absorption by the antireflection-coated windows limits the enhancement factor. Some recent applications of laser-based CEAS methods in shock tubes12,13 demonstrated the feasibility of this approach. Furthermore, no systematic variation in the effective path length was observed over time during the experiments reported in this Article, indicating that deterioration in the transmittance of the windows was negligible. However, a small but measurable gradual decrease (less than 1% per single shot on average) in leff was detected when toluene (diluted with Ar to 100 ppm) was used as the sample gas under reflected shock conditions with T5 = 1740 K and p5 = 100 kPa. This reduction was possibly caused by condensation of some reaction products such as polycyclic aromatic hydrocarbons on the window surfaces, and degradation of the dielectric coating on the windows by some heterogeneous reactions. By cleaning the window surfaces using methanol, the performance could be recovered partially but not completely. Therefore, directly installing higher reflectivity mirrors in the place of the windows would produce a significant improvement on the detection sensitivity but could potentially cause irreversible degradation of the expensive mirrors depending on the experimental conditions. Application: High-Temperature Kinetics and Spectroscopy of Formaldehyde. The applicability of the method developed has been evaluated by investigating the kinetics and spectroscopy of formaldehyde (CH2O) at high temperatures. Formaldehyde is an important intermediate product in the

Figure 3. Time-resolved absorption spectra of formaldehyde observed following the pyrolysis of 1,3,5-trioxane behind the shock waves at p5 = 100 ± 2 kPa and T5 = 955, 1265, and 1708 K.

mainly to wavelength dependence of the mirror reflectivity, leff varies from 60 to 200 cm across the wavelength range 280−420 nm, corresponding to a cavity enhancement factor of 12−40. This factor is lower than the ideal enhancement factor of 20−50, which is expected from the mirror reflectivity specified by the manufacturer, due to light absorption by the dielectric antireflection coatings of the windows as well as imperfect coupling of the light with the cavity (including that caused by small residual reflectivity of the antireflection coated surfaces). In the shock-tube experiments described below, leff was measured 2073

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The Journal of Physical Chemistry A Table 1. Absorption Cross Sections of Formaldehyde at High Temperatures absorption cross section (10−21 cm2 molecule−1) wavelength (nm) 282.4 284.6 286.7 288.8 291.0 293.1 295.2 297.3 299.5 301.6 303.7 305.9 308.0 310.1 312.3 314.4 315.9 317.9 320.0 322.1 324.1 326.2 328.3 330.3 332.4 334.5 336.6 338.6 340.7 342.8 344.8 346.9

955 K 18.8 28.2 24.8 28.7 24.8 29.3 33.3 30.5 28.4 25.5 37.2 40.7 34.3 30.9 27.6 36.6 40.2 35.4 27.4 21.1 23.2 38.6 36.9 28.8 18.1 12.5 14.2 30.7 31.1 25.0 15.6 10.0

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2.4 3.3 2.9 3.3 2.9 3.3 3.7 3.4 3.1 1.3 1.8 1.9 1.6 1.5 1.3 1.7 1.9 1.7 1.3 1.0 1.1 1.8 1.7 1.4 0.9 0.7 0.7 1.4 1.4 1.2 0.7 0.5

1265 K 23.5 27.4 27.9 31.6 29.0 31.4 34.8 35.9 34.7 34.5 38.1 43.1 41.6 40.6 39.0 41.5 41.8 42.5 37.5 32.8 33.6 42.7 43.5 39.0 29.7 24.0 24.8 35.2 38.9 34.3 25.9 19.5

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

2.9 3.3 3.2 3.6 3.3 3.5 3.8 3.9 3.8 1.7 1.8 2.0 1.9 1.9 1.8 1.9 2.0 2.0 1.8 1.6 1.6 2.0 2.0 1.8 1.4 1.1 1.2 1.6 1.8 1.6 1.2 0.9

absorption cross section (10−21 cm2 molecule−1)

1708 K

wavelength (nm)

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

348.3 350.3 352.3 354.3 356.3 358.3 360.3 362.4 364.4 366.4 368.4 370.4 372.4 374.4 376.4 378.4 380.7 382.7 384.6 386.6 388.5 390.5 392.4 394.4 396.3 398.3 400.2 402.2 404.1 406.1 408.0 410.0

33.0 32.7 33.2 39.5 37.2 37.4 39.8 41.6 41.4 41.2 44.0 46.5 48.0 48.1 48.5 50.5 49.6 50.9 48.2 46.0 46.6 49.8 51.8 49.5 43.8 39.4 39.2 45.0 46.8 45.2 39.2 35.4

4.6 4.7 4.5 4.9 4.6 4.4 4.6 4.7 4.7 2.2 2.3 2.4 2.4 2.3 2.3 2.4 2.4 2.4 2.3 2.3 2.3 2.4 2.5 2.4 2.1 1.9 1.9 2.1 2.2 2.1 1.8 1.7

955 K 6.2 7.2 17.4 20.6 13.6 8.0 5.3 3.5 3.3 4.1 7.1 8.3 5.4 3.6 3.0 2.3 1.60 1.57 2.2 1.64 1.18 0.98 0.80 1.01 1.07 0.70 0.50 0.45 0.48 0.37 0.32 0.23

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.3 0.3 0.7 0.8 0.5 0.3 0.2 0.2 0.2 0.2 0.3 0.3 0.2 0.2 0.1 0.1 0.09 0.09 0.1 0.09 0.08 0.08 0.08 0.08 0.08 0.07 0.06 0.06 0.07 0.06 0.05 0.05

1265 K 14.6 14.3 21.8 25.6 21.2 15.8 12.1 9.6 8.4 9.2 12.4 13.2 10.8 8.7 7.5 6.4 5.0 4.8 5.6 5.0 4.0 3.6 3.2 3.3 3.4 2.8 2.4 2.2 2.1 1.74 1.67 1.51

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

0.7 0.6 0.8 1.0 0.8 0.6 0.5 0.4 0.4 0.4 0.5 0.5 0.4 0.4 0.3 0.3 0.2 0.2 0.2 0.2 0.2 0.2 0.1 0.1 0.2 0.1 0.1 0.1 0.1 0.09 0.09 0.08

1708 K 29.5 28.2 32.0 34.5 31.8 28.3 24.5 22.1 20.4 20.4 22.1 21.9 20.1 18.4 16.6 15.4 13.8 12.5 12.7 12.0 10.9 10.3 9.4 9.1 9.1 8.4 7.3 6.9 7.2 5.8 5.7 5.4

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

1.4 1.1 1.2 1.3 1.2 1.1 0.9 0.8 0.8 0.8 0.8 0.8 0.8 0.7 0.6 0.6 0.5 0.5 0.5 0.5 0.4 0.4 0.4 0.4 0.4 0.3 0.3 0.3 0.3 0.2 0.2 0.2

Figure 3 shows the temporal profiles of the absorption coefficients recorded in the wavelength range 280−410 nm. The channel (wavelength) specific time profiles are also shown in Figures S1−S3 (Supporting Information). Time (t) zero in the profiles indicates the arrival of the reflected shock waves. The thin horizontal lines visible in Figure 3 at t = 0 and near t = −0.1 ms correspond to the schlieren spikes resulting from the passage of the reflected and incident shock fronts, respectively. Several absorption bands were observed behind the reflected shock waves under all three conditions. At 955 K, the absorption coefficients rise following the passage of the reflected waves and reach plateaus near t = 0.5 ms. The absorptions are almost instantly developed and remain nearly constant at 1265 K. At the highest temperature, the instantly developed absorptions gradually decrease on the sub-millisecond time scale. Under this condition, small absorptions were also observed behind the incident shock waves due to the slow decomposition of 1,3,5trioxane at a post-incident-shock temperature of ∼900 K. These three types of the temporal behaviors are consistent with those reported in the literature.33 The unimolecular decomposition of 1,3,5-trioxane proceeds with a concerted mechanism and exclusively produces three formaldehyde molecules:34

oxidation of hydrocarbon fuels, especially in cool-flame regions.30 This species was selected as a first example for the evaluation because it has characteristic weak absorption bands over a wide spectral region at near-UV wavelengths with an average absorption cross section of the order of 10−20 cm2 molecule−1.31,32 Here, the UV−visible absorption of formaldehyde was detected behind reflected shock waves using 1,3,5trioxane (C3H6O3) as a precursor.33,34 In the following experiments, the absorption cross sections of the formaldehyde and the rate constants for the decomposition of 1,3,5-trioxane and formaldehyde were determined from the time-resolved BBCEAS measurements and compared with literature data. The sample gas used was a mixture of 2000 ppm of 1,3,5trioxane (>99%; Tokyo Chemical Industry; degassed by several freeze−pump−thaw cycles before use) diluted in Ar (>99.9999%; Taiyo Nippon Sanso). The mixtures were prepared from pressure measurements using capacitance manometers (MKS Instruments, Baratron 626), stored in glass vessels, and allowed to homogenize overnight or longer. The experiments were performed at a postshock pressure of p5 = 100 ± 2 kPa and three representative temperatures: T5 = 955, 1265, and 1708 K; the formation and consumption of formaldehyde were observed at the lowest and highest temperatures, respectively, whereas uniform temporal profiles of near-instantly formed formaldehyde were obtained at the intermediate temperature.

C3H6O3 → 3CH 2O 2074

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temperatures, they were determined through kinetic analyses of the profiles. For the kinetic analyses, the time profiles were weighted averaged over the wavelengths (or the MAPMT channels). Since the detection sensitivity significantly depends on the wavelength, a weight defined by the square of the signalto-noise ratio was applied. Time profiles of the weighted averaged absorption coefficient, αw̅ , are shown in Figure 4. At 955 K, reaction R1 was the sole reaction responsible for the time history of formaldehyde. The decomposition rate constant k1 was determined by a nonlinear least-squares fit of the profile to a form of C[1 − exp(−k1t)], where C is a proportional constant equivalent to the plateau value of the absorption coefficient and hence is related to the absorption cross section. The fit gave a rate constant of k1 = 9.3 × 103 s−1 with a standard error of only 1% owing to the high signal-to-noise ratio. The actual uncertainty is dominated by the uncertainty in the postshock temperature (1%). The value of the derived rate constant lies in line with those of two recent evaluations33,34 within the specified uncertainties (the comparison is shown in Figure S4 in the Supporting Information). The profile at 1708 K was analyzed using the reaction mechanism of USC-Mech II.35 As reported in a recent study,33 a simulation using this mechanism slightly underpredicted the observed decay rate and showed high sensitivities to the following reactions (where M represents a third body): Figure 4. Time profiles of the weighted averaged absorption coefficients observed following the pyrolysis of 1,3,5-trioxane behind the shock waves at p5 = 100 ± 2 kPa and T5 = 955, 1265, and 1708 K. The righthand axes represent the corresponding concentrations of formaldehyde relative to the initial concentration of 1,3,5-trioxane. The dashed lines (almost superimposed on the solid lines) are the fitted profiles.

CH 2O + M = HCO + H + M

(R2)

CH 2O + H = HCO + H 2

(R3)

HCO + M = H + CO + M

(R4)

HCO + H = CO + H 2

(R5)

Here, the rate constants for reactions R3−R5 have been updated to the values reported by Friedrichs et al.36,37 and a nonlinear least-squares fit was performed to determine the rate constant for R2, k2, and the absorption cross section. The resultant rate constant was k2 = 2.4 × 10−18 cm3 molecule−1 s−1 for M = Ar, which is comparable to the value in another study by Friedrichs et al.,38 k2 = 2.7 × 10−18 cm3 molecule−1 s−1 at 1708 K and a total pressure of 100 kPa with argon, deduced from their rate expression derived from a Rice−Ramsperger−Kassel−Marcus (RRKM) calculation. The simulation using the updated mechanism agreed well with the observed profile within the noise level, as shown in Figure 4c. It can also reproduce wavelength-specific time profiles (see Figure S3 in the Supporting Information), indicating the absence of interference absorption from the reaction products (H2, CO, and small fractions of H and HCO radicals; see Figure S5 in the Supporting Information). The absorption cross sections of formaldehyde are plotted in Figure 5 together with the literature data.31,33 The present values are also listed in Table 1 with the 95% confidence intervals deduced from the uncertainties in the fit, effective path lengths, sample compositions, and postshock gas densities. The spectra exhibit clear band structures, which are broadened as the temperature rises due to the increased number of populated rovibronic states. The absorption cross section increases with temperature, notably at the long wavelength side due to the contribution of the transition from the high vibrational levels of the ground electronic state. The spectral feature matches that reported by Mackey et al.,31 which was taken in a flow tube cell at 873 K with a spectral resolution of 0.3 nm. The data is also consistent with the cross-section value reported by Wang et al.,33

Figure 5. Absorption cross sections of formaldehyde at high temperatures determined in this study (dashed lines with symbols; 2 nm resolution), by Mackey et al.31 (solid line; 0.3 nm resolution; taken from their Figure 2), and by Wang et al.33 (diamond; measured with a narrow line laser at 306.7 nm).

Therefore, the absorption cross sections of formaldehyde can be quantitatively inferred from the observed absorption coefficients. At the intermediate temperature, the wavelength-dependent cross sections were directly determined from the post-reflectedshock absorption coefficients. At the lowest and highest 2075

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The Journal of Physical Chemistry A

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which was measured using a narrow-line laser at 306.7 nm, considering the difference in the spectral resolutions.

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CONCLUSION Time-resolved broadband cavity-enhanced absorption spectroscopy has been successfully applied for fast and sensitive broadband absorption measurements behind shock waves. The method developed enables time-resolved absorption measurements over an ∼32 nm spectral bandpass in a single experiment with temporal and spectral resolutions of 5 μs and 2 nm, respectively. The spectral region can be further extended by combining the data taken at different center wavelengths, utilizing the high reproducibility of the diaphragmless shock tube employed. The effective absorption path lengths of 60−200 cm have been achieved across the wavelength range 280−420 nm. The applicability of the method developed to kinetic and spectroscopic measurements has been investigated through timeand wavelength-resolved absorption measurements of formaldehyde behind the reflected shock waves. The results presented validate this new technique.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b01069. Figures showing wavelength-specific time profiles of the absorption coefficients, a comparison of the present and literature rate constants, and simulated time profiles (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81-29-861-2735. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by JSPS KAKENHI Grant Numbers 15K17991 and 15K01231.

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REFERENCES

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Article

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DOI: 10.1021/acs.jpca.6b01069 J. Phys. Chem. A 2016, 120, 2070−2077