Characterization of two photon excited fragment spectroscopy (TPEFS) for HNO₃ detection in gas-phase kinetic experiments

Abstract

We have developed and tested two-photon excited fragment spectroscopy (TPEFS) for detecting HNO₃ in pulsed laser photolysis kinetic experiments. Dispersed (220–330 nm) and time-dependent emission at (310 ± 5) nm following the 193 nm excitation of HNO₃ in N₂, air and He was recorded and analysed to characterise the OH(A²Σ) and NO(A²Σ⁺) electronic excited states involved. The limit of detection for HNO₃ using TPEFS was ∼5 × 10⁹ molecule cm⁻³ (at 60 torr N₂ and 180 μs integration time). Detection of HNO₃ using the emission at (310 ± 5 nm) was orders of magnitude more sensitive than detection of NO and NO₂, especially in the presence of O₂ which quenches NO(A²Σ⁺) more efficiently than OH(A²Σ). While H₂O₂ (and possibly HO₂) could also be detected by 193 nm TPEFS, the relative sensitivity (compared to HNO₃) was very low. The viability of real-time TPEFS detection of HNO₃ using emission at (310 ± 5) nm was demonstrated by monitoring HNO₃ formation in the reaction of OH + NO₂ and deriving the rate coefficient, k₂. The value of k₂ obtained at 293 K and pressures of 50–200 torr is entirely consistent with that obtained by simultaneously measuring the OH decay and is in very good agreement with the most recent literature values.

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1. Introduction

HNO₃ is an important atmospheric trace gas and its ultra-violet photo-dissociation has been the subject of numerous studies.¹ The photo-dissociation of HNO₃ can be divided into three channels, leading to formation of OH, O-atoms or H-atoms, the relative importance of which depends on the wavelength.

HNO₃ + hν (I) → OH(X) + NO₂(X²A₁) (R1a)

→ OH(X) + NO₂(1²B₂) (R1b)

HNO₃ + hν (II) → O(¹D) + HONO(X¹A′) (R1c)

→ O(³P) + HONO(a³A′′) (R1d)

→ O(³P) + HONO(X¹A′) (R1e)

HNO₃ + hν (III) → H(²S) + NO₃ (R1f)

At wavelengths (λ) greater than 250 nm, the n–π* transition (to the 1 ¹A′′ electronic excited state) in HNO₃ leads to photo-dissociation into predominantly OH + NO₂ (Φ^I_250nm > 0.97) with a weak contribution from O-atom formation (Φ^II_250nm = 0.03). The formation of NO₃ and H photo-fragments (Channel III) at these wavelengths has been assigned an upper limit of Φ^III_250nm < 0.012.²

At λ < 250 nm, HNO₃ is excited to the 2¹A′ electronic excited through an π–π* transition. At 193 nm, channel II becomes the main photo-dissociation channel with quantum yields of Φ^II_193nm = 0.67 and Φ^I_193nm = 0.33.^2–5 OH fragments formed in channel I are produced in their vibrational ground state with little rotational excitation,^6–9 whereas the NO₂ co-fragment is formed either in its ground state, or in its 1²B₂ electronically excited state (yield < 1.0%). The ground state NO₂ thus formed is sufficiently energy rich to decompose to NO and O(³P). Experimental determinations of the yield of O(¹D) in channel II vary between 0.54 and 0.28.^2,5 At shorter wavelengths, λ < 155 nm, OH can be formed in an electronically excited state^10,11 in a single photon process.

In a series of papers by Stuhl and co-workers studying the excitation of HNO₃ at 193 nm,^12–14 it was shown that electronically excited OH, OH(A), was produced in a sequential, two-photon process. From experimental observations, spin conservation and energy considerations the authors were able to demonstrate that OH(A) was not formed directly but via the photolysis of electronically excited HONO, probably in its metastable lower triplet state (a³A′′). They used these findings to develop a new method (laser-photolysis fragment-fluorescence, LPFF) for the measurement of HNO₃ in the atmosphere.^15,16 Recently, Winiberg et al.¹⁷ reported results from the multi-photon photolysis of HNO₃ at 193 and 248 nm and reported dispersed OH and NO fluorescence spectra. They demonstrated that OH emission from a 2-photon excitation of HNO₃ was not only observed upon excitation at 193 nm but also at 248 nm. In a previous study¹⁸ from our group (on the reaction between OH and HNO₃), the TPEFS method was used to check for HNO₃ concentration gradients across the reactor at low temperature (220 K < T < 250 K).

In this paper, we investigate the two-photon photodissociation of HNO₃ at 193 nm and demonstrate the application of two-photon excited fragment spectroscopy (TPEFS) detection of HNO₃ in real-time (flash photolysis) kinetic studies. For the latter we re-measured the well-known rate coefficient^19,20 of the reaction between OH and NO₂ (R2) by monitoring the HNO₃ product by TPEFS and also by near-simultaneous detection of OH via Laser Induced Fluorescence (LIF):

OH + NO₂ + M → HNO₃ + M (R2a)

→ HOONO + M (R2b)

The three-body association reaction of OH with NO₂ is known to proceed via two product channels ((R2a) and (R2b)) forming mainly nitric acid (HNO₃) but with a contribution from peroxynitrous-acid (HOONO).^21,22 At room temperature and a pressure of 100 mbar the rate coefficients of the two reactions have been evaluated as: k_2a = 3.0 × 10⁻¹² cm³ molecule⁻¹ s⁻¹ and k_2b = 2.0 × 10⁻¹³ cm³ molecule⁻¹ s⁻¹. ²³ HOONO is thermally unstable with a room-temperature lifetime w.r.t. decomposition to OH + NO₂ of ≈10 s. However, on the milli-second timescale of our experiments it can be considered a stable product. As the application of TPEFS in kinetic studies of HNO₃ will depend on its selectivity, we characterisd the sensitivity of TPEFS at 193 nm for detection of several other trace gases, including NO and NO₂ which are often present (as impurities or products) in reaction systems involving HNO₃.

2. Experimental

All measurements were performed at 293 K on the PLP-LIF apparatus shown in Fig. 1. Several features of the setup have been described in detail elsewhere.²⁴ The main modifications to the present set-up are (1) the incorporation of a gated CCD camera for dispersed fluorescence measurement and (2) an additional (193 nm) excimer laser.

Fig. 1 Schematic of the combined PLP-LIF and PLP-TPEFS set-up. PMT: photomultiplier, IF: interference filter, AC1: absorption cell with l = 110 cm (240–400 nm), AC2: absorption cell with l = 34.8 cm (213.86 nm): AC2: absorption cell with l = 43.8 cm (184.95 nm). MC: monochromator with diode-array detector. H4: Halogen lamp. 193, 248 and 282 nm pulses were provided by excimer lasers and a YAG-pumped dye-laser, respectively. Dispersed fluorescence was collected on an axis orthogonal to the page using a lens/optical-fibre set-up. Dashed lines indicate direction of gas-flow.

2.1 Radical generation, fluorescence excitation and detection

Laser-light is coupled in/out of the thermostatted, multi-axis reaction cell (volume ∼500 cm³) via Brewster-angle quartz windows. Pulsed (∼20 ns) 248 nm light from a KrF-excimer laser (Coherent COMPex 205F) provided a source of OH radicals (e.g. via H₂O₂ photolysis, see later).

HNO₃ was detected following excitation/dissociation at 193 nm using an ArF excimer laser (Coherent COMPex Pro 201F). A focal lens (f = 50 cm) was used to mildly focus the laser in the middle of the reactor to enhance the HNO₃ detection sensitivity. Typical photon fluxes at 193 nm varied from 30 to 50 mJ cm⁻² (measured at the exit of the photolysis cell). OH was excited at 282 nm using a YAG-pumped Dye-Laser (Quantel Brilliant B/Lambda-Physik ScanMate II). All three lasers operated at 10 Hz. The PMT signal was accumulated using either a box-car integrator (Stanford Research Systems, SR 250) for kinetic measurements or a digital oscilloscope (Tektronix TDS 3014C, 100 MHz) for recording time-resolved fluorescence signals.

The fluorescing volume at the reactor centre was imaged via a 5 cm diameter quartz lens on the major axis of the cell onto a photomultiplier tube screened with a 280 nm long-pass filter (BG26) and a (310 ± 5) nm interference filter. A lens/optical fibre set up on an orthogonal axis transmitted fluorescence from the same volume to the entrance slit of a 0.5 m monochromator (Acton Research 500) equipped with a gated, intensified CCD camera (Roper Scientific, PMax) for measurement of dispersed fluorescence. Spectra were recorded using gratings with either 300 or 1200 lines mm⁻¹ resulting in spectral ranges of ∼80 nm (at ∼1.2 nm resolution) or ∼20 nm (at ∼0.4 nm resolution), respectively. Spectral resolution determination and wavelength calibration was carried out using a low pressure Hg-lamp.

2.2 Reagent gas concentrations

The concentrations of reagent gases were monitored using three different, on-line optical absorption set-ups. Absorption by NO₂ (400–450 nm) was measured in an absorption cell (l = 110 cm) using a halogen lamp as light source and a 0.5 m monochromator/diode array camera as detector. NO₂ concentrations were derived by least-squares fitting to a literature reference spectrum degraded to the same resolution.²⁵ The concentration of H₂O₂ was determined from its optical absorption at 213.86 nm (low pressure Zn-lamp, l = 34.8 cm) using an absorption cross-section of σ_213.9(H₂O₂) = 3.3 × 10⁻¹⁹ cm² molecule⁻¹.²⁶ The concentrations of HNO₃ and H₂O were determined from their optical absorption at 184.95 nm (low pressure Hg-lamp, l = 43.8 cm) using σ_184.95(HNO₃) = 1.63 × 10⁻¹⁷ cm² molecule^{−1 18,27,28} and σ_184.95(H₂O) = 7.14 × 10⁻²⁰ cm² molecule⁻¹.²⁹ In the same set-up, the ozone concentration was measured at 253.65 nm using a cross-section of 1.1 × 10⁻¹⁷ cm² molecule⁻¹.²³

2.3 Chemicals

Bottled N₂ (Westfalen, 5.0) was used without further purification. H₂O₂ (AppliChem, 50 wt%) was concentrated by vacuum distillation. NO₂ was prepared by reacting ∼50 torr of NO with a large excess of O₂ in a dried glass bulb. The NO₂ was then condensed at liquid N₂ temperature and excess O₂ and NO were removed by pumping. The resulting NO₂ was stored as a mixture of 5% NO₂, 10% O₂ and 85% N₂. Anhydrous nitric acid was prepared by mixing KNO₃ (Sigma Aldrich, 99%) and H₂SO₄ (Roth, 98%), and condensing the HNO₃ vapour into a liquid nitrogen trap. Anhydrous nitric acid was kept at 252 K between experiments.

3. Results and discussion

3.1 Fluorescence from HNO₃ at (310 ± 5) nm in N₂

Our TPEFS measurement of HNO₃ monitors a fluorescence signal that is transmitted through an interference filter (310 ± 5 nm) that biases detection to the strong OH (0,0) emission lines. Fig. 2 (upper panel) displays the averaged (500 laser pulses), time-resolved signal due to three different concentrations of HNO₃ (in a flow of N₂ at a total pressure of 100 torr) which were quantified by absorption at 184.95 nm. The integrated fluorescence signals are plotted against HNO₃ concentration in the lower panel of Fig. 2 which indicates that, for [HNO₃] up to 2 × 10¹⁴ molecule cm⁻³ and under these experimental settings (PMT voltage, focused 193 nm laser light), the fluorescence signal is proportional to [HNO₃]. At 60 torr N₂, we achieved a limit of detection for HNO₃ of 5 × 10⁹ molecule cm⁻³ at 1σ for 2 min of signal accumulation, which results (at 10 Hz) in a total signal integration time of 180 μs.

Fig. 2 Upper panel: Time resolved fluorescence signal detected by the PMT and (310 ± 5) nm interference filter at 100 torr N₂ and room temperature (298 ± 2 K). Lower panel: TPEFS signal (0–150 ns) versus HNO₃ concentration. The straight line is a linear regression to the data.

The dependence of the TPEFS signal on the 193 nm laser energy (E_193nm, varied by changing the high-voltage of the excimer laser or placing fine metal mesh in the beam at the exit of the laser) is displayed in Fig. 3. The relative change in energy was measured by splitting part of the laser-beam to a photo-diode with a linear response in the range measured.

Fig. 3 TPEFS signal as a function of 193 nm laser energy. The solid line is a linear regression. The experimental conditions were: 100 torr [N₂] and [HNO₃] = 1.1 × 10¹³ molecule cm⁻³.

The signal does not follow the expected quadratic dependence on laser energy for a two-photon process, but varies linearly, with a negative offset. This is a result of saturation of the first electronic transition due to the focused 193 nm radiation and the large absorption cross-section of HNO₃. The apparent, negative offset is a manifestation of non-linearity at low laser energy where the first transition is not yet saturated. Our energy dependence contrasts that reported by Winiberg et al.¹⁷ who observed a quadratic dependence on laser fluence. This difference is likely related to their use of much lower laser fluences (factor ∼15) and (potentially) a less focused laser beam.

A series of auxiliary experiments was conducted to examine the quenching of the fluorescence by N₂. The fluorescence signals, recorded for [HNO₃] = 5.0 × 10¹² molecule cm⁻³, at N₂ densities between 1.5 and 10 × 10¹⁷ molecule cm⁻³ (∼4 and ∼30 torr at 293 K), are displayed in the upper panel of Fig. 4.

Fig. 4 Upper panel: Time resolved fluorescence signal detected by the PMT through the (310 ± 5) nm interference filter following the 193 nm excitation of HNO₃. The black, solid lines correspond to fits using (E2). Lower panel: Fluorescence decay constant (τ_f) versus bath gas (N₂) concentration. The black solid line corresponds to a linear regression used for fitting τ_f. Error bars are 2σ statistical only.

Assuming that the fluorescence corresponds to the (0,0) transition from the OH(A) state we can write:

d[OH(A)]/dt = k_f + k_q(N₂)[N₂] + k_q(HNO₃)[HNO₃] (1)

where k_f is the fluorescence decay rate constant (s⁻¹) and is the inverse of the radiative lifetime, τ_f. k_q(N₂) is the quenching rate constant for N₂ bath gas, k_q(HNO₃) is the quenching rate constant for HNO₃ (k_q in units of cm³ molecule⁻¹ s⁻¹), [HNO₃] and [N₂] are the concentrations of HNO₃ and N₂ (both in molecule cm⁻³). The fluorescence profiles in Fig. 4 were fitted to eqn (E2), which is a convolution of a Gaussian function and a simple exponential decay:where S₀ is the signal intensity, α (s) is the width of the Gaussian function, β is the fluorescence decay lifetime in s and thus the reciprocal of the decay constant (τ_f), t₀ is the time (s) at the onset of the signal rise and erf is the error function. This equation allows us to account for the finite pulse width of the 193 nm excimer laser (∼20 ns), the response time for the PMT (∼20 ns) and the oscilloscope bandwidth (100 MHz) which result in non-instantaneous build-up of signal. The slope of the plot of τ_fversus [N₂] (lower panel of Fig. 4), is the quenching rate constant, here determined as k_q(N₂) = (1.1 ± 0.1) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹. This is in good agreement with the value of (1.3 ± 0.4) × 10⁻¹¹ cm³ molecule⁻¹ s⁻¹ reported by Kenner et al.¹⁴ for collisional deactivation of rotational levels N′ = 1–16 of the v′ = 0 state of OH(A) generated by the 193 nm excitation of HNO₃. It is approximately 3 times smaller than those derived from experiments in which OH(A, v′ = 0) was formed rotationally cold (N′ < 4)^30,31 and thus in qualitative agreement with previous observations that the electronic quenching rate coefficient decreases as the rotational level increases.^32,33

At an HNO₃ concentration of 5 × 10¹² molecule cm⁻³ and using the quenching rate constant reported by Kenner et al.¹⁴ of k_q(HNO₃) = 5.9 × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹, we calculate k_q(HNO₃)[HNO₃] ≈ 3000 s⁻¹ which thus represents a negligible contribution (<1%) to the intercept of (1.2 ± 0.1) × 10⁶ s⁻¹. The inercept can thus be equated to k_f and results in a radiative lifetime of about (840 ± 90) ns (errors are 2σ statistical). This value is somewhat larger than the natural fluorescence lifetime of (688 ± 21) ns³⁴ for the A²Σ(v′ = 0) → X²Π(v′′= 0) transition, indicating that the nascent OH(A²Σ(v′ = 1,2)) formed from 193 nm, two-photo excitation of HNO₃ undergoes vibrational energy transfer down to A²Σ(v′ = 0) on the same timescale as the fluorescence emission and the electronic quenching. This was confirmed by the observation of an increase in the signal intensity as the pressure was increased although [HNO₃] was kept constant.

3.2 Dispersed fluorescence spectrum of HNO₃

In Fig. 5 we display the emission spectrum (220 to 330 nm) obtained in the excitation of HNO₃ at 193 nm in He bath gas at 90 torr. The individual spectra for each ∼20 nm wide spectral region are the average of 2000 single spectra (obtained at 10 Hz) with a gate width (i.e. CCD exposure time) of 1 μs and were recorded 45 ns after the 193 nm laser pulse. The features are assigned to emission from excited OH and NO. Note that the final spectrum is not corrected for the wavelength dependent sensitivity of the detector or wavelength dependent transmission of either the monochromator or the optical fibre used. This will result in a positive bias to longer wavelength fluorescence and thus features such as the NO emission lines between 225 and 280 nm are stronger (relative to the OH(A) lines) than depicted in this figure. Under these experimental conditions, we were able to observe the OH(0,0) emission centred at 310 nm and emissions of vibrationally excited OH at ∼282 nm OH(1,0), ∼287 nm OH(2,1) and ∼315 nm OH(1,1).

Fig. 5 Fluorescence emission spectrum (black line) following excitation of 7 × 10¹³ molecule cm⁻³ HNO₃ in 90 torr He at 193 nm. The inset has an expanded y-scale showing NO fluorescence emission lines from 220 to 280 nm. The red line is a simulation (LIFBASE³⁵) of the relative line intensities for the OH A²Σ(v′ = 0,1,2) → X²Π(v′′= 0,1,2) transition using T_vib = 3200 K and T_rot = 700 K.

Using LIFBASE³⁵ we could approximately reproduce the measured OH fluorescence spectra with a vibrational temperature (T_vib) of ∼3200 K and a rotational temperature (T_rot) of ∼700 K. The former value is in qualitative agreement with Kenner et al.¹⁴ who also observed a high degree of vibrational excitation in OH and reported a vibrational temperature of 375 K.

The NO emission lines have been observed previously in the 193 nm excitation of HNO₃ and were thought to be the result of the excitation of NO₂, which was present as an impurity in the experiments of Papenbrock et al.¹² However, our measurement of the NO* fluorescence emission resulting from the excitation of NO₂ at 193 nm (see Fig. 6) showed that the intensities of the NO emission lines are much smaller than those observed in the excitation of similar amounts of HNO₃, which leads us to conclude that NO* is formed via 193 nm excitation of HNO₃ and not from NO₂ impurity.

Fig. 6 Upper panel: NO fluorescence emission spectrum following 193 nm excitation of NO with assignment to vibrational transitions from the A to X electronic states. Lower panel: As upper panel but following 193 nm NO₂ excitation. Experiments were carried out at ∼298 K and a bath gas-pressure of 60 torr (N₂) with [NO] = 3.0 × 10¹⁵ molecule cm⁻³ or [NO₂] = 2.4 × 10¹⁵ molecule cm⁻³. The 310 nm interference filter transmission curve (used for selective detection of emission from OH(A)) is represented by the dashed line.

Indeed, this additional channel, in which the co-product would be OH in its electronic ground state, is energetically feasible and has been proposed previously.³⁶ Recent work by Winiberg et al.¹⁷ also showed that NO(A) was observed from the two photon photolysis of HNO₃ at 248 nm.

3.3 TPEFS detection of selected NO_X and HO_X trace gases

In this section we discuss the relative detection sensitivity of TPEFS to HNO₃, NO and NO₂. The results are summarised in Table 1. As described above, the NO(A) emission lines seen when exciting HNO₃ samples at 193 nm may arise from the presence of impurities such as NO or NO₂. Here, we examine the relative detection sensitivity for NO and NO₂, identify the origin of these lines and assess the potential interference of NO and NO₂ whilst monitoring HNO₃ as OH(A).

Table 1 TPEFS sensitivity (S) to NO, NO₂, HO₂ and H₂O₂

	HNO3	NO	NO2	H2O2	HO2
a σ is the single-photon absorption cross-section at 193 nm (units of 10^−20 cm^2 molecule^−1). Detection sensitivity is relative to HNO3. Uncertainties are 2σ statistical only.
σ	1100^23	<0.001	29^37	61^23	390^38
S (N2)	10 000	(30 ± 10)	(50 ± 20)	—	<(3 ± 1)
S (air)	10 000	(5 ± 1)	—	(0.6 ± 0.2)
S (He)	10 000	<1	—	—

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For both NO and NO₂, we performed a series of experiments in different bath gases (N₂ and He) and with and without O₂ in order to assess the excitation mechanism at the origin of emission around 310 nm. To minimize HNO₃ interference from NO and NO₂ excitation spectra, we coated the gas line leading to the reactor with NaHCO₃. The removal of HNO₃ was confirmed by the non-observation of OH emission lines.

In experiments designed to investigate the kinetics of HNO₃ formation via the reaction between OH and NO₂ (Section 3.4) we used H₂O₂ as the photolytic source of OH. In these experiments, HO₂ was also formed and we therefore report the sensitivity (relative to HNO₃) of TPEFS to both HO₂ and H₂O₂.

The experiments on NO, NO₂, HO₂ and H₂O₂ are described in Sections 3.3.1–3.3.4, the results are summarized in Table 1.

3.3.1 NO emission spectrum. In Fig. 6 (upper panel), we present the dispersed NO fluorescence emission (recorded 45 ns after the 193 nm laser pulse) observed upon 193 nm excitation of NO in N₂. Vibronic transitions were assigned using LIFBASE.³⁵ In Fig. S1 (ESI†) we present absorption cross-sections (185–230 nm) of NO obtained at a spectral resolution of 0.16 nm (as derived from the measured full width (at half maximum) of the 253.65 nm line from a low-pressure Hg lamp). The spectrum was recorded at 19 torr of N₂ with [NO] = 3.1 × 10¹⁶ molecule cm⁻³ using a 10 cm absorption cell. In this wavelength range, the NO spectrum shows discrete transitions from the ground state to the A, B, C and D electronic states which were assigned using LIFBASE.³⁵ In Fig. S1 (ESI†), we also indicate the position of the 193 nm ArF laser pulse which lies between the NO absorption features centered around ∼191 nm and ∼195 nm, thus highlighting the lack of NO absorption at the excitation wavelength. At 193 nm, the single-photon absorption cross-section of NO is very low (see Table 1).

Shibuya and Stuhl³⁹ and Hack et al.⁴⁰ measured the dispersed fluorescence from a few mTorr of pure NO upon excitation with an ArF laser and reported that the emission (in the 200 to 300 nm range) arose mainly from the B²Π(v′ = 7) state, but identified weaker features from the adjacent A(v′ = 3) and C(v′ = 0) states. Shibuya and Stuhl hypothesized that at 193 nm the absorption arose from the transition from high rotational states (R₁₁, P₁₁, Q₁₁, R₂₂ and P₂₂) of the ground state (X²Π, v′′ = 0) to the B2 Π(v′ = 7) state.

Additionally, we measured the dependence of the NO fluorescence signal (as measured through the (310 ± 5) nm interference filter and PMT) as a function of the 193 nm laser energy, which is displayed in Fig. S2 (ESI†). There is a strictly proportional dependence of the NO fluorescence signal as a function of E_193nm, which (given the weak absorption of NO at this wavelength) may indicate that the process leading to NO fluorescence involves one photon.

In Fig. S3 (ESI†), we display a series of spectra showing the effect of changing bath gas (He to N₂) and of adding O₂ on the distribution of the NO emission lines upon 193 nm excitation of either NO or NO₂. All spectra were recorded at a total pressure of 65 torr with similar concentrations of either NO or NO₂ ([NO] = 2.6 × 10¹⁵ molecule cm⁻³, [NO₂] = 2.1 × 10¹⁵ molecule cm⁻³) and [O₂] = 4.0 × 10¹⁶ molecule cm⁻³. In Fig. S3a (ESI†) (NO₂ excitation) we observed that the fluorescence emission is ∼5 times more intense in He than in N₂ for the A(v′ = 0) → X vibrational series. For NO (Fig. S3b, ESI†), we also observed a stronger quenching effect of He relative to N₂ but observed that in He fluorescence was mainly from the A(v′ = 3) electronic state while in N₂ it was from the A(v′ = 0) state.

The relative intensity of the emission lines indicates that 85% of the vibrational population was located in the A(v′ = 3) state. The replacement of He with N₂ leads to the depopulation, through vibrational energy transfer, of the A(v′ = 3) electronic state to form A(v′ = 0, 1, 2). We did not observe any evidence of emission down from the B²Π(v′ = 7) state as reported previously^39,40 however it appears that under our pressure and bath gas conditions that the B²Π(v′ = 7) is quenched down to the observed A²Σ(v′ = 3) state in agreement with Hack et al.⁴⁰ We note that the quenching rate constants were reported to be larger for N₂ (see Settersen et al.⁴¹ and references therein) than for He.^42,43

In Fig. S3c to f (ESI†), we present spectra highlighting the strong O₂ quenching effect on NO fluorescence from both NO₂ and NO excitation.

We also examined the quenching of NO fluorescence (as measured by the PMT through the (310 ± 5) nm interference filter) by O₂. As shown in Fig. 6, in this wavelength window, NO fluorescence arises from NO A(v′ = 0, 1, 2, 3) emission to the ground state. In Fig. S4 (ESI†) we show the relative change in fluorescence intensity while the concentration of O₂ was varied from 0 to 4 × 10¹⁷ molecule cm⁻³ (in N₂ bath gas at a total pressure of 60 torr). From this we derive a quenching rate constant for O₂ of (1.5 ± 0.1) × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹, where the uncertainty is 2σ statistical only (more details in ESI†). This result is in excellent agreement with previous measurements which reported a quenching rate constant for O₂ of 1.5 × 10⁻¹⁰ cm³ molecule⁻¹ s⁻¹ (see Nee et al.⁴² and references therein) for NO (A, v′ = 0). Quenching rate constants were reported as being only weakly dependent on the vibrational level of the A state, with values of k_q within 30% for (A, v′ = 0, 1, 2, 3) for N₂ and O₂.⁴² Our experiments indicate that the numerous quenching rate constant determinations reported in the literature can reproduce our observations at 310 nm.

3.3.2 NO₂ emission spectrum. At 193 nm, the single-photon absorption cross-section of NO₂ is not accurately known with reported values ranging from 2.7 to 5.4 × 10⁻¹⁹ cm² molecule⁻¹,⁴⁴ the most recent measurement reported a cross-section of (2.9 ± 1.2) × 10⁻¹⁹ cm² molecule⁻¹ at this wavelength.⁴⁵

Excitation of NO₂ at 193 nm (6.42 eV) leads to its photo-dissociation to vibrationally excited, electronic ground-state NO(X ²Π) and both O(¹D) and O(³P)^37,46 as well as N(⁴S) and O₂.⁴⁷ As shown in Fig. 6 (lower panel), upon excitation of NO₂ at 193 nm, we observed fluorescence emission from NO(A²Σ⁺), as previously reported.⁴⁸

The energy thresholds for the formation of NO A²Σ⁺ and NO B²Π are 8.60 and 8.75 eV respectively.^49–51 Welge⁵² reported the formation of NO(A²Σ⁺ and B²Π) after exciting NO₂ to Rydberg states at 116.5 nm (10.64 eV), 123.6 nm (10.03 eV) and 129.5 nm (9.57 eV) but not at 147 nm (8.43 eV). This indicates that single-photon processes at 193 nm cannot explain the formation of NO(A²Σ⁺). On the other hand, simultaneous absorption of two-photons at 193 nm (12.84 eV) appears unlikely to be the source of NO(A²Σ⁺) as the ionization energy threshold for the formation of NO⁺ is only 12.38 eV.⁵¹ We conclude that a sequential, two-photon absorption mechanism involving a sufficiently long-lived intermediate state (i.e. similar to the formation of excited OH in the 2-photon photolysis of HNO₃) might be at the origin of the observed NO(A²Σ⁺) in NO₂ photolysis at 193 nm.

3.3.3 Relative TPEFS sensitivity of NO, NO₂ and HNO₃. Initial experiments indicated that the TPEFS detection of HNO₃ around 310 nm (i.e. non-dispersed fluorescence) was orders of magnitude more sensitive than for NO or NO₂. In order to extend the dynamic range to measure relative signals from NO, NO₂ and HNO₃ under the same settings (i.e. PMT voltage) we reduced the sensitivity (by a factor of 5.4) when monitoring signals from HNO₃ by adding a BG26 optical filter in front of the PMT and using concentrations of HNO₃ that were roughly 10 times smaller than those of NO and NO₂: [HNO₃] = 0.2–1.2 × 10¹³ molecule cm⁻³, [NO] = 2.1–9.9 × 10¹³ molecule cm⁻³, [NO₂] = 2.1–8.5 × 10¹³ molecule cm⁻³. Under these conditions, saturation of the signal at the PMT was avoided when using HNO₃ although the TPEFS signals observed were still roughly 100 times larger for HNO₃ than for NO and NO₂.

In Fig. 7, we present calibration curves in which TPEFS signals are plotted as a function of NO, NO₂ and HNO₃ concentrations.

Fig. 7 HNO₃ TPEFS signal (left y-axis) and NO and NO₂ TPEFS signal (right y-axis) as a function of concentration. These results were obtained in N₂ (62 torr) and at room temperature (298 ± 2 K).

Note that the right y-axis (for NO and NO₂ detection) is scaled by a factor 0.01 compared to that for HNO₃ (left y-axis). Concentrations of NO₂ and HNO₃ were obtained by in situ optical absorption (Section 2.2), whereas the concentration of NO was derived from the mixing ratio in the storage bulb, its dilution in bath gas and the total pressure. The solid-line fits to the data indicate a sensitivity for detection of NO relative to HNO₃ of (3 ± 1) × 10⁻³ in N₂. The values obtained in air and He were (5 ± 1) × 10⁻⁴ and <10⁻⁴, respectively.

The lower relative sensitivity in air compared to N₂ is readily explained by the more efficient quenching of O₂ on NO fluorescence than on OH fluorescence. It is also amplified by the very low quenching rate constant of NO fluorescence by N₂.⁴¹

In He, the TPEFS sensitivity to HNO₃ increased (compared to N₂) much more than it did for NO or NO₂. This forced us to reduce the PMT-voltage when monitoring HNO₃ whereby usable signals from NO and NO₂ were only obtained by adding much larger concentrations for which fluorescence self-quenching was an issue. In He we were thus unable to extend the dynamic range of the experiment to measure signals from HNO₃ and NO or NO₂ under the same conditions and we only report a lower limit of 10⁻⁴ to the relative sensivity.

In order to perform similar experiments on NO₂, we initially used diluted NO₂ samples. However, we found that a small but variable fraction (around 0.1–1%) of the NO₂ was converted to HNO₃ on the inlet and reactor surfaces. We therefore generated NO₂in situ in a pre-reactor by reacting NO with O₃. The latter, at a concentration of 1.0 × 10¹³ molecule cm⁻³, was generated by the photolysis of O₂ at 185 nm using a Hg lamp.

The conversion of NO to NO₂ was 92 to 95%. We thus obtained a relative detection efficiency (in N₂) of NO₂ compared to HNO₃ of (5 ± 3) × 10⁻³.

3.3.4 Detection of H₂O₂. The single-photon cross-section of H₂O₂ at 193 nm is 6.1 × 10⁻¹⁹ cm² molecule⁻¹. ²³ In a series of experiments in 50 torr N₂ at ∼298 K we observed a linear dependence of the TPEFS signal on the H₂O₂ concentration (varied from 0.11 to 1.1 × 10¹⁶ molecule cm⁻³) as shown in Fig. S5 (ESI†). The TPEFS detection sensitivity of H₂O₂ relative to that of HNO₃ of was found to be (6 ± 2) × 10⁻⁵, where the uncertainty is 2σ statistical only.

Previous studies on the VUV photolysis of H₂O₂^53–56 indicate that OH, H and O-atoms are formed:

H₂O₂ + hν → 2 OH(X²Π) (R3a)

→ OH(X²Π) + OH(X² Π, v′′ > 0) (R3b)

→ H(²S) + HO₂ (R3c)

→ H₂O + O(³P) (R3d)

→ H₂O + O(¹D) (R3e)

→ H₂O + O(¹S) (R3f)

At λ < 198 nm excitation, the main dissociation pathways lead to two OH (R5a and R5b) and to H(²S) atom and HO₂ (R5c). At 193 nm, the yields for the OH + OH channel (R5a) and the H + HO₂ (R5c) are 0.8 and 0.2, respectively and an upper limit of 0.15 was given for the formation of vibrationally excited OH(X² Π, v′′ > 0) (R5b).⁵⁴ The yields of O-atoms are very low with upper limits of 0.001 for O(³P) + O(¹D) and 0.02 for O(¹S) channels. OH(A) is formed at wavelength below 172 nm.⁵⁷

Formation of OH(A), has however been observed in the two-photon excitation of H₂O₂ at 193 nm^58,59 which, via analysis of the state resolved internal distribution of OH(A), was demonstrated to originate from a resonant, 2-photon sequential absorption process.

3.3.5 Detection of HO₂. HO₂ was formed in the 248 nm photolysis of H₂O₂ whereby the initially formed OH radicals were converted to HO₂ in (R4).

OH + H₂O₂ → HO₂ + H₂O (R4)

The sensitivity for detection of HO₂ at 193 nm was examined in 60 torr of N₂ with [H₂O₂] = 2.4 × 10¹⁵ molecule cm⁻³. The photon density at 248 nm was measured using a calibrated Joulemeter as 6.8 × 10¹⁶ photon cm⁻². Under these conditions, ∼1.6 × 10¹³ molecule cm⁻³ of HO₂ were generated. The observed TPEFS signal was modelled as the sum of the signals originating directly from H₂O₂ and from HO₂ formed in R4. The kinetic model included R4 and R5 with diffusion coefficients for OH and HO₂ set to 30 s⁻¹. In Fig. S6 (ESI†), we show the signal expected when assuming that HO₂ was not detected. The slight depletion in signal at time = zero is explained by the loss of H₂O₂ by photolysis (∼1.5%) and in the subsequent OH + H₂O₂ reaction. From this data we were only able to report an upper limit HO₂ detection sensitivity (relative to HNO₃) of (3.2 ± 1.2) × 10⁻⁴ (2σ statistical only, including a 15% uncertainty on the photon density).

3.4 Rate coefficient for the OH + NO₂ reaction

Rate coefficients for OH + NO₂ were measured by both conventional pulsed laser photolytic formation of OH with its detection in real time by laser induced fluorescence (PLP-LIF, with 282 nm excitation of OH and PLP-TPEFS with 193 nm excitation for detection of the HNO₃ product).

OH radicals were generated either in the 248 nm photolysis of H₂O₂ (R5) or by the 248 nm photolysis of O₃ in the presence of H₂O (R6 and R7).

H₂O₂ + hv→ 2 OH (R5)

O₃ + hv → O(¹D) + O₂ (R6)

O(¹D) + H₂O → 2 OH (R7)

The concentrations used were [H₂O₂] ∼1 × 10¹⁴ molecule cm⁻³, [O₃] = (2–7) × 10¹³ molecule cm⁻³ and [H₂O] = (1.5–6.0) × 10¹⁶ molecule cm⁻³ (corresponding to a mixing ratio of ∼4.2% at the total pressure of 50 to 200 torr, see Table 2). Using a laser-fluence of ∼50 mJ cm⁻², 1–3 × 10¹² molecule cm⁻³ [OH] were generated per pulse such that the experiments were conducted under pseudo-first order conditions (i.e. [NO₂] ≫ [OH]).

Table 2 Determination of k₂ in air

Pressure (torr)	H2O (%)	k 2 (10^−12 cm^3 molecule^−1 s^−1)
a OH LIF measurement. Errors are 2σ statistical only.
O3/H2O as OH precursor
50	4.5	(3.2± 0.7)
100	4.1	(4.5± 0.4)
150	3.8	(5.7± 0.8)
200	4.5	(6.6± 0.3)
H2O2 as OH precursor
50	0	(2.3± 0.3)
100	0	(3.9± 0.3)
100	0	(4.0± 0.1)^a

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We observed that small amounts of NO₂ (<0.1%) were converted into HNO₃ on the surfaces of the reactor adding a background signal to the kinetics profile. The effect became more pronounced when water vapour was added to the reactor where as much as a few percent of NO₂ were converted to HNO₃. We note that the build-up of background HNO₃ occurred on a longer time scale (∼2–3 hours) than the time necessary to gather the data necessary to derive a rate constant for one particular set of conditions. However, it did prevent conducting a long-time series of measurements (e.g. over the course of a day) as the background became too large and the reactor cell needed to be flushed with dry N₂ for several hours to return to favourable conditions. The use of NaHCO3 to coat the surface was impractical in these experiments as its efficiency to remove HNO₃ also changed over time.

In both schemes, OH is generated quasi-instantaneously compared to its loss rate and the time profiles for OH loss and HNO₃/HOONO production in the cell are then given by:

[OH]_t = [OH]₀ exp(−[k₂[NO₂] + d_OH]t) (3)

[HNO₃]_t = αC(exp(−d_HNO3t) − exp(−[k₂[NO₂] + d_OH]t)) (4)

[HOONO]_t = (1 − α)C(exp(−d_HOONOt) − exp(−[k₂[NO₂] + d_OH]t)) (5)

where k₂ is the rate coefficient for reaction (R2), d_OH and d_HNO3 are first-order rate constants (s⁻¹) for the diffusive loss of OH and HNO₃ from the reaction volume, respectively and C is equal to [OH]₀(k₂[NO₂] + d_OH)/(k₂[NO₂] + d_OH + d_HNO3). We do not know if TPEFS detects HOONO but note that, to a very good approximation, the first-order constant for formation of HOONO will be the same as for HNO₃ as both are very long-lived compared to the time-scale of the decay of OH. Only the absolute concentrations of HNO₃ and HOONO are defined by the branching ratio and thus the kinetic parameters would not be impacted whether HOONO is detected or not.

The pseudo-first-order loss rate coefficient for OH is:

k₂′ = k₂[NO₂] + d_OH (6)

Experiments to derive k₂ were carried out at room temperature and at a number of different pressures of air (50–200 torr) using the two different OH precursors described above. We worked in air rather than in N₂ as this improves the relative sensitivity to HNO₃ compared to NO₂.

Fig. 8 shows time profiles for both OH decay (upper panel) and HNO₃ production (lower panel) obtained for the same chemical system using H₂O₂ as a precursor. The HNO₃ TPEFS signals displayed were accumulated for 40 scans (∼10 min) while OH LIF signal were accumulated for 25 scans (∼5 min). The profiles were obtained by computer-controlled variation of the delay-time between the 248 nm excimer laser pulse (generating OH at time zero) and either the 282 nm laser exciting OH or the 193 nm excimer-laser exciting HNO₃.

Fig. 8 Time dependent signals from OH (upper panel, LIF) and HNO₃ (lower panel, TPEFS) obtained in measurements at 100 torr of air using H₂O₂ as a OH precursor. The solid lines are fits to the OH (eqn (3)) and HNO₃ signals (eqn (4)). The reaction time for the HNO₃ formation datasets was adjusted (i.e. shorter at high [NO₂]) to get sufficient datapoints in the early part of the profile.

The pseudo first-order rate coefficients, k₂′, were obtained by fitting the observed time profiles to eqn (3) and (4) for OH loss and HNO₃ production, respectively. The bimolecular rate coefficients were then obtained by plotting k₂′ against [NO₂] as shown in Fig. 9, which displays data from an experiment at a total pressure of 100 torr of air whereby [NO₂] was varied between 0.5 and 3 × 10¹⁴ molecule cm⁻³.

Fig. 9 Plot of k^′₂versus [NO₂] for the reaction (R2) of OH with NO₂ at 100 torr of air using H₂O₂ as OH precursor. The solid lines represent a linear regression returning k₂ = (4.0 ± 0.1) × 10⁻¹² cm³ molecule⁻¹ s⁻¹ using OH detection by LIF (red line) and k₂ = (3.9 ± 0.3) × 10⁻¹² cm³ molecule⁻¹ s⁻¹ using HNO₃ detection by TPEFS (black line). Error bars are 2σ statistical only.

The values of k₂ obtained from the slopes of least-squares fits to these datasets are (4.0 ± 0.1) and (3.9 ± 0.3) × 10⁻¹² cm³ molecule⁻¹ s⁻¹, respectively.

Fig. 10 shows the measured rate coefficients as a function of pressure along with fall-off expression (see the ESI†) used to parameterize data recently measured in this laboratory.^19,20

Fig. 10 Upper panel: Measurement of k₂ for the OH reaction with NO₂ in air using 248 nm photolysis of H₂O₂ as a OH precursor and either TPEFS detection of HNO₃ or conventional LIF detection of OH. The solid red line is a fall-off parameterisation (see ESI†). Lower panel: Measurement of k₂ for the OH reaction with NO₂ in air using 248 nm photolysis of O₃–H₂O to generate OH. The solid red line is a fall-off parameterization (see the ESI†) using a mixing ratio for H₂O of 4.2% while the solid black line corresponds to the same parametrisation in dry air.

The results displayed in the upper panel of Fig. 10 indicate that the rate coefficients obtained using detection of HNO₃ using TPEFS are in excellent agreement (better than 10%) with that obtained using OH-LIF and also with the parameterisation presented in our previous, comprehensive study (using OH-LIF). The lower panel indicates that larger rate coefficients are obtained when using O₃/H₂O as OH-precursor. This observation is entirely consistent with the enhancement of k₂ in the presence of H₂O described in detail by Amedro et al.¹⁹ and the parameterisation of k₂ presented by those authors (red line). Note that the overall aim of the kinetic investigations described in Section 3.4 was not to strengthen the database on the OH + NO₂ reaction, but to show that time resolved detection of HNO₃ by TPEFS can be used to derive accurate rate coefficients. For more details about the OH reaction with NO₂ rate constants measurements, including an extended comparison with previous works and a newly developed parametrization, we invite the interested reader to view our previous studies.^19,20 We are unaware of any reason why TPEFS detection of HNO₃ could not be extended to kinetic studies at e.g. different temperatures.

4. Conclusions

We have characterized the detection of HNO₃ using TPEFS as part of a study to assess its viability for detection of HNO₃ in real-time (e.g. pulsed laser) kinetic studies. We have shown that detection of HNO₃ (via OH(A) emission at ∼310 nm is orders of magnitude more sensitive than detection NO or NO₂ (via NO* emission) at the same wavelength, especially in air where the quenching of NO fluorescence is most efficient owing to the presence of O₂. As a test case, we have used TPEFS for real-time detection of HNO₃ in the reaction between OH and NO₂. The rate constant obtained (293 K, 50–200 torr) is entirely consistent with that obtained by simultaneously measuring the OH decay and is in very good agreement with the most recent literature values.

Author contributions

DA, TD and JC set up the apparatus, DA, TD and AB performed the experiments. DA analysed the data. JC conceptualised the experiments and helped DA write the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

We thank the Deutsche Forschungsgemeinschaft (DFG) for partial financial support of this research (CR 246/2-1). Open Access funding provided by the Max Planck Society.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1cp00297j

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