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Absorption cross-section measurements of the vinyl radical in the 440–460 nm region by cavity ring-down spectroscopy
19 November 1999
Chemical Physics Letters 313 Ž1999. 771–776 www.elsevier.nlrlocatercplett
Absorption cross-section measurements of the vinyl radical in the 440–460 nm region by cavity ring-down spectroscopy Kenichi Tonokura ) , Satoshi Marui, Mitsuo Koshi Department of Chemical System Engineering, School of Engineering, The UniÕersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Received 28 June 1999; in final form 28 July 1999
Abstract Absorption cross-sections of the vinyl radical ŽC 2 H 3 . have been determined in the spectral range 440–460 nm, using laser photolysis coupled with a cavity ring-down spectroscopic detection technique. The disappearance rate of vinyl radical ˜ 2AY –X˜ 2AX transition was probed by visible cavity ring-down spectroscopy. Based on a reaction kinetics by its absorption in A simulation, the absorption cross-sections of the vinyl radical were estimated. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Knowledge of the kinetics of unsaturated hydrocarbon free radicals is of primary importance in the modeling of atmospheric and combustion reactions. Vinyl radicals have been found in abundance in interstellar space, and they have been detected in low-temperature planetary atmospheres w1x. They also play a key role in high-temperature hydrocarbon combustion systems where they are involved in the formation of polyacetylenes and possibly of polycyclic aromatic hydrocarbons and hence of soot w2x. Kinetic absorption measurements of the vinyl radical have been applied in the vacuum ultraviolet region w3,4x. Due to difficulties in detecting the vinyl radical using standard optical detection techniques, the reaction kinetics database of the vinyl radical has ) Corresponding author. Tel.: q81-3-5841-7296; fax: q81-35841-7488; e-mail: [email protected]
been determined mainly by mass spectroscopy w5–8x. Electronic spectral properties of the vinyl radical in the visible region have been studied previously. Hunziker et al. w9x observed a visible absorption band assigned to the electronic transition between the ˜ 2AX . and first excited state ŽA˜ 2AY . of the ground ŽX vinyl radical with the band origin at 499.5 nm. Most recently, Pibel et al. w10x, using cavity ring-down spectroscopy ŽCRDS., have observed the visible transition of the vinyl radical between 530 and 415 nm. Mebel et al. w11x calculated the vibrational fre˜ 2AY state and Franck–Condon facquencies of the A ˜ 2AY § X˜ 2AX tors and the oscillator strength for the A transition. In the present work, we report the absorption cross-sections of the vinyl radical in the range 440– 460 nm. Vinyl radical was generated by 193 nm photolysis of methyl vinyl ketone. Based on the reaction kinetic simulation of the methyl–vinyl system, absorption cross-sections for the vinyl radical
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 1 0 7 0 - 2
772
K. Tonokura et al.r Chemical Physics Letters 313 (1999) 771–776
have been determined. The objective of the present work is to determine the absorption cross-sections and detection sensitivity of the vinyl radical using the visible CRDS technique. It will be shown that, using visible CRDS, the vinyl radical can be detected with sufficient sensitivity to enable kinetic investigation of its reactions.
The photolysis and CRDS system was used for the production and detection of vinyl radical. The basic principle of the cavity ring-down method applied to the kinetic studies has been described by Yu and Lin w12x. Fig. 1 shows a schematic diagram of the CRDS apparatus. The ring-down cavity is 0.625 m long with a pair of high-reflectance mirrors Ž R ) 0.9999 at 450 nm. with 1.2 m radius of curvature and 25.4 mm diameter Žcovering the range 430–470 nm.. For fine optical adjustment, the mirror mounts are adjustable with two pairs of micrometer screws. A He–Ne laser was used to aid alignment. The vinyl radicals were produced by ArF excimer laser ŽLambda Physik COMPex 102. stimulated pho-
tolysis of methyl vinyl ketone ŽMVK. and vinyl bromide ŽVB.. The photolysis laser power used was 3–10 mJ cmy2 per pulse. The output of the excimer pumped dye laser ŽLambda Physik LPX 110 q Lambda Physik LPD 3002. was used for the probe laser. The photolysis laser beam entered the reaction cell at a right angle to the cavity and overlapped the probe laser beam at the center of the reaction cell. The probe laser beam was injected into the cavity through one of the mirrors. The photon intensity decay inside the cavity was monitored by measuring the weak transmission of light through the other mirror with a photomultiplier tube ŽHamamatsu R955.. The output of the signal from a photomultiplier tube was fed to a digital oscilloscope ŽTektronix TDS 520C. and transferred to a PC via a GPIB interface. The ring-down waveforms were averaged over 20 laser pulses. Absorption spectra were obtained by scanning the wavelength of the probe laser. For time-dependent studies, timing between the photolysis and probe laser beams was controlled by a pulse generator ŽStanford Research Systems DG535.. Decay of the intensity of the laser light trapped within the cavity follows a simple exponential function w13x
Fig. 1. Schematic diagram of laser photolysis in combination with CRDS.
It s I0 exp Ž yb t . Ž 1. where It is intensity at time t, I0 is intensity at time zero, b is intensity decay rate in the optical cavity. The average b is calculated from the linear average over N pulses, that is ² b : s Ý birN. In the photolysis experiments, the average absorbance ² A: is calculated as follows: l ² A: s Ž² babs :y² b base :. Ž 2. c where l is the cavity length and c is the speed of light. ² babs : is decay rate in the presence of an absorber, and ² b base : is base decay rate under nonabsorbing conditions. Typical ring-down waveforms are shown in Fig. 2. The gases were regulated by calibrated mass flow controllers, and the typical total flow rate was 3800 sccm. In order to protect the mirrors and photolysis beam entrance windows from deposition of reaction products, a flow of Ar was introduced over these optics. The sample gases used in the present experiments were premixed Žca. 5% diluted in argon.. The total pressure was measured at the center of the
2. Experimental
K. Tonokura et al.r Chemical Physics Letters 313 (1999) 771–776
773
that measured by Hunziker et al. w9x in same spectral region. This electronic transition was assigned to ˜ 2AY § X˜ 2AX transition. vinyl A An initial concentration of vinyl radical in the photolysis experiments is estimated from the relation
w C 2 H 3 x 0 s Np w C 2 H 3 X x sC193 f 2H 3X
Ž 3.
where wC 2 H 3 Xx and s are vinyl precursor concentration and absorption cross-section, respectively, and Np is number density of laser photons as determined from laser pulse energy measurements. The production yield of vinyl radical Ž f . was estimated from the 193 nm photodissociation processes of MVK as follows: C 2 H 3 COCH 3 q 193 nm ™ C 2 H 3) q CO q CH 3 , Ž R1. Fig. 2. Ring-down decay waveforms observed at 446.5 nm Ža. without 193 nm photolysis of MVK, Žb. with 193 nm photolysis of MVK. The solid line marks that part of the waveform that is a single-exponential fit to the experimental data.
reaction cell with a capacitance manometer ŽMKS Baratron 122AA.. Reagent concentrations were calculated from the total pressure and the calibrated flow rates. Spectroscopic and kinetics experiments were carried out at a laser repetition rate of 1–6 Hz to ensure complete removal of the reacted mixture and replenishment of the gas sample between successive laser shots. Experiments were carried out at room temperature Ž297 " 2 K..
C 2 H 3) ™ C 2 H 2 q H ,
Ž R2.
C 2 H 3) q M ™ C 2 H 3 q M ,
Ž R3.
where C 2 H 3) represents a hot vinyl radical. The production yields of methyl and vinyl radicals were determined to be 22.8 " 3.3 and 20.4 " 2.7%, respectively w14x. The initial methyl and vinyl radical
3. Results and discussion The vinyl radical has been confirmed as being a primary photoproduct in 193 nm photolysis of MVK and VB w14–17x. Fig. 3 shows the measured absorption spectrum of vinyl radical produced in 193 nm photolysis of MVK at a total pressure of 30 Torr. No dependence on the total pressure Ž10–30 Torr. in the absorption spectrum was observed. The same absorption spectrum was observed when the system of 193 nm photolysis of VB is used as a source of vinyl radical production, which is strong evidence for the production and detection of vinyl radical in these systems. The spectrum is in excellent agreement with
Fig. 3. Absorption spectrum of vinyl radical observed from 193 nm photolysis of MVK Ž5=10 14 molecules cmy3 .. The time delay between the photolysis and probe laser beams is 1 ms. The spectrum was measured with 0.1 nm spectral resolution.
K. Tonokura et al.r Chemical Physics Letters 313 (1999) 771–776
774
yields were in good agreement with the photolysis yield of MVK Ž23.6 " 1.1%. w14x. The production of C 2 H 2 q H from C 2 H 3) represents a minor fraction of the C 2 H 3 yield w14x. For 193 nm photolysis of VB, the quantum yield of vinyl radical formation has not been determined to our knowledge. In the absorption cross-section measurements, therefore, MVK is used as a source of vinyl radical. Fig. 4 shows a typical time profile of vinyl radical absorption at 446.5 nm. The points represent the averaged absorbance of vinyl radical as a function of time delay between photolysis and probe laser. Assuming the Beer–Lambert law, the average absorbance ² A: is given by ² A : s sC
2H3
wC 2 H 3 x ls
Ž 4.
where sC 2 H 3 is absorption cross-section of vinyl radical at wavelength l, and l s is absorption pathlength induced by photolysis laser beam Ž; 38 mm.. This time dependence would be governed by the vinyl–vinyl, methyl–methyl, and vinyl–methyl reaction w14,18x. Contribution of the reaction of vinyl and methyl radicals with H atom is negligibly small because of the low quantum yield of H atom compared to vinyl and methyl radicals, and following
Fig. 4. Time profile of vinyl radical absorbance at 446.5 nm with time delay between photolysis and probe laser. The solid curve is the best fit of these data using s s 4.9=10y1 9 cm2 moleculey1 and wC 2 H 3 x 0 s 5=10 13 molecules cmy3.
reactions have to be considered: C 2 H 3 q C 2 H 3 ™ Products ,
Ž R4.
CH 3 q CH 3 ™ Products ,
Ž R5.
C 2 H 3 q CH 3 ™ Products .
Ž R6.
For this multicomponent reaction system, the rate equations are as follows: d wC 2 H 3 x dt
2
s y2 k 4 w C 2 H 3 x y k 6 w CH 3 xw C 2 H 3 x ,
Ž 5. d w CH 3 x dt
2
s y2 k 5 w CH 3 x y k 6 w CH 3 xw C 2 H 3 x .
Ž 6.
The coupled differential equations are solved by numerical integration routines. The rate constants for the reactions ŽR4. to ŽR6. have previously been determined w18,19x and were used as fixed parameters. Since the disappearance rate of vinyl radical is very sensitive to its initial concentration, the initial concentrations of vinyl radical can be determined by fitting the calculated decay rates to the experimental values, and therefore the absorption cross-section can be estimated. The solid curve shown in Fig. 4 represents the fit to the experimental data using the parameters. The initial radical concentrations were controlled by changing the precursor concentration and photolysis laser power. Fig. 5 shows the results of the analysis for the absorption cross-sections of vinyl radical as a function of the initial vinyl radical concentrations. No dependence of the absorption cross-section on the initial radical concentrations nor the ArF laser power was observed. The line shown in Fig. 5 represents the average value of s446.5 s Ž4.8 " 0.3. = 10y1 9 cm2 moleculey1. Based on this value, the absorption cross-sections in the range 440–460 nm are obtained ŽFig. 3.. From the results of Hunziker et al. w9x the absorption cross-section at 446.5 nm is deduced to be Ž0.8 " 0.3. = 10y1 9 cm2 moleculey1 . In the experiments of Hunziker et al. w9x, the determination of the absorption cross-section is sensitive to the estimate of the radical concentrations produced from the Hg-photosensitized reactions. On the other hand, in our study, the initial concentration of the vinyl radicals is directly determined from well-established rate constants. The present absorption cross-section measurement was carried out at
K. Tonokura et al.r Chemical Physics Letters 313 (1999) 771–776
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The detection sensitivity of the CRDS method is limited by the mirror reflectivity and minimum change in the ring-down time that can be detected. Zalicki and Zare w20x showed that, for a change in the ring-down time Dt upon tuning to an absorption feature, the corresponding absorbance per pass is Dt
Ž a l s . min s Ž 1 y R .
ž / t
.
Ž 7.
min
The reflectivity of the mirrors used in the current study is 0.9999, and the accuracy in the ring-down time determination of Ž Dtrt . min s 0.03, the minimum measured absorbance Ž a l s . min is calculated to be 3 = 10y6 . On the basis of the absorption crosssection of 4.8 = 10y1 9 cm2 moleculey1 for the vinyl radical and l s of 3.8 cm, the detection limit of vinyl radical with the present apparatus is estimated to be 2 = 10 12 molecules cmy3 .
Acknowledgements We thank C.A. Taatjes for a preprint of Ref. w10x. This work is supported in part by a Grant-in-Aid from the ministry of Education, Science, Sports and Culture ŽNo. 10640483. and Sumitomo Foundation. Fig. 5. Plots of calculated absorption cross-section of vinyl radical at 446.5 nm as a function of Ža. photolysis laser power and Žb. MVK concentration.
References
higher spectral resolution than in the previous study. These differences should be emphasized in comparing our results with previous studies. The reliability of the value determined in the present study was checked as follows. The initial concentration of vinyl radical is estimated from Eq. Ž3.. The absorbance at 446.5 nm is about 80 ppm ŽFig. 3.. From Eq. Ž4., the absorption cross-section is estimated to be Ž4 " 1. = 10y1 9 cm2 moleculey1 , which is consistent with the value estimated from the analytical simulation. Pibel et al. w10x reported the crude estimate of the absorption cross-section of vinyl radicals, which agrees with Hunziker et al. However, the cross-section calculated from their results using Eqs. Ž3. and Ž4. is also consistent with our results.
w1x D. Toublanc, J.P. Parisot, J. Brillet, D. Gautier, F. Raulin, C.P. McKay, Icarus 113 Ž1995. 2. w2x P.R. Westmoreland, A.M. Dean, J.B. Howard, J.P. Longwell, J. Phys. Chem. 93 Ž1989. 817. w3x A. Fahr, A.H. Laufer, J. Phys. Chem. 92 Ž1988. 7229. w4x A. Fahr, A.H. Laufer, J. Phys. Chem. 94 Ž1990. 726. w5x I.R. Slagle, J.-Y. Park, M.C. Heaven, D. Gutman, J. Am. Chem. Soc. 106 Ž1984. 4356. w6x R.P. Thorn, W.P. Payne, L.J. Stief, D.C. Trady, J. Phys. Chem. 100 Ž1996. 13594. w7x W.A. Payne, P.S. Monks, F.L. Nesbitt, L.J. Stief, J. Chem. Phys. 104 Ž1996. 9808. w8x V.D. Knyazev, I.R. Slagle, J. Phys. Chem. 100 Ž1996. 16899. w9x H.E. Hunziker, H. Kneppe, A.D. McLean, P. Siegbahn, H.R. Wendt, Can. J. Chem. 61 Ž1983. 993. w10x C.D. Pibel, A. McIlroy, C.A. Taatjes, S. Alfred, K. Patrick, J.B. Halpern, J. Chem. Phys. 110 Ž1999. 1841.
776
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w11x A.M. Mebel, Y.-T. Chen, S.H. Lin, Chem. Phys. Lett. 275 Ž1997. 19. w12x T. Yu, M.C. Lin, Int. J. Chem. Kinet. 26 Ž1994. 771. w13x D.B. Atkinson, J.W. Hudgens, J. Phys. Chem. A 101 Ž1997. 3901. w14x A. Fahr, W. Braum, A. Laufer, J. Phys. Chem. A 97 Ž1993. 1502. w15x A. Fahr, A. Laufer, J. Phys. Chem. 99 Ž1995. 262.
w16x A.M. Wodtke, E.J. Hintsa, J. Somarjai, Y.T. Lee, Isr. J. Chem. 29 Ž1989. 383. w17x A. Fahr, A. Laufer, M. Krauss, R. Osman, J. Phys. Chem. 101 Ž1997. 4885. w18x A. Fahr, W. Braun, Int. J. Chem. Kinet. 20 Ž1994. 20. w19x A. Fahr, A. Laufer, R. Klein, W. Braum, J. Phys. Chem. 95 Ž1991. 3218. w20x P. Zalicki, R. Zare, J. Chem. Phys. 102 Ž1995. 2708.
Chemical Physics Letters 313 Ž1999. 771–776 www.elsevier.nlrlocatercplett
Absorption cross-section measurements of the vinyl radical in the 440–460 nm region by cavity ring-down spectroscopy Kenichi Tonokura ) , Satoshi Marui, Mitsuo Koshi Department of Chemical System Engineering, School of Engineering, The UniÕersity of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan Received 28 June 1999; in final form 28 July 1999
Abstract Absorption cross-sections of the vinyl radical ŽC 2 H 3 . have been determined in the spectral range 440–460 nm, using laser photolysis coupled with a cavity ring-down spectroscopic detection technique. The disappearance rate of vinyl radical ˜ 2AY –X˜ 2AX transition was probed by visible cavity ring-down spectroscopy. Based on a reaction kinetics by its absorption in A simulation, the absorption cross-sections of the vinyl radical were estimated. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Knowledge of the kinetics of unsaturated hydrocarbon free radicals is of primary importance in the modeling of atmospheric and combustion reactions. Vinyl radicals have been found in abundance in interstellar space, and they have been detected in low-temperature planetary atmospheres w1x. They also play a key role in high-temperature hydrocarbon combustion systems where they are involved in the formation of polyacetylenes and possibly of polycyclic aromatic hydrocarbons and hence of soot w2x. Kinetic absorption measurements of the vinyl radical have been applied in the vacuum ultraviolet region w3,4x. Due to difficulties in detecting the vinyl radical using standard optical detection techniques, the reaction kinetics database of the vinyl radical has ) Corresponding author. Tel.: q81-3-5841-7296; fax: q81-35841-7488; e-mail: [email protected]
been determined mainly by mass spectroscopy w5–8x. Electronic spectral properties of the vinyl radical in the visible region have been studied previously. Hunziker et al. w9x observed a visible absorption band assigned to the electronic transition between the ˜ 2AX . and first excited state ŽA˜ 2AY . of the ground ŽX vinyl radical with the band origin at 499.5 nm. Most recently, Pibel et al. w10x, using cavity ring-down spectroscopy ŽCRDS., have observed the visible transition of the vinyl radical between 530 and 415 nm. Mebel et al. w11x calculated the vibrational fre˜ 2AY state and Franck–Condon facquencies of the A ˜ 2AY § X˜ 2AX tors and the oscillator strength for the A transition. In the present work, we report the absorption cross-sections of the vinyl radical in the range 440– 460 nm. Vinyl radical was generated by 193 nm photolysis of methyl vinyl ketone. Based on the reaction kinetic simulation of the methyl–vinyl system, absorption cross-sections for the vinyl radical
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 1 0 7 0 - 2
772
K. Tonokura et al.r Chemical Physics Letters 313 (1999) 771–776
have been determined. The objective of the present work is to determine the absorption cross-sections and detection sensitivity of the vinyl radical using the visible CRDS technique. It will be shown that, using visible CRDS, the vinyl radical can be detected with sufficient sensitivity to enable kinetic investigation of its reactions.
The photolysis and CRDS system was used for the production and detection of vinyl radical. The basic principle of the cavity ring-down method applied to the kinetic studies has been described by Yu and Lin w12x. Fig. 1 shows a schematic diagram of the CRDS apparatus. The ring-down cavity is 0.625 m long with a pair of high-reflectance mirrors Ž R ) 0.9999 at 450 nm. with 1.2 m radius of curvature and 25.4 mm diameter Žcovering the range 430–470 nm.. For fine optical adjustment, the mirror mounts are adjustable with two pairs of micrometer screws. A He–Ne laser was used to aid alignment. The vinyl radicals were produced by ArF excimer laser ŽLambda Physik COMPex 102. stimulated pho-
tolysis of methyl vinyl ketone ŽMVK. and vinyl bromide ŽVB.. The photolysis laser power used was 3–10 mJ cmy2 per pulse. The output of the excimer pumped dye laser ŽLambda Physik LPX 110 q Lambda Physik LPD 3002. was used for the probe laser. The photolysis laser beam entered the reaction cell at a right angle to the cavity and overlapped the probe laser beam at the center of the reaction cell. The probe laser beam was injected into the cavity through one of the mirrors. The photon intensity decay inside the cavity was monitored by measuring the weak transmission of light through the other mirror with a photomultiplier tube ŽHamamatsu R955.. The output of the signal from a photomultiplier tube was fed to a digital oscilloscope ŽTektronix TDS 520C. and transferred to a PC via a GPIB interface. The ring-down waveforms were averaged over 20 laser pulses. Absorption spectra were obtained by scanning the wavelength of the probe laser. For time-dependent studies, timing between the photolysis and probe laser beams was controlled by a pulse generator ŽStanford Research Systems DG535.. Decay of the intensity of the laser light trapped within the cavity follows a simple exponential function w13x
Fig. 1. Schematic diagram of laser photolysis in combination with CRDS.
It s I0 exp Ž yb t . Ž 1. where It is intensity at time t, I0 is intensity at time zero, b is intensity decay rate in the optical cavity. The average b is calculated from the linear average over N pulses, that is ² b : s Ý birN. In the photolysis experiments, the average absorbance ² A: is calculated as follows: l ² A: s Ž² babs :y² b base :. Ž 2. c where l is the cavity length and c is the speed of light. ² babs : is decay rate in the presence of an absorber, and ² b base : is base decay rate under nonabsorbing conditions. Typical ring-down waveforms are shown in Fig. 2. The gases were regulated by calibrated mass flow controllers, and the typical total flow rate was 3800 sccm. In order to protect the mirrors and photolysis beam entrance windows from deposition of reaction products, a flow of Ar was introduced over these optics. The sample gases used in the present experiments were premixed Žca. 5% diluted in argon.. The total pressure was measured at the center of the
2. Experimental
K. Tonokura et al.r Chemical Physics Letters 313 (1999) 771–776
773
that measured by Hunziker et al. w9x in same spectral region. This electronic transition was assigned to ˜ 2AY § X˜ 2AX transition. vinyl A An initial concentration of vinyl radical in the photolysis experiments is estimated from the relation
w C 2 H 3 x 0 s Np w C 2 H 3 X x sC193 f 2H 3X
Ž 3.
where wC 2 H 3 Xx and s are vinyl precursor concentration and absorption cross-section, respectively, and Np is number density of laser photons as determined from laser pulse energy measurements. The production yield of vinyl radical Ž f . was estimated from the 193 nm photodissociation processes of MVK as follows: C 2 H 3 COCH 3 q 193 nm ™ C 2 H 3) q CO q CH 3 , Ž R1. Fig. 2. Ring-down decay waveforms observed at 446.5 nm Ža. without 193 nm photolysis of MVK, Žb. with 193 nm photolysis of MVK. The solid line marks that part of the waveform that is a single-exponential fit to the experimental data.
reaction cell with a capacitance manometer ŽMKS Baratron 122AA.. Reagent concentrations were calculated from the total pressure and the calibrated flow rates. Spectroscopic and kinetics experiments were carried out at a laser repetition rate of 1–6 Hz to ensure complete removal of the reacted mixture and replenishment of the gas sample between successive laser shots. Experiments were carried out at room temperature Ž297 " 2 K..
C 2 H 3) ™ C 2 H 2 q H ,
Ž R2.
C 2 H 3) q M ™ C 2 H 3 q M ,
Ž R3.
where C 2 H 3) represents a hot vinyl radical. The production yields of methyl and vinyl radicals were determined to be 22.8 " 3.3 and 20.4 " 2.7%, respectively w14x. The initial methyl and vinyl radical
3. Results and discussion The vinyl radical has been confirmed as being a primary photoproduct in 193 nm photolysis of MVK and VB w14–17x. Fig. 3 shows the measured absorption spectrum of vinyl radical produced in 193 nm photolysis of MVK at a total pressure of 30 Torr. No dependence on the total pressure Ž10–30 Torr. in the absorption spectrum was observed. The same absorption spectrum was observed when the system of 193 nm photolysis of VB is used as a source of vinyl radical production, which is strong evidence for the production and detection of vinyl radical in these systems. The spectrum is in excellent agreement with
Fig. 3. Absorption spectrum of vinyl radical observed from 193 nm photolysis of MVK Ž5=10 14 molecules cmy3 .. The time delay between the photolysis and probe laser beams is 1 ms. The spectrum was measured with 0.1 nm spectral resolution.
K. Tonokura et al.r Chemical Physics Letters 313 (1999) 771–776
774
yields were in good agreement with the photolysis yield of MVK Ž23.6 " 1.1%. w14x. The production of C 2 H 2 q H from C 2 H 3) represents a minor fraction of the C 2 H 3 yield w14x. For 193 nm photolysis of VB, the quantum yield of vinyl radical formation has not been determined to our knowledge. In the absorption cross-section measurements, therefore, MVK is used as a source of vinyl radical. Fig. 4 shows a typical time profile of vinyl radical absorption at 446.5 nm. The points represent the averaged absorbance of vinyl radical as a function of time delay between photolysis and probe laser. Assuming the Beer–Lambert law, the average absorbance ² A: is given by ² A : s sC
2H3
wC 2 H 3 x ls
Ž 4.
where sC 2 H 3 is absorption cross-section of vinyl radical at wavelength l, and l s is absorption pathlength induced by photolysis laser beam Ž; 38 mm.. This time dependence would be governed by the vinyl–vinyl, methyl–methyl, and vinyl–methyl reaction w14,18x. Contribution of the reaction of vinyl and methyl radicals with H atom is negligibly small because of the low quantum yield of H atom compared to vinyl and methyl radicals, and following
Fig. 4. Time profile of vinyl radical absorbance at 446.5 nm with time delay between photolysis and probe laser. The solid curve is the best fit of these data using s s 4.9=10y1 9 cm2 moleculey1 and wC 2 H 3 x 0 s 5=10 13 molecules cmy3.
reactions have to be considered: C 2 H 3 q C 2 H 3 ™ Products ,
Ž R4.
CH 3 q CH 3 ™ Products ,
Ž R5.
C 2 H 3 q CH 3 ™ Products .
Ž R6.
For this multicomponent reaction system, the rate equations are as follows: d wC 2 H 3 x dt
2
s y2 k 4 w C 2 H 3 x y k 6 w CH 3 xw C 2 H 3 x ,
Ž 5. d w CH 3 x dt
2
s y2 k 5 w CH 3 x y k 6 w CH 3 xw C 2 H 3 x .
Ž 6.
The coupled differential equations are solved by numerical integration routines. The rate constants for the reactions ŽR4. to ŽR6. have previously been determined w18,19x and were used as fixed parameters. Since the disappearance rate of vinyl radical is very sensitive to its initial concentration, the initial concentrations of vinyl radical can be determined by fitting the calculated decay rates to the experimental values, and therefore the absorption cross-section can be estimated. The solid curve shown in Fig. 4 represents the fit to the experimental data using the parameters. The initial radical concentrations were controlled by changing the precursor concentration and photolysis laser power. Fig. 5 shows the results of the analysis for the absorption cross-sections of vinyl radical as a function of the initial vinyl radical concentrations. No dependence of the absorption cross-section on the initial radical concentrations nor the ArF laser power was observed. The line shown in Fig. 5 represents the average value of s446.5 s Ž4.8 " 0.3. = 10y1 9 cm2 moleculey1. Based on this value, the absorption cross-sections in the range 440–460 nm are obtained ŽFig. 3.. From the results of Hunziker et al. w9x the absorption cross-section at 446.5 nm is deduced to be Ž0.8 " 0.3. = 10y1 9 cm2 moleculey1 . In the experiments of Hunziker et al. w9x, the determination of the absorption cross-section is sensitive to the estimate of the radical concentrations produced from the Hg-photosensitized reactions. On the other hand, in our study, the initial concentration of the vinyl radicals is directly determined from well-established rate constants. The present absorption cross-section measurement was carried out at
K. Tonokura et al.r Chemical Physics Letters 313 (1999) 771–776
775
The detection sensitivity of the CRDS method is limited by the mirror reflectivity and minimum change in the ring-down time that can be detected. Zalicki and Zare w20x showed that, for a change in the ring-down time Dt upon tuning to an absorption feature, the corresponding absorbance per pass is Dt
Ž a l s . min s Ž 1 y R .
ž / t
.
Ž 7.
min
The reflectivity of the mirrors used in the current study is 0.9999, and the accuracy in the ring-down time determination of Ž Dtrt . min s 0.03, the minimum measured absorbance Ž a l s . min is calculated to be 3 = 10y6 . On the basis of the absorption crosssection of 4.8 = 10y1 9 cm2 moleculey1 for the vinyl radical and l s of 3.8 cm, the detection limit of vinyl radical with the present apparatus is estimated to be 2 = 10 12 molecules cmy3 .
Acknowledgements We thank C.A. Taatjes for a preprint of Ref. w10x. This work is supported in part by a Grant-in-Aid from the ministry of Education, Science, Sports and Culture ŽNo. 10640483. and Sumitomo Foundation. Fig. 5. Plots of calculated absorption cross-section of vinyl radical at 446.5 nm as a function of Ža. photolysis laser power and Žb. MVK concentration.
References
higher spectral resolution than in the previous study. These differences should be emphasized in comparing our results with previous studies. The reliability of the value determined in the present study was checked as follows. The initial concentration of vinyl radical is estimated from Eq. Ž3.. The absorbance at 446.5 nm is about 80 ppm ŽFig. 3.. From Eq. Ž4., the absorption cross-section is estimated to be Ž4 " 1. = 10y1 9 cm2 moleculey1 , which is consistent with the value estimated from the analytical simulation. Pibel et al. w10x reported the crude estimate of the absorption cross-section of vinyl radicals, which agrees with Hunziker et al. However, the cross-section calculated from their results using Eqs. Ž3. and Ž4. is also consistent with our results.
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