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Absolute Absorption Cross-Section of the Ã←X˜ Electronic Transition of the Ethyl Peroxy Radical and Rate Constant of Its Cross Reaction with HO2

Absolute Absorption Cross-Section of the Ã←X˜ Electronic Transition of the Ethyl Peroxy Radical... hv photonics Article Absolute Absorption Cross-Section of the à X Electronic Transition of the Ethyl Peroxy Radical and Rate Constant of Its Cross Reaction with HO 1 , 2 , 3 1 1 2 , 3 2 , 3 1 Cuihong Zhang , Mirna Shamas , Mohamed Assali , Xiaofeng Tang , Weijun Zhang , Laure Pillier , 1 1 , Coralie Schoemaecker and Christa Fittschen * Université Lille, CNRS, UMR 8522-PC2A-Physicochimie des Processus de Combustion et de l’Atmosphère, F-59000 Lille, France; cuihong.zhang@univ-lille.fr (C.Z.); mirna.shamas@univ-lille.fr (M.S.); mohamed.assali@univ-lille.fr (M.A.); laure.pillier@univ-lille.fr (L.P.); coralie.schoemaecker@univ-lille.fr (C.S.) Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics and Fine Mechanics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China; tangxf@aiofm.ac.cn (X.T.); wjzhang@aiofm.ac.cn (W.Z.) Science Island Branch, Graduate School, University of Science and Technology of China, Hefei 230026, China * Correspondence: Christa.Fittschen@univ-lille.fr Abstract: The absolute absorption cross-section of the ethyl peroxy radical C H O in the à X 2 5 2 electronic transition with the peak wavelength at 7596 cm has been determined by the method of dual wavelengths time resolved continuous wave cavity ring down spectroscopy. C H O radicals 2 5 2 were generated from pulsed 351 nm photolysis of C H /Cl mixture in presence of 100 Torr O 2 6 2 2 at T = 295 K. C H O radicals were detected on one of the CRDS paths. Two methods have been 2 5 2 applied for the determination of the C H O absorption cross-section: (i) based on Cl-atoms being 2 5 2 converted alternatively to either C H O by adding C H or to hydro peroxy radicals, HO , by 2 5 2 2 6 2 adding CH OH to the mixture, whereby HO was reliably quantified on the second CRDS path in the 3 2 2 vibrational overtone at 6638.2 cm (ii) based on the reaction of C H O with HO , measured 1 2 5 2 2 Citation: Zhang, C.; Shamas, M.; under either excess HO or under excess C H O concentration. Both methods lead to the same peak 2 2 5 2 Assali, M.; Tang, X.; Zhang, W.; Pillier, 1 20 2 absorption cross-section for C H O at 7596 cm of  = (1.0  0.2)  10 cm . The rate constant L.; Schoemaecker, C.; Fittschen, C. 2 5 2 12 3 Absolute Absorption Cross-Section of for the cross reaction between of C H O and HO has been measured to be (6.2  1.5)  10 cm 2 5 2 2 1 1 the à X Electronic Transition of the molecule s . Ethyl Peroxy Radical and Rate Constant of Its Cross Reaction with e Keywords: peroxy radicals; near-infrared spectroscopy; à X electronic transition; cavity ring HO . Photonics 2021, 8, 296. https:// down spectroscopy doi.org/10.3390/photonics8080296 Received: 24 June 2021 Accepted: 21 July 2021 1. Introduction Published: 24 July 2021 The oxidation of volatile organic compounds (VOCs) in the troposphere is mainly driven by hydroxyl radicals (OH) and leads, after addition of O , to the formation of Publisher’s Note: MDPI stays neutral organic peroxy radicals (RO ). The fate of these RO radicals depends on the chemical com- 2 2 with regard to jurisdictional claims in position of the environment. In a polluted atmosphere they react mainly with nitric oxide published maps and institutional affil- (NO) to form alkoxy radicals or react with nitrogen dioxide (NO ) to form peroxynitrates iations. (RO NO ). Subsequent to the reaction with NO, alkoxy radicals react with O to form 2 2 2 hydro peroxy radicals (HO ). HO further oxidises NO into NO and thus regenerates 2 2 2 OH, closing the quasi-catalytic cycle. The photolysis of produced NO is the only relevant chemical source of tropospheric ozone. In clean environments with low NO (NO = NO x x Copyright: © 2021 by the authors. + NO ) concentrations, the dominant loss of RO is due to its reaction with HO forming 2 2 2 Licensee MDPI, Basel, Switzerland. hydroperoxides ROOH and terminating the radical reaction chain. In addition, RO radi- This article is an open access article cals can react either with themselves as self-reaction (RO + RO ) or with other R’O as 2 2 2 distributed under the terms and cross-reaction (RO + R’O ) or with OH radicals (RO + OH) [1–5]. conditions of the Creative Commons 2 2 2 Ethane is one of the most abundant non-methane hydrocarbons in the atmosphere, Attribution (CC BY) license (https:// and its atmospheric oxidation leads to the formation of the ethyl peroxy radical, C H O . A creativecommons.org/licenses/by/ 2 5 2 reliable detection of this radical is therefore highly desirable for studying its reactivity and 4.0/). Photonics 2021, 8, 296. https://doi.org/10.3390/photonics8080296 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 296 2 of 17 thus understanding its embedded chemistry. Previous studies of peroxy chemistry have e e mostly been carried out by UV absorption spectroscopy in the B X electronic transition: this method gives a good sensitivity for peroxy radicals due to large absorption cross- sections, but the selectivity is poor because the absorption spectra are unstructured and the spectra of many different species are overlapping. The à X electronic transition of peroxy radicals is located in the near IR region. At room temperature, these transitions form rotationally unresolved envelopes with typical features about 1 cm or more wide and allow a more selective detection of peroxy radicals, compared to UV absorption. The shape of such unresolved absorption features is typically only very little influenced by temperature or pressure, in contrast to the resolved spectra of small species like OH or HO : sharp lines are observed for transitions between different rotational or vibration states, where pressure is broadening the lines and temperature can change the relative populations of the different states and thus the cross-sections of the lines. However, due to small absorption cross-sections of the à X electronic transition of 20 21 2 peroxy radicals (~10 –10 cm ), these transitions have not attracted much attention after they had been located for the first time by Hunziker and Wendt in 1976 [6,7]. Interest has been revived many years later when the highly sensitive absorption technique of cavity ring down spectroscopy (CRDS) has been developed [8,9], which can make up for the small absorption cross-sections. The first report on using this technique for the detection of peroxy radicals was in 2000 [10]: T. Miller and coworkers obtained pulsed near IR radiation by stimulated Raman shifting of the output of a pulsed dye laser in molecular hydrogen. The output of such a laser source has a typical bandwidth of about 0.03 cm and is thus much narrower than the à X electronic transition of peroxy radicals. They measured the absorption spectra of the methyl and ethyl peroxy radicals, but determined only the absorption cross-section for the methyl peroxy radical. The peak of the à X transition for C H O was found around 7596 cm . 2 5 2 A few years later, Atkinson and Spillman [11] measured again the spectra of both radicals, now using a continuous external cavity diode laser to perform cw-CRDS with 5 1 a much narrower bandwidth (~3  10 cm ). They confirmed the overall shape of the absorption spectrum, and measured for the first time the absorption cross-section for C H O using the kinetic method [12–15]. This method can be applied, if the rate 2 5 2 constant of a radical-radical reaction is known, because the initial concentration and thus the absorption cross-section can in principle be determined from the shape of the kinetic decay. The self-reaction can be described as follows. A + A ! B d[A] = 2k A (1) [ ] dt Integration of Equation (1) leads to 1 1 = + 2kt (2) [A] [A] Hence, plotting 1/[A] as a function of time leads to a straight line with the slope being 2k. In the case where the rate constant is known, but not the absolute concentration of A, the absorption coefficient =   [A] can be used in Equation (2) instead of [A], leading to 1 1 2k = + t (3) [A]  [A] Plotting 1/  [A] leads to a straight line with the slope being m = 2k/ while the intercept I = 1/  [A] . However, different complications can arise from this method: radicals can be lost through other processes too, for example through diffusion out of the photolysed volume or through unidentified secondary reactions in which case the decays are faster than expected from pure self-reaction only, and the retrieved absorption Photonics 2021, 8, 296 3 of 17 cross-section would be too small. In the case of peroxy radicals, this method has another complication: the self-reaction of peroxy radicals (R1) has several product pathways, and one of them leads to the formation of HO radicals: 2 C H O ! 2 C H O + O (R1a) 2 5 2 2 5 2 ! C H OH + CH CHO + O (R1b) 2 5 3 2 followed, in presence of O , by (R2): C H O + O ! CH CHO + HO (R2) 2 5 2 3 2 The HO radicals react with C H O 2 2 5 2 C H O + HO ! C H OOH + O (R3) 2 5 2 2 2 5 2 with (R3) having a rate constant faster than (R1). As a result, the C H O decays are 2 5 2 accelerated by the formation of HO , and therefore when using Equation (3) for (R1), the obtained rate constant k is called k , and the acceleration has to be taken into account 1 1 obs to retrieve the “real” rate constant k from C H O decays. Using the recommended 1 2 5 2 value of k , in the kinetic method, Atkinson and Spillman [11] obtained an absorption 1 obs 1 21 2 cross-section for C H O at 7596 cm of  = (3.0  1.5)  10 cm . 2 5 2 Another work on the ethyl peroxy spectrum from the Miller group [16] scanned the à X electronic transition over a large wavelength range and identified the transitions for the two different isomers. Indeed, ethyl peroxy radicals exist in an equilibrium between two stable conformers with the dihedral angles between the O-O-C and O-C-C planes being 0 for the T (trans) and 120 for the G (gauche) conformer. The peak absorptions for 1 1 both conformers were located well separated at 7362 cm for the T- and 7592 cm for the G-conformer. In this work, they used a different method to estimate the absorption cross-section: peroxy radicals were generated by the reaction of Cl-atoms with C H , with 2 6 the Cl-atoms being generated by 193 nm photolysis of oxalylchloride, (COCl) . To obtain the concentration of C H O , they measured the photolysis laser energy with and without 2 5 2 precursor, and calculated the Cl-atom concentration from the difference. Supposing that 21 2 each Cl-atom generated one C H O radical, they obtained  = 4.4 10 cm for C H O 2 5 2 2 5 2 at 7596 cm . The next work on the ethyl peroxy spectrum from the Miller group [17] used a different method to obtain the absorption cross-section: in a dual-path CRDS set-up, the concentration of HCl (generated from the reaction of Cl-atoms with C H ) was measured 2 6 on one path while the absorption of C H O was measured simultaneously on the other 2 5 2 path. Again supposing that each HCl-molecule had generated one C H O radical, they 2 5 2 21 2 1 obtained  = (5.29  0.20)  10 cm for C H O at 7596 cm . 2 5 2 In the most recent work from the Miller group [18], the above absorption cross-section was validated indirectly through the kinetic method: the C H O absorption profiles were 2 5 2 converted to C H O concentration-time profiles using the above absorption cross-section, 2 5 2 and the rate constant k , for the self-reaction was extracted. Good agreement with other obs literature data was found, which was taken as an indication that the absorption cross- section is valid. A summary of previous results as well as the results obtained in this work is presented in Table 1. In this work we present a new determination of the absorption cross-section, based on two different approaches. The first one is comparable to one of the Miller methods [17] and will be called back-to-back method: in our dual-path CRDS set-up we generate Cl-atoms and transform them to HO through reaction with CH OH, with HO being quantified 2 3 2 on one path at 6638.2 cm . Directly after, the Cl-atoms were transformed to C H O 2 5 2 by adding C H instead of CH OH to the reaction mixture and the C H O absorption 2 6 3 2 5 2 was measured on the second path. Supposing that the Cl concentration stays the same between both experiments and that in both cases all Cl-atoms are converted to either HO 2 Photonics 2021, 8, x FOR PEER REVIEW 4 of 17 Photonics 2021, 8, 296 4 of 17 can be quantified reliably) or to C2H5O2, the absorption cross-section of C2H5O2 is deter- mined relative to the one of HO2. The second approach is a variation of the kinetic method (which can be quantified reliably) or to C H O , the absorption cross-section of C H O is 2 5 2 2 5 2 such as used by Atkinson and Spillman [11] and Melnik et al. [18], but not based on the determined relative to the one of HO . The second approach is a variation of the kinetic sel method f-react such ion of asC used 2H5Oby 2, bAtkinson ut on the cross and Spillman reaction between HO [11] and Melnik 2 and C et al. 2H [18 5O ], 2. This but not reaction based has be on theen me self-reaction asured in of a wide r C H O a , nge but of c on the oncentrations under cross reaction between either HO excess of and C HO H 2 or exce O . This ss 2 5 2 2 2 5 2 of C reaction 2H5O has 2. In the fi been measur rst case, the ra ed in a wide te consta range nt is retr of concentrations ieved by adj under usting the C either excess 2H5O2 of decay HOs wi or th the a excess of bsol C u H te concentra O . In the first tion of case, HO the 2 being f rate constant ixed, while is retrieved in the second case t by adjusting the he rat C e H con- O 2 5 2 2 5 2 decays with the absolute concentration of HO being fixed, while in the second case the stant is fixed to the value determined just before, and now the best fit of the HO2 decay is rate constant is fixed to the value determined just before, and now the best fit of the HO achieved by adjusting the absolute concentration of C2H5O2, i.e., the absorption cross-sec- decay is achieved by adjusting the absolute concentration of C H O , i.e., the absorption tion. 2 5 2 cross-section. −1. Table 1. Summary of the C2H5O2 absorption cross-section at 7596 cm Table 1. Summary of the C H O absorption cross-section at 7596 cm . 2 5 2 −21 2 σ/10 cm Method Reference Method Reference /10 cm Kinetic method, no other radical losses Atkinson and Spillman 3.0 ± 1.5 Atkinson and Spillman considered [11] 3.0  1.5 Kinetic method, no other radical losses considered [11] Depletion of photolysis energy through precursor Depletion of photolysis energy through precursor 4.4 with [Cl] = [C2H5O2], i.e., no secondary reactions Rupper et al. [16] 4.4 with [Cl] = [C H O ], i.e., no secondary reactions Rupper et al. [16] 2 5 2 considered considered Measurement of HCl in dual path CRDS with [Cl] Measurement of HCl in dual path CRDS with [Cl] = 5.5.29 29 ± 0.20  0.20 = [C2H5O2], i.e., no secondary reactions Meln Melnik ik et et al al. . [ [1 17 7]] [C H O ], i.e., no secondary reactions considered 2 5 2 considered 5.29 Kinetic method used for validation of Ref. [17] Melnik et al. [18] 5.29 Kinetic method used for validation of Ref. [17] Melnik et al. [18] Measurement of HO /C H O in dual path CRDS 2 2 5 2 Measurement of HO2/C2H5O2 in dual path CRDS 10  2 This work 10 ± 2 with [Cl] = [HO ] = [C H O ] This work 2 2 5 2 with [Cl] = [HO2] = [C2H5O2] 10  2 Kinetic method from C H O + HO This work 2 5 2 2 10 ± 2 Kinetic method from C2H5O2 + HO2 This work 2. Materials and Methods 2. Materials and Methods The setup has been described in detail before [19–23] and is only briefly discussed The setup has been described in detail before [19-23] and is only briefly discussed here (Figure 1). here (Figure 1). Figure 1. Schematic view of the used experimental setup: AOM, Acousto-Optic Modulator; APD, Avalanche Photo Diode; Figure 1. Schematic view of the used experimental setup: AOM, Acousto-Optic Modulator; APD, Avalanche Photo Diode; M, Mirror; L, Lens. Both cw-CRDS systems are equipped with identical trigger circuits and data acquisition systems. M, Mirror; L, Lens. Both cw-CRDS systems are equipped with identical trigger circuits and data acquisition systems. The setup consisted of a 0.79 m long flow reactor made of stainless steel. The photol- The setup consisted of a 0.79 m long flow reactor made of stainless steel. The photolysis ysi laser s la(Lambda ser (Lamb Physik da Phys LPX ik LPX 202i, 202 XeF i, Xe at F at 351 35nm) 1 nm widt ) widt h h is de is delimited limited t too2 2 cm cm and p and passes asses t thr hrough t ough the her r ee aact ctor or longitudinally longitudinal.ly The . The flow flow reactor reaccontains tor contai two ns two i identical denti continuous cal continwave uous cavity ring-down spectroscopy (cw-CRDS) absorption paths, which were installed in a wave cavity ring-down spectroscopy (cw-CRDS) absorption paths, which were installed small angle with respect to the photolysis path. An overlap of the absorption path with the in a small angle with respect to the photolysis path. An overlap of the absorption path photolysis beam of 0.288 m is achieved. Both beam paths were tested for a uniform overlap with the photolysis beam of 0.288 m is achieved. Both beam paths were tested for a uni- with the photolysis beam before experiments were done. For this purpose, both cw-CRDS form overlap with the photolysis beam before experiments were done. For this purpose, instruments were operated to simultaneously measure HO concentrations. Deviations between HO concentrations were less than 5%, demonstrating that the photolysis laser Photonics 2021, 8, 296 5 of 17 was very well aligned, i.e., both light paths probed a very similar photolysed volume in the reactor. A small helium purge flow prevented the mirrors from being contaminated. Two different DFB lasers are used for the detection of the two species and each one is coupled into one of the cavities by systems of lenses and mirrors. Each probe beam passed an st acousto-optic modulator (AOM, AAoptoelectronic) to rapidly turn off the 1 order beam once a user-set threshold for light intensity in the cavity was reached, in order to measure the ring-down event. A home-made tracking system is used to increase the number of ring-down events [21]. Then, the decay of light intensity is recorded and an exponential fit is applied to retrieve the ring-down time. The absorption coefficient is derived from Equation (4). R 1 1 = [A]   = (4) where  is the ring-down time with an absorber present;  is the ring-down time with no absorber present;  is the absorption cross-section of the absorbing species A; R is the A L ratio between cavity length (79 cm) and effective absorption path (28.8 cm); c is the speed of light. Ethyl peroxy radicals were generated by pulsed 351 nm photolysis of C H /Cl O 2 6 2/ 2 mixtures initiating the reaction sequence (R4), (R5) and (R6): Cl + h ! 2 Cl (R4) 2 351 nm C H + Cl ! C H + HCl (R5) 2 6 2 5 C H + O + M ! C H O + M (R6a) 2 5 2 2 5 2 C H + O ! C H + HO (R6b) 2 5 2 2 4 2 For studying the cross reaction with HO , methanol, CH OH, has been added in 2 3 varying concentrations to the mixture. CH OH + Cl ! CH OH + HCl (R7) 3 2 CH OH + O ! CH O + HO (R8) 2 2 2 2 In order to rapidly convert C H O into HO through (R2), all experiments have been 2 5 2 carried out in 100 Torr O (Air Liquide, Alphagaz 2). The Cl concentration was typically 2 2 16 3 2 around 1  10 cm , leading with a photolysis energy of 20 mJ/cm to initial Cl-atom 14 3 concentrations of around 1  10 cm . A small flow of pure ethane was added directly from the cylinder (Mitry-Mory, N35) to the mixture through a calibrated flow meter (Bronkhorst, Tylan). Methanol (Sigma-Aldrich) was added to the mixture by flowing a small fraction of the main flow through a bubbler containing liquid methanol, kept in ice or in a thermostated water bath. All experiments were carried out at 298 K. 3. Results In the following, the two different methods applied in this work for the determination of the absorption cross-section of C H O at its peak wavelength 7596 cm are described. 2 5 2 3.1. Quantification of C H O in Back-to-Back Experiments 2 5 2 In the first method, the absorption cross-section of C H O is measured in a rather 2 5 2 direct way in back-to-back experiments relative to the absorption cross-section of HO . Therefore, the reliability of the measurement depends on the reliability of the absorption cross-section of HO . The absorption spectrum and cross-sections of HO in the near 2 2 IR have been measured several times [15,22,24,25] and pressure broadening of selected lines has also been carried out [26–28]. In this work, HO was quantified on two different absorption lines with the cross-section varying about a factor of 9 between both lines: for most experiments, HO has been detected on the strongest line of the 2 band at 2 1 Photonics 2021, 8, x FOR PEER REVIEW 6 of 17 has also been carried out [26-28]. In this work, HO2 was quantified on two different ab- Photonics 2021, 8, 296 6 of 17 sorption lines with the cross-section varying about a factor of 9 between both lines: for most experiments, HO2 has been detected on the strongest line of the 21 band at 6638.2 −1 cm , but for experiments with high initial radical concentrations a small line at 6638.58 −1 cm 6638.2 has been cm used , but to foravoid satur experiments ation. with The ab highsorptio initialnradical cross-sconcentrations ection of the stron a small gest line line −19 2 in he at 6638.58 lium (σcm 50 Torr hehas = 2.been 72 × 10 used cm to ) [1 avoid 5,24saturation. ] and in syntheti The absorption c air [26-28] ( crσ oss-section 100 Torr air = 1.44 of the × 19 2 −19 2 strongest line in helium ( = 2.72  10 cm ) [15,24] and in synthetic air [26–28] 10 cm ) has been measured several times, the cross-section of the small line has only 50 Torr he 19 2 −20 2 ( = 1.44  10 cm ) has been measured several times, the cross-section of the been measured once in 50 and 100 Torr helium (2.8 and 2.1 × 10 cm , respectively) 100 Torr air 20 2 small line has only been measured once in 50 and 100 Torr helium (2.8 and 2.1 10 cm , [27][29], but no measurements in pure O2 have been carried out. Therefore, we have de- respectively) [27,29], but no measurements in pure O have been carried out. Therefore, termined both cross-sections in 100 Torr O2 in the frame of this work, using the kinetic we have determined both cross-sections in 100 Torr O in the frame of this work, using the method. 2 kinetic method. Figure 2 shows a typical example: HO2 decays have been measured for 3 different Figure 2 shows a typical example: HO decays have been measured for 3 different initial Cl-atom concentrations and the raw signals are presented in graph (a). The decays initial Cl-atom concentrations and the raw signals are presented in graph (a). The decays have then been plotted following Equation (3) and the result is shown in graph (b). The have then been plotted following Equation (3) and the result is shown in graph (b). The slope of a linear regression of this plot can in principle be converted to the absorption slope of a linear regression of this plot can in principle be converted to the absorption cross-section using the known rate constant of the HO2 self-reaction. However, as has been cross-section using the known rate constant of the HO self-reaction. However, as has been mentioned above, radicals can be lost also through other processes, and in the case of laser mentioned above, radicals can be lost also through other processes, and in the case of laser photolysis experiments one possible loss is diffusion out of the photolysis volume. The photolysis experiments one possible loss is diffusion out of the photolysis volume. The relative impact of this loss process decreases with increasing initial HO2 concentration and relative impact of this loss process decreases with increasing initial HO concentration in order to correct this influence, an extrapolation to infinite [HO2]0 is used, shown in and in order to correct this influence, an extrapolation to infinite [HO ] is used, shown 2 0 graph (c): the slope m from graph (b) is plotted as a function of the intercept I (=1/α0). in graph (c): the slope m from graph (b) is plotted as a function of the intercept I (=1/ ). Extrapolating the m-values to I = 0 therefore removes the influence of the diffusion on the Extrapolating the m-values to I = 0 therefore removes the influence of the diffusion on the slope m. In the example of Figure 2, using the slope m obtained from extrapolation instead slope m. In the example of Figure 2, using the slope m obtained from extrapolation instead of using the directly determined slope m leads to an increase in the absorption cross-sec- of using the directly determined slope m leads to an increase in the absorption cross-section tion of 6% for the highest initial concentration and 13% for the lowest initial concentration. of 6% for the highest initial concentration and 13% for the lowest initial concentration. Error Error bars in graph (c) correspond to 95% confidence interval of the linear regression from bars in graph (c) correspond to 95% confidence interval of the linear regression from the the graph (b): the error bars on the x-values are too small to be seen within the symbols. graph (b): the error bars on the x-values are too small to be seen within the symbols. Several Several such series have been measured for both absorption lines, and the following ab- such series have been measured for both absorption lines, and the following absorption sorption cross-sections in 100 Torr O2 have been deduced for HO2 for the two lines: cross-sections in 100 Torr O have been deduced for HO for the two lines: 2 2 −1 −19 2 6638.2 cm :σ = (2.0 ± 0.3) × 10 cm . 1 19 2 6638.2 cm : = (2.0  0.3)  10 cm . −1 −20 2 6638.58 cm :σ = (2.1 ± 0.3) × 10 cm . 1 20 2 6638.58 cm : = (2.1  0.3)  10 cm . The uncertainty on σ reflect the uncertainty of ±15% on the rate constant of the HO2 The uncertainty on  reflect the uncertainty of 15% on the rate constant of the HO self-reaction, such as estimated by the IUPAC committee [30]. self-reaction, such as estimated by the IUPAC committee [30]. -6 8? 0 6? 0 (b) -6 6? 0 (a) 4? 0 -6 4? 0 2? 0 -6 2? 0 0 0 0.000 0.005 0.010 0.015 0.020 0.00 0.01 0.02 0.03 0.04 0.05 t / s t / s 1.8? 0 (c) 1.7? 0 1.6? 0 1.5? 0 5 5 5 01?0 2? 0 3? 0 I / cm Figure 2. Example of measurement of HO absorption cross-section using the kinetic method: graph (a) shows kinetic decays for 3 different Cl-atom concentrations, graph (b) shows the same signals plotted following Equation (3) with the linear regression over the first 20 ms, graph (c) shows the plot of slope m as a function of I, obtained in graph (b) for the 3 experiments. -1  (HO ) / cm -1 m / cm s (1 / (HO )) / cm 2 Photonics 2021, 8, x FOR PEER REVIEW 7 of 17 Figure 2. Example of measurement of HO2 absorption cross-section using the kinetic method: graph (a) shows kinetic decays for 3 different Cl-atom concentrations, graph (b) shows the same signals plotted following Equation (3) with the linear regression over the first 20 ms, graph (c) shows the Photonics 2021, 8, 296 7 of 17 plot of slope m as a function of I, obtained in graph (b) for the 3 experiments. These absorption cross-sections are now used to obtain the absorption cross-section These absorption cross-sections are now used to obtain the absorption cross-section of of C2H5O2 in back-to-back experiments. Figure 3 shows the principle of these measure- C H O in back-to-back experiments. Figure 3 shows the principle of these measurements: 2 5 2 ments: Cl2 is first photolysed in the presence of excess CH3OH, leading to quantitative Cl is first photolysed in the presence of excess CH OH, leading to quantitative formation format 2 ion of HO2 radicals: typical absorption-time prof 3 iles for 4 different Cl2 concentra- of HO radicals: typical absorption-time profiles for 4 different Cl concentrations are tions are shown i 2 n the upper right graph (b) of Figure 3. In the next step, C 2 H3OH is re- shown in the upper right graph (b) of Figure 3. In the next step, CH OH is removed from moved from the gas flow, and excess C2H6 is added instead, all other conditions are kept the gas flow, and excess C H is added instead, all other conditions are kept constant. 2 6 constant. The corresponding C2H5O2 absorption time profiles are shown in the upper left The corresponding C H O absorption time profiles are shown in the upper left graph (a). 2 5 2 graph (a). It can be seen that the HO2 profiles decay much faster than the corresponding It can be seen that the HO profiles decay much faster than the corresponding C H O 2 2 5 2 C2H5O2 profiles: this is in line with the rate constant of the HO2 self-reaction being around profiles: this is in line with the rate constant of the HO self-reaction being around 10 times 10 times faster than the rate constant of the C2H5O2 self-reaction. In order to get a reliable faster than the rate constant of the C H O self-reaction. In order to get a reliable extrap- 2 5 2 extrapolation of αt=0 ms, a plot of 1/α = f(t) is generated for both species (graph (c) and (d) olation of , a plot of 1/ = f(t) is generated for both species (graph (c) and (d) for t=0 ms for C2H5O2 and HO2, respectively) and a linear regression allows retrieving αt=0 ms from the C H O and HO , respectively) and a linear regression allows retrieving from the 2 5 2 2 t=0 ms intercept, as shown in Equation (3). For HO2, the αt=0 ms values can now be converted to intercept, as shown in Equation (3). For HO , the values can now be converted to 2 t=0 ms absolute concentrations ([HO2]t=0 ms) using the above determined absorption cross-section. absolute concentrations ([HO ] ) using the above determined absorption cross-section. 2 t=0 ms Supposing that each Cl-atom is converted into either one HO2 radical or into one C2H5O2 Supposing that each Cl-atom is converted into either one HO radical or into one C H O 2 2 5 2 radical, i.e., [HO2]t=0 ms = [C2HO5]t=0 ms, a plot of α(C2H5O2)t=0 ms = f([HO2]t=0 ms) leads to a linear radical, i.e., [HO ] = [C HO ] , a plot of (C H O ) = f([HO ] ) leads 2 t=0 ms 2 5 t=0 ms 2 5 2 t=0 ms 2 t=0 ms relationship with the slope equal to the absolute absorption cross-section of C2H5O2. The to a linear relationship with the slope equal to the absolute absorption cross-section of lower graph (e) in Figure 3 summarizes the results, obtained on four different days using C H O . The lower graph (e) in Figure 3 summarizes the results, obtained on four different 2 5 2 −1 either the big HO2 line at 6638.2 cm (open circles and open diamonds) or the small line days using either the big HO line at 6638.2 cm (open circles and open diamonds) or the −1 at 6635.58 cm (all other symbols, with the coloured symbols representing the results from small line at 6635.58 cm (all other symbols, with the coloured symbols representing the the experiment in Figure 3). results from the experiment in Figure 3). Figure 3. Example of measurement of the C H O absorption cross-section relative to the HO 2 5 2 2 Figure 3. Example of measurement of the C2H5O2 absorption cross-section relative to the HO2 ab- absorption cross-section. Upper graphs: C H O (a) and HO (b) absorption time profiles. Graphs (c) 2 5 2 2 sorption cross-section. Upper graphs: C2H5O2 (a) and HO2 (b) absorption time profiles. Graphs (c) and (d): same profiles, converted to 1/ (see Equation (3)) and linear regression over the first 20 ms following the photolysis pulse. Lower graph (e) shows plot of (C H O ) = f ([HO ] ): 2 5 2 t=0 ms 2 t=0 ms open circles and open diamonds are obtained using HO measurements at 6638.2 cm , coloured points (from above graphs) and crosses are obtained using HO measurements at 6638.58 cm . [O ] 2 2 18 3 16 3 = 2.8  10 cm , [C H ] = 3.7  10 cm for all experiments. 2 6 Photonics 2021, 8, x FOR PEER REVIEW 8 of 17 and (d): same profiles, converted to 1/α (see Equation (3)) and linear regression over the first 20 ms following the photolysis pulse. Lower graph (e) shows plot of α (C2H5O2)t=0 ms = f ([HO2]t=0 ms): open −1 circles and open diamonds are obtained using HO2 measurements at 6638.2 cm , coloured points Photonics 2021, 8, 296 −1 8 of 17 (from above graphs) and crosses are obtained using HO2 measurements at 6638.58 cm . [O2] = 2.8 × 18 −3 16 −3 10 cm , [C2H6] = 3.7 × 10 cm for all experiments. −1 From these experiments, an absorption cross-section for C2H5O2 at 7596 cm of σ = From these experiments, an absorption cross-section for C H O at 7596 cm of 2 5 2 −20 2 (1.0 ± 0.2) × 10 cm is obtained. The error bar is mostly due to the uncertainty in the rate 20 2 = (1.0  0.2)  10 cm is obtained. The error bar is mostly due to the uncertainty in constant of the HO2 self-reaction, to which the absorption cross-section of C2H5O2 is di- the rate constant of the HO self-reaction, to which the absorption cross-section of C H O 2 2 5 2 rectly linked. is directly linked. In imitation of the kinetic method such as used by Melnik et al.[18], the above exper- In imitation of the kinetic method such as used by Melnik et al. [18], the above iments can also be used to validate the absorption cross-section obtained using the back- experiments can also be used to validate the absorption cross-section obtained using the to-back method by determining k3,obs and comparing it with data from the literature. In- back-to-back method by determining k and comparing it with data from the literature. 3,obs deed, the C2H5O2 data from Figure 3c can be treated with the same method as shown for Indeed, the C H O data from Figure 3c can be treated with the same method as shown for 2 5 2 the HO2 data in Figure 2, and the obtained intercept is then equal to 2 × kobs/σ. Figure 4 the HO data in Figure 2, and the obtained intercept is then equal to 2  k /. Figure 4 obs shows this type of plot for the data from Figure 3c. shows this type of plot for the data from Figure 3c. Figure 4. Plot of slope m as a function of I from the linear regressions obtained in Figure 3c. Figure 4. Plot of slope m as a function of I from the linear regressions obtained in Figure 3c. Now, using the above retrieved absorption cross-section for C H O at 7596 cm of 2 5 2 −1 Now, using the above retrieved absorption cross-section for C2H5O2 at 7596 cm of σ 20 2 = (1.0  0.2)  10 cm , we can obtain from the intercept of the linear regression in −20 2 = (1.0 ± 0.2) × 10 cm , we can obtain from the intercept of the linear regression in Figure 13 3 1 1 Figure 4 a value for k = (1.3 0.3) 10 cm molecule s , in good agreement with 1,obs −13 3 −1 −1 4 a value for k1,obs = (1.3 ± 0.3) × 10 cm molecule s , in good agreement with the currently 13 3 1 1 the currently recommended literature value (1.24  10 cm molecule s ) [31]. −13 3 −1 −1 recommended literature value (1.24 × 10 cm molecule s ) [31]. 3.2. Quantification of C H O by Measuring the Rate Constant of C H O + HO 2 5 2 2 5 2 2 3.2. Quantification of C2H5O2 by Measuring the Rate Constant of C2H5O2 + HO2 Another way to determine the absorption cross-section of C H O has been applied by 2 5 2 Another way to determine the absorption cross-section of C2H5O2 has been applied determining the rate constant of the cross reaction between C H O and HO . Indeed, the 2 5 2 2 by determining the rate constant of the cross reaction between C2H5O2 and HO2. Indeed, rate constant can be determined under different conditions: using an excess of HO over the rate constant can be determined under different conditions: using an excess of HO2 C H O leads to C H O decays that are sensitive to the absolute concentration of HO , 2 5 2 2 5 2 2 over C2H5O2 leads to C2H5O2 decays that are sensitive to the absolute concentration of HO2, while in the reverse case the HO decay will be sensitive to the absolute C H O concen- 2 2 5 2 while in the reverse case the HO2 decay will be sensitive to the absolute C2H5O2 concen- tration, and thus to its absorption cross-section. Therefore, measuring simultaneously the tration, and thus to its absorption cross-section. Therefore, measuring simultaneously the decays of both species over a large range of concentration ratio allows determining the rate decays of both species over a large range of concentration ratio allows determining the constant (from excess HO experiments) and the absorption cross-section of C H O (from 2 2 5 2 rate constant (from excess HO2 experiments) and the absorption cross-section of C2H5O2 excess C H O experiments). Figure 5 illustrates this using two examples from Figure 6. 2 5 2 (from excess C2H5O2 experiments). Figure 5 illustrates this using two examples from Fig- ure 6. Photonics 2021, 8, x FOR PEER REVIEW 9 of 17 Photonics 2021, 8, x FOR PEER REVIEW 9 of 17 Photonics 2021, 8, 296 9 of 17 Figure 5. Figure 5.Experimental profiles taken under Experimental profiles taken under excess C excess C 2H H 5OO 2 conditions (upper graphs) and under conditions (upper graphs) and under 2 5 2 Figure 5. Experimental profiles taken under excess C2H5O2 conditions (upper graphs) and under excess HO2 conditions (lower graph). The dashed lines represent modelled profiles of C2H5OOH, excess HO conditions (lower graph). The dashed lines represent modelled profiles of C H OOH, 2 2 5 excess HO2 conditions (lower graph). The dashed lines represent modelled profiles of C2H5OOH, the product from (R3), while the full lines represent the product of the corresponding self-reaction the product from (R3), while the full lines represent the product of the corresponding self-reaction the product from (R3), while the full lines represent the product of the corresponding self-reaction (C2H5OH for C2H5O2 and H2O2 for HO2). Different colours represent the result from a model with (C H OH for C H O and H O for HO ). Different colours represent the result from a model with (C22 H5OH for 5 C2H 2 5O 5 2 and 2 H2O 2 2 for 2 HO2).2 Different colours represent the result from a model with different k3. different k . different k3. 14 14 1×10 1×10 14 14 1×10 1×10 -12 3 -1 k = 5.5 10 cm s -12 3 -1 13 13 7.5×10 k = 5.5 10 cm s 7.5×10 13 13 7.5×10 7.5×10 (a) (a) 13 13 5×10 5×10 13 13 5×10 5×10 13 13 2.5×10 2.5×10 13 13 2.5×10 2.5×10 0 0 0.000 0 0.005 0.010 0.015 0.020 0.0 000 0.005 0.010 0.015 0.020 0.000 0.005 0.010 0.015 0.020 0.000 0.005 0.010 0.015 0.020 t / s t / s t / s t / s 1×10 1×10 7.5×10 7.5×10 (c) (c) 5×10 5×10 2.5×10 2.5×10 0.000 0.005 0.010 0.015 0.020 0.000 0.005 0.010 0.015 0.020 t / s t / s Figure 6. C H O (left graphs) and HO (right graphs) concentration time profiles for a total radical 2 5 2 2 Figure 6. C2H5O2 (left graphs) and HO2 (right graphs) concentration time profiles for a total radical 14 3 Figure 6. concentration C2H5O of 2 (left graphs) and HO 1.2  10 cm . C2 (rig H O ht g absorption raphs) concentration tim time profiles have e profiles for a to been converted tal radica using l 2 5 2 14 −3 concentration of 1.2 × 10 cm . C2H5O2 absorption time profiles have been converted using σ = 1.0 20 2 14 −3 12 3 1 1 concentration  = 1.0  10 of 1 cm .2 × 10 . Centr cm e graphs . C2H5O (b 2 ab ): best sorption time fit with k pro = 6.2 files have  10 becm en conv molecule erted using s ,σupper = 1.0 −20 2 −12 3 −1 −1 × 10 cm . Centre graphs (b): best fit with k3 = 6.2 × 10 cm molecule s , upper graphs (a): model −20 2 −12 3 −1 −1 12 3 1 1 × 10 cm . Centre graphs (b): best fit with k3 = 6.2 × 10 cm molecule s , upper graphs (a): model graphs (a): model with of k = 5.5  10 cm molecule s , lower graphs (c): model with −12 3 −1 −1 −12 3 −1 with of k3 = 5.5 × 10 cm molecule s , lower graphs (c): model with k3 = 8.0 × 10 cm molecule −12 3 −1 −1 −12 3 −1 with of k3 = 5. 5 12 × 10 3 cm mole cu 1le1s , lower graphs (c): model with k3 = 8.0 × 10 cm molecule −k 1. = 8.0  10 cm molecule s . −1. -3 -3 [C H O ] / cm [C H O ] / cm 2 5 2 -3 2 5 2 -3 [C H O ] / cm [C H O ] / cm 2 5 2 2 5 2 -3 [HO ] / cm 2 -3 [HO ] / cm 2 Photonics 2021, 8, 296 10 of 17 Both species show different behaviour: C H O always decreases rapidly over the 2 5 2 first few ms, given by the loss through (R3) (C H OOH concentration time profile given 2 5 as dashed lines). Then the decays slow down at longer reaction times, when HO con- centration gets low, because the self-reaction becomes the major loss process, and this reaction is slow for C H O radicals (C H OH concentration time profile given as full 2 5 2 2 5 lines). This behaviour is especially visible when C H O is the excess species (upper graph 2 5 2 in Figure 5 and pink and orange circles in Figure 6: [C H O ]  3  [HO ]). HO on the 2 5 2 2 2 other hand approaches low concentrations at longer reaction times under all conditions, even when it is the excess species (lower graph in Figure 5 and black circles in Figure 6: [HO ]  3  [C H O ]): its self-reaction (H O concentration time profile given as full 2 2 5 2 2 2 lines) is around 20 times faster than the self-reaction of C H O and is a major loss process 2 5 2 under all conditions and all reaction times, the reaction with C H O (dashed lines) plays 2 5 2 a major role only under excess C H O conditions. Under excess HO concentrations, the 2 5 2 2 HO profile is barely influenced by (R3): an increased loss through an increase in k is 2 3 counterbalanced by a decreased loss through self-reaction. The profiles of all condition shown in Figure 6 have simultaneously been fitted to a simple mechanism, with the experimental conditions given in Table 2 and the mechanism 14 3 given in Table 3. The initial Cl-atom concentration was fixed to 1.2  10 cm for all experiments, obtained in initial experiments from measuring pure HO decays (no C H 2 2 6 15 3 added). [C H ] has been varied between 1.9–7.5  10 cm and [CH OH] has been 2 6 3 15 3 varied between 2.8–5.0  10 cm . Using these conditions, the ratio of [HO ]/[C H O ] 2 2 5 2 has been varied between 0.3 (pink circles) and 2.5 (black circles). Table 2. Conditions for experiments shown in Figure 6. Initial Cl-atom concentration was for all 14 3 2 experiments 1.2  10 cm , total pressure was 100 Torr O , T = 295 K. [C H O ] and [HO ] 2 2 5 2 concentration taken from the model. Total radical concentrations are slightly below initial Cl- concentration due to (R10). 15 15 13 13 3 3 3 3 [C H ]/10 cm [CH OH]/10 cm [C H O ] /10 cm [HO ] /10 cm 2 6 3 2 5 2 max 2 max 1.94 5.0 3.4 8.3 2.74 5.0 4.3 7.4 3.45 5.0 5.0 6.7 4.30 5.0 5.6 6.1 5.91 2.8 8.1 3.6 7.50 2.8 8.6 3.0 For all graphs in Figure 6, the above determined absorption cross-section ( = 20 2 1.0  10 cm ) has been used to convert the C H O absorption coefficients into ab- 2 5 2 solute concentrations. The profiles for both species could be well reproduced over the entire concentration 12 3 1 1 range using a rate constant of k = 6.2  10 cm molecule s , shown in the centre graph (b). In a next step, different rate constants for the cross reaction have been tested: indeed, despite several measurements of this rate constant over the last decades [32–38], there is no good agreement for this rate constant. An excellent summary on previous measurements of this rate constant can be found in Noell et al. [32] and will not be repeated here. The two recent determinations from Noell et al. [32] and Boyd et al. [33] are considered by the IUPAC committee as being carried out by the most reliable methods, however they 12 3 1 1 vary by about a factor of 1.5 (8.14  10 cm molecule s for Boyd et al. [33] from 12 3 1 1 UV absorption and 5.57  10 cm molecule s for Noell et al. [32] from UV/near IR absorption). We have tested these two limits by trying to adjust both profiles over the entire concentration range. In the upper graphs (a), the rate constant k has been set to the lower 12 3 1 1 limit such as obtained by Noell et al. [32] (5.5  10 cm molecule s ), leading to C H O and (less pronounced) HO decays that are too slow. Increasing the initial C H O 2 5 2 2 2 5 2 Photonics 2021, 8, 296 11 of 17 concentration by about 10% (corresponding to a decreased absorption cross-section for 20 2 C H O :  = 0.9  10 cm ) can lead again to less good, but still acceptable HO and 2 5 2 2 C H O decays (which would also imply a slight deviation of the overall initial radical 2 5 2 14 3 concentration from 1.2  10 cm ). In the lower graphs (c), the upper limit has been 12 3 1 1 tested by setting k = 8  10 cm molecule s : decays of both species are too fast and a decrease in concentration does not lead to an acceptable adjustment of both species. Table 3. Reaction mechanism used to fit all experiments in this work. 3 1 1 Reaction k/cm molecule s Reference 1a 2 C H O ! 2 C H O + O 2.6  10 Ref [32] * 2 5 2 2 5 2 1b 2 C H O ! C H OH + CH CHO + O 6.7  10 Ref [32] * 2 5 2 2 5 3 2 2 C H O + O ! CH CHO + HO 8  10 Ref [39] 2 5 2 3 2 3 C H O + HO ! C H OOH + O This work 6.2  10 2 5 2 2 2 5 2 5 Cl + C H ! C H + HCl 5.9  10 Ref [31] 2 6 2 5 6a C H + O + M ! C H O + M 4.8  10 Ref [40] 2 5 2 2 5 2 6b C H + O ! C H + HO 3-4 10 This work ** 2 5 2 2 4 2 7 Cl + CH OH ! CH OH + HCl 5.5  10 Ref [31] 3 2 8 CH OH + O ! CH O + HO 9.6  10 Ref [31] 2 2 2 2 9 2 HO ! H O + O Ref [30] 1.7  10 2 2 2 2 10 C H O + Cl ! products 1.5  10 Ref [41] 2 5 2 11 C H O ! diffusion 2 s This work 2 5 2 12 HO ! diffusion 3 s This work * The branching ratio for (R1) is currently contradictory, IUPAC currently recommends the radical path (R1a) as the major path. However, we have chosen here to use the most recent determination: (a) the self-reaction is very minor in our system (see Figure 5) and thus a change in branching ratio has a negligible impact on the retrieved profiles and (b) we have confirmed in separate experiments (to be published) the low branching ratio for the radical path. ** This reaction is likely due to excited C H radicals and the branching ratio between (R6a) and 2 5 (R6b) depends on pressure and also on the mode of generation of the C H radicals. 2 5 In conclusion, using the absorption cross-section for C H O obtained in back-to-back 2 5 2 experiments leads in these kinetic experiments to the best fit for both species over the entire concentration range. However, it should of course be noted, that in the end both methods rely on the absorption cross-section of HO and therefore both approaches cannot be considered as independent methods: the initial Cl-atom concentration used as input parameter in the model and being vital for retrieving the rate constant k and with this the absorption cross-section for C H O depend entirely on the rate constant for the HO 2 5 2 2 self-reaction. The absorption cross-section of HO varies through pressure broadening (which is taken into account), but it might also vary during the experiment through small and unnoted shifts in the wavelength of the DFB laser emission (the linewidth of the HO absorption lines are on the order of 0.02 cm FWHM at 50 Torr he). However, in our experiments the absorption cross-section of HO is under most conditions constantly being “measured”: a major HO loss in most experiments is the self-reaction, and thus the HO 2 2 decays are sensitive to the absolute HO concentration, i.e., to the absorption cross-section that has been used to convert the absorption time profiles to concentration time profiles. Therefore, it can be said that both methods have determined the C H O absorption cross- 2 5 2 section relative to the rate constant of the HO self-reaction. The IUPAC committee [30] estimates the uncertainty of this rate constant to 15%, which we use as a basis to estimate the uncertainty of our rate constant, with an additional 10% for uncertainties in the fitting 12 3 1 1 of the rate constant: k = (6.2  1.5)  10 cm molecule s . 3 Photonics 2021, 8, x FOR PEER REVIEW 12 of 17 Photonics 2021, 8, 296 12 of 17 3.3. Measuring the Relative Absorption Spectrum 3.3. Measuring the Relative Absorption Spectrum In order to obtain the shape of the C2H5O2 absorption spectrum, kinetic decays have In order to obtain the shape of the C H O absorption spectrum, kinetic decays 2 5 2 been measured under identical conditions at 15 different wavelengths in the range acces- have been measured under identical −1 conditions at 15 different wavelengths in the range sible with our DFB laser (7596–7630 cm ). The relative absorption coefficients are put on accessible with our DFB laser (7596–7630 cm ). The relative absorption coef −1 ficients are an absolute scale by comparison with the absorption cross-section at 7596.47 cm . Table 4 put on an absolute scale by comparison with the absorption cross-section at 7596.47 cm . summarizes the obtained results, and Figure 7 compares the present data with two litera- Table 4 summarizes the obtained results, and Figure 7 compares the present data with two ture results. literature results. Figure 7. C H O absorption coefficients at different wavelengths obtained in this work (green 2 5 2 Figure 7. C2H5O2 absorption coefficients at different wavelengths obtained in this work (green crosses and green axis), overlaid onto the spectrum obtained by Melnik et al. [17] (upper graph, crosses and green axis), overlaid onto the spectrum obtained by Melnik et al. [17] (upper graph, Reprinted with permission from [17], Copyright 2010 American Chemical Society) and Atkinson Reprinted with permission from [17], Copyright 2010 American Chemical Society) and Atkinson and Spillman [11] (lower graph, Reprinted with permission from [11], Copyright 2002 American and Spillman [11] (lower graph, Reprinted with permission from [11], Copyright 2002 American −1 Chemical Society). In the upper graph the data have been shifted by 4 cm , and in both graphs our Chemical Society). In the upper graph the data have been shifted by 4 cm , and in both graphs our data have data have beenbeen scaled scaled on the onythe -axiy s, -axis, i.e., appa i.e., appar rently ently there is ther a ba e is sel a baseline ine shift in shift both in both comcomparisons. parisons. The upper graph shows that our spectrum (green symbols and green axis apply) The upper graph shows that our spectrum (green symbols and green axis apply) agrees well with the results of Melnik et al. [17] if our data are shifted by 4 cm . Possibly, −1 agrees well with the results of Melnik et al. [17] if our data are shifted by 4 cm . Possibly, there is a mistake in the Melnik figure (T. Miller, private communication), because the there is a mistake in the Melnik figure (T. Miller, private communication), because the peak absorption is given in the text at 7596 cm , just as in our case, however in the figure −1 peak absorption is given in the text at 7596 cm , just as in our case, however in the figure the peak is located at 7600 cm , indicated by a blue vertical line. In the lower graph, −1 the peak is located at 7600 cm , indicated by a blue vertical line. In the lower graph, our our data (again in green) are overlaid to the spectrum of Atkinson and Spillman [11]. A data (again in green) are overlaid to the spectrum of Atkinson and Spillman [11]. A good good agreement of the shape in both comparisons can be obtained, when our data are agreement of the shape in both comparisons can be obtained, when our data are scaled on scaled on the y-axis, i.e., when we suppose a shift in the baseline of both literature spectra the y-axis, i.e., when we suppose a shift in the baseline of both literature spectra (around (around 23% of the peak absorption for Atkinson and Spillman and 15% for Melnik et al.). 23% of the peak absorption for Atkinson and Spillman and 15% for Melnik et al.). Melnik Melnik et al. discussed in their paper such baseline shift (dashed line in their figure) and et al. discussed in their paper such baseline shift (dashed line in their figure) and at- attributed it to a broadband absorber, generated simultaneously during the photolysis. tributed it to a broadband absorber, generated simultaneously during the photolysis. In- Indeed, they obtained their baseline by measuring ring-down events with the photolysis deed, they obtained their baseline by measuring ring-down events with the photolysis laser blocked. In this case, a broadband absorber generated simultaneously to the C H O 2 5 2 laser blocked. In this case, a broadband absorber generated simultaneously to the C2H5O2 radical would induce a baseline shift. To take into account this shift (horizontal dashed line radical would induce a baseline shift. To take into account this shift (horizontal dashed in the upper graph of Figure 7), they have calculated the absorption cross-section above Photonics 2021, 8, 296 13 of 17 this plateau. No explanation for a possible baseline shift in the work of Atkinson and Spillman can be given. Table 4. C H O Absorption cross-sections at different wavelengths. 2 5 2 1 20 2 Wavenumber/cm /10 cm 7596.47 10.0 7597.20 8.7 7597.44 8.1 7598.40 7.4 7602.02 6.7 7602.38 6.8 7606.25 5.8 7609.16 5.0 7610.66 4.2 7619.28 3.7 7622.36 3.1 7624.28 2.9 7626.72 2.3 7630.50 2.0 7489.16 2.0 4. Discussion Comparison of the Absorption Cross-Section with Literature Data The absorption cross-section of C H O was first determined by Atkinson and Spill- 2 5 2 man [11] using 193 nm photolysis of 3-pentanone as precursor. Using the kinetic method, 21 2 they determined at the peak  = (3  1.5)  10 cm , which is 3 times smaller than the present value. A higher absorption cross-section had also been measured previously by our group for the CH O radical [12]. One possible reason might be that the determina- 3 2 tion from Atkinson and Spillman is based on the kinetic method using low initial radical concentrations, hence the C H O concentration has to be measured over long reaction 2 5 2 times in order to observe a sizeable decay, but the possible loss due to diffusion out of the photolysis volume or due to wall loss, possibly non-negligible over such long reaction times, has not been considered in the data evaluation. This can induce an overestimation of the radical concentration and therefore an underestimation of the absorption cross-section (see Figures 2c and 4). Another reason might be the precursor: the reaction of C H + O 2 5 2 can also lead to small amounts of HO through (R6b), around 1% of the initial Cl-atom concentration led to formation of HO in the experiments of this work. Atkinson and Spill- man used 193 nm photolysis of 3-pentanone, which leaves considerably higher amounts of excess energy in the fragments than our method, based on H-atom abstraction. Therefore, the fraction of C H radicals that react through (R6b) might be considerably higher than in 2 5 our case. This could induce a non-negligible initial HO concentration which participates in the removal of C H O and would thus induce a systematic error when using the kinetic 2 5 2 method. This is also in line with the observation of Atkinson and Spillman, that in their experiments the apparent rate constant of the C H O self-reaction was inversely pressure 2 5 2 dependent: the rate constant decreased with increasing pressure (D. Atkinson, private com- munication). An increased cooling of the hot C H radical with increasing pressure would 2 5 lead to a decreasing HO concentration and thus to a slow-down of the C H O decay. 2 2 5 2 Rupper et al. [16] estimated the absolute absorption cross-section to  = 4.4  10 cm from calculating the initial Cl-atom concentration by measuring the decrease of photolysis energy in absence and presence of the Cl-atom precursor, assuming that all Photonics 2021, 8, x FOR PEER REVIEW 14 of 17 Photonics 2021, 8, 296 14 of 17 energy in absence and presence of the Cl-atom precursor, assuming that all generated Cl- atoms lead to formation of one C2H5O2. In a more recent work from the same group, Melnik et al. [18] have determined the absorption cross-section by dual-CRDS method: on generated Cl-atoms lead to formation of one C H O . In a more recent work from the 2 5 2 one absorption path they measured the absorption of C2H5O2 while on the other path the same group, Melnik et al. [18] have determined the absorption cross-section by dual- concentration of HC CRDS l was method: quantifi on ed tha one absorption nks to its known a path they bsorp measur tion cross- ed thesecti absorption on. As- of C H O while 2 5 2 suming again that on one the Cother 2H5O2path has b the een concentration generated foof r eHCl ach m was olequantified cule of HCthanks l, they f to ou its nd known absorption −21 −2 cross-section. Assuming again that one C H O has been generated for each molecule an absorption cross-section of σ = 5.29 × 10 cm . This is nearly 2 times lower than the 2 5 2 21 2 value obtained in t of his wo HCl, rthey k. It is found unlike an lyabsorption that the difference in the cross-section of bandwidth o  = 5.29  f10 the exci cm - . This is nearly −1 −4 −1 2 times lower than the value obtained in this work. It is unlikely that the difference in the tation laser sources (0.01 cm for Melnik and <1 × 10 cm for this work) can explain the 1 4 1 bandwidth of the excitation laser sources (0.01 cm for Melnik and <1  10 cm for difference, because the absorption band is unstructured and much larger than the band- this work) can explain the difference, because the absorption band is unstructured and width of both laser sources. Also, the overall shape is, after consideration of a baseline much larger than the bandwidth of both laser sources. Also, the overall shape is, after shift, in excellent agreement between both works (see Figure 7). consideration of a baseline shift, in excellent agreement between both works (see Figure 7). A possible explanation might be that Melnik et al. and Rupper et al. both consider A possible explanation might be that Melnik et al. and Rupper et al. both consider the the complete conversion of Cl-atoms into C2H5O2 radicals: a simple model is presented by complete conversion of Cl-atoms into C H O radicals: a simple model is presented by Melnik et al. [17] showing the complete conversion of Cl- 2ato 5ms in 2 to C2H5O2. However, Melnik et al. [17] showing the complete conversion −10 3 of Cl-atoms −1 −1into C H O . However, the 2 5 2 the very fast reactions of Cl-atoms with C2H5O2 (k10 = 1.5 × 10 cm molecule s ) [41] and 10 3 1 1 −10 very 3fast reactions −1 −1 of Cl-atoms with C H O (k = 1.5  10 cm molecule s ) [41] 2 5 2 10 C2H5 (k = 3 × 10 cm molecule s ) [42] are omitted in this model, even though these 10 3 1 1 and C H (k = 3  10 cm molecule s ) [42] are omitted in this model, even though 2 5 reactions are non-negligible under their conditions of very high initial Cl-atom concentra- these reactions are non-negligible under their conditions of very high initial Cl-atom con- 15 −3 16 tions, well above 10 cm , combined with relatively low C2H6 concentrations (1 × 10 15 3 centrations, well above 10 cm , combined with relatively low C H concentrations −3 2 6 cm ). These reactions result in a C2H5O2 concentration that might be well below the initial 16 3 (1  10 cm ). These reactions result in a C H O concentration that might be well 2 5 2 Cl-atom concentration, depending on the overall radical concentration as well as on the below the initial Cl-atom concentration, depending on the overall radical concentration C2H6 concentration. Figure 8 shows a simulation using the model from Melnik et al., but as well as on the C H concentration. Figure 8 shows a simulation using the model 2 6 completed by the two fast reactions. The left graph shows the result using initial concen- from Melnik et al., but completed by the two fast reactions. The left graph shows the 15 −3 16 −3 trations such as given by Melnik et al. ([Cl]0 = 2 × 10 cm and [C2H6]0 = 1 × 10 cm ), the 15 3 result using initial concentrations such as given by Melnik et al. ([Cl] = 2  10 cm right graph shows the model result with typical conditions such as used in this work for 16 3 and [C H ] = 1  10 cm ), the right graph shows the model result with typical con- 2 6 0 13 −3 16 the determination of the absorption cross-section ([Cl]0 = 5 × 10 cm and [C2H6]0 = 3 × 10 ditions such as used in this work for the determination of the absorption cross-section −3 cm ). Under the high Cl/low C2H6 conditions of Melnik et al., only 63% of the Cl-atoms 13 3 16 3 ([Cl] = 5  10 cm and [C H ] = 3  10 cm ). Under the high Cl/low C H con- 0 2 6 0 2 6 have been converted to C2H5O2, while 28% of the Cl-atoms have reacted with C2H5O2 and ditions of Melnik et al., only 63% of the Cl-atoms have been converted to C H O , while 2 5 2 8% have reacted with C2H5. Under the low Cl/high C2H6 conditions (right graph), virtually 28% of the Cl-atoms have reacted with C H O and 8% have reacted with C H . Under 2 5 2 2 5 all Cl-atoms have been converted to C2H5O2, less than 1% of the Cl-atoms have reacted the low Cl/high C H conditions (right graph), virtually all Cl-atoms have been converted 2 6 with either C2H5O2 or C2H5. From this model one can suspect that the absorption cross- to C H O , less than 1% of the Cl-atoms have reacted with either C H O or C H . From 2 5 2 2 5 2 2 5 sections of Melnik et al. [17] and Rupper et al. [16] are strongly underestimated, and a this model one can suspect that the absorption cross-sections of Melnik et al. [17] and correction of the Melnik et al. value, based on the more complete model presented here, Rupper et al. [16] are strongly underestimated, and a correction of the Melnik et al. value, −21 −2 would lead to σ = 8.8 × 10 cm , which gets into good agreement with the value found in 21 2 based on the more complete model presented here, would lead to  = 8.8  10 cm , this work. which gets into good agreement with the value found in this work. Figure 8. Simulation of conversion of Cl-atoms (violet dashed dot) into HCl (black) and C H O (blue dashed): model Figure 8. Simulation of conversion of Cl-atoms (violet dashed dot) into HCl (black 2 ) an 5 d C 2 2H5O2 10 3 1 taken from Melnik et al., completed with the reactions of Cl with C H O (k = 1.5  10 cm s ) [41] (red dotted) and (blue dashed): model taken from Melnik et al., completed w 2ith the rea 5 2 ctions of Cl with C2H5O2 (k = 10 3 1 −10 3 −1 −10 3 −1 C H (k = 3 10 cm s ) [42] (green dashed dotted): left graph conditions such as used in Melnik et al. [17], right graph 2 5 1.5 × 10 cm s ) [41] (red dotted) and C2H5 (k = 3 × 10 cm s ) [42] (green dashed dotted): left conditions such as used in this work. The products from the reaction of Cl with C H O (red) and with C H (green) are graph conditions such as used in Melnik et al.[17], right graph conditions such as used in this work. 2 5 2 2 5 zoomedThe products in the right graph from the reaction of Cl w by a factor of 100 (right ith yC -axis 2H5O applies). 2 (red) and with C2H5 (green) are zoomed in the right graph by a factor of 100 (right y-axis applies). 5. Conclusions We have presented in this work a new determination of the absorption cross-section of the à X electronic transition of the C H O radical. The cross-section at the peak 2 5 2 Photonics 2021, 8, 296 15 of 17 wavelength 7596.4 cm has in a first approach been determined by direct comparison with the well-known HO absorption cross-section in back-to-back experiments to be 20 2 (1.0  0.2)  10 cm . In further experiments, the absorption cross-section has been validated by measuring the rate constant of C H O with HO in a wide range of con- 2 5 2 2 centration: the ratio of [HO ]/[C H O ] has been varied between 0.3 and 2.5 and the 2 2 5 2 concentration time profiles could be reproduced very well using the same absorption cross-section for all C H O profiles, which returned a rate constant for the cross reaction 2 5 2 12 3 1 1 of 6.2  10 cm molecule s . Sensitivity analysis in the upper and lower range of previous literature values did not allow for good reproduction of the concentration-time profiles for both species over the entire concentration range and confirm the reliability of our results. Smaller absorption cross-sections such as obtained in previous works can convincingly be explained by unidentified secondary reaction, not having been taken into account in the data evaluations. Author Contributions: Conceptualization, C.F.; methodology, C.F., C.Z., M.S., M.A.; validation, C.F., L.P., C.S.; formal analysis, C.Z., M.S.; investigation, C.Z., M.S., M.A.; resources, C.F., M.A.; data curation, C.F.; writing—original draft preparation, C.F.; writing—review and editing, all authors; visualization, C.Z., M.S., C.F.; supervision, C.F., L.P., X.T., W.Z.; project administration, C.F.; funding acquisition, C.F., L.P., C.S., X.T., W.Z. All authors have read and agreed to the published version of the manuscript. Funding: This project was supported by the French ANR agency under contract No. ANR-11- Labx-0005-01 CaPPA (Chemical and Physical Properties of the Atmosphere), the Région Hauts-de- France, the Ministère de l’Enseignement Supérieur et de la Recherche (CPER Climibio) and the European Fund for Regional Economic Development. C.F. is grateful to the Chinese Academy of Sciences President’s International Fellowship Initiative (No. 2018VMA0055). C.Z. thanks the Chinese Scholarship Council for financial support (No. 202006340125). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Raw data are available on request. Conflicts of Interest: The authors declare no conflict of interest. References 1. Orlando, J.J.; Tyndall, G.S. Laboratory studies of organic peroxy radical chemistry: An overview with emphasis on recent issues of atmospheric significance. Chem. Soc. Rev. 2012, 41, 6294–6317. [CrossRef] [PubMed] 2. Fittschen, C. The reaction of peroxy radicals with OH radicals. Chem. Phys. Lett. 2019, 725, 102–108. [CrossRef] 3. Assaf, E.; Song, B.; Tomas, A.; Schoemaecker, C.; Fittschen, C. Rate Constant of the Reaction between CH O Radicals and OH 3 2 Radicals revisited. J. Phys. Chem. A 2016, 120, 8923–8932. [CrossRef] 4. Hasson, A.S.; Tyndall, G.S.; Orlando, J.J. 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[CrossRef] 2 2 22. Assaf, E.; Asvany, O.; Votava, O.; Batut, S.; Schoemaecker, C.; Fittschen, C. Measurement of line strengths in the à A’ X A” transition of HO and DO . J. Quant. Spectrosc. Radiat. Transfer 2017, 201, 161–170. [CrossRef] 2 2 23. Thiebaud, J.; Aluculesei, A.; Fittschen, C. Formation of HO Radicals from the Photodissociation of H O at 248 nm. J. Chem. 2 2 2 Phys. 2007, 126, 186101. [CrossRef] [PubMed] 24. Tang, Y.; Tyndall, G.S.; Orlando, J.J. Spectroscopic and Kinetic Properties of HO Radicals and the Enhancement of the HO Self 2 2 Reaction by CH OH and H O. J. Phys. Chem. A 2010, 114, 369–378. [CrossRef] 3 2 25. DeSain, J.D.; Ho, A.D.; Taatjes, C.A. High-resolution diode laser absorption spectroscopy of the O–H stretch overtone band (2,0,0)(0,0,0) of the HO radical. J. Mol. Spectrosc. 2003, 219, 163–169. [CrossRef] 26. Ibrahim, N.; Thiebaud, J.; Orphal, J.; Fittschen, C. Air-Broadening Coefficients of the HO Radical in the 2v Band Measured 2 1 Using cw-CRDS. J. Mol. 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A laser flash photolysis, time-resolved Fourrier Transform Infrared Emission study of the reaction Cl + C H –> HCl + C H . J. Phys. Chem. 1993, 97, 5633–5642. [CrossRef] 2 5 2 4 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Photonics Multidisciplinary Digital Publishing Institute

Absolute Absorption Cross-Section of the Ã←X˜ Electronic Transition of the Ethyl Peroxy Radical and Rate Constant of Its Cross Reaction with HO2

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hv photonics Article Absolute Absorption Cross-Section of the à X Electronic Transition of the Ethyl Peroxy Radical and Rate Constant of Its Cross Reaction with HO 1 , 2 , 3 1 1 2 , 3 2 , 3 1 Cuihong Zhang , Mirna Shamas , Mohamed Assali , Xiaofeng Tang , Weijun Zhang , Laure Pillier , 1 1 , Coralie Schoemaecker and Christa Fittschen * Université Lille, CNRS, UMR 8522-PC2A-Physicochimie des Processus de Combustion et de l’Atmosphère, F-59000 Lille, France; cuihong.zhang@univ-lille.fr (C.Z.); mirna.shamas@univ-lille.fr (M.S.); mohamed.assali@univ-lille.fr (M.A.); laure.pillier@univ-lille.fr (L.P.); coralie.schoemaecker@univ-lille.fr (C.S.) Laboratory of Atmospheric Physico-Chemistry, Anhui Institute of Optics and Fine Mechanics, HFIPS, Chinese Academy of Sciences, Hefei 230031, China; tangxf@aiofm.ac.cn (X.T.); wjzhang@aiofm.ac.cn (W.Z.) Science Island Branch, Graduate School, University of Science and Technology of China, Hefei 230026, China * Correspondence: Christa.Fittschen@univ-lille.fr Abstract: The absolute absorption cross-section of the ethyl peroxy radical C H O in the à X 2 5 2 electronic transition with the peak wavelength at 7596 cm has been determined by the method of dual wavelengths time resolved continuous wave cavity ring down spectroscopy. C H O radicals 2 5 2 were generated from pulsed 351 nm photolysis of C H /Cl mixture in presence of 100 Torr O 2 6 2 2 at T = 295 K. C H O radicals were detected on one of the CRDS paths. Two methods have been 2 5 2 applied for the determination of the C H O absorption cross-section: (i) based on Cl-atoms being 2 5 2 converted alternatively to either C H O by adding C H or to hydro peroxy radicals, HO , by 2 5 2 2 6 2 adding CH OH to the mixture, whereby HO was reliably quantified on the second CRDS path in the 3 2 2 vibrational overtone at 6638.2 cm (ii) based on the reaction of C H O with HO , measured 1 2 5 2 2 Citation: Zhang, C.; Shamas, M.; under either excess HO or under excess C H O concentration. Both methods lead to the same peak 2 2 5 2 Assali, M.; Tang, X.; Zhang, W.; Pillier, 1 20 2 absorption cross-section for C H O at 7596 cm of  = (1.0  0.2)  10 cm . The rate constant L.; Schoemaecker, C.; Fittschen, C. 2 5 2 12 3 Absolute Absorption Cross-Section of for the cross reaction between of C H O and HO has been measured to be (6.2  1.5)  10 cm 2 5 2 2 1 1 the à X Electronic Transition of the molecule s . Ethyl Peroxy Radical and Rate Constant of Its Cross Reaction with e Keywords: peroxy radicals; near-infrared spectroscopy; à X electronic transition; cavity ring HO . Photonics 2021, 8, 296. https:// down spectroscopy doi.org/10.3390/photonics8080296 Received: 24 June 2021 Accepted: 21 July 2021 1. Introduction Published: 24 July 2021 The oxidation of volatile organic compounds (VOCs) in the troposphere is mainly driven by hydroxyl radicals (OH) and leads, after addition of O , to the formation of Publisher’s Note: MDPI stays neutral organic peroxy radicals (RO ). The fate of these RO radicals depends on the chemical com- 2 2 with regard to jurisdictional claims in position of the environment. In a polluted atmosphere they react mainly with nitric oxide published maps and institutional affil- (NO) to form alkoxy radicals or react with nitrogen dioxide (NO ) to form peroxynitrates iations. (RO NO ). Subsequent to the reaction with NO, alkoxy radicals react with O to form 2 2 2 hydro peroxy radicals (HO ). HO further oxidises NO into NO and thus regenerates 2 2 2 OH, closing the quasi-catalytic cycle. The photolysis of produced NO is the only relevant chemical source of tropospheric ozone. In clean environments with low NO (NO = NO x x Copyright: © 2021 by the authors. + NO ) concentrations, the dominant loss of RO is due to its reaction with HO forming 2 2 2 Licensee MDPI, Basel, Switzerland. hydroperoxides ROOH and terminating the radical reaction chain. In addition, RO radi- This article is an open access article cals can react either with themselves as self-reaction (RO + RO ) or with other R’O as 2 2 2 distributed under the terms and cross-reaction (RO + R’O ) or with OH radicals (RO + OH) [1–5]. conditions of the Creative Commons 2 2 2 Ethane is one of the most abundant non-methane hydrocarbons in the atmosphere, Attribution (CC BY) license (https:// and its atmospheric oxidation leads to the formation of the ethyl peroxy radical, C H O . A creativecommons.org/licenses/by/ 2 5 2 reliable detection of this radical is therefore highly desirable for studying its reactivity and 4.0/). Photonics 2021, 8, 296. https://doi.org/10.3390/photonics8080296 https://www.mdpi.com/journal/photonics Photonics 2021, 8, 296 2 of 17 thus understanding its embedded chemistry. Previous studies of peroxy chemistry have e e mostly been carried out by UV absorption spectroscopy in the B X electronic transition: this method gives a good sensitivity for peroxy radicals due to large absorption cross- sections, but the selectivity is poor because the absorption spectra are unstructured and the spectra of many different species are overlapping. The à X electronic transition of peroxy radicals is located in the near IR region. At room temperature, these transitions form rotationally unresolved envelopes with typical features about 1 cm or more wide and allow a more selective detection of peroxy radicals, compared to UV absorption. The shape of such unresolved absorption features is typically only very little influenced by temperature or pressure, in contrast to the resolved spectra of small species like OH or HO : sharp lines are observed for transitions between different rotational or vibration states, where pressure is broadening the lines and temperature can change the relative populations of the different states and thus the cross-sections of the lines. However, due to small absorption cross-sections of the à X electronic transition of 20 21 2 peroxy radicals (~10 –10 cm ), these transitions have not attracted much attention after they had been located for the first time by Hunziker and Wendt in 1976 [6,7]. Interest has been revived many years later when the highly sensitive absorption technique of cavity ring down spectroscopy (CRDS) has been developed [8,9], which can make up for the small absorption cross-sections. The first report on using this technique for the detection of peroxy radicals was in 2000 [10]: T. Miller and coworkers obtained pulsed near IR radiation by stimulated Raman shifting of the output of a pulsed dye laser in molecular hydrogen. The output of such a laser source has a typical bandwidth of about 0.03 cm and is thus much narrower than the à X electronic transition of peroxy radicals. They measured the absorption spectra of the methyl and ethyl peroxy radicals, but determined only the absorption cross-section for the methyl peroxy radical. The peak of the à X transition for C H O was found around 7596 cm . 2 5 2 A few years later, Atkinson and Spillman [11] measured again the spectra of both radicals, now using a continuous external cavity diode laser to perform cw-CRDS with 5 1 a much narrower bandwidth (~3  10 cm ). They confirmed the overall shape of the absorption spectrum, and measured for the first time the absorption cross-section for C H O using the kinetic method [12–15]. This method can be applied, if the rate 2 5 2 constant of a radical-radical reaction is known, because the initial concentration and thus the absorption cross-section can in principle be determined from the shape of the kinetic decay. The self-reaction can be described as follows. A + A ! B d[A] = 2k A (1) [ ] dt Integration of Equation (1) leads to 1 1 = + 2kt (2) [A] [A] Hence, plotting 1/[A] as a function of time leads to a straight line with the slope being 2k. In the case where the rate constant is known, but not the absolute concentration of A, the absorption coefficient =   [A] can be used in Equation (2) instead of [A], leading to 1 1 2k = + t (3) [A]  [A] Plotting 1/  [A] leads to a straight line with the slope being m = 2k/ while the intercept I = 1/  [A] . However, different complications can arise from this method: radicals can be lost through other processes too, for example through diffusion out of the photolysed volume or through unidentified secondary reactions in which case the decays are faster than expected from pure self-reaction only, and the retrieved absorption Photonics 2021, 8, 296 3 of 17 cross-section would be too small. In the case of peroxy radicals, this method has another complication: the self-reaction of peroxy radicals (R1) has several product pathways, and one of them leads to the formation of HO radicals: 2 C H O ! 2 C H O + O (R1a) 2 5 2 2 5 2 ! C H OH + CH CHO + O (R1b) 2 5 3 2 followed, in presence of O , by (R2): C H O + O ! CH CHO + HO (R2) 2 5 2 3 2 The HO radicals react with C H O 2 2 5 2 C H O + HO ! C H OOH + O (R3) 2 5 2 2 2 5 2 with (R3) having a rate constant faster than (R1). As a result, the C H O decays are 2 5 2 accelerated by the formation of HO , and therefore when using Equation (3) for (R1), the obtained rate constant k is called k , and the acceleration has to be taken into account 1 1 obs to retrieve the “real” rate constant k from C H O decays. Using the recommended 1 2 5 2 value of k , in the kinetic method, Atkinson and Spillman [11] obtained an absorption 1 obs 1 21 2 cross-section for C H O at 7596 cm of  = (3.0  1.5)  10 cm . 2 5 2 Another work on the ethyl peroxy spectrum from the Miller group [16] scanned the à X electronic transition over a large wavelength range and identified the transitions for the two different isomers. Indeed, ethyl peroxy radicals exist in an equilibrium between two stable conformers with the dihedral angles between the O-O-C and O-C-C planes being 0 for the T (trans) and 120 for the G (gauche) conformer. The peak absorptions for 1 1 both conformers were located well separated at 7362 cm for the T- and 7592 cm for the G-conformer. In this work, they used a different method to estimate the absorption cross-section: peroxy radicals were generated by the reaction of Cl-atoms with C H , with 2 6 the Cl-atoms being generated by 193 nm photolysis of oxalylchloride, (COCl) . To obtain the concentration of C H O , they measured the photolysis laser energy with and without 2 5 2 precursor, and calculated the Cl-atom concentration from the difference. Supposing that 21 2 each Cl-atom generated one C H O radical, they obtained  = 4.4 10 cm for C H O 2 5 2 2 5 2 at 7596 cm . The next work on the ethyl peroxy spectrum from the Miller group [17] used a different method to obtain the absorption cross-section: in a dual-path CRDS set-up, the concentration of HCl (generated from the reaction of Cl-atoms with C H ) was measured 2 6 on one path while the absorption of C H O was measured simultaneously on the other 2 5 2 path. Again supposing that each HCl-molecule had generated one C H O radical, they 2 5 2 21 2 1 obtained  = (5.29  0.20)  10 cm for C H O at 7596 cm . 2 5 2 In the most recent work from the Miller group [18], the above absorption cross-section was validated indirectly through the kinetic method: the C H O absorption profiles were 2 5 2 converted to C H O concentration-time profiles using the above absorption cross-section, 2 5 2 and the rate constant k , for the self-reaction was extracted. Good agreement with other obs literature data was found, which was taken as an indication that the absorption cross- section is valid. A summary of previous results as well as the results obtained in this work is presented in Table 1. In this work we present a new determination of the absorption cross-section, based on two different approaches. The first one is comparable to one of the Miller methods [17] and will be called back-to-back method: in our dual-path CRDS set-up we generate Cl-atoms and transform them to HO through reaction with CH OH, with HO being quantified 2 3 2 on one path at 6638.2 cm . Directly after, the Cl-atoms were transformed to C H O 2 5 2 by adding C H instead of CH OH to the reaction mixture and the C H O absorption 2 6 3 2 5 2 was measured on the second path. Supposing that the Cl concentration stays the same between both experiments and that in both cases all Cl-atoms are converted to either HO 2 Photonics 2021, 8, x FOR PEER REVIEW 4 of 17 Photonics 2021, 8, 296 4 of 17 can be quantified reliably) or to C2H5O2, the absorption cross-section of C2H5O2 is deter- mined relative to the one of HO2. The second approach is a variation of the kinetic method (which can be quantified reliably) or to C H O , the absorption cross-section of C H O is 2 5 2 2 5 2 such as used by Atkinson and Spillman [11] and Melnik et al. [18], but not based on the determined relative to the one of HO . The second approach is a variation of the kinetic sel method f-react such ion of asC used 2H5Oby 2, bAtkinson ut on the cross and Spillman reaction between HO [11] and Melnik 2 and C et al. 2H [18 5O ], 2. This but not reaction based has be on theen me self-reaction asured in of a wide r C H O a , nge but of c on the oncentrations under cross reaction between either HO excess of and C HO H 2 or exce O . This ss 2 5 2 2 2 5 2 of C reaction 2H5O has 2. In the fi been measur rst case, the ra ed in a wide te consta range nt is retr of concentrations ieved by adj under usting the C either excess 2H5O2 of decay HOs wi or th the a excess of bsol C u H te concentra O . In the first tion of case, HO the 2 being f rate constant ixed, while is retrieved in the second case t by adjusting the he rat C e H con- O 2 5 2 2 5 2 decays with the absolute concentration of HO being fixed, while in the second case the stant is fixed to the value determined just before, and now the best fit of the HO2 decay is rate constant is fixed to the value determined just before, and now the best fit of the HO achieved by adjusting the absolute concentration of C2H5O2, i.e., the absorption cross-sec- decay is achieved by adjusting the absolute concentration of C H O , i.e., the absorption tion. 2 5 2 cross-section. −1. Table 1. Summary of the C2H5O2 absorption cross-section at 7596 cm Table 1. Summary of the C H O absorption cross-section at 7596 cm . 2 5 2 −21 2 σ/10 cm Method Reference Method Reference /10 cm Kinetic method, no other radical losses Atkinson and Spillman 3.0 ± 1.5 Atkinson and Spillman considered [11] 3.0  1.5 Kinetic method, no other radical losses considered [11] Depletion of photolysis energy through precursor Depletion of photolysis energy through precursor 4.4 with [Cl] = [C2H5O2], i.e., no secondary reactions Rupper et al. [16] 4.4 with [Cl] = [C H O ], i.e., no secondary reactions Rupper et al. [16] 2 5 2 considered considered Measurement of HCl in dual path CRDS with [Cl] Measurement of HCl in dual path CRDS with [Cl] = 5.5.29 29 ± 0.20  0.20 = [C2H5O2], i.e., no secondary reactions Meln Melnik ik et et al al. . [ [1 17 7]] [C H O ], i.e., no secondary reactions considered 2 5 2 considered 5.29 Kinetic method used for validation of Ref. [17] Melnik et al. [18] 5.29 Kinetic method used for validation of Ref. [17] Melnik et al. [18] Measurement of HO /C H O in dual path CRDS 2 2 5 2 Measurement of HO2/C2H5O2 in dual path CRDS 10  2 This work 10 ± 2 with [Cl] = [HO ] = [C H O ] This work 2 2 5 2 with [Cl] = [HO2] = [C2H5O2] 10  2 Kinetic method from C H O + HO This work 2 5 2 2 10 ± 2 Kinetic method from C2H5O2 + HO2 This work 2. Materials and Methods 2. Materials and Methods The setup has been described in detail before [19–23] and is only briefly discussed The setup has been described in detail before [19-23] and is only briefly discussed here (Figure 1). here (Figure 1). Figure 1. Schematic view of the used experimental setup: AOM, Acousto-Optic Modulator; APD, Avalanche Photo Diode; Figure 1. Schematic view of the used experimental setup: AOM, Acousto-Optic Modulator; APD, Avalanche Photo Diode; M, Mirror; L, Lens. Both cw-CRDS systems are equipped with identical trigger circuits and data acquisition systems. M, Mirror; L, Lens. Both cw-CRDS systems are equipped with identical trigger circuits and data acquisition systems. The setup consisted of a 0.79 m long flow reactor made of stainless steel. The photol- The setup consisted of a 0.79 m long flow reactor made of stainless steel. The photolysis ysi laser s la(Lambda ser (Lamb Physik da Phys LPX ik LPX 202i, 202 XeF i, Xe at F at 351 35nm) 1 nm widt ) widt h h is de is delimited limited t too2 2 cm cm and p and passes asses t thr hrough t ough the her r ee aact ctor or longitudinally longitudinal.ly The . The flow flow reactor reaccontains tor contai two ns two i identical denti continuous cal continwave uous cavity ring-down spectroscopy (cw-CRDS) absorption paths, which were installed in a wave cavity ring-down spectroscopy (cw-CRDS) absorption paths, which were installed small angle with respect to the photolysis path. An overlap of the absorption path with the in a small angle with respect to the photolysis path. An overlap of the absorption path photolysis beam of 0.288 m is achieved. Both beam paths were tested for a uniform overlap with the photolysis beam of 0.288 m is achieved. Both beam paths were tested for a uni- with the photolysis beam before experiments were done. For this purpose, both cw-CRDS form overlap with the photolysis beam before experiments were done. For this purpose, instruments were operated to simultaneously measure HO concentrations. Deviations between HO concentrations were less than 5%, demonstrating that the photolysis laser Photonics 2021, 8, 296 5 of 17 was very well aligned, i.e., both light paths probed a very similar photolysed volume in the reactor. A small helium purge flow prevented the mirrors from being contaminated. Two different DFB lasers are used for the detection of the two species and each one is coupled into one of the cavities by systems of lenses and mirrors. Each probe beam passed an st acousto-optic modulator (AOM, AAoptoelectronic) to rapidly turn off the 1 order beam once a user-set threshold for light intensity in the cavity was reached, in order to measure the ring-down event. A home-made tracking system is used to increase the number of ring-down events [21]. Then, the decay of light intensity is recorded and an exponential fit is applied to retrieve the ring-down time. The absorption coefficient is derived from Equation (4). R 1 1 = [A]   = (4) where  is the ring-down time with an absorber present;  is the ring-down time with no absorber present;  is the absorption cross-section of the absorbing species A; R is the A L ratio between cavity length (79 cm) and effective absorption path (28.8 cm); c is the speed of light. Ethyl peroxy radicals were generated by pulsed 351 nm photolysis of C H /Cl O 2 6 2/ 2 mixtures initiating the reaction sequence (R4), (R5) and (R6): Cl + h ! 2 Cl (R4) 2 351 nm C H + Cl ! C H + HCl (R5) 2 6 2 5 C H + O + M ! C H O + M (R6a) 2 5 2 2 5 2 C H + O ! C H + HO (R6b) 2 5 2 2 4 2 For studying the cross reaction with HO , methanol, CH OH, has been added in 2 3 varying concentrations to the mixture. CH OH + Cl ! CH OH + HCl (R7) 3 2 CH OH + O ! CH O + HO (R8) 2 2 2 2 In order to rapidly convert C H O into HO through (R2), all experiments have been 2 5 2 carried out in 100 Torr O (Air Liquide, Alphagaz 2). The Cl concentration was typically 2 2 16 3 2 around 1  10 cm , leading with a photolysis energy of 20 mJ/cm to initial Cl-atom 14 3 concentrations of around 1  10 cm . A small flow of pure ethane was added directly from the cylinder (Mitry-Mory, N35) to the mixture through a calibrated flow meter (Bronkhorst, Tylan). Methanol (Sigma-Aldrich) was added to the mixture by flowing a small fraction of the main flow through a bubbler containing liquid methanol, kept in ice or in a thermostated water bath. All experiments were carried out at 298 K. 3. Results In the following, the two different methods applied in this work for the determination of the absorption cross-section of C H O at its peak wavelength 7596 cm are described. 2 5 2 3.1. Quantification of C H O in Back-to-Back Experiments 2 5 2 In the first method, the absorption cross-section of C H O is measured in a rather 2 5 2 direct way in back-to-back experiments relative to the absorption cross-section of HO . Therefore, the reliability of the measurement depends on the reliability of the absorption cross-section of HO . The absorption spectrum and cross-sections of HO in the near 2 2 IR have been measured several times [15,22,24,25] and pressure broadening of selected lines has also been carried out [26–28]. In this work, HO was quantified on two different absorption lines with the cross-section varying about a factor of 9 between both lines: for most experiments, HO has been detected on the strongest line of the 2 band at 2 1 Photonics 2021, 8, x FOR PEER REVIEW 6 of 17 has also been carried out [26-28]. In this work, HO2 was quantified on two different ab- Photonics 2021, 8, 296 6 of 17 sorption lines with the cross-section varying about a factor of 9 between both lines: for most experiments, HO2 has been detected on the strongest line of the 21 band at 6638.2 −1 cm , but for experiments with high initial radical concentrations a small line at 6638.58 −1 cm 6638.2 has been cm used , but to foravoid satur experiments ation. with The ab highsorptio initialnradical cross-sconcentrations ection of the stron a small gest line line −19 2 in he at 6638.58 lium (σcm 50 Torr hehas = 2.been 72 × 10 used cm to ) [1 avoid 5,24saturation. ] and in syntheti The absorption c air [26-28] ( crσ oss-section 100 Torr air = 1.44 of the × 19 2 −19 2 strongest line in helium ( = 2.72  10 cm ) [15,24] and in synthetic air [26–28] 10 cm ) has been measured several times, the cross-section of the small line has only 50 Torr he 19 2 −20 2 ( = 1.44  10 cm ) has been measured several times, the cross-section of the been measured once in 50 and 100 Torr helium (2.8 and 2.1 × 10 cm , respectively) 100 Torr air 20 2 small line has only been measured once in 50 and 100 Torr helium (2.8 and 2.1 10 cm , [27][29], but no measurements in pure O2 have been carried out. Therefore, we have de- respectively) [27,29], but no measurements in pure O have been carried out. Therefore, termined both cross-sections in 100 Torr O2 in the frame of this work, using the kinetic we have determined both cross-sections in 100 Torr O in the frame of this work, using the method. 2 kinetic method. Figure 2 shows a typical example: HO2 decays have been measured for 3 different Figure 2 shows a typical example: HO decays have been measured for 3 different initial Cl-atom concentrations and the raw signals are presented in graph (a). The decays initial Cl-atom concentrations and the raw signals are presented in graph (a). The decays have then been plotted following Equation (3) and the result is shown in graph (b). The have then been plotted following Equation (3) and the result is shown in graph (b). The slope of a linear regression of this plot can in principle be converted to the absorption slope of a linear regression of this plot can in principle be converted to the absorption cross-section using the known rate constant of the HO2 self-reaction. However, as has been cross-section using the known rate constant of the HO self-reaction. However, as has been mentioned above, radicals can be lost also through other processes, and in the case of laser mentioned above, radicals can be lost also through other processes, and in the case of laser photolysis experiments one possible loss is diffusion out of the photolysis volume. The photolysis experiments one possible loss is diffusion out of the photolysis volume. The relative impact of this loss process decreases with increasing initial HO2 concentration and relative impact of this loss process decreases with increasing initial HO concentration in order to correct this influence, an extrapolation to infinite [HO2]0 is used, shown in and in order to correct this influence, an extrapolation to infinite [HO ] is used, shown 2 0 graph (c): the slope m from graph (b) is plotted as a function of the intercept I (=1/α0). in graph (c): the slope m from graph (b) is plotted as a function of the intercept I (=1/ ). Extrapolating the m-values to I = 0 therefore removes the influence of the diffusion on the Extrapolating the m-values to I = 0 therefore removes the influence of the diffusion on the slope m. In the example of Figure 2, using the slope m obtained from extrapolation instead slope m. In the example of Figure 2, using the slope m obtained from extrapolation instead of using the directly determined slope m leads to an increase in the absorption cross-sec- of using the directly determined slope m leads to an increase in the absorption cross-section tion of 6% for the highest initial concentration and 13% for the lowest initial concentration. of 6% for the highest initial concentration and 13% for the lowest initial concentration. Error Error bars in graph (c) correspond to 95% confidence interval of the linear regression from bars in graph (c) correspond to 95% confidence interval of the linear regression from the the graph (b): the error bars on the x-values are too small to be seen within the symbols. graph (b): the error bars on the x-values are too small to be seen within the symbols. Several Several such series have been measured for both absorption lines, and the following ab- such series have been measured for both absorption lines, and the following absorption sorption cross-sections in 100 Torr O2 have been deduced for HO2 for the two lines: cross-sections in 100 Torr O have been deduced for HO for the two lines: 2 2 −1 −19 2 6638.2 cm :σ = (2.0 ± 0.3) × 10 cm . 1 19 2 6638.2 cm : = (2.0  0.3)  10 cm . −1 −20 2 6638.58 cm :σ = (2.1 ± 0.3) × 10 cm . 1 20 2 6638.58 cm : = (2.1  0.3)  10 cm . The uncertainty on σ reflect the uncertainty of ±15% on the rate constant of the HO2 The uncertainty on  reflect the uncertainty of 15% on the rate constant of the HO self-reaction, such as estimated by the IUPAC committee [30]. self-reaction, such as estimated by the IUPAC committee [30]. -6 8? 0 6? 0 (b) -6 6? 0 (a) 4? 0 -6 4? 0 2? 0 -6 2? 0 0 0 0.000 0.005 0.010 0.015 0.020 0.00 0.01 0.02 0.03 0.04 0.05 t / s t / s 1.8? 0 (c) 1.7? 0 1.6? 0 1.5? 0 5 5 5 01?0 2? 0 3? 0 I / cm Figure 2. Example of measurement of HO absorption cross-section using the kinetic method: graph (a) shows kinetic decays for 3 different Cl-atom concentrations, graph (b) shows the same signals plotted following Equation (3) with the linear regression over the first 20 ms, graph (c) shows the plot of slope m as a function of I, obtained in graph (b) for the 3 experiments. -1  (HO ) / cm -1 m / cm s (1 / (HO )) / cm 2 Photonics 2021, 8, x FOR PEER REVIEW 7 of 17 Figure 2. Example of measurement of HO2 absorption cross-section using the kinetic method: graph (a) shows kinetic decays for 3 different Cl-atom concentrations, graph (b) shows the same signals plotted following Equation (3) with the linear regression over the first 20 ms, graph (c) shows the Photonics 2021, 8, 296 7 of 17 plot of slope m as a function of I, obtained in graph (b) for the 3 experiments. These absorption cross-sections are now used to obtain the absorption cross-section These absorption cross-sections are now used to obtain the absorption cross-section of of C2H5O2 in back-to-back experiments. Figure 3 shows the principle of these measure- C H O in back-to-back experiments. Figure 3 shows the principle of these measurements: 2 5 2 ments: Cl2 is first photolysed in the presence of excess CH3OH, leading to quantitative Cl is first photolysed in the presence of excess CH OH, leading to quantitative formation format 2 ion of HO2 radicals: typical absorption-time prof 3 iles for 4 different Cl2 concentra- of HO radicals: typical absorption-time profiles for 4 different Cl concentrations are tions are shown i 2 n the upper right graph (b) of Figure 3. In the next step, C 2 H3OH is re- shown in the upper right graph (b) of Figure 3. In the next step, CH OH is removed from moved from the gas flow, and excess C2H6 is added instead, all other conditions are kept the gas flow, and excess C H is added instead, all other conditions are kept constant. 2 6 constant. The corresponding C2H5O2 absorption time profiles are shown in the upper left The corresponding C H O absorption time profiles are shown in the upper left graph (a). 2 5 2 graph (a). It can be seen that the HO2 profiles decay much faster than the corresponding It can be seen that the HO profiles decay much faster than the corresponding C H O 2 2 5 2 C2H5O2 profiles: this is in line with the rate constant of the HO2 self-reaction being around profiles: this is in line with the rate constant of the HO self-reaction being around 10 times 10 times faster than the rate constant of the C2H5O2 self-reaction. In order to get a reliable faster than the rate constant of the C H O self-reaction. In order to get a reliable extrap- 2 5 2 extrapolation of αt=0 ms, a plot of 1/α = f(t) is generated for both species (graph (c) and (d) olation of , a plot of 1/ = f(t) is generated for both species (graph (c) and (d) for t=0 ms for C2H5O2 and HO2, respectively) and a linear regression allows retrieving αt=0 ms from the C H O and HO , respectively) and a linear regression allows retrieving from the 2 5 2 2 t=0 ms intercept, as shown in Equation (3). For HO2, the αt=0 ms values can now be converted to intercept, as shown in Equation (3). For HO , the values can now be converted to 2 t=0 ms absolute concentrations ([HO2]t=0 ms) using the above determined absorption cross-section. absolute concentrations ([HO ] ) using the above determined absorption cross-section. 2 t=0 ms Supposing that each Cl-atom is converted into either one HO2 radical or into one C2H5O2 Supposing that each Cl-atom is converted into either one HO radical or into one C H O 2 2 5 2 radical, i.e., [HO2]t=0 ms = [C2HO5]t=0 ms, a plot of α(C2H5O2)t=0 ms = f([HO2]t=0 ms) leads to a linear radical, i.e., [HO ] = [C HO ] , a plot of (C H O ) = f([HO ] ) leads 2 t=0 ms 2 5 t=0 ms 2 5 2 t=0 ms 2 t=0 ms relationship with the slope equal to the absolute absorption cross-section of C2H5O2. The to a linear relationship with the slope equal to the absolute absorption cross-section of lower graph (e) in Figure 3 summarizes the results, obtained on four different days using C H O . The lower graph (e) in Figure 3 summarizes the results, obtained on four different 2 5 2 −1 either the big HO2 line at 6638.2 cm (open circles and open diamonds) or the small line days using either the big HO line at 6638.2 cm (open circles and open diamonds) or the −1 at 6635.58 cm (all other symbols, with the coloured symbols representing the results from small line at 6635.58 cm (all other symbols, with the coloured symbols representing the the experiment in Figure 3). results from the experiment in Figure 3). Figure 3. Example of measurement of the C H O absorption cross-section relative to the HO 2 5 2 2 Figure 3. Example of measurement of the C2H5O2 absorption cross-section relative to the HO2 ab- absorption cross-section. Upper graphs: C H O (a) and HO (b) absorption time profiles. Graphs (c) 2 5 2 2 sorption cross-section. Upper graphs: C2H5O2 (a) and HO2 (b) absorption time profiles. Graphs (c) and (d): same profiles, converted to 1/ (see Equation (3)) and linear regression over the first 20 ms following the photolysis pulse. Lower graph (e) shows plot of (C H O ) = f ([HO ] ): 2 5 2 t=0 ms 2 t=0 ms open circles and open diamonds are obtained using HO measurements at 6638.2 cm , coloured points (from above graphs) and crosses are obtained using HO measurements at 6638.58 cm . [O ] 2 2 18 3 16 3 = 2.8  10 cm , [C H ] = 3.7  10 cm for all experiments. 2 6 Photonics 2021, 8, x FOR PEER REVIEW 8 of 17 and (d): same profiles, converted to 1/α (see Equation (3)) and linear regression over the first 20 ms following the photolysis pulse. Lower graph (e) shows plot of α (C2H5O2)t=0 ms = f ([HO2]t=0 ms): open −1 circles and open diamonds are obtained using HO2 measurements at 6638.2 cm , coloured points Photonics 2021, 8, 296 −1 8 of 17 (from above graphs) and crosses are obtained using HO2 measurements at 6638.58 cm . [O2] = 2.8 × 18 −3 16 −3 10 cm , [C2H6] = 3.7 × 10 cm for all experiments. −1 From these experiments, an absorption cross-section for C2H5O2 at 7596 cm of σ = From these experiments, an absorption cross-section for C H O at 7596 cm of 2 5 2 −20 2 (1.0 ± 0.2) × 10 cm is obtained. The error bar is mostly due to the uncertainty in the rate 20 2 = (1.0  0.2)  10 cm is obtained. The error bar is mostly due to the uncertainty in constant of the HO2 self-reaction, to which the absorption cross-section of C2H5O2 is di- the rate constant of the HO self-reaction, to which the absorption cross-section of C H O 2 2 5 2 rectly linked. is directly linked. In imitation of the kinetic method such as used by Melnik et al.[18], the above exper- In imitation of the kinetic method such as used by Melnik et al. [18], the above iments can also be used to validate the absorption cross-section obtained using the back- experiments can also be used to validate the absorption cross-section obtained using the to-back method by determining k3,obs and comparing it with data from the literature. In- back-to-back method by determining k and comparing it with data from the literature. 3,obs deed, the C2H5O2 data from Figure 3c can be treated with the same method as shown for Indeed, the C H O data from Figure 3c can be treated with the same method as shown for 2 5 2 the HO2 data in Figure 2, and the obtained intercept is then equal to 2 × kobs/σ. Figure 4 the HO data in Figure 2, and the obtained intercept is then equal to 2  k /. Figure 4 obs shows this type of plot for the data from Figure 3c. shows this type of plot for the data from Figure 3c. Figure 4. Plot of slope m as a function of I from the linear regressions obtained in Figure 3c. Figure 4. Plot of slope m as a function of I from the linear regressions obtained in Figure 3c. Now, using the above retrieved absorption cross-section for C H O at 7596 cm of 2 5 2 −1 Now, using the above retrieved absorption cross-section for C2H5O2 at 7596 cm of σ 20 2 = (1.0  0.2)  10 cm , we can obtain from the intercept of the linear regression in −20 2 = (1.0 ± 0.2) × 10 cm , we can obtain from the intercept of the linear regression in Figure 13 3 1 1 Figure 4 a value for k = (1.3 0.3) 10 cm molecule s , in good agreement with 1,obs −13 3 −1 −1 4 a value for k1,obs = (1.3 ± 0.3) × 10 cm molecule s , in good agreement with the currently 13 3 1 1 the currently recommended literature value (1.24  10 cm molecule s ) [31]. −13 3 −1 −1 recommended literature value (1.24 × 10 cm molecule s ) [31]. 3.2. Quantification of C H O by Measuring the Rate Constant of C H O + HO 2 5 2 2 5 2 2 3.2. Quantification of C2H5O2 by Measuring the Rate Constant of C2H5O2 + HO2 Another way to determine the absorption cross-section of C H O has been applied by 2 5 2 Another way to determine the absorption cross-section of C2H5O2 has been applied determining the rate constant of the cross reaction between C H O and HO . Indeed, the 2 5 2 2 by determining the rate constant of the cross reaction between C2H5O2 and HO2. Indeed, rate constant can be determined under different conditions: using an excess of HO over the rate constant can be determined under different conditions: using an excess of HO2 C H O leads to C H O decays that are sensitive to the absolute concentration of HO , 2 5 2 2 5 2 2 over C2H5O2 leads to C2H5O2 decays that are sensitive to the absolute concentration of HO2, while in the reverse case the HO decay will be sensitive to the absolute C H O concen- 2 2 5 2 while in the reverse case the HO2 decay will be sensitive to the absolute C2H5O2 concen- tration, and thus to its absorption cross-section. Therefore, measuring simultaneously the tration, and thus to its absorption cross-section. Therefore, measuring simultaneously the decays of both species over a large range of concentration ratio allows determining the rate decays of both species over a large range of concentration ratio allows determining the constant (from excess HO experiments) and the absorption cross-section of C H O (from 2 2 5 2 rate constant (from excess HO2 experiments) and the absorption cross-section of C2H5O2 excess C H O experiments). Figure 5 illustrates this using two examples from Figure 6. 2 5 2 (from excess C2H5O2 experiments). Figure 5 illustrates this using two examples from Fig- ure 6. Photonics 2021, 8, x FOR PEER REVIEW 9 of 17 Photonics 2021, 8, x FOR PEER REVIEW 9 of 17 Photonics 2021, 8, 296 9 of 17 Figure 5. Figure 5.Experimental profiles taken under Experimental profiles taken under excess C excess C 2H H 5OO 2 conditions (upper graphs) and under conditions (upper graphs) and under 2 5 2 Figure 5. Experimental profiles taken under excess C2H5O2 conditions (upper graphs) and under excess HO2 conditions (lower graph). The dashed lines represent modelled profiles of C2H5OOH, excess HO conditions (lower graph). The dashed lines represent modelled profiles of C H OOH, 2 2 5 excess HO2 conditions (lower graph). The dashed lines represent modelled profiles of C2H5OOH, the product from (R3), while the full lines represent the product of the corresponding self-reaction the product from (R3), while the full lines represent the product of the corresponding self-reaction the product from (R3), while the full lines represent the product of the corresponding self-reaction (C2H5OH for C2H5O2 and H2O2 for HO2). Different colours represent the result from a model with (C H OH for C H O and H O for HO ). Different colours represent the result from a model with (C22 H5OH for 5 C2H 2 5O 5 2 and 2 H2O 2 2 for 2 HO2).2 Different colours represent the result from a model with different k3. different k . different k3. 14 14 1×10 1×10 14 14 1×10 1×10 -12 3 -1 k = 5.5 10 cm s -12 3 -1 13 13 7.5×10 k = 5.5 10 cm s 7.5×10 13 13 7.5×10 7.5×10 (a) (a) 13 13 5×10 5×10 13 13 5×10 5×10 13 13 2.5×10 2.5×10 13 13 2.5×10 2.5×10 0 0 0.000 0 0.005 0.010 0.015 0.020 0.0 000 0.005 0.010 0.015 0.020 0.000 0.005 0.010 0.015 0.020 0.000 0.005 0.010 0.015 0.020 t / s t / s t / s t / s 1×10 1×10 7.5×10 7.5×10 (c) (c) 5×10 5×10 2.5×10 2.5×10 0.000 0.005 0.010 0.015 0.020 0.000 0.005 0.010 0.015 0.020 t / s t / s Figure 6. C H O (left graphs) and HO (right graphs) concentration time profiles for a total radical 2 5 2 2 Figure 6. C2H5O2 (left graphs) and HO2 (right graphs) concentration time profiles for a total radical 14 3 Figure 6. concentration C2H5O of 2 (left graphs) and HO 1.2  10 cm . C2 (rig H O ht g absorption raphs) concentration tim time profiles have e profiles for a to been converted tal radica using l 2 5 2 14 −3 concentration of 1.2 × 10 cm . C2H5O2 absorption time profiles have been converted using σ = 1.0 20 2 14 −3 12 3 1 1 concentration  = 1.0  10 of 1 cm .2 × 10 . Centr cm e graphs . C2H5O (b 2 ab ): best sorption time fit with k pro = 6.2 files have  10 becm en conv molecule erted using s ,σupper = 1.0 −20 2 −12 3 −1 −1 × 10 cm . Centre graphs (b): best fit with k3 = 6.2 × 10 cm molecule s , upper graphs (a): model −20 2 −12 3 −1 −1 12 3 1 1 × 10 cm . Centre graphs (b): best fit with k3 = 6.2 × 10 cm molecule s , upper graphs (a): model graphs (a): model with of k = 5.5  10 cm molecule s , lower graphs (c): model with −12 3 −1 −1 −12 3 −1 with of k3 = 5.5 × 10 cm molecule s , lower graphs (c): model with k3 = 8.0 × 10 cm molecule −12 3 −1 −1 −12 3 −1 with of k3 = 5. 5 12 × 10 3 cm mole cu 1le1s , lower graphs (c): model with k3 = 8.0 × 10 cm molecule −k 1. = 8.0  10 cm molecule s . −1. -3 -3 [C H O ] / cm [C H O ] / cm 2 5 2 -3 2 5 2 -3 [C H O ] / cm [C H O ] / cm 2 5 2 2 5 2 -3 [HO ] / cm 2 -3 [HO ] / cm 2 Photonics 2021, 8, 296 10 of 17 Both species show different behaviour: C H O always decreases rapidly over the 2 5 2 first few ms, given by the loss through (R3) (C H OOH concentration time profile given 2 5 as dashed lines). Then the decays slow down at longer reaction times, when HO con- centration gets low, because the self-reaction becomes the major loss process, and this reaction is slow for C H O radicals (C H OH concentration time profile given as full 2 5 2 2 5 lines). This behaviour is especially visible when C H O is the excess species (upper graph 2 5 2 in Figure 5 and pink and orange circles in Figure 6: [C H O ]  3  [HO ]). HO on the 2 5 2 2 2 other hand approaches low concentrations at longer reaction times under all conditions, even when it is the excess species (lower graph in Figure 5 and black circles in Figure 6: [HO ]  3  [C H O ]): its self-reaction (H O concentration time profile given as full 2 2 5 2 2 2 lines) is around 20 times faster than the self-reaction of C H O and is a major loss process 2 5 2 under all conditions and all reaction times, the reaction with C H O (dashed lines) plays 2 5 2 a major role only under excess C H O conditions. Under excess HO concentrations, the 2 5 2 2 HO profile is barely influenced by (R3): an increased loss through an increase in k is 2 3 counterbalanced by a decreased loss through self-reaction. The profiles of all condition shown in Figure 6 have simultaneously been fitted to a simple mechanism, with the experimental conditions given in Table 2 and the mechanism 14 3 given in Table 3. The initial Cl-atom concentration was fixed to 1.2  10 cm for all experiments, obtained in initial experiments from measuring pure HO decays (no C H 2 2 6 15 3 added). [C H ] has been varied between 1.9–7.5  10 cm and [CH OH] has been 2 6 3 15 3 varied between 2.8–5.0  10 cm . Using these conditions, the ratio of [HO ]/[C H O ] 2 2 5 2 has been varied between 0.3 (pink circles) and 2.5 (black circles). Table 2. Conditions for experiments shown in Figure 6. Initial Cl-atom concentration was for all 14 3 2 experiments 1.2  10 cm , total pressure was 100 Torr O , T = 295 K. [C H O ] and [HO ] 2 2 5 2 concentration taken from the model. Total radical concentrations are slightly below initial Cl- concentration due to (R10). 15 15 13 13 3 3 3 3 [C H ]/10 cm [CH OH]/10 cm [C H O ] /10 cm [HO ] /10 cm 2 6 3 2 5 2 max 2 max 1.94 5.0 3.4 8.3 2.74 5.0 4.3 7.4 3.45 5.0 5.0 6.7 4.30 5.0 5.6 6.1 5.91 2.8 8.1 3.6 7.50 2.8 8.6 3.0 For all graphs in Figure 6, the above determined absorption cross-section ( = 20 2 1.0  10 cm ) has been used to convert the C H O absorption coefficients into ab- 2 5 2 solute concentrations. The profiles for both species could be well reproduced over the entire concentration 12 3 1 1 range using a rate constant of k = 6.2  10 cm molecule s , shown in the centre graph (b). In a next step, different rate constants for the cross reaction have been tested: indeed, despite several measurements of this rate constant over the last decades [32–38], there is no good agreement for this rate constant. An excellent summary on previous measurements of this rate constant can be found in Noell et al. [32] and will not be repeated here. The two recent determinations from Noell et al. [32] and Boyd et al. [33] are considered by the IUPAC committee as being carried out by the most reliable methods, however they 12 3 1 1 vary by about a factor of 1.5 (8.14  10 cm molecule s for Boyd et al. [33] from 12 3 1 1 UV absorption and 5.57  10 cm molecule s for Noell et al. [32] from UV/near IR absorption). We have tested these two limits by trying to adjust both profiles over the entire concentration range. In the upper graphs (a), the rate constant k has been set to the lower 12 3 1 1 limit such as obtained by Noell et al. [32] (5.5  10 cm molecule s ), leading to C H O and (less pronounced) HO decays that are too slow. Increasing the initial C H O 2 5 2 2 2 5 2 Photonics 2021, 8, 296 11 of 17 concentration by about 10% (corresponding to a decreased absorption cross-section for 20 2 C H O :  = 0.9  10 cm ) can lead again to less good, but still acceptable HO and 2 5 2 2 C H O decays (which would also imply a slight deviation of the overall initial radical 2 5 2 14 3 concentration from 1.2  10 cm ). In the lower graphs (c), the upper limit has been 12 3 1 1 tested by setting k = 8  10 cm molecule s : decays of both species are too fast and a decrease in concentration does not lead to an acceptable adjustment of both species. Table 3. Reaction mechanism used to fit all experiments in this work. 3 1 1 Reaction k/cm molecule s Reference 1a 2 C H O ! 2 C H O + O 2.6  10 Ref [32] * 2 5 2 2 5 2 1b 2 C H O ! C H OH + CH CHO + O 6.7  10 Ref [32] * 2 5 2 2 5 3 2 2 C H O + O ! CH CHO + HO 8  10 Ref [39] 2 5 2 3 2 3 C H O + HO ! C H OOH + O This work 6.2  10 2 5 2 2 2 5 2 5 Cl + C H ! C H + HCl 5.9  10 Ref [31] 2 6 2 5 6a C H + O + M ! C H O + M 4.8  10 Ref [40] 2 5 2 2 5 2 6b C H + O ! C H + HO 3-4 10 This work ** 2 5 2 2 4 2 7 Cl + CH OH ! CH OH + HCl 5.5  10 Ref [31] 3 2 8 CH OH + O ! CH O + HO 9.6  10 Ref [31] 2 2 2 2 9 2 HO ! H O + O Ref [30] 1.7  10 2 2 2 2 10 C H O + Cl ! products 1.5  10 Ref [41] 2 5 2 11 C H O ! diffusion 2 s This work 2 5 2 12 HO ! diffusion 3 s This work * The branching ratio for (R1) is currently contradictory, IUPAC currently recommends the radical path (R1a) as the major path. However, we have chosen here to use the most recent determination: (a) the self-reaction is very minor in our system (see Figure 5) and thus a change in branching ratio has a negligible impact on the retrieved profiles and (b) we have confirmed in separate experiments (to be published) the low branching ratio for the radical path. ** This reaction is likely due to excited C H radicals and the branching ratio between (R6a) and 2 5 (R6b) depends on pressure and also on the mode of generation of the C H radicals. 2 5 In conclusion, using the absorption cross-section for C H O obtained in back-to-back 2 5 2 experiments leads in these kinetic experiments to the best fit for both species over the entire concentration range. However, it should of course be noted, that in the end both methods rely on the absorption cross-section of HO and therefore both approaches cannot be considered as independent methods: the initial Cl-atom concentration used as input parameter in the model and being vital for retrieving the rate constant k and with this the absorption cross-section for C H O depend entirely on the rate constant for the HO 2 5 2 2 self-reaction. The absorption cross-section of HO varies through pressure broadening (which is taken into account), but it might also vary during the experiment through small and unnoted shifts in the wavelength of the DFB laser emission (the linewidth of the HO absorption lines are on the order of 0.02 cm FWHM at 50 Torr he). However, in our experiments the absorption cross-section of HO is under most conditions constantly being “measured”: a major HO loss in most experiments is the self-reaction, and thus the HO 2 2 decays are sensitive to the absolute HO concentration, i.e., to the absorption cross-section that has been used to convert the absorption time profiles to concentration time profiles. Therefore, it can be said that both methods have determined the C H O absorption cross- 2 5 2 section relative to the rate constant of the HO self-reaction. The IUPAC committee [30] estimates the uncertainty of this rate constant to 15%, which we use as a basis to estimate the uncertainty of our rate constant, with an additional 10% for uncertainties in the fitting 12 3 1 1 of the rate constant: k = (6.2  1.5)  10 cm molecule s . 3 Photonics 2021, 8, x FOR PEER REVIEW 12 of 17 Photonics 2021, 8, 296 12 of 17 3.3. Measuring the Relative Absorption Spectrum 3.3. Measuring the Relative Absorption Spectrum In order to obtain the shape of the C2H5O2 absorption spectrum, kinetic decays have In order to obtain the shape of the C H O absorption spectrum, kinetic decays 2 5 2 been measured under identical conditions at 15 different wavelengths in the range acces- have been measured under identical −1 conditions at 15 different wavelengths in the range sible with our DFB laser (7596–7630 cm ). The relative absorption coefficients are put on accessible with our DFB laser (7596–7630 cm ). The relative absorption coef −1 ficients are an absolute scale by comparison with the absorption cross-section at 7596.47 cm . Table 4 put on an absolute scale by comparison with the absorption cross-section at 7596.47 cm . summarizes the obtained results, and Figure 7 compares the present data with two litera- Table 4 summarizes the obtained results, and Figure 7 compares the present data with two ture results. literature results. Figure 7. C H O absorption coefficients at different wavelengths obtained in this work (green 2 5 2 Figure 7. C2H5O2 absorption coefficients at different wavelengths obtained in this work (green crosses and green axis), overlaid onto the spectrum obtained by Melnik et al. [17] (upper graph, crosses and green axis), overlaid onto the spectrum obtained by Melnik et al. [17] (upper graph, Reprinted with permission from [17], Copyright 2010 American Chemical Society) and Atkinson Reprinted with permission from [17], Copyright 2010 American Chemical Society) and Atkinson and Spillman [11] (lower graph, Reprinted with permission from [11], Copyright 2002 American and Spillman [11] (lower graph, Reprinted with permission from [11], Copyright 2002 American −1 Chemical Society). In the upper graph the data have been shifted by 4 cm , and in both graphs our Chemical Society). In the upper graph the data have been shifted by 4 cm , and in both graphs our data have data have beenbeen scaled scaled on the onythe -axiy s, -axis, i.e., appa i.e., appar rently ently there is ther a ba e is sel a baseline ine shift in shift both in both comcomparisons. parisons. The upper graph shows that our spectrum (green symbols and green axis apply) The upper graph shows that our spectrum (green symbols and green axis apply) agrees well with the results of Melnik et al. [17] if our data are shifted by 4 cm . Possibly, −1 agrees well with the results of Melnik et al. [17] if our data are shifted by 4 cm . Possibly, there is a mistake in the Melnik figure (T. Miller, private communication), because the there is a mistake in the Melnik figure (T. Miller, private communication), because the peak absorption is given in the text at 7596 cm , just as in our case, however in the figure −1 peak absorption is given in the text at 7596 cm , just as in our case, however in the figure the peak is located at 7600 cm , indicated by a blue vertical line. In the lower graph, −1 the peak is located at 7600 cm , indicated by a blue vertical line. In the lower graph, our our data (again in green) are overlaid to the spectrum of Atkinson and Spillman [11]. A data (again in green) are overlaid to the spectrum of Atkinson and Spillman [11]. A good good agreement of the shape in both comparisons can be obtained, when our data are agreement of the shape in both comparisons can be obtained, when our data are scaled on scaled on the y-axis, i.e., when we suppose a shift in the baseline of both literature spectra the y-axis, i.e., when we suppose a shift in the baseline of both literature spectra (around (around 23% of the peak absorption for Atkinson and Spillman and 15% for Melnik et al.). 23% of the peak absorption for Atkinson and Spillman and 15% for Melnik et al.). Melnik Melnik et al. discussed in their paper such baseline shift (dashed line in their figure) and et al. discussed in their paper such baseline shift (dashed line in their figure) and at- attributed it to a broadband absorber, generated simultaneously during the photolysis. tributed it to a broadband absorber, generated simultaneously during the photolysis. In- Indeed, they obtained their baseline by measuring ring-down events with the photolysis deed, they obtained their baseline by measuring ring-down events with the photolysis laser blocked. In this case, a broadband absorber generated simultaneously to the C H O 2 5 2 laser blocked. In this case, a broadband absorber generated simultaneously to the C2H5O2 radical would induce a baseline shift. To take into account this shift (horizontal dashed line radical would induce a baseline shift. To take into account this shift (horizontal dashed in the upper graph of Figure 7), they have calculated the absorption cross-section above Photonics 2021, 8, 296 13 of 17 this plateau. No explanation for a possible baseline shift in the work of Atkinson and Spillman can be given. Table 4. C H O Absorption cross-sections at different wavelengths. 2 5 2 1 20 2 Wavenumber/cm /10 cm 7596.47 10.0 7597.20 8.7 7597.44 8.1 7598.40 7.4 7602.02 6.7 7602.38 6.8 7606.25 5.8 7609.16 5.0 7610.66 4.2 7619.28 3.7 7622.36 3.1 7624.28 2.9 7626.72 2.3 7630.50 2.0 7489.16 2.0 4. Discussion Comparison of the Absorption Cross-Section with Literature Data The absorption cross-section of C H O was first determined by Atkinson and Spill- 2 5 2 man [11] using 193 nm photolysis of 3-pentanone as precursor. Using the kinetic method, 21 2 they determined at the peak  = (3  1.5)  10 cm , which is 3 times smaller than the present value. A higher absorption cross-section had also been measured previously by our group for the CH O radical [12]. One possible reason might be that the determina- 3 2 tion from Atkinson and Spillman is based on the kinetic method using low initial radical concentrations, hence the C H O concentration has to be measured over long reaction 2 5 2 times in order to observe a sizeable decay, but the possible loss due to diffusion out of the photolysis volume or due to wall loss, possibly non-negligible over such long reaction times, has not been considered in the data evaluation. This can induce an overestimation of the radical concentration and therefore an underestimation of the absorption cross-section (see Figures 2c and 4). Another reason might be the precursor: the reaction of C H + O 2 5 2 can also lead to small amounts of HO through (R6b), around 1% of the initial Cl-atom concentration led to formation of HO in the experiments of this work. Atkinson and Spill- man used 193 nm photolysis of 3-pentanone, which leaves considerably higher amounts of excess energy in the fragments than our method, based on H-atom abstraction. Therefore, the fraction of C H radicals that react through (R6b) might be considerably higher than in 2 5 our case. This could induce a non-negligible initial HO concentration which participates in the removal of C H O and would thus induce a systematic error when using the kinetic 2 5 2 method. This is also in line with the observation of Atkinson and Spillman, that in their experiments the apparent rate constant of the C H O self-reaction was inversely pressure 2 5 2 dependent: the rate constant decreased with increasing pressure (D. Atkinson, private com- munication). An increased cooling of the hot C H radical with increasing pressure would 2 5 lead to a decreasing HO concentration and thus to a slow-down of the C H O decay. 2 2 5 2 Rupper et al. [16] estimated the absolute absorption cross-section to  = 4.4  10 cm from calculating the initial Cl-atom concentration by measuring the decrease of photolysis energy in absence and presence of the Cl-atom precursor, assuming that all Photonics 2021, 8, x FOR PEER REVIEW 14 of 17 Photonics 2021, 8, 296 14 of 17 energy in absence and presence of the Cl-atom precursor, assuming that all generated Cl- atoms lead to formation of one C2H5O2. In a more recent work from the same group, Melnik et al. [18] have determined the absorption cross-section by dual-CRDS method: on generated Cl-atoms lead to formation of one C H O . In a more recent work from the 2 5 2 one absorption path they measured the absorption of C2H5O2 while on the other path the same group, Melnik et al. [18] have determined the absorption cross-section by dual- concentration of HC CRDS l was method: quantifi on ed tha one absorption nks to its known a path they bsorp measur tion cross- ed thesecti absorption on. As- of C H O while 2 5 2 suming again that on one the Cother 2H5O2path has b the een concentration generated foof r eHCl ach m was olequantified cule of HCthanks l, they f to ou its nd known absorption −21 −2 cross-section. Assuming again that one C H O has been generated for each molecule an absorption cross-section of σ = 5.29 × 10 cm . This is nearly 2 times lower than the 2 5 2 21 2 value obtained in t of his wo HCl, rthey k. It is found unlike an lyabsorption that the difference in the cross-section of bandwidth o  = 5.29  f10 the exci cm - . This is nearly −1 −4 −1 2 times lower than the value obtained in this work. It is unlikely that the difference in the tation laser sources (0.01 cm for Melnik and <1 × 10 cm for this work) can explain the 1 4 1 bandwidth of the excitation laser sources (0.01 cm for Melnik and <1  10 cm for difference, because the absorption band is unstructured and much larger than the band- this work) can explain the difference, because the absorption band is unstructured and width of both laser sources. Also, the overall shape is, after consideration of a baseline much larger than the bandwidth of both laser sources. Also, the overall shape is, after shift, in excellent agreement between both works (see Figure 7). consideration of a baseline shift, in excellent agreement between both works (see Figure 7). A possible explanation might be that Melnik et al. and Rupper et al. both consider A possible explanation might be that Melnik et al. and Rupper et al. both consider the the complete conversion of Cl-atoms into C2H5O2 radicals: a simple model is presented by complete conversion of Cl-atoms into C H O radicals: a simple model is presented by Melnik et al. [17] showing the complete conversion of Cl- 2ato 5ms in 2 to C2H5O2. However, Melnik et al. [17] showing the complete conversion −10 3 of Cl-atoms −1 −1into C H O . However, the 2 5 2 the very fast reactions of Cl-atoms with C2H5O2 (k10 = 1.5 × 10 cm molecule s ) [41] and 10 3 1 1 −10 very 3fast reactions −1 −1 of Cl-atoms with C H O (k = 1.5  10 cm molecule s ) [41] 2 5 2 10 C2H5 (k = 3 × 10 cm molecule s ) [42] are omitted in this model, even though these 10 3 1 1 and C H (k = 3  10 cm molecule s ) [42] are omitted in this model, even though 2 5 reactions are non-negligible under their conditions of very high initial Cl-atom concentra- these reactions are non-negligible under their conditions of very high initial Cl-atom con- 15 −3 16 tions, well above 10 cm , combined with relatively low C2H6 concentrations (1 × 10 15 3 centrations, well above 10 cm , combined with relatively low C H concentrations −3 2 6 cm ). These reactions result in a C2H5O2 concentration that might be well below the initial 16 3 (1  10 cm ). These reactions result in a C H O concentration that might be well 2 5 2 Cl-atom concentration, depending on the overall radical concentration as well as on the below the initial Cl-atom concentration, depending on the overall radical concentration C2H6 concentration. Figure 8 shows a simulation using the model from Melnik et al., but as well as on the C H concentration. Figure 8 shows a simulation using the model 2 6 completed by the two fast reactions. The left graph shows the result using initial concen- from Melnik et al., but completed by the two fast reactions. The left graph shows the 15 −3 16 −3 trations such as given by Melnik et al. ([Cl]0 = 2 × 10 cm and [C2H6]0 = 1 × 10 cm ), the 15 3 result using initial concentrations such as given by Melnik et al. ([Cl] = 2  10 cm right graph shows the model result with typical conditions such as used in this work for 16 3 and [C H ] = 1  10 cm ), the right graph shows the model result with typical con- 2 6 0 13 −3 16 the determination of the absorption cross-section ([Cl]0 = 5 × 10 cm and [C2H6]0 = 3 × 10 ditions such as used in this work for the determination of the absorption cross-section −3 cm ). Under the high Cl/low C2H6 conditions of Melnik et al., only 63% of the Cl-atoms 13 3 16 3 ([Cl] = 5  10 cm and [C H ] = 3  10 cm ). Under the high Cl/low C H con- 0 2 6 0 2 6 have been converted to C2H5O2, while 28% of the Cl-atoms have reacted with C2H5O2 and ditions of Melnik et al., only 63% of the Cl-atoms have been converted to C H O , while 2 5 2 8% have reacted with C2H5. Under the low Cl/high C2H6 conditions (right graph), virtually 28% of the Cl-atoms have reacted with C H O and 8% have reacted with C H . Under 2 5 2 2 5 all Cl-atoms have been converted to C2H5O2, less than 1% of the Cl-atoms have reacted the low Cl/high C H conditions (right graph), virtually all Cl-atoms have been converted 2 6 with either C2H5O2 or C2H5. From this model one can suspect that the absorption cross- to C H O , less than 1% of the Cl-atoms have reacted with either C H O or C H . From 2 5 2 2 5 2 2 5 sections of Melnik et al. [17] and Rupper et al. [16] are strongly underestimated, and a this model one can suspect that the absorption cross-sections of Melnik et al. [17] and correction of the Melnik et al. value, based on the more complete model presented here, Rupper et al. [16] are strongly underestimated, and a correction of the Melnik et al. value, −21 −2 would lead to σ = 8.8 × 10 cm , which gets into good agreement with the value found in 21 2 based on the more complete model presented here, would lead to  = 8.8  10 cm , this work. which gets into good agreement with the value found in this work. Figure 8. Simulation of conversion of Cl-atoms (violet dashed dot) into HCl (black) and C H O (blue dashed): model Figure 8. Simulation of conversion of Cl-atoms (violet dashed dot) into HCl (black 2 ) an 5 d C 2 2H5O2 10 3 1 taken from Melnik et al., completed with the reactions of Cl with C H O (k = 1.5  10 cm s ) [41] (red dotted) and (blue dashed): model taken from Melnik et al., completed w 2ith the rea 5 2 ctions of Cl with C2H5O2 (k = 10 3 1 −10 3 −1 −10 3 −1 C H (k = 3 10 cm s ) [42] (green dashed dotted): left graph conditions such as used in Melnik et al. [17], right graph 2 5 1.5 × 10 cm s ) [41] (red dotted) and C2H5 (k = 3 × 10 cm s ) [42] (green dashed dotted): left conditions such as used in this work. The products from the reaction of Cl with C H O (red) and with C H (green) are graph conditions such as used in Melnik et al.[17], right graph conditions such as used in this work. 2 5 2 2 5 zoomedThe products in the right graph from the reaction of Cl w by a factor of 100 (right ith yC -axis 2H5O applies). 2 (red) and with C2H5 (green) are zoomed in the right graph by a factor of 100 (right y-axis applies). 5. Conclusions We have presented in this work a new determination of the absorption cross-section of the à X electronic transition of the C H O radical. The cross-section at the peak 2 5 2 Photonics 2021, 8, 296 15 of 17 wavelength 7596.4 cm has in a first approach been determined by direct comparison with the well-known HO absorption cross-section in back-to-back experiments to be 20 2 (1.0  0.2)  10 cm . In further experiments, the absorption cross-section has been validated by measuring the rate constant of C H O with HO in a wide range of con- 2 5 2 2 centration: the ratio of [HO ]/[C H O ] has been varied between 0.3 and 2.5 and the 2 2 5 2 concentration time profiles could be reproduced very well using the same absorption cross-section for all C H O profiles, which returned a rate constant for the cross reaction 2 5 2 12 3 1 1 of 6.2  10 cm molecule s . Sensitivity analysis in the upper and lower range of previous literature values did not allow for good reproduction of the concentration-time profiles for both species over the entire concentration range and confirm the reliability of our results. Smaller absorption cross-sections such as obtained in previous works can convincingly be explained by unidentified secondary reaction, not having been taken into account in the data evaluations. Author Contributions: Conceptualization, C.F.; methodology, C.F., C.Z., M.S., M.A.; validation, C.F., L.P., C.S.; formal analysis, C.Z., M.S.; investigation, C.Z., M.S., M.A.; resources, C.F., M.A.; data curation, C.F.; writing—original draft preparation, C.F.; writing—review and editing, all authors; visualization, C.Z., M.S., C.F.; supervision, C.F., L.P., X.T., W.Z.; project administration, C.F.; funding acquisition, C.F., L.P., C.S., X.T., W.Z. All authors have read and agreed to the published version of the manuscript. Funding: This project was supported by the French ANR agency under contract No. ANR-11- Labx-0005-01 CaPPA (Chemical and Physical Properties of the Atmosphere), the Région Hauts-de- France, the Ministère de l’Enseignement Supérieur et de la Recherche (CPER Climibio) and the European Fund for Regional Economic Development. C.F. is grateful to the Chinese Academy of Sciences President’s International Fellowship Initiative (No. 2018VMA0055). C.Z. thanks the Chinese Scholarship Council for financial support (No. 202006340125). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Raw data are available on request. Conflicts of Interest: The authors declare no conflict of interest. References 1. Orlando, J.J.; Tyndall, G.S. Laboratory studies of organic peroxy radical chemistry: An overview with emphasis on recent issues of atmospheric significance. Chem. Soc. Rev. 2012, 41, 6294–6317. [CrossRef] [PubMed] 2. Fittschen, C. The reaction of peroxy radicals with OH radicals. Chem. Phys. Lett. 2019, 725, 102–108. [CrossRef] 3. Assaf, E.; Song, B.; Tomas, A.; Schoemaecker, C.; Fittschen, C. Rate Constant of the Reaction between CH O Radicals and OH 3 2 Radicals revisited. J. Phys. Chem. A 2016, 120, 8923–8932. [CrossRef] 4. Hasson, A.S.; Tyndall, G.S.; Orlando, J.J. 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Journal

PhotonicsMultidisciplinary Digital Publishing Institute

Published: Jul 24, 2021

Keywords: peroxy radicals; near-infrared spectroscopy; Ã←X˜electronic transitio; cavity ring down spectroscopy

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