# The absorption spectrum and absolute absorption cross sections of acetylperoxy radicals, CH3C(O)O2 in the near IR

Michael Rolletter, Emmanuel Assaf, Mohamed Assali, Hendrik Fuchs, Christa Fittschen

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Michael Rolletter, Emmanuel Assaf, Mohamed Assali, Hendrik Fuchs, Christa Fittschen. The absorption spectrum and absolute absorption cross sections of acetylperoxy radicals, CH3C(O)O2 in the near IR. Journal of Quantitative Spectroscopy and Radiative Transfer, 2020, Journal of Quantitative Spectroscopy and Radiative Transfer, 245, 10.1016/j.jqsrt.2020.106877. hal-02960888

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Submitted on 8 Oct 2020

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<figure><img src="image_1.png" /></figure>

Distributed under a Creative Commons Attribution 4.0 International License
<figure><img src="image_2.png" /><figcaption>Fig. 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.</figcaption></figure>

This additional OH radical regeneration could improve the model-measurement agreement in low NOx environments with high VOC emission rates.

For an accurate understanding of the CH3C(O)O2 + HO2 reaction, it is necessary to understand the secondary chemistry. For example, the CH3C(O)O2 self-reaction (R4) competes with the reaction with HO2, forming the same product CH3C(O)O as (R3) making it hard to distinguish between both reactions.

$$2 \mathrm{CH_3(O)O_2} \rightarrow 2 \mathrm{CH_3C(O)O} + \mathrm{O_2} \quad (\mathrm{R4})$$

In addition, reaction rate constants of the self-reaction ($k_4 = 2.9 \times 10^{-12} \exp(500/T) \mathrm{cm}^3 \mathrm{molecule}^{-1} \mathrm{s}^{-1}$ [13]) and of the reaction with HO2 ($k_{1-3} = 3.14 \times 10^{-12} \exp(580/T) \mathrm{cm}^3 \mathrm{molecule}^{-1} \mathrm{s}^{-1}$ [13]) are in the same order of magnitude which makes it complicated to study those reaction kinetics.

The detection of RO2 in previous kinetic laboratory studies was mainly done in the UV region. The spectral overlap of different peroxy species in this region is prone to systematic errors in the quantitative detection [14–18]. Therefore, experiments analysing different RO2 are difficult to evaluate, if they are detected by UV absorption.

Here, we use absorption of CH3C(O)O2 in the Ā-Ā̄ electronic transition located in the near infrared region. This results in absorption cross sections that are up to several orders of magnitude smaller compared to values in the UV, but the detection is more selective due to less spectral overlap with formed products. In order to measure these small absorption cross sections, very sensitive detection methods need to be used, in our case continuous wave-Cavity Ring Down Spectroscopy (cw-CRDS). While the relative spectrum has already been measured by Zalyubovsky et al. [19] in a large wavelength range and the absolute absorption cross section of the strongest band at 5582 cm⁻¹ has been estimated, we present here the determination of absolute absorption cross sections in two ranges from 6094 cm⁻¹ - 6180 cm⁻¹ and from 6420 cm⁻¹ - 6600 cm⁻¹, corresponding to the COO bend and to the OO stretch transition, respectively, relative to the absorption cross section of HO2. These cross sections can be used in future works for the quantitative detection of this radical.

## 2. Experimental

### 2.1. Experimental setup

The setup has been described in detail before [20–23] and is briefly discussed here (Fig. 1).

The setup consisted of a 0.79 m long flow reactor made of stainless steel. The beam of a pulsed excimer laser (Lambda Physik LPX 202i) passed the reactor longitudinally. The flow reactor contained

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 with the photolysis beam of 0.377 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. For measuring the CH3C(O)O2 spectrum, a tunable laser source (Agilent 81680A) was coupled into one of the cavities by systems of lenses and mirrors. On the other path, a DFB laser was coupled into the cavity for the detection of HO2 radicals during the calibration measurements. The calibration of the acetylperoxy absorption cross section at 6497.94 and 6638.30 cm⁻¹ in 67 hPa helium has also been carried out using a DFB laser instead of the Agilent module. Each probe beam passed an acousto-optic modulator (AOM, AAoptoelectronic) to rapidly turn off the 1st order beam once a threshold for light intensity in the cavity was reached, in order to measure the ring-down event. Then, the decay of light intensity was recorded and an exponential fit is applied to retrieve the ring-down time. The absorption coefficient α is derived from Eq. (1).

$$\alpha = [A] * \sigma_A = \frac{R_L}{c} \left( \frac{1}{\tau} - \frac{1}{\tau_0} \right) \quad (1)$$

where τ is the ring-down time with an absorber present; τ0 is the ring-down time with no absorber present; σA is the absorption cross section of the absorbing species A; Rl is the ratio between cavity length (79 cm) and effective absorption path (37.7 cm); c is the speed of light. To calculate the absorption cross section it is necessary to know the absorber concentration.

Acetylperoxy radicals were generated by pulsed 351 nm photolysis of acetaldehyde (CH3CHO) / Cl2 / O2 mixtures:

$$\mathrm{Cl_2} + h\nu \rightarrow 2 \mathrm{Cl} \quad (\mathrm{R5})$$

$$\mathrm{CH_3CHO} + \mathrm{Cl} \rightarrow \mathrm{CH_3CO} + \mathrm{HCl} \quad (\mathrm{R6})$$

$$\mathrm{CH_3CO} + \mathrm{O_2} + \mathrm{M} \rightarrow \mathrm{CH_3C(O)O_2} + \mathrm{M} \quad (\mathrm{R7})$$

The Cl radical concentration for the measurement of the spectrum was around 1.7 × 10¹² cm⁻³ and was varied for the calibration measurements between (1 and 8) × 10¹² cm⁻³. Acetaldehyde was prepared as a diluted mixture in a glass bulb. A small flow was added to the mixture through a calibrated flow meter giving a concentration of 2.5 × 10¹⁴ cm⁻³. Nearly all experiments were performed in synthetic air, at 298 K and 67 hPa total pressure,
<figure><img src="image_3.png" /><figcaption>Fig. 2. Typical series of ring-down times for CH₃C(O)O₂, the insert shows the zoom of the gray-shaded area (+/-15 ms). The dashed line represents the time of the photolysis pulse (t=0s). Ring-down events before the photolysis pulse (black) are used to determine τ₀, extrapolation to t=0s of a bi-exponential fit of the ring-down times occurring during the first 50 ms after the photolysis pulse (black line in the insert) are used to determine τ.</figcaption></figure>

the absorption cross sections at 6697.94 and 6638.30 cm⁻¹ were also determined at 67 hPa helium. N₂ (Praxair, 4.5), He (Praxair 4.5) and O₂ (Praxair, 4.5) were used without further purification. All gas flows were controlled by calibrated mass flow controllers (Bronkhorst, Tylan).

## 2.2. Absorption spectra measurements

The procedure to measure absorption spectra has been described before [24,25] and is only briefly discussed here. The spectrum was measured with a point spacing of 0.1 cm⁻¹ for the wavelength range from 6094 - 6180 cm⁻¹ and 0.2 cm⁻¹ for the wavelength range from 6420 - 6600 cm⁻¹, corresponding to the COO bend and the OO stretch, respectively [19]. Both wavelength regions have been sampled by changing incrementally the wavelength of the laser while a constant amount of CH₃C(O)O₂ was generated in the reactor.

For each wavelength, a time series of ring-down measurements testing the acetylperoxy radical absorption was recorded. After the data acquisition was triggered ring-down events were usually recorded 0.5 s each before and after the photolysis laser shot which led to the formation of acetylperoxy radicals. A typical trace is shown in Fig. 2, where ring-down times from ring-down events occurring before the photolysis pulse are shown in black, and those after the photolysis pulse are shown in green. The loss of CH₃C(O)O₂ radicals is for the first tens of ms mostly due to self-reaction and to the reaction with the radical products of this self-reaction (CH₃O₂ and HO₂). With decreasing radical concentrations on the longer time scale, diffusion out of the photolysis volume becomes the major loss process. To derive the absorbance of the initially produced acetylperoxy radicals, the time-resolved series of ring-down events was extrapolated to the moment of the photolysis pulse (t=0s). Different fitting procedures were tested, and it turned out that a bi-exponential fit over the first 50 ms following the photolysis pulse reproduced the data very well and allowed a reliable extrapolation to t=0s. However, it has to be kept in mind that the decay of the CH₃C(O)O₂ concentration is due to a complex reaction scheme, and the decay constants from the fit have no physical meaning. The quality of the fit is shown as a black line in the insert of Fig. 2. τ₀, that is required to calculate the absorbance (Eq. (1)), was derived from the average of all detected ring-down events that occurred before the photolysis pulse when no CH₃C(O)O₂ was present. The ring-down events are randomly distributed in time at each photolysis shot because of the

<figure><img src="image_4.png" /><figcaption>Fig. 3. Portion of the relative absorption spectrum: each dot, corresponding to one wavelength, is extracted from a kinetic decay such as shown in Fig. 2. Black dots represent baseline (τ₀), green dots obtained from extrapolation of bi-exponential fitting such as shown in Fig. 2 (τt=0), blue dots (α) obtained by applying equation (Eq. (1)).</figcaption></figure>

random nature of when exactly an efficient coupling of the laser into the cavity was achieved. Ring-down events were therefore accumulated over several laser pulses (10 - 20 generally) to get a better coverage of the whole time range.

## 3. Results and discussion

A portion of the relative absorption spectrum of the OO stretch region is shown in Fig. 3. For each wavenumber, measurements were evaluated as shown in Fig. 2. Ring-down times extrapolated to t=0s (green) and τ₀ as the average of all ring-down times before the photolysis pulse (black) are shown for each wavenumber in Fig. 3. The absorption coefficients (blue) are calculated by applying equation (Eq. (1)) to each data pair τ and τ₀.

In order to convert the absorption coefficient α into absolute cross sections σ, the knowledge of the exact CH₃C(O)O₂ concentration is necessary. Therefore, a series of experiments was conducted to quantify the initial amount of radicals. This was achieved by quantitatively converting all Cl-atoms to HO₂ radicals, which can be reliably measured by cw-CRDS on a strong absorption line at 6638.205 cm⁻¹ [23,26–29]. The measurement of the HO₂ absorption cross section is based on the measurement of HO₂ decays during self-reaction, which allows for retrieval of the initial concentration, and thus the absorption cross section, if the rate constant is known. While the uncertainty of the measured HO₂ decays itself is small (<10%), the uncertainty of the rate constant is currently recommended by the IUPAC committee to ±40%. This same uncertainty has to be considered for the absorption cross sections obtained in this work, as they are measured relative to the HO₂ absorption cross section. The quantitative conversion of Cl-atoms to HO₂ is done by photolysing a Cl₂ / methanol (CH₃OH) mixture:

$$Cl + CH_3OH \rightarrow HCl + CH_2OH \quad (R9)$$

$$CH_2OH + O_2 \rightarrow CH_2O + HO_2 \quad (R10)$$

Then, CH₃OH is substituted by CH₃CHO to form CH₃C(O)O₂ following reactions (R11) and (R12), while keeping conditions for the generation of Cl radicals constant.

$$Cl + CH_3CHO \rightarrow HCl + CH_3CO \quad (R11)$$

$$CH_3CO + O_2 \rightarrow CH_3C(O)O_2 \quad (R12a)$$

Assuming that the concentration of HO₂ radicals corresponds to the concentration of Cl atoms, the ratio of absorbance measured
<figure><img src="image_5.png" /><figcaption>**Fig. 4.** Left plot shows HO₂ absorption coefficient online (6638.20 cm⁻¹, black dots) and offline (6638.30 cm⁻¹, open black symbols, right y-axis apply for both) and HO₂ concentration (blue symbols, left y-axis) measured after photolysing a Cl₂ / CH₃CHO / O₂ mixture. Right graph shows the HO₂ concentration from the photolysis of Cl₂ / CH₃OH / O₂ mixture (blue symbols) and the CH₃C(O)O₂ concentration time profile from the photolysis of the Cl₂ / CH₃CHO / O₂ mixture (black symbols). Both experiments used the same Cl₂ concentration.</figcaption></figure>

for CH₃C(O)O₂ and HO₂ can be used to calculate the CH₃C(O)O₂ absorption cross section relative to the well known HO₂ absorption cross section according to:

$$ \sigma_{\text{CH}_3\text{C(O)O}_2} = \alpha_{\text{CH}_3\text{C(O)O}_2} \frac{\sigma_{\text{HO}_2}}{\alpha_{\text{HO}_2}} \qquad (2) $$

However, the assumption does not entirely apply, because the reaction of CH₃CO + O₂ leads also to the formation of some OH radicals, the yield depending on pressure and nature of the CH₃CO precursor [30–32]. An OH yield of 0.25 is expected in nitrogen at 67 hPa [30].

$$ \mathrm{CH_3CO} + \mathrm{O_2} \rightarrow \mathrm{OH} + \text{products} \qquad (\mathrm{R12b}) $$

OH radical concentrations can in principle be measured by cw-CRDS in the experimental set-up [33]. However, concentrations in these experiments were below the limit of detection likely due to the fast reaction with acetaldehyde [13]:

$$ \mathrm{CH_3CHO} + \mathrm{OH} \rightarrow \mathrm{CH_3CO} + \mathrm{H_2O} \qquad (\mathrm{R13}) $$

Because under our experimental conditions ([CH₃CHO] = 2.5 × 10¹⁴ cm⁻³), (R13) is leading with k₁₃ = 1.5 × 10⁻¹¹ cm³ s⁻¹ to an OH lifetime of 250 µs, and can thus, in absence of other potential reaction partners, be considered as the nearly exclusive fate of OH radicals. And because (R13) leads to formation of another CH₃CO radical, this reaction does not introduce an error in the calculation of the absorption cross section using equation (Eq. (2)).

However, it was observed in our experiments that small amounts of HO₂ radicals are formed immediately from the initial reaction of CH₃CHO + Cl. Radical concentrations measured in a typical experiment are shown in Fig. 4: the left graph shows the HO₂ signal obtained from photolysis of Cl₂ / CH₃CHO / O₂ mixture. Because CH₃C(O)O₂ has a broad absorption spectrum [19], it still absorbs in the wavelength range where HO₂ is detected (6638.2 cm⁻¹). Therefore, absolute HO₂ concentrations (blue symbols) are obtained from the difference of the online (6638.2 cm⁻¹) and the offline (6638.3 cm⁻¹) absorption signal. It can be seen that the HO₂ concentration immediately after the photolysis pulse is not zero. The blue symbols on the right graph show the HO₂ concentration time profile under the same conditions, but with CH₃OH instead of CH₃CHO. Comparing the HO₂ concentrations measured from methanol mixtures ([HO₂]ₐ₄₃OH) and acetaldehyde mixtures ([HO₂]ₐ₄₃C(H)O) shows that around 3% of the Cl-atoms are con-

<caption>**Table 1**</caption>

Absorption coefficient α for CH₃C(O)O₂ from the measurement of the full spectrum for eight wavenumbers (marked by lines in the full spectrum of Fig. 6) and absorption cross sections σ for the same lines, determined relative to the HO₂ cross section at 67 hPa N₂ and for two wavenumbers at 67 hPa helium.

<table><thead><tr><th>Wavenumber / cm<sup>-1</sup></th><th>α / 10<sup>-8</sup> cm<sup>-1</sup></th><th>σ / 10<sup>-20</sup> cm<sup>2</sup></th></tr></thead><tbody><tr><td>6121.08</td><td>5.65 ± 0.28</td><td>3.4 ± 1.7</td></tr><tr><td>6164.75</td><td>2.75 ± 0.14</td><td>1.7 ± 0.8</td></tr><tr><td>6108.74</td><td>4.01 ± 0.20</td><td>2.2 ± 1.1</td></tr><tr><td>6114.53</td><td>1.59 ± 0.08</td><td>0.9 ± 0.5</td></tr><tr><td>6497.94</td><td>5.35 ± 0.27</td><td>3.2 ± 1.6</td></tr><tr><td>6697.94 (helium)</td><td></td><td>3.3 ± 1.7</td></tr><tr><td>6502.80</td><td>3.03 ± 0.15</td><td>1.7 ± 0.9</td></tr><tr><td>6552.76</td><td>4.29 ± 0.21</td><td>2.5 ± 1.3</td></tr><tr><td>6510.74</td><td>8.49 ± 0.42</td><td>4.9 ± 2.4</td></tr><tr><td>6638.30 (helium)</td><td></td><td>0.8 ± 0.4</td></tr></tbody></table>

verted to HO₂ (δₐ₄₃O₂) in the presence of CH₃CHO.

$$ \delta_{\text{HO}_2} = \frac{[\text{HO}_2]_{\text{CH}_3\text{CHO}}}{[\text{HO}_2]_{\text{CH}_3\text{OH}}} \qquad (3) $$

This small correction of the initial CH₃C(O)O₂ concentration was taken into account when converting the absorption coefficient of CH₃C(O)O₂ into absorption cross sections:

$$ \sigma_{\text{CH}_3\text{C(O)O}_2} = \alpha_{\text{CH}_3\text{C(O)O}_2} \frac{\sigma_{\text{HO}_2}}{\alpha_{\text{HO}_2}} \times \frac{1}{(1 - \delta_{\text{HO}_2})} \qquad (4) $$

The origin of this rapid HO₂ formation is not clear, but is formed possibly through the reaction

$$ \mathrm{CH_3CO} + \mathrm{O_2} \rightarrow \mathrm{CH_2CO} + \mathrm{HO_2} \qquad (\mathrm{R12c}) $$

Such a rapid HO₂ formation with similar yields had already been observed by Morajkar et al. [34], with a yield of around 7%, independent of pressure between 10 and 90 Torr helium, following the 248 nm photolysis of CH₃CHO, and also by Hui et al. [35], with a yield of 2–3% following the reaction of Cl-atoms with CH₃CHO at 100 Torr N₂. HO₂ concentrations at 67 hPa N₂ have been calculated using an absorption cross section of σₐ₄₃O₂₄₆₃₈.20cm⁻¹ = 2.01 × 10⁻¹⁹ cm², obtained from the empirical expression of Assaf et al. [27].

This way, absorption cross sections σ were measured for 8 wavenumbers in synthetic air and for 2 wavenumbers in helium, given in Table 1 together with the absorption coefficients α for the same wavelengths in synthetic air, such as found during the measurement of the full spectrum. Also given in Table 1 are the absorption cross sections for two wavenumbers, obtained in 67 hPa
<figure><img src="image_6.png" /><figcaption>**Fig. 5.** Absorption coefficients $\alpha$ as a function of the absorption cross sections $\sigma$ from Table 1. Error bars are statistical for absorption coefficients $\alpha$ (5%), and an uncertainty of 45% is added for the absorption cross section $\sigma$, taking into account the uncertainty in the absorption cross section for HO$_2$.</figcaption></figure>

helium: 6697.94 cm$^{-1}$ corresponds to one peak of the OO-stretch transition band, while 6638.30 cm$^{-1}$ corresponds to the wavenumber that we commonly use for the measurement of the HO$_2$-offline signal, i.e. the open circles in Fig. 4. The error bars of the absorption coefficients $\alpha$ are statistical only and are given with ±5%, obtained from the 95% confidence interval of the extrapolation of the bi-exponential fit to $t=0$ s (black curve in the insert of Fig. 2, typically below 4%) as well as the $\tau_0$ (average of all ring down events before the photolysis pulse: typically less than 1%). The error bars for the absorption cross sections are given with ±50% and are composed of twice the uncertainty of extrapolating $\alpha$ to $t=0$ s (once for $\alpha_{CH_3C(O)O_2}$ and once for $\alpha_{HO_2}$) and the 40% uncertainty given by the IUPAC committee [36] for the rate constant of the HO$_2$ self-reaction, that was used to determine the absorption cross section of HO$_2$.

In Fig. 5 the absorption coefficients are plotted for all eight wavenumbers as a function of the absorption cross sections $\sigma$. A good linearity is found, assuring that the CH$_3C(O)O_2$ concentration was stable during the measurement of the full spectrum.

The slope from the linear regression of Fig. 5 leads to the concentration of CH$_3C(O)O_2$ radicals that was generated during the measurement of the full spectrum: $1.7 \times 10^{12}$ cm$^{-3}$. This value was used for the conversion of the absorption coefficients from the relative spectra (blue line in Fig. 3) of the two wavelength ranges into absolute absorption cross sections, shown in Fig. 6. A comparison with a previously published spectrum [19] shows an excellent agreement of the positions and relative intensities of the different absorption maxima.

Zalyubovsky et al. [19] determined an absorption cross section of $\sigma = (1 \pm 0.5) \times 10^{-19}$ cm$^2$ at 5582.5 cm$^{-1}$. This is consistent with our absorption cross section of $(4.9 \pm 2.4) \times 10^{-20}$ cm$^2$ at the absorption maximum 6510.71 cm$^{-1}$, which has in the spectrum of Zalyubovsky et al. a relative intensity of approximately a factor 2 less than the absorption maximum at 5582.5 cm$^{-1}$.

The results obtained in this work will be used in future studies on the reaction kinetics of CH$_3C(O)O_2$ radicals. Depending on the quality of alignment, cleanliness of mirrors, etc. a decrease of the ring-down time of $\Delta\tau = 0.5$ µs on a typical $\tau_0 = 50$ µs can be achieved in time-resolved experiments, leading to a limit of detection below [CH$_3C(O)O_2$] = $4 \times 10^{11}$ cm$^{-3}$, making this technique more sensitive than typical UV-absorption measurements. And even though the spectrum features a rather broad background, i.e. lacks the high selectivity that can be achieved for HO$_2$ or OH measurements, its main absorption peaks are red-shifted compared to other small peroxy radicals such as HO$_2$, CH$_3O_2$ [24,37,38], C$_2H_5O_2$ [37] and should thus allow a selective detection for measuring the rate constants and branching ratios of self- and cross-reactions.

<figure><img src="image_7.png" /></figure>

<figure><img src="image_8.png" /><figcaption>**Fig. 6.** Absolute absorption spectrum of CH$_3C(O)O_2$. Vertical lines indicate the wavelengths where absolute absorption cross sections have been determined relative to the absorption cross section of HO$_2$ (see Table 1). The data can be downloaded as supplementary data.</figcaption></figure>

## 4. Conclusion

We measured the CH$_3C(O)O_2$ absorption spectrum in the ranges from 6094 cm$^{-1}$ - 6180 cm$^{-1}$ and 6420 cm$^{-1}$ - 6600 cm$^{-1}$. Measurements were performed in 67 hPa synthetic air or helium total pressure. Radicals were generated by the pulsed photolysis of acetaldehyde / Cl$_2$ / O$_2$ mixtures at 351 nm.

Some large peaks on top of a broad absorption spectrum were obtained, in good agreement with an earlier measurement by Zalyubovsky et al. [19]. Absolute absorption cross sections were measured for eight different wavelengths and are in good agreement relative to the only available measurement by Zalyubovsky et al. [19] performed at a lower wavenumber.

## Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## CRediT authorship contribution statement

**Michael Rolletter:** Data curation, Writing - original draft.
**Emmanuel Assaf:** Investigation, Data curation, Resources.
**Mohamed Assali:** Investigation, Data curation. **Hendrik Fuchs:** Conceptualization, Writing - review & editing, Supervision, Funding acquisition. **Christa Fittschen:** Conceptualization, Writing - original draft, Supervision, Project administration, Funding acquisition.

## Acknowledgments

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 Climbio) and the European Fund for Regional Economic Development. This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (SARLEP grant agreement No. 681529) and from the exchange program of the Deutscher Akademischer Austauschdienst (DAAD) (project number 57316518) and PHC Procope project no. 37666WA.

## Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jqsrt.2020.106877.

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