Absolute Absorption Cross-Section of the Ã←$\tilde{X}$ Electronic Transition of the Ethyl Peroxy Radical and Rate Constant of Its Cross Reaction with HO₂

Abstract

The absolute absorption cross-section of the ethyl peroxy radical C₂H₅O₂ in the Ã←$\tilde{X}$ electronic transition with the peak wavelength at 7596 cm⁻¹ has been determined by the method of dual wavelengths time resolved continuous wave cavity ring down spectroscopy. C₂H₅O₂ radicals were generated from pulsed 351 nm photolysis of C₂H₆/Cl₂ mixture in presence of 100 Torr O₂ at T = 295 K. C₂H₅O₂ radicals were detected on one of the CRDS paths. Two methods have been applied for the determination of the C₂H₅O₂ absorption cross-section: (i) based on Cl-atoms being converted alternatively to either C₂H₅O₂ by adding C₂H₆ or to hydro peroxy radicals, HO₂, by adding CH₃OH to the mixture, whereby HO₂ was reliably quantified on the second CRDS path in the 2ν₁ vibrational overtone at 6638.2 cm⁻¹ (ii) based on the reaction of C₂H₅O₂ with HO₂, measured under either excess HO₂ or under excess C₂H₅O₂ concentration. Both methods lead to the same peak absorption cross-section for C₂H₅O₂ at 7596 cm⁻¹ of σ = (1.0 ± 0.2) × 10⁻²⁰ cm². The rate constant for the cross reaction between of C₂H₅O₂ and HO₂ has been measured to be (6.2 ± 1.5) × 10⁻¹² cm³ molecule⁻¹ s⁻¹.

1. Introduction

The oxidation of volatile organic compounds (VOCs) in the troposphere is mainly driven by hydroxyl radicals (OH) and leads, after addition of O₂, to the formation of organic peroxy radicals (RO₂). The fate of these RO₂ radicals depends on the chemical composition of the environment. In a polluted atmosphere they react mainly with nitric oxide (NO) to form alkoxy radicals or react with nitrogen dioxide (NO₂) to form peroxynitrates (RO₂NO₂). Subsequent to the reaction with NO, alkoxy radicals react with O₂ to form hydro peroxy radicals (HO₂). HO₂ further oxidises NO into NO₂ and thus regenerates OH, closing the quasi-catalytic cycle. The photolysis of produced NO₂ is the only relevant chemical source of tropospheric ozone. In clean environments with low NO_x (NO_x = NO + NO₂) concentrations, the dominant loss of RO₂ is due to its reaction with HO₂ forming hydroperoxides ROOH and terminating the radical reaction chain. In addition, RO₂ radicals can react either with themselves as self-reaction (RO₂ + RO₂) or with other R’O₂ as cross-reaction (RO₂ + R’O₂) or with OH radicals (RO₂ + OH) [1,2,3,4,5].

Ethane is one of the most abundant non-methane hydrocarbons in the atmosphere, and its atmospheric oxidation leads to the formation of the ethyl peroxy radical, C₂H₅O₂. A reliable detection of this radical is therefore highly desirable for studying its reactivity and thus understanding its embedded chemistry. Previous studies of peroxy chemistry have mostly been carried out by UV absorption spectroscopy in the $\tilde{B}$←$\tilde{X}$ 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 Ã←$\tilde{X}$ 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⁻¹ 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 HO₂: 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 Ã←$\tilde{X}$ electronic transition of peroxy radicals (~10⁻²⁰–10⁻²¹ cm²), 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⁻¹ and is thus much narrower than the Ã←$\tilde{X}$ 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 Ã←$\tilde{X}$ transition for C₂H₅O₂ was found around 7596 cm⁻¹.

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 a much narrower bandwidth (~3 × 10⁻⁵ cm⁻¹). They confirmed the overall shape of the absorption spectrum, and measured for the first time the absorption cross-section for C₂H₅O₂ using the kinetic method [12,13,14,15]. This method can be applied, if the rate 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

$$\frac{d\left[\mathrm{A}\right]}{dt}=-2k{\left[\mathrm{A}\right]}^2$$

(1)

Integration of Equation (1) leads to

$$\frac{1}{\left[\mathrm{A}\right]}=\frac{1}{{\left[\mathrm{A}\right]}_0}+2kt$$

(2)

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 α = σ × [A] can be used in Equation (2) instead of [A], leading to

$$\frac{1}{\mathsf{\sigma }\times \left[\mathrm{A}\right]}=\frac{1}{\mathsf{\sigma }\times {\left[\mathrm{A}\right]}_0}+\frac{2k}{\mathsf{\sigma }}t$$

(3)

Plotting 1/σ × [A] leads to a straight line with the slope being m = 2k/σ while the intercept I = 1/σ × [A]₀. 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 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 HO₂ radicals:

2 C₂H₅O₂ → 2 C₂H₅O + O₂

(R1a)

→ C₂H₅OH + CH₃CHO + O₂

(R1b)

followed, in presence of O₂, by (R2):

C₂H₅O + O₂→ CH₃CHO + HO₂

(R2)

The HO₂ radicals react with C₂H₅O₂

C₂H₅O₂ + HO₂→ C₂H₅OOH + O₂

(R3)

with (R3) having a rate constant faster than (R1). As a result, the C₂H₅O₂ decays are accelerated by the formation of HO₂, and therefore when using Equation (3) for (R1), the obtained rate constant k₁ is called k₁,_obs and the acceleration has to be taken into account to retrieve the “real” rate constant k₁ from C₂H₅O₂ decays. Using the recommended value of k₁,_obs in the kinetic method, Atkinson and Spillman [11] obtained an absorption cross-section for C₂H₅O₂ at 7596 cm⁻¹ of σ = (3.0 ± 1.5) × 10⁻²¹ cm².

Another work on the ethyl peroxy spectrum from the Miller group [16] scanned the Ã←$\tilde{X}$ 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 both conformers were located well separated at 7362 cm⁻¹ for the T- and 7592 cm⁻¹ 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 C₂H₆, with the Cl-atoms being generated by 193 nm photolysis of oxalylchloride, (COCl)₂. To obtain the concentration of C₂H₅O₂, they measured the photolysis laser energy with and without precursor, and calculated the Cl-atom concentration from the difference. Supposing that each Cl-atom generated one C₂H₅O₂ radical, they obtained σ = 4.4 × 10⁻²¹ cm² for C₂H₅O₂ at 7596 cm⁻¹.

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 C₂H₆) was measured on one path while the absorption of C₂H₅O₂ was measured simultaneously on the other path. Again supposing that each HCl-molecule had generated one C₂H₅O₂ radical, they obtained σ = (5.29 ± 0.20) × 10⁻²¹ cm² for C₂H₅O₂ at 7596 cm⁻¹.

In the most recent work from the Miller group [18], the above absorption cross-section was validated indirectly through the kinetic method: the C₂H₅O₂ absorption profiles were converted to C₂H₅O₂ concentration-time profiles using the above absorption cross-section, and the rate constant k₁,_obs for the self-reaction was extracted. Good agreement with other 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. Summary of the C₂H₅O₂ absorption cross-section at 7596 cm⁻¹.

σ/10−21 cm2	Method	Reference
3.0 ± 1.5	Kinetic method, no other radical losses considered	Atkinson and Spillman [11]
4.4	Depletion of photolysis energy through precursor with [Cl] = [C2H5O2], i.e., no secondary reactions considered	Rupper et al. [16]
5.29 ± 0.20	Measurement of HCl in dual path CRDS with [Cl] = [C2H5O2], i.e., no secondary reactions considered	Melnik et al. [17]
5.29	Kinetic method used for validation of Ref. [17]	Melnik et al. [18]
10 ± 2	Measurement of HO2/C2H5O2 in dual path CRDS with [Cl] = [HO2] = [C2H5O2]	This work
10 ± 2	Kinetic method from C2H5O2 + HO2	This work

.

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 HO₂ through reaction with CH₃OH, with HO₂ being quantified on one path at 6638.2 cm⁻¹. Directly after, the Cl-atoms were transformed to C₂H₅O₂ by adding C₂H₆ instead of CH₃OH to the reaction mixture and the C₂H₅O₂ absorption 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 HO₂ (which can be quantified reliably) or to C₂H₅O₂, the absorption cross-section of C₂H₅O₂ is determined relative to the one of HO₂. The second approach is a variation of the kinetic method such as used by Atkinson and Spillman [11] and Melnik et al. [18], but not based on the self-reaction of C₂H₅O₂, but on the cross reaction between HO₂ and C₂H₅O₂. This reaction has been measured in a wide range of concentrations under either excess of HO₂ or excess of C₂H₅O₂. In the first case, the rate constant is retrieved by adjusting the C₂H₅O₂ decays with the absolute concentration of HO₂ being fixed, while in the second case the rate constant is fixed to the value determined just before, and now the best fit of the HO₂ decay is achieved by adjusting the absolute concentration of C₂H₅O₂, i.e., the absorption cross-section.

2. Materials and Methods

The setup has been described in detail before [19,20,21,22,23] and is only briefly discussed here (Figure 1).

The setup consisted of a 0.79 m long flow reactor made of stainless steel. The photolysis laser (Lambda Physik LPX 202i, XeF at 351 nm) width is delimited to 2 cm and passes through the reactor longitudinally. The flow reactor contains two identical continuous wave cavity ring-down spectroscopy (cw-CRDS) absorption paths, which were installed in a small angle with respect to the photolysis path. An overlap of the absorption path with the photolysis beam of 0.288 m is achieved. Both beam paths were tested for a uniform overlap with the photolysis beam before experiments were done. For this purpose, both cw-CRDS instruments were operated to simultaneously measure HO₂ concentrations. Deviations between HO₂ concentrations were less than 5%, demonstrating that the photolysis laser 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 acousto-optic modulator (AOM, AAoptoelectronic) to rapidly turn off the 1^st 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 α is derived from Equation (4).

$$\mathsf{\alpha }=\left[\mathrm{A}\right]\times {\mathsf{\sigma }}_{\mathrm{A}}=\frac{R_{\mathrm{L}}}{\mathrm{c}}\left(\frac{1}{\mathsf{\tau }}-\frac{1}{{\mathsf{\tau }}_0}\right)$$

(4)

where τ is the ring-down time with an absorber present; τ₀ is the ring-down time with no absorber present; σ_A is the absorption cross-section of the absorbing species A; R_L is the 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 C₂H₆/Cl_2/O₂ mixtures initiating the reaction sequence (R4), (R5) and (R6):

Cl₂ + hν_{351 nm} → 2 Cl

(R4)

C₂H₆ + Cl → C₂H₅ + HCl

(R5)

C₂H₅ + O₂ + M → C₂H₅O₂ + M

(R6a)

C₂H₅ + O₂ → C₂H₄ + HO₂

(R6b)

For studying the cross reaction with HO₂, methanol, CH₃OH, has been added in varying concentrations to the mixture.

CH₃OH + Cl → CH₂OH + HCl

(R7)

CH₂OH + O₂ → CH₂O + HO₂

(R8)

In order to rapidly convert C₂H₅O into HO₂ through (R2), all experiments have been carried out in 100 Torr O₂ (Air Liquide, Alphagaz 2). The Cl₂ concentration was typically around 1 × 10¹⁶ cm⁻³, leading with a photolysis energy of 20 mJ/cm² to initial Cl-atom concentrations of around 1 × 10¹⁴ cm⁻³.

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 C₂H₅O₂ at its peak wavelength 7596 cm⁻¹ are described.

3.1. Quantification of C₂H₅O₂ in Back-to-Back Experiments

In the first method, the absorption cross-section of C₂H₅O₂ is measured in a rather direct way in back-to-back experiments relative to the absorption cross-section of HO₂. Therefore, the reliability of the measurement depends on the reliability of the absorption cross-section of HO₂. The absorption spectrum and cross-sections of HO₂ in the near IR have been measured several times [15,22,24,25] and pressure broadening of selected lines has also been carried out [26,27,28]. In this work, HO₂ was quantified on two different absorption 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 2ν₁ band at 6638.2 cm⁻¹, but for experiments with high initial radical concentrations a small line at 6638.58 cm⁻¹ has been used to avoid saturation. The absorption cross-section of the strongest line in helium (σ_{50 Torr he} = 2.72 × 10⁻¹⁹ cm²) [15,24] and in synthetic air [26,27,28] (σ_{100 Torr air} = 1.44 × 10⁻¹⁹ cm²) has been measured several times, the cross-section of the small line has only been measured once in 50 and 100 Torr helium (2.8 and 2.1 × 10⁻²⁰ cm², respectively) [27,29], but no measurements in pure O₂ have been carried out. Therefore, we have determined both cross-sections in 100 Torr O₂ in the frame of this work, using the kinetic method.

Figure 2 shows a typical example: HO₂ decays have been measured for 3 different 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 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 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 relative impact of this loss process decreases with increasing initial HO₂ concentration and in order to correct this influence, an extrapolation to infinite [HO₂]₀ is used, shown in graph (c): the slope m from graph (b) is plotted as a function of the intercept I (=1/α₀). 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 of using the directly determined slope m leads to an increase in the absorption cross-section of 6% for the highest initial concentration and 13% for the lowest initial concentration. Error bars in graph (c) correspond to 95% confidence interval of the linear regression from the graph (b): the error bars on the x-values are too small to be seen within the symbols. Several such series have been measured for both absorption lines, and the following absorption cross-sections in 100 Torr O₂ have been deduced for HO₂ for the two lines:

6638.2 cm⁻¹:σ = (2.0 ± 0.3) × 10⁻¹⁹ cm².

6638.58 cm⁻¹:σ = (2.1 ± 0.3) × 10⁻²⁰ cm².

The uncertainty on σ reflect the uncertainty of ±15% on the rate constant of the HO₂ self-reaction, such as estimated by the IUPAC committee [30].

These absorption cross-sections are now used to obtain the absorption cross-section of C₂H₅O₂ in back-to-back experiments. Figure 3 shows the principle of these measurements: Cl₂ is first photolysed in the presence of excess CH₃OH, leading to quantitative formation of HO₂ radicals: typical absorption-time profiles for 4 different Cl₂ concentrations are shown in the upper right graph (b) of Figure 3. In the next step, CH₃OH is removed from the gas flow, and excess C₂H₆ is added instead, all other conditions are kept constant. The corresponding C₂H₅O₂ absorption time profiles are shown in the upper left graph (a). It can be seen that the HO₂ profiles decay much faster than the corresponding C₂H₅O₂ profiles: this is in line with the rate constant of the HO₂ self-reaction being around 10 times faster than the rate constant of the C₂H₅O₂ self-reaction. In order to get a reliable extrapolation of α_{t=0 ms}, a plot of 1/α = f(t) is generated for both species (graph (c) and (d) for C₂H₅O₂ and HO₂, respectively) and a linear regression allows retrieving α_{t=0 ms} from the intercept, as shown in Equation (3). For HO₂, the α_{t=0 ms} values can now be converted to absolute concentrations ([HO₂]_{t=0 ms}) using the above determined absorption cross-section. Supposing that each Cl-atom is converted into either one HO₂ radical or into one C₂H₅O₂ 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 relationship with the slope equal to the absolute absorption cross-section of C₂H₅O₂. The lower graph (e) in Figure 3 summarizes the results, obtained on four different days using either the big HO₂ line at 6638.2 cm⁻¹ (open circles and open diamonds) or the small line at 6635.58 cm⁻¹ (all other symbols, with the coloured symbols representing the results from the experiment in Figure 3).

From these experiments, an absorption cross-section for C₂H₅O₂ at 7596 cm⁻¹ of σ = (1.0 ± 0.2) × 10⁻²⁰ cm² is obtained. The error bar is mostly due to the uncertainty in the rate constant of the HO₂ self-reaction, to which the absorption cross-section of C₂H₅O₂ is directly linked.

In imitation of the kinetic method such as used by Melnik et al. [18], the above experiments can also be used to validate the absorption cross-section obtained using the back-to-back method by determining k_3,obs and comparing it with data from the literature. Indeed, the C₂H₅O₂ data from Figure 3c can be treated with the same method as shown for the HO₂ data in Figure 2, and the obtained intercept is then equal to 2 × k_obs/σ. Figure 4 shows this type of plot for the data from Figure 3c.

Now, using the above retrieved absorption cross-section for C₂H₅O₂ at 7596 cm⁻¹ of σ = (1.0 ± 0.2) × 10⁻²⁰ cm², we can obtain from the intercept of the linear regression in Figure 4 a value for k_1,obs = (1.3 ± 0.3) × 10⁻¹³ cm³molecule⁻¹ s⁻¹, in good agreement with the currently recommended literature value (1.24 × 10⁻¹³ cm³molecule⁻¹ s⁻¹) [31].

3.2. Quantification of C₂H₅O₂ by Measuring the Rate Constant of C₂H₅O₂ + HO₂

Another way to determine the absorption cross-section of C₂H₅O₂ has been applied by determining the rate constant of the cross reaction between C₂H₅O₂ and HO₂. Indeed, the rate constant can be determined under different conditions: using an excess of HO₂ over C₂H₅O₂ leads to C₂H₅O₂ decays that are sensitive to the absolute concentration of HO₂, while in the reverse case the HO₂ decay will be sensitive to the absolute C₂H₅O₂ concentration, 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 constant (from excess HO₂ experiments) and the absorption cross-section of C₂H₅O₂ (from excess C₂H₅O₂ experiments). Figure 5 illustrates this using two examples from Figure 6.

Both species show different behaviour: C₂H₅O₂ always decreases rapidly over the first few ms, given by the loss through (R3) (C₂H₅OOH concentration time profile given as dashed lines). Then the decays slow down at longer reaction times, when HO₂ concentration gets low, because the self-reaction becomes the major loss process, and this reaction is slow for C₂H₅O₂ radicals (C₂H₅OH concentration time profile given as full lines). This behaviour is especially visible when C₂H₅O₂ is the excess species (upper graph in Figure 5 and pink and orange circles in Figure 6: [C₂H₅O₂] ≈ 3 × [HO₂]). HO₂ on the 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: [HO₂] ≈ 3 × [C₂H₅O₂]): its self-reaction (H₂O₂ concentration time profile given as full lines) is around 20 times faster than the self-reaction of C₂H₅O₂ and is a major loss process under all conditions and all reaction times, the reaction with C₂H₅O₂ (dashed lines) plays a major role only under excess C₂H₅O₂ conditions. Under excess HO₂ concentrations, the HO₂ profile is barely influenced by (R3): an increased loss through an increase in k₃ is 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. Conditions for experiments shown in Figure 6. Initial Cl-atom concentration was for all experiments 1.2 × 10¹⁴ cm⁻³, total pressure was 100 Torr O₂, T = 295 K. [C₂H₅O₂] and [HO²] concentration taken from the model. Total radical concentrations are slightly below initial Cl-concentration due to (R10).

[C2H6]/1015 cm−3	[CH3OH]/1015 cm−3	[C2H5O2]max/1013 cm−3	[HO2]max/1013 cm−3
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

and the mechanism given in Table 3. The initial Cl-atom concentration was fixed to 1.2 × 10¹⁴ cm⁻³ for all experiments, obtained in initial experiments from measuring pure HO₂ decays (no C₂H₆ added). [C₂H₆] has been varied between 1.9–7.5 × 10¹⁵ cm⁻³ and [CH₃OH] has been varied between 2.8–5.0 × 10¹⁵ cm⁻³. Using these conditions, the ratio of [HO₂]/[C₂H₅O₂] has been varied between 0.3 (pink circles) and 2.5 (black circles).

For all graphs in Figure 6, the above determined absorption cross-section (σ = 1.0 × 10⁻²⁰ cm²) has been used to convert the C₂H₅O₂ absorption coefficients into absolute concentrations.

The profiles for both species could be well reproduced over the entire concentration range using a rate constant of k₃ = 6.2 × 10⁻¹² cm³ molecule⁻¹ s⁻¹, 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 [32,33,34,35,36,37,38], 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 vary by about a factor of 1.5 (8.14 × 10⁻¹² cm³ molecule⁻¹ s⁻¹ for Boyd et al. [33] from UV absorption and 5.57 × 10⁻¹² cm³ molecule⁻¹ s⁻¹ 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 k₃ has been set to the lower limit such as obtained by Noell et al. [32] (5.5 × 10⁻¹² cm³molecule⁻¹ s⁻¹), leading to C₂H₅O₂ and (less pronounced) HO₂ decays that are too slow. Increasing the initial C₂H₅O₂ concentration by about 10% (corresponding to a decreased absorption cross-section for C₂H₅O₂: σ = 0.9 × 10⁻²⁰ cm²) can lead again to less good, but still acceptable HO₂ and C₂H₅O₂ decays (which would also imply a slight deviation of the overall initial radical concentration from 1.2 × 10¹⁴ cm⁻³). In the lower graphs (c), the upper limit has been tested by setting k₃ = 8 × 10⁻¹² cm³molecule⁻¹ s⁻¹: 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.

	Reaction	k/cm3molecule−1s−1	Reference
1a	2 C2H5O2 → 2 C2H5O + O2	2.6 × 10−14	Ref [32] *
1b	2 C2H5O2 → C2H5OH + CH3CHO + O2	6.7 × 10−14	Ref [32] *
2	C2H5O + O2 → CH3CHO + HO2	8 × 10−15	Ref [39]
3	C2H5O2 + HO2 → C2H5OOH + O2	6.2 × 10−12	This work
5	Cl + C2H6 → C2H5 + HCl	5.9 × 10−11	Ref [31]
6a	C2H5 + O2 + M → C2H5O2 + M	4.8 × 10−12	Ref [40]
6b	C2H5 + O2 → C2H4 + HO2	3-4× 10−14	This work **
7	Cl + CH3OH → CH2OH + HCl	5.5 × 10−11	Ref [31]
8	CH2OH + O2 → CH2O + HO2	9.6 × 10−12	Ref [31]
9	2 HO2 → H2O2 + O2	1.7 × 10−12	Ref [30]
10	C2H5O2 + Cl → products	1.5 × 10−10	Ref [41]
11	C2H5O2 → diffusion	2 s−1	This work
12	HO2 → diffusion	3 s−1	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 C₂H₅ radicals and the branching ratio between (R6a) and (R6b) depends on pressure and also on the mode of generation of the C₂H₅ radicals.

Table 3. Reaction mechanism used to fit all experiments in this work.

	Reaction	k/cm3molecule−1s−1	Reference
1a	2 C2H5O2 → 2 C2H5O + O2	2.6 × 10−14	Ref [32] *
1b	2 C2H5O2 → C2H5OH + CH3CHO + O2	6.7 × 10−14	Ref [32] *
2	C2H5O + O2 → CH3CHO + HO2	8 × 10−15	Ref [39]
3	C2H5O2 + HO2 → C2H5OOH + O2	6.2 × 10−12	This work
5	Cl + C2H6 → C2H5 + HCl	5.9 × 10−11	Ref [31]
6a	C2H5 + O2 + M → C2H5O2 + M	4.8 × 10−12	Ref [40]
6b	C2H5 + O2 → C2H4 + HO2	3-4× 10−14	This work **
7	Cl + CH3OH → CH2OH + HCl	5.5 × 10−11	Ref [31]
8	CH2OH + O2 → CH2O + HO2	9.6 × 10−12	Ref [31]
9	2 HO2 → H2O2 + O2	1.7 × 10−12	Ref [30]
10	C2H5O2 + Cl → products	1.5 × 10−10	Ref [41]
11	C2H5O2 → diffusion	2 s−1	This work
12	HO2 → diffusion	3 s−1	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 C₂H₅ radicals and the branching ratio between (R6a) and (R6b) depends on pressure and also on the mode of generation of the C₂H₅ radicals.

In conclusion, using the absorption cross-section for C₂H₅O₂ obtained in back-to-back 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 HO₂ 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 k₃ and with this the absorption cross-section for C₂H₅O₂ depend entirely on the rate constant for the HO₂ self-reaction. The absorption cross-section of HO₂ 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 HO₂ absorption lines are on the order of 0.02 cm⁻¹ FWHM at 50 Torr he). However, in our experiments the absorption cross-section of HO₂ is under most conditions constantly being “measured”: a major HO₂ loss in most experiments is the self-reaction, and thus the HO₂ decays are sensitive to the absolute HO₂ 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 C₂H₅O₂ absorption cross-section relative to the rate constant of the HO₂ 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 of the rate constant: k₃ = (6.2 ± 1.5) × 10⁻¹² cm³molecule⁻¹ s⁻¹.

3.3. Measuring the Relative Absorption Spectrum

In order to obtain the shape of the C₂H₅O₂ absorption spectrum, kinetic decays have been measured under identical conditions at 15 different wavelengths in the range accessible with our DFB laser (7596–7630 cm⁻¹). The relative absorption coefficients are put on an absolute scale by comparison with the absorption cross-section at 7596.47 cm⁻¹.

Table 4. C₂H₅O₂ Absorption cross-sections at different wavelengths.

Wavenumber/cm−1	σ/10−20 cm2
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

summarizes the obtained results, and Figure 7 compares the present data with two literature results.

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⁻¹. Possibly, there is a mistake in the Melnik figure (T. Miller, private communication), because the peak absorption is given in the text at 7596 cm⁻¹, just as in our case, however in the figure the peak is located at 7600 cm⁻¹, indicated by a blue vertical line. In the lower graph, our data (again in green) are overlaid to the spectrum of Atkinson and Spillman [11]. A good agreement of the shape in both comparisons can be obtained, when our data are scaled on the y-axis, i.e., when we suppose a shift in the baseline of both literature spectra (around 23% of the peak absorption for Atkinson and Spillman and 15% for Melnik et al.). Melnik et al. discussed in their paper such baseline shift (dashed line in their figure) and attributed it to a broadband absorber, generated simultaneously during the photolysis. Indeed, they obtained their baseline by measuring ring-down events with the photolysis 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 in the upper graph of Figure 7), they have calculated the absorption cross-section above this plateau. No explanation for a possible baseline shift in the work of Atkinson and Spillman can be given.

4. Discussion

Comparison of the Absorption Cross-Section with Literature Data

The absorption cross-section of C₂H₅O₂ was first determined by Atkinson and Spillman [11] using 193 nm photolysis of 3-pentanone as precursor. Using the kinetic method, they determined at the peak σ = (3 ± 1.5) × 10⁻²¹ cm², which is 3 times smaller than the present value. A higher absorption cross-section had also been measured previously by our group for the CH₃O₂ radical [12]. One possible reason might be that the determination from Atkinson and Spillman is based on the kinetic method using low initial radical concentrations, hence the C₂H₅O₂ concentration has to be measured over long reaction 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 Figure 2c and Figure 4). Another reason might be the precursor: the reaction of C₂H₅ + O₂ can also lead to small amounts of HO₂ through (R6b), around 1% of the initial Cl-atom concentration led to formation of HO₂ in the experiments of this work. Atkinson and Spillman 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 C₂H₅ radicals that react through (R6b) might be considerably higher than in our case. This could induce a non-negligible initial HO₂ concentration which participates in the removal of C₂H₅O₂ and would thus induce a systematic error when using the kinetic method. This is also in line with the observation of Atkinson and Spillman, that in their experiments the apparent rate constant of the C₂H₅O₂ self-reaction was inversely pressure dependent: the rate constant decreased with increasing pressure (D. Atkinson, private communication). An increased cooling of the hot C₂H₅ radical with increasing pressure would lead to a decreasing HO₂ concentration and thus to a slow-down of the C₂H₅O₂ decay.

Rupper et al. [16] estimated the absolute absorption cross-section to σ = 4.4 × 10⁻²¹ cm⁻² 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 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 one absorption path they measured the absorption of C₂H₅O₂ while on the other path the concentration of HCl was quantified thanks to its known absorption cross-section. Assuming again that one C₂H₅O₂ has been generated for each molecule of HCl, they found an absorption cross-section of σ = 5.29 × 10⁻²¹ cm⁻². This is nearly 2 times lower than the value obtained in this work. It is unlikely that the difference in the bandwidth of the excitation laser sources (0.01 cm⁻¹ for Melnik and <1 × 10⁻⁴ cm⁻¹ for this work) can explain the difference, because the absorption band is unstructured and much larger than the bandwidth of both laser sources. Also, the overall shape is, after 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 the complete conversion of Cl-atoms into C₂H₅O₂ radicals: a simple model is presented by Melnik et al. [17] showing the complete conversion of Cl-atoms into C₂H₅O₂. However, the very fast reactions of Cl-atoms with C₂H₅O₂ (k₁₀ = 1.5 × 10⁻¹⁰ cm³molecule⁻¹ s⁻¹) [41] and C₂H₅ (k = 3 × 10⁻¹⁰ cm³molecule⁻¹ s⁻¹) [42] are omitted in this model, even though these reactions are non-negligible under their conditions of very high initial Cl-atom concentrations, well above 10¹⁵ cm⁻³, combined with relatively low C₂H₆ concentrations (1 × 10¹⁶ cm⁻³). These reactions result in a C₂H₅O₂ concentration that might be well below the initial Cl-atom concentration, depending on the overall radical concentration as well as on the C₂H₆ concentration. Figure 8 shows a simulation using the model from Melnik et al., but completed by the two fast reactions. The left graph shows the result using initial concentrations such as given by Melnik et al. ([Cl]₀ = 2 × 10¹⁵ cm⁻³ and [C₂H₆]₀ = 1 × 10¹⁶ cm⁻³), the right graph shows the model result with typical conditions such as used in this work for the determination of the absorption cross-section ([Cl]₀ = 5 × 10¹³ cm⁻³and [C₂H₆]₀ = 3 × 10¹⁶ cm⁻³). Under the high Cl/low C₂H₆ conditions of Melnik et al., only 63% of the Cl-atoms have been converted to C₂H₅O₂, while 28% of the Cl-atoms have reacted with C₂H₅O₂ and 8% have reacted with C₂H₅. Under the low Cl/high C₂H₆ conditions (right graph), virtually all Cl-atoms have been converted to C₂H₅O₂, less than 1% of the Cl-atoms have reacted with either C₂H₅O₂ or C₂H₅. From this model one can suspect that the absorption cross-sections of Melnik et al. [17] and Rupper et al. [16] are strongly underestimated, and a correction of the Melnik et al. value, based on the more complete model presented here, would lead to σ = 8.8 × 10⁻²¹ cm⁻², which gets into good agreement with the value found in this work.

5. Conclusions

We have presented in this work a new determination of the absorption cross-section of the Ã←$\tilde{X}$ electronic transition of the C₂H₅O₂ radical. The cross-section at the peak wavelength 7596.4 cm⁻¹ has in a first approach been determined by direct comparison with the well-known HO₂ absorption cross-section in back-to-back experiments to be (1.0 ± 0.2) × 10⁻²⁰ cm². In further experiments, the absorption cross-section has been validated by measuring the rate constant of C₂H₅O₂ with HO₂ in a wide range of concentration: the ratio of [HO₂]/[C₂H₅O₂] has been varied between 0.3 and 2.5 and the concentration time profiles could be reproduced very well using the same absorption cross-section for all C₂H₅O₂ profiles, which returned a rate constant for the cross reaction of 6.2 × 10⁻¹² cm³ molecule⁻¹ s⁻¹. 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.