Production of HONO from NO₂ uptake on illuminated TiO₂ aerosol particles and following the illumination of mixed TiO₂∕ammonium nitrate particles

The rate of production of HONO from illuminated TiO₂ aerosols in the presence of NO₂ was measured using an aerosol flow tube system coupled to a photo-fragmentation laser-induced fluorescence detection apparatus. The reactive uptake coefficient of NO₂ to form HONO, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, was determined for NO₂ mixing ratios in the range 34–400 ppb, with ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ spanning the range (9.97 ± 3.52) × 10⁻⁶ to (1.26 ± 0.17) × 10⁻⁴ at a relative humidity of 15 ± 1 % and for a lamp photon flux of (1.63 ± 0.09) ×10¹⁶ photons cm⁻² s⁻¹ (integrated between 290 and 400 nm), which is similar to midday ambient actinic flux values. ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ increased as a function of NO₂ mixing ratio at low NO₂ before peaking at (1.26 ± 0.17) $\times {\mathrm{10}}^{-\mathrm{4}}$ at ∼ 51 ppb NO₂ and then sharply decreasing at higher NO₂ mixing ratios rather than levelling off, which would be indicative of surface saturation. The dependence of HONO production on relative humidity was also investigated, with a peak in production of HONO from TiO₂ aerosol surfaces found at ∼ 25 % RH. Possible mechanisms consistent with the observed trends in both the HONO production and reactive uptake coefficient were investigated using a zero-dimensional kinetic box model. The modelling studies supported a mechanism for HONO production on the aerosol surface involving two molecules of NO₂, as well as a surface HONO loss mechanism which is dependent upon NO₂. In a separate experiment, significant production of HONO was observed from illumination of mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ aerosols in the absence of NO₂. However, no production of HONO was seen from the illumination of nitrate aerosols alone. The rate of production of HONO observed from mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ aerosols was scaled to ambient conditions found at the Cape Verde Atmospheric Observatory (CVAO) in the remote tropical marine boundary layer. The rate of HONO production from aerosol particulate nitrate photolysis containing a photocatalyst was found to be similar to the missing HONO production rate necessary to reproduce observed concentrations of HONO at CVAO. These results provide evidence that particulate nitrate photolysis may have a significant impact on the production of HONO and hence NO_x in the marine boundary layer where mixed aerosols containing nitrate and a photocatalytic species such as TiO₂, as found in dust, are present.

1 Introduction

A dominant source of OH radicals in polluted environments is the photolysis of nitrous acid (HONO) (Platt et al., 1980; Winer and Biermann, 1994; Harrison et al., 1996; Alicke et al., 2002; Whalley et al., 2018; Crilley et al., 2019; Lu et al., 2019; Slater et al., 2020; Whalley et al., 2021). During a recent study in winter in central Beijing, HONO photolysis accounted for over 90 % of the primary production of OH averaged over the day (Slater et al., 2020). Oxidation by OH radicals is the dominant removal mechanism for many tropospheric trace gases, such as tropospheric methane, as well as the formation of secondary species, including tropospheric ozone (Levy, 1971), nitric and sulfuric acids which condense to form aerosols, and secondary organic aerosols. Understanding the formation of HONO in highly polluted environments is crucial to fully understand both the concentration and distribution of key atmospheric radical species, as well as secondary products in the gas and aerosol phases associated with climate change and poor air quality.

Atmospheric concentrations of HONO range from a few parts per trillion by volume (pptv) in remote clean environments (Reed et al., 2017) to more than 10 ppb in highly polluted areas such as Beijing (Crilley et al., 2019). The main gas-phase source of HONO in the troposphere is the reaction of nitric oxide (NO) with the OH radical. HONO has also been shown to be directly emitted from vehicles (Kurtenbach et al., 2001; Li et al., 2008), for which the rate of emission is often estimated as a fraction of known NO_x (NO₂+NO) emissions. Many heterogeneous HONO sources have also been postulated, including the conversion of nitric acid (HNO₃) on ground or canopy surfaces (Zhou et al., 2003; George et al., 2005), bacterial production of nitrite on soil surfaces (Su et al., 2011; Oswald et al., 2013), and, more recently, particulate nitrate photolysis, thought to be an important source in marine environments (Ye et al., 2016; Reed et al., 2017; Ye et al., 2017a, b). Rapid cycling of gas-phase nitric acid to gas-phase nitrous acid via particulate nitrate photolysis in the clean marine boundary layer has been observed during the 2013 NOMADSS aircraft measurement campaign over the North Atlantic Ocean (Ye et al., 2016). Ground-based measurements of HONO made at Cabo Verde in the tropical Atlantic Ocean (Reed et al., 2017) provided evidence that a mechanism for renoxification in low-NO_x areas is required (Reed et al., 2017; Ye et al., 2017a).

Recent model calculations show a missing daytime source of HONO, which is not consistent with known gas-phase production mechanisms, direct emissions or dark heterogeneous formation (e.g. prevalent at night). It has been suggested that this source could be light driven and dependent on NO₂ (Kleffmann, 2007; Michoud et al., 2014; Spataro and Ianniello, 2014; Lee et al., 2016).

It is estimated that between 1604 and 1960 Tg yr⁻¹ of dust particles are emitted into the atmosphere (Ginoux et al., 2001). Titanium dioxide (TiO₂) is a photocatalytic compound found in dust particles at mass mixing ratios of between 0.1 % and 10 % depending on the location where the particles were suspended (Hanisch and Crowley, 2003). When exposed to UV light (λ < 390 nm) TiO₂ promotes an electron ($e_{\mathrm{CB}}^{-}$) from the conduction band to the valence band, leaving behind a positively charged hole ($h_{\mathrm{VB}}^{+}$) in the valence band (Chen et al., 2012):

$$\begin{array}{}\text{(R1)}& {\mathrm{TiO}}_{\mathrm{2}}+h\mathit{\nu }\to e_{\mathrm{CB}}^{-}+h_{\mathrm{VB}}^{+},\end{array}$$

which can then lead to both reduction and oxidation reactions of any surface-adsorbed gas-phase species such as NO₂ leading to HONO.

In previous studies of the reaction of NO₂ on TiO₂ aerosol surfaces, HONO was observed as a major gas-phase product (Gustafsson et al., 2006; Dupart et al., 2014). Gustafsson et al. (2006) observed a yield of gas-phase HONO of ∼ 75 % (for each NO₂ removed) and showed the rate of the photoreaction of NO₂ on pure TiO₂ aerosols dependent on relative humidity, emphasising the superhydrophilic nature of TiO₂ surfaces under UV irradiation. Dupart et al. (2014) also reported a relative humidity dependence of the uptake of NO₂ onto Arizona test dust containing TiO₂, with the main gas-phase products measured being NO and HONO, with a HONO yield of 30 % in experiments with 110 ppb NO₂. Dupart et al. (2014) postulated the following mechanism of HONO production, which is consistent with the formation of the NO${}_{\mathrm{2}}^{-}$ anion seen in a previous study on TiO₂ surfaces (Nakamura et al., 2000):

$$\begin{array}{}\text{(R2)}& {\displaystyle }{\mathrm{h}}_{\mathrm{VB}}^{+}+{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\to {\mathrm{H}}^{+}+\mathrm{OH},\text{(R3)}& {\displaystyle }{e}_{\mathrm{CB}}^{-}+{\mathrm{O}}_{\mathrm{2}}\to {\mathrm{O}}_{\mathrm{2}}^{-},\text{(R4)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}}^{-}\left(\text{or}{e}_{\mathrm{CB}}^{-}\right)\to {\mathrm{NO}}_{\mathrm{2}}^{-}+{\mathrm{O}}_{\mathrm{2}},\text{(R5)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}^{-}+{\mathrm{H}}^{+}\to \mathrm{HONO},\text{(R6)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{2}}+\mathrm{OH}\to {\mathrm{HNO}}_{\mathrm{3}}.\end{array}$$

In areas with high mineral dust loading, such as desert regions, far from anthropogenic sources, NO₂ concentrations are typically low. However, when dust is transported to urban areas, this source of HONO may become significant. One study reported that TiO₂ composed 0.75–1.58 µg m⁻³ when aerosol loadings were 250–520 µg m⁻³ over the same time period in southeast Beijing, when air had been transported from the Gobi desert (Schleicher et al., 2010).

In this study, the production of HONO on the surface of TiO₂ particles in the presence of NO₂ is investigated as a function of NO₂ mixing ratio, aerosol surface area density and relative humidity using an aerosol flow tube system coupled to a photo-fragmentation laser-induced fluorescence detector (Boustead, 2019). The uptake coefficient of NO₂ to generate HONO is then determined, and a mechanistic interpretation of the experimental observations is presented. The production of HONO directly in the absence of NO₂ from the illumination of a mixed sample of nitrate and TiO₂ aerosol is also presented. Using a similar apparatus, previous work had showed that TiO₂ particles produce OH and HO₂ radicals directly under UV illumination (Moon et al., 2019). The atmospheric implications of these results and the role of photocatalysts for the formation of HONO are also discussed.

2 Method

2.1 Overview of the experimental setup

The production of HONO from illuminated aerosol surfaces is studied using an aerosol flow tube system coupled to a photo-fragmentation laser-induced fluorescence (PF-LIF) cell which allows the highly sensitive detection of the OH radical formed through photo-fragmentation of HONO into OH and NO followed by laser-induced fluorescence (LIF) detection at low pressure. The experimental setup used in this investigation is described in detail in Boustead (2019), as well as similar systems having been used to measure HONO in the field (Liao et al., 2006; Wang et al., 2020), and therefore only a brief description of the setup is given here. A schematic of the experimental setup is shown in Fig. 1.

Figure 1 Schematic of the Leeds aerosol flow tube system coupled to a laser-fragmentation laser-induced fluorescence detector for HONO. The paths of the 355 nm (blue) and 308 nm (purple, depicted as travelling out of the page perpendicular to the 355 nm light) light are also shown. CPC: condensation particle counter; DMA: differential mobility analyser; HEPA: high-efficiency particle air filter; FAGE: fluorescence assay by gas expansion; MCP: microchannel plate photomultiplier; MFC: mass flow controller; RH/T: relative humidity/temperature probe; SMPS: scanning mobility particle sizer.

All experiments were conducted at room temperature (295 ± 3 K) using nitrogen (BOC, 99.998 %) or air (BOC, 21 ± 0.5 % O₂) as the carrier gas. A humidified flow of aerosols, ∼ 6 L min⁻¹ (total residence time of 104 s in the flow tube), was introduced through an inlet at the rear of the aerosol flow tube (Quartz, 100 cm long, 11.5 cm i.d.), which was covered by a black box to eliminate the presence of room light during experiments. A 15 W UV lamp (XX-15LW bench lamp, λ_peak=365 nm) was situated on the outside of the flow tube to illuminate aerosols and promote the production of HONO (half the length of the flow tube was illuminated, leading to an illumination time of 52 s). The concentration of HONO is measured by PF-LIF with sampling from the end of the flow tube via a protruding turret containing a 1 mm diameter pinhole, through which the gas exiting the flow tube was drawn into the detection cell at 5 L min⁻¹. The detection cell was kept at low pressure, ∼ 1.5 Torr, using a rotary pump (Edwards, E1M80) in combination with a roots blower (Edwards, EH1200). All gas flows in the experiment were controlled using mass flow controllers (MKS and Brooks). The relative humidity (RH) and temperature of the aerosol flow was measured using a probe (Rotronics HC2-S, accuracy ±1 % RH) the former calibrated against the H₂O vapour concentration measured by a chilled mirror hygrometer (General Eastern Optica) in the exhaust from the flow tube.

2.2 Aerosol generation and detection

Solutions for the generation of TiO₂ aerosol solutions were prepared by dissolving 5 g of titanium dioxide (Aldrich Chemistry 718467, 99.5 % Degussa, 80 % anatase : 20 % rutile) into 500 mL of Milli-Q water. Polydisperse aerosols were then generated from this solution using an atomiser (TSI model 3076), creating a 1 L min⁻¹ flow of TiO₂ aerosol particles in nitrogen hereafter referred to as the aerosol flow. This aerosol flow was then passed through a silica drying tube (TSI 3062, capable of reducing 60 % RH incoming flow to 20 % RH) to remove water vapour and then passed through a neutraliser to apply a known charge distribution and reduce loss of aerosols to the walls. After the neutraliser the aerosol flow was mixed with both a dry and a humidified N₂ flow (controlled by mass flow controllers) to regulate the relative humidity of the system by changing the ratio of dry to humid nitrogen flows. A conditioning tube was then used to allow for equilibration of water vapour adsorption and re-evaporation to and from the aerosol surfaces for the chosen RH, which was controlled within the range ∼ 10 %–70 % RH. A portion of the aerosol flow was then passed through a high-efficiency particle filter (HEPA) fitted with a bypass loop and bellows valve allowing control of the aerosol number concentration entering the aerosol flow tube. Previous studies (George et al., 2013; Boustead, 2019) have shown the loss of aerosol to the walls of the flow tube to be negligible. Aerosol size distributions were measured for aerosols exiting the flow tube using a scanning mobility particle sizer (SMPS, TSI 3081) and a condensation particle counter (CPC, TSI 3775) which was calibrated using latex beads. Any aerosol surface area not counted due to the upper diameter range of the combined SMPS/CPC (14.6–661.2 nm, sheath flow of 3 L min⁻¹, instrumental particle counting error of 10 %–20 %) was corrected for during analysis by assuming a log-normal distribution, which was verified for TiO₂ aerosols generated in this manner (Matthews et al., 2014). However, the majority of aerosols, > 90 %, had diameters in the range that could be directly detected. In addition to the experiments with single-component TiO₂, mixed ammonium $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ and single-component ammonium nitrate aerosols were also generated using the atomiser for investigations of HONO production from nitrate aerosols without NO₂ present. An example of an aerosol size distribution from this work for single-component ammonium nitrate aerosols, mixed ammonium $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ and single-component TiO₂ aerosols is shown in Fig. 2.

Figure 2 Typical aerosol surface area distribution for pure ammonium nitrate aerosols (green) and pure TiO₂ aerosols (red) and 50:50 mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ aerosols (purple) measured after the flow tube.

2.3 Detection of HONO

As HONO is not directly detectable via LIF, it was necessary to fragment the HONO produced into OH and NO (Liao et al., 2007), with detection of OH via LIF. A 355 nm photolysis laser (Spectron Laser Systems, SL803) with a pulse repetition frequency (PRF) of 10 Hz and pulse duration ∼ 10 ns was used to fragment HONO into OH. This fragmentation wavelength was chosen as HONO has a strong absorption peak at ∼ 355 nm, leading to the breakage of the HO–NO bond to form NO and OH in their electronic ground states (Shan et al., 1989). A Nd:YAG pumped dye probe laser (JDSU Q201-HD, Q series, Sirah Cobra Stretch) with a PRF of 5000 Hz was used for the detection of OH via the fluorescence assay by gas expansion (FAGE) technique, which employs the expansion of gas through a small pinhole into the detection cell. The OH radical was measured using on-resonance detection by LIF via the excitation of the A²Σ⁺ (${\mathit{\nu }}^{\prime }=\mathrm{0}$) ←X²Π_i (${\mathit{\nu }}^{\prime \prime }=\mathrm{0}$) Q₁(2) transition at 308 nm (Heard, 2006). A multi-channel plate (MCP) photomultiplier (Photek, MCP 325) equipped with an interference filter at 308 nm (Barr Associates, 308 nm, FWHM – 8 nm, ∼ 50 % transmission) was used to measure the fluorescence signal. A reference OH cell in which a large LIF signal could be generated was utilised to ensure the wavelength of the probe laser remained tuned to the peak of the OH transition at 308 nm. OH measurements are taken both before and after each photolysis laser pulse, allowing measurement of any OH already present in the gas flow to be determined as a background signal for subtraction. The OH generated from HONO photolysis was measured promptly (∼ 800 ns) after the 355 nm pulse to maximise sensitivity to OH before it was spatially diluted away from the measurement region (Boustead, 2019). Offline measurements, with the probe laser wavelength moved away from the OH transition (by 0.02 nm), were taken to allow the signal generated from detector dark counts and scattered laser light to be measured and subtracted from the online signal. To determine an absolute value of the HONO concentration, [HONO], a calibration was performed, in order to convert from the HONO signal, S_HONO, using S_HONO=C_HONO [HONO], as described fully in Boustead (2019). A glass calibration wand was used to produce OH and HO₂ in equal concentrations from the photolysis of water vapour at 185 nm:

$$\begin{array}{}\text{(R7)}& {\displaystyle }{\mathrm{H}}_{\mathrm{2}}\mathrm{O}+h\mathit{\nu }\stackrel{\mathit{\lambda }=\mathrm{185}\mathrm{nm}}{⟶}\mathrm{OH}+\mathrm{H},\text{(R8)}& {\displaystyle }\mathrm{H}+{\mathrm{O}}_{\mathrm{2}}+M\to {\mathrm{HO}}_{\mathrm{2}}+M.\end{array}$$

An excess flow of NO was then added to generate HONO, which was then detected as OH in the cell. The excess flow of NO (BOC, 99.5 %) ensures rapid and complete conversion of OH and HO₂ to HONO. The concentration of OH and HO₂ produced, and therefore the amount of HONO produced in the wand, is calculated using

$$\begin{array}{}\text{(1)}& \left[\mathrm{OH}\right]=\left[{\mathrm{HO}}_{\mathrm{2}}\right]=\left[{\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right]{\mathit{\sigma }}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}{\mathit{\varphi }}_{\mathrm{OH}}Ft,\end{array}$$

where [H₂O] is the concentration of water vapour in the humidified gas flow, ${\mathit{\sigma }}_{{\mathrm{H}}_{\mathrm{2}}\mathrm{O}}$ is the absorption cross section of H₂O at 185 nm 7.14 × 10⁻²⁰ cm² molec.⁻¹ (Cantrell et al., 1997), ϕ_OH is the quantum yield of OH for the photo-dissociation of H₂O at 185 nm (=1), F is the lamp flux and t is the irradiation time (the product of which is determined using ozone actinometry (Boustead, 2019).

A typical value of the calibration factor was $C_{\mathrm{HONO}}=(\mathrm{3.63}\pm \mathrm{0.51})\times {\mathrm{10}}^{-\mathrm{9}}$ counts mW⁻¹ for N₂, leading to a calculated limit of detection of 12 ppt for a 50 s averaging period and a signal-to-noise ratio (SNR) of 1 (Boustead, 2019). The typical error in the HONO concentration was 15 % at 1σ, determined by the error in the calibration.

2.4 Experimental procedure and data analysis

The experiments were performed with a minimum flow of 6 L min⁻¹ through the aerosol flow tube, giving a Reynolds number of ∼ 150, which ensured a laminar flow regime. The HONO signal, converted to an absolute concentration using a calibration factor, was measured over a range of aerosol surface area densities, both in the presence and absence of illumination, and background measurements without aerosols present were also performed.

The HONO signal originates from several sources: the illuminated aerosol surface, the illuminated quartz flow tube walls, dark reactions on aerosol surfaces, dark reactions on the flow tube surface, and finally from impurities in the NO₂ (Sigma Aldrich, > 99.5 %, freeze pump thawed to further remove any remaining NO or O₂) and N₂ flows (either HONO itself or a species which photolyses at 355 nm to give OH). Of interest here is the HONO production from both dark and illuminated aerosol surfaces which is atmospherically relevant. Following transit through the flow tube, and in the presence of NO₂, the total concentration of HONO measured by the PF-LIF detector is given by

$$\begin{array}{}\text{(2)}& \begin{array}{rl}& \left[\mathrm{HONO}\right]={\left[\mathrm{HONO}\right]}_{\text{illuminated\hspace{0.17em} aerosols}}\\ & +[\mathrm{HONO}{]}_{\text{illuminated walls}}+[\mathrm{HONO}{]}_{\text{dark aerosols}}\\ & +[\mathrm{HONO}{]}_{\text{dark walls}}+[\mathrm{HONO}{]}_{\text{impurities}}.\end{array}\end{array}$$

Any HONO seen without the presence of aerosol was therefore due to HONO impurities in the N₂ or NO₂ gas, the dark production of HONO from the flow tube walls or from the production of HONO from the illuminated reactor walls, which may include production from TiO₂ aerosols coating the flow tube in the presence of NO₂. This background HONO concentration depended on the experimental conditions and on how recently the flow tube and PF-LIF cell had been cleaned to remove any build-up of TiO₂ deposits. However, the build-up of TiO₂ on the flow tube walls was relatively slow, and back-to-back measurements were made in the presence and absence of aerosols to obtain an accurate background. Additional experiments showed no significant production of HONO on TiO₂ aerosol surfaces without the presence of NO₂. Even though the aerosol surface area density (∼ 0.02 m² m⁻³) was small compared to the surface area density of the reactor walls (35 m² m⁻³), very little HONO signal was produced without the presence of aerosols and was always subtracted from the signal in the presence of aerosols. The HONO signal was measured both with the lamp on and off for each aerosol surface area density to investigate the production of HONO from illuminated aerosol surfaces. The HONO signal was averaged over 50 s (average of 500 of the 355 nm photolysis laser pulses with a PRF of 10 Hz). Once aerosols were introduced into the flow tube system, a period of ∼ 30 min was allowed for equilibration and the measured aerosol surface area density to stabilise. In general, the relative humidity of the system was kept constant at RH ∼ 15 % for all experiments investigating HONO production as a function of NO₂ mixing ratio over the range 34–400 ppb. In a number of experiments, however, RH was varied in the range ∼ 12 %–37 %.

The mixing ratio of NO₂ entering the flow tube was calculated using the concentration of the NO₂ in the cylinder and the degree of dilution. The NO₂ mixing ratio within the cylinder was determined using a commercial instrument based on UV–Vis absorption spectroscopy (Thermo Fisher 42TL, limit of detection 50 pptv, precision 25 pptv). For each individual experiment, the mixing ratio of NO₂ was kept constant (within the range 34–400 ppb), and the aerosol surface area density was varied from zero up to a maximum of 0.04 m² m⁻³, in order to obtain the HONO produced from illuminated aerosol surfaces in the flow tube for a given mixing ratio of NO₂. As well as subtraction of any background HONO, a correction must be made for any loss of HONO owing to its photolysis occurring within the flow tube.

In order to determine the rate of photolysis of HONO, the rate of photolysis of NO₂ was first determined using chemical actinometry, and the known spectral output of the lamp and the literature values of the absorption cross sections and photo-dissociation quantum yields for NO₂ and HONO were used to determine the rate of photolysis of HONO. When just flowing NO₂ in the flow tube, the loss of NO₂ within the illuminated region is determined only by photolysis and is given by

$$\begin{array}{}\text{(3)}& -{\displaystyle \frac{\mathrm{d}\left[{\mathrm{NO}}_{\mathrm{2}}\right]}{\mathrm{d}t}}=j\left({\mathrm{NO}}_{\mathrm{2}}\right)\left[{\mathrm{NO}}_{\mathrm{2}}\right],\end{array}$$

where j(NO₂) is the photolysis frequency of NO₂ for the lamp used in these experiments. From the measured loss of NO₂ in the illuminated region, and with knowledge of the residence time, the photolysis frequency, j(NO₂), was determined to be (6.43 ± 0.30) × 10⁻³ s⁻¹ for the set of experiments using one lamp to illuminate the flow tube. j(NO₂) is given by

$$\begin{array}{}\text{(4)}& j\left({\mathrm{NO}}_{\mathrm{2}}\right)=\underset{{\mathit{\lambda }}_{\mathrm{1}}}{\overset{{\mathit{\lambda }}_{\mathrm{2}}}{\int }}{\mathit{\sigma }}_{\mathit{\lambda }}{\mathit{\varphi }}_{\mathit{\lambda }}{F}_{\mathit{\lambda }}\mathrm{d}\mathit{\lambda },\end{array}$$

where λ₁ and λ₂ represent the range of wavelengths over which the lamp emits, and σ_λ and ϕ_λ are the wavelength-dependent absorption cross section and photo-dissociation quantum yield of NO₂, respectively, and F_λ is the flux of the lamp at a given wavelength. The flux of the lamp, the spectral intensity of which was measured using a spectral radiometer (Ocean Optics QE65000) as a function of wavelength, is shown in Fig. 3.

Figure 3 UVA emission spectrum for the 15 W bench lamp used in these experiments between 290–400 nm. The integrated photon flux over this wavelength range is (1.63 ± 0.09) ×  10¹⁶ photons cm⁻² s⁻¹ determined from the measured j(NO₂) of (6.43 ± 0.30) × 10⁻³ s⁻¹.

From the measured j(NO₂), and with knowledge of σ_λ and φ_λ for NO₂, the flux of the lamp was determined to be (1.63 ± 0.09) × 10¹⁶ photons cm⁻² s⁻¹ integrated over the 290–400 nm wavelength range of the lamp. Using this flux, and the known σ_λ and φ_λ for HONO over the same wavelength range, j(HONO) was determined to be (1.66 ± 0.10) × 10⁻³ s⁻¹.

In the presence of aerosols under illuminated conditions, the rate of heterogeneous removal of NO₂ at the aerosol surface to generate HONO is given by

$$\begin{array}{}\text{(5)}& -{\displaystyle \frac{\mathrm{d}\left[{\mathrm{NO}}_{\mathrm{2}}\right]}{\mathrm{d}t}}=k\left[{\mathrm{NO}}_{\mathrm{2}}\right],\end{array}$$

where k is the pseudo-first-order rate coefficient for loss of NO₂ at the aerosol surface, which leads to the generation of HONO. The postulated mechanism for HONO production from NO₂ is discussed in Sect. 3.3.2 below, but for the definition of k it is assumed to be a first-order process for NO₂. Integration of Eq. (5) gives

$$\begin{array}{}\text{(6)}& k=-{\displaystyle \frac{\ln \left(\frac{{\left[{\mathrm{NO}}_{\mathrm{2}}\right]}_{\mathrm{0}}-{\left[\mathrm{HONO}\right]}_t}{{\left[{\mathrm{NO}}_{\mathrm{2}}\right]}_{\mathrm{0}}}\right)}{t}},\end{array}$$

where ${\left[{\mathrm{NO}}_{\mathrm{2}}\right]}_{\mathrm{0}}-[\mathrm{HONO}{]}_t$ is the concentration of NO₂ at time t, assuming that each NO₂ molecule is quantitatively converted to a HONO molecule following surface uptake (see Sect. 3.3.2 for the proposed mechanism), and ${\left[{\mathrm{NO}}_{\mathrm{2}}\right]}_{\mathrm{0}}$ is the initial concentration of NO₂. Hence k can be determined from Eq. (6) using the measurement of the concentration of HONO, [HONO], that has been generated from TiO₂ aerosol surfaces for an illumination time of t (and after subtraction of any background HONO produced from other sources and after correction for loss via photolysis; see above) and with knowledge of [NO₂]₀.

The reactive uptake coefficient of NO₂ to generate HONO, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, defined as the probability that upon collision of NO₂ with the TiO₂ aerosol surface a gas-phase HONO molecule is generated, is given by

$$\begin{array}{}\text{(7)}& {\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}={\displaystyle \frac{\mathrm{4}\times k}{\mathit{\nu }\times \mathrm{SA}}},\end{array}$$

where ν is the mean thermal velocity of NO₂, given by $\mathit{\nu }=\sqrt{\left(\right(\mathrm{8}RT)/(\mathit{\pi }M\left)\right)}$ with R, T and M as the gas constant, the absolute temperature and the molar mass of NO₂, respectively; SA is the aerosol surface area density (m² m⁻³); and k is defined as above. Rearrangement of Eq. (7) gives

$$\begin{array}{}\text{(8)}& k={\displaystyle \frac{{\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}\times \mathrm{SA}\times \mathit{\nu }}{\mathrm{4}}}.\end{array}$$

Figure 4 shows the variation of k,determined from Eq. (6) above with t=52 s (illumination time in the flow tube), against aerosol surface area density, SA, for [NO₂]₀=200 ppb and RH = 15 %, from which the gradient using Eq. (8) yields ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}=(\mathrm{2.17}\pm \mathrm{0.09})\times {\mathrm{10}}^{-\mathrm{5}}$.

Figure 4 Pseudo-first-order rate coefficient for HONO production, k (open circles), as a function of aerosol surface area for [NO₂] = 200 ppb and RH = 15 ± 1 %, T=293 ± 3 K, and a photolysis time of 52 ± 2 s. The red line is a linear-least-squares fit including 1σ confidence bands (dashed lines) weighted to both x and y errors (1σ), the gradient of which yields ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}=$ (2.17 ± 0.09) × 10⁻⁵, with the uncertainty representing (1σ). The non-zero y-axis intercept is due to a background HONO signal owing to the presence of a HONO impurity in the NO₂ cylinder, which is not subtracted. The total photon flux of the lamp (see Fig. 2 for its spectral output) = (1.63 ± 0.09) × 10¹⁶ photons cm⁻² s⁻¹.

The uncertainty in k (∼ 20 %) shown in Fig. 4 and determined by Eq. (6) is mainly controlled by the uncertainty in the HONO concentration (the HONO signal typically varies between repeated runs for a given SA by ∼ 10 % coupled with the 15 % error in the calibration factor), the initial NO₂ mixing ratio (10 %), and the photolysis time, t (∼ 3 %). The uncertainty in SA is determined by the uncertainty in the SMPS (15 %). The error in the value of ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ (typically 20 %) is calculated from the 1σ statistical error of the weighted fit shown in Fig. 4. An experiment performed using air yielded an uptake coefficient value within 7 % of the equivalent experiment done in N₂, which is well within the experimental error.

2.5 Box model description

A kinetic scheme within the framework of a box model was used together with the differential equation solver Facsimile 4.3.53 (MCPA Software Ltd., 2020) to investigate the mechanism of NO₂ adsorption on TiO₂ in the presence of light to produce HONO. The models were only semi-explicit, focusing on determining the stoichiometric amounts of NO₂ needed to produce a single HONO molecule in the gas phase for comparison with the experimental dependence of HONO production upon NO₂ mixing ratio and to provide a predictive framework for parameterising the HONO production rate with NO₂ mixing ratio in the atmosphere. Three model scenarios were designed. The simplest model (Model 1) considered only the adsorption of a single molecule of NO₂ to the TiO₂ surface, the surface conversion to HONO in the presence of light and subsequent desorption of HONO – the latter was assumed to occur rapidly. The two further model scenarios investigated the effect of a 2:1 stoichiometric relationship between the NO₂ adsorbed to the surface of TiO₂ and the HONO produced, via the formation of an NO₂ dimer. Model 2 incorporated an Eley–Rideal mechanism reliant on the adsorption of one NO₂ molecule to the surface followed by the subsequent adsorption of a second NO₂ molecule directly onto the first (Fig. 5). Model 3, however, features a Langmuir–Hinshelwood mechanism of adsorption in which two NO₂ molecules adsorb to the surface and then diffuse to one another before colliding on the surface and forming the cis-ONO-NO₂ dimer (Finlayson-Pitts et al., 2003; de Jesus Madeiros and Pimentel, 2011; Liu and Goddard, 2012; Varner et al., 2014). The formation of the asymmetric cis-ONO-NO₂ dimer followed by isomerisation to form the asymmetric trans-ONO-NO₂ dimer has been suggested to have an enthalpic barrier that is ∼ 170 kJ mol⁻¹ lower than for direct isomerisation to trans-ONO-NO₂ from the symmetric N₂O₄ dimer (Liu and Goddard, 2012). The dimerisation of NO₂ and subsequent isomerisation to form trans-ONO-NO₂ has been suggested under dark conditions to lead to the formation of both HONO and HNO₃ in the presence of water vapour (Finlayson-Pitts et al., 2003; de Jesus Madeiros and Pimentel, 2011; Liu and Goddard, 2012; Varner et al., 2014). Although the interaction of light with TiO₂ with the concomitant production of electron–hole pairs (Reaction R1) is central to HONO formation, we do not specify here the exact mechanism by which the electron–hole pairs interact with surface-bound species to generate HONO. We propose that the interaction with light speeds up the autoionisation of trans-ONO-NO₂ to form (NO⁺)(NO${}_{\mathrm{3}}^{-}$), which is represented by Reactions (R13) and (R15) in Model 2 and Model 3 respectively. (NO⁺)(NO${}_{\mathrm{3}}^{-}$) can then react rapidly with surface-adsorbed water, leading to HONO formation (Varner et al., 2014).

A schematic of the proposed mechanism investigated with Model 2 and Model 3 is shown in Fig. 5 and consists of (i) the adsorption of NO₂ onto a surface site, (ii) the conversion of NO₂ to form HONO via the formation of an NO₂ dimer intermediate on the surface via either a Eley–Rideal or Langmuir–Hinshelwood-type mechanism, (iii) subsequent desorption of HONO from the surface, and finally (iv) competitive removal processes for HONO both on the surface and in the gas phase that are either dependent or independent on the NO₂ mixing ratio. The model includes the gas-phase photolysis of NO₂ and HONO and the gas-phase reactions of both HONO and NO₂ with OH and O(³P) atoms.

Figure 5 Schematic diagram of proposed mechanism of uptake of NO₂ on an aerosol surface in the presence of water to form HONO. Both Eley–Rideal, Model 2, and Langmuir–Hinshelwood, Model 3, mechanisms are shown with relevant estimated and calculated rate coefficients used in the models. NO₂-dependent and independent loss reactions of HONO are also depicted. Nitrogen is shown in black, oxygen is shown in red and hydrogen is shown in blue. ^* denotes intermediate steps of the isomerisation of symmetric N₂O₄ to trans-ONO-NO₂, which is then predicted to form HONO.

To the best of our knowledge neither the enthalpy of adsorption of NO₂ onto a TiO₂ surface nor the bimolecular rate coefficients for the chemical steps on the surface shown in Fig. 5 have been determined. Hence, for each of the steps a rate coefficient (s⁻¹ or cm³ molec.⁻¹ s⁻¹) was assigned, as given in Table 1, and with the exception of the experimentally determined j(NO₂) and the calculated j(HONO), and the gas-phase rate coefficients which are known, the rate coefficients were estimated, with the aim of reproducing the experimental NO₂ dependence of the HONO production and NO₂ reactive uptake coefficient; justification of chosen values is given below.

Table 1 Reactions included in the chemical mechanism used to model NO₂ uptake onto TiO₂ aerosols. All rate coefficients are estimated, as described in Sect. 2.5, with the exception of the NO₂ and HONO photolysis rate coefficient and the gas-phase rate coefficient which are known.

^a Measured using chemical actinometry with the knowledge of the experimentally determined spectral output of the lamp and the cross sections and quantum yields of NO₂ and HONO; see Sect. 2.4 for more detail. ^b Calculated using a photon flux of (1.63 ± 0.09) × 10¹⁶ photons cm⁻² s⁻¹. ^c Sander et al. (2003). ^d Rate coefficients are in the units of s⁻¹ for first-order processes or cm³ molec.⁻¹ s⁻¹ for second-order processes. T for all k values is 298 K.

The modelled Gibbs free energy barrier for the isomerisation of N₂O₄ to form the asymmetric ONO-NO₂ isomer (cis or trans conformation not specified) was estimated by Pimental et al. (2007) to be 87 kJ mol⁻¹ with a rate coefficient as large as 2 × 10⁻³ s⁻¹ in the aqueous phase at 298 K, stated in the study to confirm the Finlayson-Pitts model for the hydrolysis of NO₂ on surfaces via the asymmetric trans-ONO-NO₂ dimer (Finlayson-Pitts et al., 2003). Using this study as a guide, we estimated k_R13 and k_R15 as 5 × 10⁻³ s⁻¹, slightly larger than that estimated by Pimental et al. (2007) due to the presence of light. A study into the decomposition of HONO on borosilicate glass surfaces suggested a rate coefficient for the loss HONO on the non-conditioned chamber walls to be (1.0 ± 0.2) × 10⁻⁴ s⁻¹ increasing to (3.9 ± 1.1) × 10⁻⁴ s⁻¹ when HNO₃ was present on the walls (Syomin and Finlayson-Pitts, 2003). From this we estimated a light-accelerated loss rate coefficient of 1 × 10⁻³ s⁻¹ for the loss of HONO_(ads) by reaction with itself, k_R18, and through reaction with HNO_3(ads), k_R17. Both of these reactions will occur on the surface of the aerosol. We make the assumption that the rate of loss of HONO to the walls of the chamber for this experiment is less than that of the heterogeneous loss reactions on the photocatalytic aerosol surface, leading to a k_R22 of 1 × 10⁻⁴ s⁻¹ as reported by Syomin and Finlayson-Pitts (2003). For k_R12-k_R15, initial values were adopted and were then adjusted to fit the shape of the trend in experimental results of [HONO] and ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ versus [NO₂], discussed fully in Sect. 3.3.2. For completeness, gas-phase loss reactions of HONO and NO₂ with OH and the reactions of O(³P) with NO, NO₂ and O₂ were also included in the model, Reactions (R23)–(R27), though their inclusion had no effect on the HONO concentration. The rates of Reactions (R23)–(R27) within the model are much smaller than HONO loss reactions on the surface, Reactions (R17)–(R19), and the photolysis Reaction (R21). For both Model 2 and Model 3, the adsorption of an NO₂ molecule to the surface, k_R9, was assumed to be rapid and not the rate-determining step. Likewise, the desorption of HONO was also assumed to be rapid – faster than the loss rates of adsorbed HONO but slower than the adsorption of NO₂; this was necessary for the model to reproduce the trend in the experimental results of [HONO] versus [NO₂], discussed fully in Sect. 3.3.2.

3 Results and discussion

3.1 HONO production from TiO₂ aerosol surfaces in the presence of NO₂

The production of HONO on TiO₂ aerosol surfaces was measured as a function of the initial NO₂ mixing ratio. Figure 6 shows the dependence of the HONO concentration, measured at the end of the flow tube, on the initial NO₂ mixing ratio for an aerosol surface area of (1.6 ± 0.8) × 10⁻² m² m⁻³. A sharp increase in HONO production at a low mixing ratio of NO₂ was seen, followed by a more gradual reduction in HONO production after a peak production at ∼ 54 ± 5 ppb NO₂.

Figure 6 HONO concentration measured at the end of the flow tube as a function of the initial NO₂ mixing ratio, for the aerosol surface area density of (1.6 ± 0.8) × 10⁻² m² m⁻³, relative humidity of 15 ± 1 %, photon flux of (1.63 ± 0.09) × 10¹⁶ photons cm⁻² s⁻¹ (290–400 nm wavelength range), reaction time of 52 seconds and N₂ carrier gas. Each point is an average of up to 20 measurements at the same aerosol surface area and mixing ratio of NO_2. The highest concentration of HONO measured was 0.90 ± 0.12 ppb at [NO₂] = 54 ± 5 ppb. The y error bars represent 1σ, while the x error bars represent the sum in quadrature of the errors in the N₂ and NO₂ gas flows and the NO₂ dilution. The SA varied over the experiments at different NO₂ mixing ratios leading to a larger error in the quoted SA.

Figure 7 shows the HONO concentration measured at the end of the flow tube over a range of RH values for a fixed aerosol surface area density of (1.59 ± 0.16 × 10⁻² m² m⁻³) and at two NO₂ mixing ratios, displaying a peak in HONO production between 25 %–30 % RH. Above ∼ 37 % RH, for experiments including single-component TiO₂ aerosols, it was found that significant aerosols were lost from the system before entering the flow tube, speculated to be due to loss to the walls of the Teflon lines. As such the RH dependence was only studied up to 37 % RH; however, a clear drop-off in HONO production was seen for both NO₂ mixing ratios studied after ∼ 30 % RH.

Figure 7 RH dependence of HONO production from illuminated TiO₂ aerosol surfaces at 295 K in N₂ at 71 (black) and 170 (red) ppb initial NO₂ mixing ratio. The aerosol surface area density was kept constant at (1.59 ± 0.16) × 10⁻² m² m⁻³ with a photon flux of (1.63 ± 0.09) × 10¹⁶ photons cm⁻² s⁻¹ and an illumination time of 52 ± 2 s. The error bars represent 1σ.

A dependence of HONO production upon RH was expected due to the potential role of water as a proton donor in the production mechanism of HONO on TiO₂ surfaces (Reactions R2 and R5, as shown in Fig. 5) (Dupart et al., 2014). The fractional surface coverage of water on the TiO₂ aerosol core, $V/V_{\mathrm{m}}$, at 15 % RH and above was calculated using the parameterisation below, which was determined using transmission IR spectroscopy (Goodman et al., 2001):

$$\begin{array}{}\text{(9)}& \begin{array}{rl}& {\displaystyle \frac{V}{V_{\mathrm{m}}}}=\left[{\displaystyle \frac{c\left(\frac{P}{P_{\mathrm{0}}}\right)}{\mathrm{1}-\left(\frac{P}{P_{\mathrm{0}}}\right)}}\right]\\ & \left[{\displaystyle \frac{\mathrm{1}-\left(n+\mathrm{1}\right){\left(\frac{P}{P_{\mathrm{0}}}\right)}^n+n{\left(\frac{P}{P_{\mathrm{0}}}\right)}^{n+\mathrm{1}}}{\mathrm{1}+(c-\mathrm{1})\left(\frac{P}{P_{\mathrm{0}}}\right)-c{\left(\frac{P}{P_{\mathrm{0}}}\right)}^{n+\mathrm{1}}}}\right],\end{array}\end{array}$$

where V is the volume of water vapour adsorbed at equilibrium pressure P, V_m is the volume of gas necessary to cover the surface of TiO₂ particles with a complete monolayer, P₀ is the saturation vapour pressure, c is the temperature-dependent constant related to the enthalpies of adsorption of the first and higher layers (taken as 74.8 kJ mol⁻¹ for TiO₂, Goodman et al., 2001), and n is the asymptotic limit of monolayers (eight for TiO₂, Goodman et al., 2001) at large values of $P/P_{\mathrm{0}}$.

At 15 % RH, a fractional water coverage of 1.09 was calculated to be present on the surface, increasing to 1.50 at 35 % RH. It has been shown in previous work that HONO can be displaced from a surface by water, leading to an increase in gas-phase HONO with RH (Syomin and Finlayson-Pitts, 2003). The increase in HONO with RH to ∼ 25 %–30 % RH could therefore be attributed to both an increase in the concentration of the water reactant leading to more HONO formation and the increase in displacement of HONO from the surface due to preferential adsorption of water. A decrease in HONO production seems to occur above ∼ 30 % RH, which could be due to the increased water adsorption inhibiting either NO₂ adsorption or the electron–hole transfer process (Gustafsson et al., 2006). H₂O vapour adsorption is likely enhanced by the superhydrophilic properties of TiO₂ surfaces under UV radiation, meaning that water monolayers form more quickly on the surface of TiO₂ owing to light-induced changes in surface tension (Takeuchi et al., 2005; Gustafsson et al., 2006).

At the higher initial concentration of NO₂=170 ppb, the RH dependence showed a similar peak in HONO production between ∼ 25 %–30 % RH, but less HONO was produced overall, as expected from Fig. 6 given the higher NO₂. Previous work on the production of HONO from suspended TiO₂ aerosols reported a strong RH dependence of the uptake coefficient, γ, of NO₂ to form HONO with a peak at ∼ 15 % RH and decreasing at larger RH (Gustafsson et al., 2006). The same trend for the NO₂ uptake coefficient was observed by Dupart et al. (2014) on Arizona test dust (ATD) aerosols with a peak in γ at ∼ 25 % RH. This increase in the RH at which the uptake coefficient for NO₂ in going from TiO₂ to ATD aerosols was ascribed to the lower concentration of TiO₂ present in ATD aerosols as opposed to single-component TiO₂ aerosols used by Gustafsson et al. (2006) as well as by differences in particle size distribution. Gustafsson et al. (2006) reported a larger aerosol size distribution with a bimodal trend with mode diameters of ∼ 80 and ∼ 350 nm for single-component TiO₂ aerosols, whereas Dupart et al. (2014) reported a smaller unimodal aerosol size distribution for ATD aerosols with a mode diameter of ∼ 110 nm. In this work we also see a larger aerosol size distribution, with a lower mode diameter of ∼ 180 nm similar to Dupart et al. (2014) but for pure TiO₂ aerosols (aerosol size distribution shown in Fig. 2). Similar to the results of Dupart et al. (2014) we observe a trend inversion in [HONO] vs. RH at higher RH, between 25 %–30 %. An increase in HONO as a function of RH has also been observed on TiO₂-containing surfaces (Langridge et al., 2009; Gandolfo et al., 2015; Gandolfo et al., 2017) with a similar profile for the observed RH dependence of HONO being observed by Gandolfo et al. (2015) from photocatalytic paint surfaces with a maximum in HONO mixing ratio found at 30 % RH. In comparison, a study focusing on the products of the uptake of NO₂ on TiO₂ surfaces showed a maximum in the gas-phase HONO yield at 5 % RH, with the yield of HONO plateauing off with further increase in humidity (Bedjanian and El Zein, 2012).

3.2 Dependence of reactive uptake coefficient on initial NO₂ mixing ratio

The reactive uptake coefficient, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ for NO₂→HONO, on TiO₂ aerosol particles was determined experimentally for 18 different initial NO₂ mixing ratios and is shown in Fig. 8. For each initial NO₂ mixing ratio, the gradient of the first-order rate coefficient for HONO production, k, as a function of aerosol surface area density (e.g. Fig. 4) and in conjunction with Eq. (8) was used to obtain ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$. The uptake coefficient initially increases with NO₂, reaching a peak at ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}=(\mathrm{1.26}\pm \mathrm{0.17})\times {\mathrm{10}}^{-\mathrm{4}}$ for an initial NO₂ mixing ratio of 51±5 ppb, before sharply decreasing as the NO₂ mixing ratio continues to increase above this value.

Figure 8 Experimental results showing the reactive uptake coefficients of NO₂ to form HONO, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, onto TiO₂ aerosol surfaces as a function of the initial NO₂ mixing ratio. All experiments were conducted in N₂ at 295 K at 15 ± 1 % RH, a photon flux of (1.63 ± 0.09) × 10¹⁶ photons cm⁻² s⁻¹ and an illumination time of 52 ± 2 s. ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ was determined for each NO₂ mixing ratio from the gradient of the pseudo-first-order rate coefficient for HONO production, k, versus aerosol surface area density varied from 0–0.04 m² m⁻³ (e.g. as shown in Fig. 4) and Eq. (8).

The increase in uptake coefficient with NO₂ at low NO₂ (< 51 ppb) has not been seen previously in studies of HONO production from TiO₂-containing aerosols with similar [NO₂] ranges (Gustafsson et al., 2006; Ndour et al., 2008; Dupart et al., 2014) or with other aerosol surfaces (Bröske et al., 2003; Stemmler et al., 2007) or TiO₂ surfaces (El Zein and Bedjanian, 2012b). It is worth noting that several of these studies reported the overall uptake of NO₂ onto aerosol surfaces and not specifically the uptake to form HONO, although HONO was indirectly measured in all studies noted here (Gustafsson et al., 2006; Ndour et al., 2008; Dupart et al., 2014). For single-component TiO₂ aerosols, Gustafsson et al. (2006) reported a uptake coefficient, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}}$, of 9.6 × 10⁻⁴ at 15 % RH and 100 ppb NO₂. Taking into account the HONO yield of 0.75 given by Gustafsson et al. (2006), an estimated ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}=\mathrm{7.2}\times {\mathrm{10}}^{-\mathrm{4}}$ is determined and can be compared to the value observed in this work at 15 % RH and 100 ppb NO₂, (${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}=$ (2.68 ± 0.23) × 10⁻⁵). The ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ we determine is 27 times smaller than reported by Gustafsson et al. (2006). This difference is mostly due to the lower experimental photon flux in our setup, ∼ 19 times less at ${\mathit{\lambda }}_{max}=\mathrm{365}$ nm owing to the use of one 15 W UV lamp to irradiate the flow tube (Boustead, 2019) compared to Gustafsson et al. (2006), who utilised four 18 W UV lamps.

The origins of the increase in ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, together with reaching a maximum, and the subsequent decrease at larger NO₂ mixing ratios were investigated using the kinetic box model and postulated mechanism for HONO production described in Sect. 2.5. The aim was to compare the observed production of HONO and ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ with the modelled values, as a function of NO₂ mixing ratio. The skill of the model to reproduce the observed behaviour enables a validation of the postulated mechanism for HONO production, and variation of the kinetic parameters enables the controlling influence of different steps in the mechanism on HONO production to be evaluated.

3.3 Modelling the HONO production mechanism on illuminated TiO₂ aerosol surfaces

The HONO production on illuminated TiO₂ aerosol surfaces was investigated for each of the mechanisms outlined in Table 1.

3.3.1 Model 1

Model 1 (see Table 1 and Fig. 5), which contains the simplest mechanism, was designed to reproduce the decreasing value of the NO₂ uptake coefficient to form HONO, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, with increasing NO₂ and also the plateauing at higher NO₂ mixing ratios caused by NO₂ reaching a maximum surface coverage, as seen by Stemmler et al. (2007). A decrease in the uptake coefficient of NO₂, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}},$ onto dust aerosol surfaces was also seen in studies where the formation of HONO from NO₂ uptake was not directly studied (Ndour et al., 2008; Dupart et al., 2014). The mechanism for Model 1 which is given in Table 1 describes the adsorption of one NO₂ molecule to a surface site which then undergoes the reaction which forms HONO, followed by desorption of HONO to the gas phase, Reactions (R9)–(R11). Any representation of the specific chemical processes which convert NO₂ to HONO on the surface following the initial photo-production of electron–hole pairs in the TiO₂ structure (Reaction R2) was not included here as the primary focus was to produce the relationship between ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ and the NO₂ mixing ratio. Gustafsson et al. (2006) reported that the measured rate of photo-induced HONO production is 75 % that of the rate of NO₂ removal, whereas the dark disproportionation reaction (Reaction R28) would predict a 50 % yield, and hence that the HONO observed in their studies is not simply a photo-enhancement of

$$\begin{array}{}\text{(R28)}& \mathrm{2}{\mathrm{NO}}_{\mathrm{2}\left(\mathrm{ads}\right)}+{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\left(\mathrm{ads}\right)}\to {\mathrm{HONO}}_{\left(\mathrm{g}\right)}+{\mathrm{HNO}}_{\mathrm{3}\left(\mathrm{ads}\right)}.\end{array}$$

Gustafsson et al. (2006) suggests that an oxidant on the surface is produced following the creation of the electron–hole pair (OH is generated in Reaction R2) and suggests H₂O₂ as a possibility, which is consistent with the observation of OH and HO₂ radicals produced from the surface of illuminated TiO₂ aerosols (Moon et al., 2019). For Model 1, outputs for the predicted concentration of HONO and the reactive uptake coefficient, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, as a function of initial NO₂ mixing ratio are shown in Fig. 9.

Figure 9 Model 1 calculations for (a) the concentration of HONO and (b) the reactive uptake coefficient to form HONO, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, as a function of NO₂ mixing ratio for a model run time of 52 s. The estimated rate coefficients used in this model are shown in Table 1.

For a run time of 52 s, equal to that of the experimental illumination time, Model 1 predicts an increase in HONO production with increasing NO₂ mixing ratio until the HONO concentration begins to plateau, reaching ∼ 0.25 ppb at [NO₂] = 400 ppb, presumably owing to saturation on active aerosol surface sites by NO₂. This leads to the modelled reactive uptake coefficient, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, monotonically decreasing with increasing NO₂ mixing ratio – a variation in NO₂ uptake coefficient similar to that seen in previous photo-enhanced NO₂ aerosol uptake studies (Bröske et al., 2003; Stemmler et al., 2007; Ndour et al., 2008; Dupart et al., 2014). However, the model predictions for Model 1 do not reproduce the experimental variations shown in Figs. 6 and 8, in which there is an observed initial rise and then a fall in both the HONO concentration and ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ with increasing NO₂ mixing ratio. Hence, additional processes were considered in the model in order to try to reproduce this behaviour.

3.3.2 Model 2 and Model 3 – investigating the role of NO₂ dimerisation for the surface formation of HONO, and including additional surface losses of HONO

As the experimental ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ increases with NO₂ at low NO₂ (Fig. 8), we postulate in Model 2 and Model 3 that the production of HONO under illuminated conditions is not fully first order in NO₂ and requires more than one NO₂ molecule to form HONO, consistent with the formation of the symmetric NO₂ dimer (N₂O₄) followed by isomerisation on the surface to form the asymmetric trans-ONO-NO₂ dimer, which has been suggested to be more reactive with water than the symmetric N₂O₄ dimer (Finlayson-Pitts et al., 2003; Ramazan et al., 2004; Ramazan et al., 2006; Liu and Goddard, 2012) due to the autoionisation to form (NO⁺)(NO${}_{\mathrm{3}}^{-}$), which we propose is accelerated by the presence of light, the full mechanism for which is shown in Fig. 5. A recent rotational spectroscopy study found that the trans-ONO-NO₂ was better described as the ion pair (NO⁺)(NO${}_{\mathrm{3}}^{-}$) (Seifert et al., 2017). Reaction of the (NO⁺)(NO${}_{\mathrm{3}}^{-}$) ion pair with surface-adsorbed water can then lead to the formation of HONO and HNO₃, the feasibility of which is supported by molecular dynamics simulation studies (Varner et al., 2014). While the symmetric N₂O₄ dimer is favoured as it is the most stable conformer, the asymmetric forms have been experimentally observed in several studies (Fateley et al., 1959; Givan and Loewenschuss, 1989b, a, 1991; Pinnick et al., 1992; Forney et al., 1993; Wang and Koel, 1998, 1999; Beckers et al., 2010). A more recent ab initio study of NO₂ adsorption at the air–water interface suggested an orientational preference of NO₂ on the surface, with both oxygen atoms facing away from the interface, which may imply that the asymmetric dimer ONO-NO₂ can form directly, meaning the high barrier between the symmetric and asymmetric forms does not need to be overcome (Murdachaew et al., 2013).

The energy barrier to isomerisation of symmetric N₂O₄ in the gas phase may be reduced due to the interaction with water adsorbed on surfaces. We therefore rule out the dimer in the gas phase adsorbing onto the surface first and then reacting to form HONO (Varner et al., 2014). An interesting question is whether the first NO₂ molecule adsorbed to the surface dimerises via the addition of a gaseous NO₂ via an Eley–Rideal (ER) type process or whether a Langmuir–Hinshelwood (LH) type mechanism is operating in which both NO₂ molecules are first adsorbed and then diffuse together on the surface forming N₂O₄. Both ER and LH mechanisms to form the NO₂ dimer have been included in the model, denoted as Model 2 and Model 3, respectively. The outputs for Model 2 and Model 3 (see Table 1 for details of the processes included) for the HONO concentration and ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ as a function of NO₂ are shown in Fig. 10 together with the experimental data. The stoichiometric relationship of the requirement of two NO₂ molecules forming HONO on the surface was key to reproducing the experimental trend of first an increase and then a decrease in both the HONO concentration and the reactive uptake coefficient with the initial NO₂ mixing ratio.

Figure 10 Experimental values (open circles with 1σ error bars), Model 2 (green line) and Model 3 (pink line) calculations for (a) HONO concentration after 52 s illumination and (b) NO₂ reactive uptake coefficient, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, as a function of the initial NO₂ mixing ratio. The mechanisms used for these model runs included a 2:1 stoichiometric relationship between the NO₂ adsorbed on the TiO₂ aerosol surface and the HONO produced, as well as additional HONO loss reactions which are dependent on NO₂; see Table 1 for details. Model 2 and Model 3 use an Eley–Rideal and Langmuir–Hinshelwood mechanism, respectively, for the formation of the NO₂ dimer on the aerosol surface. Modelled ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ was calculated using Eqs. (6) and (7) with a constant surface area of 1.6 × 10⁻² m² m⁻³ chosen to match the aerosol surface area density of (1.6 ± 0.8) × 10⁻² m² m⁻³ shown in the experimental [HONO] values in panel (a).

In previous work that investigated HONO production from humic acid aerosols, a saturation effect was seen with HONO production plateauing with increasing NO₂ mixing ratio (Stemmler et al., 2007), with the decreasing uptake coefficient, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, with increasing NO₂ being attributed to NO₂ fully saturating available surface sites. However, the observed decrease in [HONO] at the high NO₂ mixing ratios shown in Figs. 8 and 10a suggests that additional reactions on the surface may remove HONO and result in the reduction of [HONO] that is measured. As [HONO] decreases with the increase in the NO₂ mixing ratio, the removal process should either involve NO₂ directly,

$$\begin{array}{}\text{(R19)}& \mathrm{HONO}+{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{NO}+{\mathrm{HNO}}_{\mathrm{3}},\end{array}$$

or involve species made rapidly from NO₂ on the surface, such as NO${}_{\mathrm{2}}^{+}$,

$$\begin{array}{}\text{(R19a)}& {\mathrm{HONO}}_{\left(\mathrm{ads}\right)}+{\mathrm{NO}}_{{\mathrm{2}}_{\left(\mathrm{ads}\right)}}^{+}\to {\mathrm{H}}^{+}+\mathrm{2}\mathrm{NO}+{\mathrm{O}}_{\mathrm{2}},\end{array}$$

which may be present at high enough concentrations of HNO₃ on the surface (Syomin and Finlayson-Pitts, 2003) or following reaction with $h_{\mathrm{VB}}^{+}$, or a product of the reaction of ${\mathrm{O}}_{\mathrm{2}}^{-}\left(\text{or}{e}_{\mathrm{CB}}^{-}\right)$ with NO₂ (Reaction R4), i.e. NO${}_{\mathrm{2}}^{-}$. Similar results were observed in a study by El Zein and Bedjanian (2012a), where NO₂ and NO were found to be formed from the heterogeneous reaction of HONO with TiO₂ surfaces in both dark and illuminated conditions, suggesting the loss of HONO via an auto-ionisation reaction between the gas-phase and adsorbed HONO to generate NO⁺ and NO${}_{\mathrm{2}}^{-}$ (El Zein and Bedjanian, 2012a). Additional HONO surface loss pathways were assumed to occur under illuminated conditions due to the presence of e⁻ and h⁺, leading to the oxidation of HONO to NO₂ and the reduction of HONO to NO (El Zein et al., 2013). Transition state theory (TST) studies of the gas-phase reaction of HONO with NO₂ to form HNO₃ calculated a large activation energy which varied depending on whether the reaction occurs via O abstraction by HONO (159 kJ mol⁻¹) or via OH abstraction via NO₂ (∼ 133–246 kJ mol⁻¹) (Lu et al., 2000). In the gas phase these reactions are too slow to be important, but they could be enhanced on the surface, potentially more so on a photoactive surface such as TiO₂. For Models 2 and 3 the shape of the trend in HONO concentration and uptake coefficient, γ, versus NO₂ concentration depended strongly on the value of k_R19 and the choice of a 2:1 stoichiometric ratio of the NO₂ molecules adsorbed to the HONO molecules produced. Without these two key processes being included, a maximum in either the HONO concentration or γ as the NO₂ concentration is increased could not be obtained in the model. A third key condition was the requirement that the desorption rate coefficient, k_R16, be larger than the rate coefficient for the loss of HONO, k_R17 and $k_{\mathrm{R}\mathrm{18}}=\mathrm{1}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹, but slower than the adsorption rate coefficient, k_R9. Changing the values of all other kinetic parameters in the model had an effect on the absolute concentration of HONO but crucially not on the shape of the trends in HONO or the uptake coefficient versus NO₂ concentration. Changing the values of the rate coefficients for the gas-phase loss Reactions (R23)–(R27) only had a very small impact on the HONO concentration. The addition of an NO₂-dependent loss reaction to both Model 2 and Model 3 had the most significant effect on the trend in modelled HONO concentration. Though it is also possible that a secondary product could remain adsorbed and therefore block active sites on the TiO₂ surface, effectively poisoning the photocatalyst, NO₂-independent loss reactions in the model, k_R17 and k_R18, had little effect on the trend in [HONO] vs. NO₂, only having an effect on the overall [HONO]. HNO₃ has however been shown to remain adsorbed to surfaces once formed (Sakamaki et al., 1983; Pitts et al., 1984; Finlayson-Pitts et al., 2003; Ramazan et al., 2004) and may also react with adsorbed HONO, further reducing the product yield (Finlayson-Pitts et al., 2003): these NO₂-independent loss reactions may therefore become more important at higher NO₂ concentrations and hence surface concentrations of HONO and HNO₃:

$$\begin{array}{}\text{(R17)}& {\text{HONO}}_{\left(\mathrm{ads}\right)}+{\mathrm{HNO}}_{\mathrm{3}\left(\mathrm{ads}\right)}\to \mathrm{2}{\mathrm{NO}}_{\left(\mathrm{g}\right)}+{\mathrm{H}}_{\mathrm{2}}{\mathrm{O}}_{\left(\mathrm{ads}\right)}+{\mathrm{O}}_{\mathrm{2}\left(\mathrm{g}\right)}.\end{array}$$

The photolysis of particulate nitrate was not considered in Model 2 or Model 3, due to the lack of particulate nitrate in the system at t=0. The gas-to-particle conversion of any HNO₃ formed was not considered to be important due to the assumption that most HNO₃ formed would remain adsorbed to the aerosol surface (Sakamaki et al., 1983; Pitts et al., 1984; Finlayson-Pitts et al., 2003; Ramazan et al., 2004).

For Model 2, which includes the production of HONO via the Eley–Rideal mechanism, in order to reproduce the experimentally observed sharp increase followed by a decrease in both [HONO] and ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ as a function of increasing NO₂ mixing ratio, the modelled rate coefficient for the adsorption of a gas-phase NO₂ molecule to another, the surface-adsorbed NO₂ to initially form the symmetric N₂O₄ dimer, k_R12, had to be larger than for the isomerisation step to form HONO and HNO₃ via trans-ONO-NO₂, k_R13. Interestingly, for HONO production via the Langmuir–Hinshelwood mechanism, Model 3, the modelled rate coefficient for the diffusion of one NO₂ molecule across the surface to form the dimer with another NO₂ molecule, k_R14, had to be smaller than for the isomerisation step, k_R15, to more closely represent the experimental results for the uptake coefficient. Additionally, in order to reproduce the experimental trend in HONO formation as a function of NO₂ mixing ratio, the rate coefficient for the NO₂-dependent loss reaction, k_R19, had to be larger than the NO₂-independent reactions, k_R17 and k_R18, leading to $k_{\mathrm{R}\mathrm{19}}=\mathrm{5}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹. The modelled HONO concentration is also sensitive to the active site surface concentration: Model 3 required an active site surface concentration 2.5 times that of Model 2 to reproduce the peak in [HONO] at ∼ 51 ppb NO₂ observed in the experimental results. The reason for this is due to the difference in active site occupation in the two models: one active site is being occupied by two NO₂ molecules per HONO formed in Model 2 as opposed to Model 3, where two active sites are occupied per HONO formed. Regardless of the choice of an Eley–Rideal or Langmuir–Hinshelwood mechanism, both models reproduce the general shape of [HONO] and ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ with NO₂, providing evidence that two NO₂ molecules are required to form HONO.

3.4 HONO production from illumination of a mixed NH₄NO₃ $/$ TiO₂ aerosol in the absence of NO₂

The photolysis of particulate nitrate has been postulated as a source of HONO under ambient sunlit conditions during several field campaigns, from both aircraft- and ground-based measurements (Reed et al., 2017; Ye et al., 2017a, b). Here, experiments were carried out to investigate the formation of HONO from particulate nitrate photolysis, with and without the addition of a photocatalyst. This is of significant interest for marine environments downwind of arid desert regions due to the availability of TiO₂ or other photocatalytic materials within aerosols in dust plumes that are transported from these regions (Hanisch and Crowley, 2003).

Using the aerosol flow tube setup described in Sect. 2.1–2.4, an aqueous solution of ammonium nitrate (5 g NH₄NO₃ in 500 mL Milli-Q water) was used to generate nitrate aerosols. At the RH used in this experiment, ∼ 50 %, the aerosols were still deliquesced. For these experiments the residence time of the aerosols in the illuminated region of the flow tube was 30 s (flow rate ∼ 6 L min⁻¹), with the production of HONO following illumination measured as a function of aerosol surface area density. The number of lamps was increased from one to four, increasing the photon flux from (1.63 ± 0.09) × 10¹⁶ to (8.21 ± 2.39) × 10¹⁶ photons cm⁻² s⁻¹ and j(NO₂) from (6.43 ± 0.30) × 10⁻³ to (3.23 ± 0.92) × 10⁻² s⁻¹. The j(NO₂), j(HONO) and flux values for four lamps were more than 4 times that of one lamp only due to the lamp casings being mirrored, and so with four lamps, with two lamps on either side of the flow tube, the casings reflected the light back into the flow tube, increasing the effective light intensity. For these experiments, no gaseous NO₂ was added to the gas entering the flow tube. As shown in Fig. 11, for the illumination of pure nitrate aerosols, although a small amount of HONO was observed at higher aerosol loadings, no statistically significant production of HONO was seen.

Figure 11 Dependence of the HONO concentration generated as a function of aerosol surface area density for pure NH₄NO₃ aerosol (black open squares, error bars represent 1σ) and 1:1 TiO₂ $/$ NH₄NO₃ mixed aerosol (red open circles, error bars represent 1σ). Both experiments were performed in N₂ at 295 K, an illuminated residence time of 30 s and a lamp photon flux of (8.29 ± 2.39) × 10¹⁶ photons cm⁻² s⁻¹. The NH₄NO₃-only experiment was performed at ∼ 50 ± 5 % RH, while the TiO₂ $/$ NH₄NO₃ mix experiment was performed at 20 ± 2 % RH. For all points, the background HONO observed without illumination has been subtracted. At zero aerosol surface area density there is no HONO generated from the walls of the flow tube.

A second set of experiments were performed with an aqueous solution of titanium dioxide and ammonium nitrate combined in a 1:1 mass ratio to give a TiO₂ $/$ NH₄NO₃ aerosol mixture (5 g NH₄NO₃ and 5 g TiO₂ in 500 mL Milli-Q water) to investigate if the photocatalytic properties of TiO₂ facilitate the production of HONO in the presence of nitrate. The RH was decreased to ensure the maximum TiO₂ photocatalytic activity (Jeong et al., 2013). A recent study using Raman micro-spectroscopy to observe phase changes in salt particles reported an efflorescence point of pure ammonium nitrate to be between 13.7 %–23.9 % RH (Wu et al., 2019). It is possible therefore that at the RH used in this experiment, ∼ 20 %, the aerosols were still deliquesced. As shown in Fig. 11, the presence of TiO₂ in the aerosol mixture showed a significant production of HONO without the presence of NO₂, a potentially significant result for the production of HONO in low-NO_xenvironments in the presence of mixed dust/nitrate aerosols, for example in oceanic regions off the coast of West Africa or in continental regions impacted by outflow from the Gobi desert. Using the Aerosol Inorganic Model (AIM) (Clegg et al., 1998; Wexler and Clegg, 2002), the nitrate content of the aerosol at both 20 % and 50 % RH was calculated, in accordance with the experimental RH conditions. From this and the aerosol volume distribution given by the SMPS, the [NO${}_{\mathrm{3}}^{-}$] within the aerosols could be calculated. The formation of HONO by photolysis of particulate nitrate is given by

$$\begin{array}{}\text{(10)}& {\displaystyle \frac{\mathrm{d}\left[\mathrm{HONO}\right]}{\mathrm{d}t}}=j\left(p{\mathrm{NO}}_{\mathrm{3}}\right)\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]\end{array}$$

and hence

$$\begin{array}{}\text{(11)}& \left[\mathrm{HONO}\right]=j\left(p{\mathrm{NO}}_{\mathrm{3}}\right)\left[{\mathrm{NO}}_{\mathrm{3}}^{-}\right]t,\end{array}$$

where j(pNO₃) is the photolysis frequency of nitrate for the lamps used in these experiments and t is the illumination time of the experiment. With knowledge of [HONO], [NO${}_{\mathrm{3}}^{-}$] and t=30 s, j(pNO₃) can be calculated from a measurement of [HONO] as a function of [NO${}_{\mathrm{3}}^{-}$], as shown in Fig. 12, for the mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ experiment.

Figure 12 Dependence of [HONO] on the calculated nitrate concentration in the aerosol (using the AIM model) for the mixed TiO${}_{\mathrm{2}}/$ammonium nitrate aerosol experiment. Using Eq. (10) and for t=30 s, the gradient gives j(pNO₃)= (3.29 ± 0.89) × 10⁻⁴ s⁻¹. Experiment performed at 15 ± 1 % RH, in N₂ at 295 K with a lamp photon flux of (8.29 ± 2.39) × 10¹⁶ photons cm⁻² s⁻¹. For all points, the background HONO observed without illumination has been subtracted.

When using the four lamps together, the experimental particulate nitrate photolysis rate, j(pNO₃), was determined to be (3.29 ± 0.89) × 10⁻⁴ s⁻¹ for the mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ aerosol. From this, it is possible to estimate j(pNO₃) for ambient conditions typical of the tropical marine boundary layer. Taking the ratio of the experimental j(HONO) for four lamps ((8.35 ± 0.18) × 10⁻³ s⁻¹) and the measured j(HONO) from the RHaMBLe campaign held at the Cape Verde Atmospheric Observatory (May–June 2007) (1.2 × 10⁻³ s⁻¹) (Carpenter et al., 2010; Whalley et al., 2010; Reed et al., 2017) and assuming that j(pNO₃) and j(HONO) scale in the same way, ambient j(pNO₃) can be determined from

$$\begin{array}{}\text{(12)}& j{\left(p{\mathrm{NO}}_{\mathrm{3}}\right)}_{\mathrm{N}}=j\left(p{\mathrm{NO}}_{\mathrm{3}}\right)\times {\displaystyle \frac{\mathrm{1.2}\times {\mathrm{10}}^{-\mathrm{3}}}{j\left(\mathrm{HONO}\right)}},\end{array}$$

where $j{\left(p{\mathrm{NO}}_{\mathrm{3}}\right)}_{\mathrm{N}}$ is the photolysis rate coefficient of particulate nitrate at Cabo Verde, j(pNO₃)  is the experimentally determined photolysis rate coefficient of particulate nitrate to form HONO and j(HONO) is the HONO photolysis rate coefficient calculated from the experimentally determined j(NO₂).

Using j(pNO₃)= (3.29 ± 0.89) × 10⁻⁴ s⁻¹, the rate of HONO production from nitrate photolysis at Cabo Verde was calculated to be $j{\left(p{\mathrm{NO}}_{\mathrm{3}}\right)}_{\mathrm{N}}=(\mathrm{4.73}\pm \mathrm{1.01})\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹ from the mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ aerosol experiment. Although for pure nitrate aerosol in the absence of TiO₂ the data were scattered and the HONO production was small (Fig. 11), an upper limit estimate of $j{\left(p{\mathrm{NO}}_{\mathrm{3}}\right)}_{\mathrm{N}}=$(1.06 ± 1.15) × 10⁻⁶ s⁻¹ under conditions at Cabo Verde could be made using Eq. (11), as done for rate of HONO production from mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ aerosols. The atmospheric implications of this will be considered below.

4 Implications of HONO production from TiO₂ for tropospheric chemistry

4.1 Production of HONO from sunlit aerosols containing TiO₂ in the presence of NO₂

For the reactive uptake of NO₂ onto illuminated TiO₂ particles as a function of the initial NO₂ mixing ratio, as shown in Fig. 8, a maximum value of ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}=$ (1.26 ± 0.17) × 10⁻⁴ was determined at 51 ± 5 ppb NO₂ for a photon flux from the lamp of (1.63 ± 0.09) × 10¹⁶ photons cm⁻² s⁻¹. These experiments were for single-component TiO₂ particles, and so for dust aerosols a value of ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}=$ (1.26 ± 0.17) × 10⁻⁵ is appropriate, assuming a 10 % fraction of TiO₂ and/or other photoactive materials (which behave similarly for HONO production) in mineral dust (Hanisch and Crowley, 2003). Dust aerosols are transported from the Gobi desert to urban areas of China where high NO_x and nitrate aerosol concentrations have been observed, and in these areas HONO production facilitated by photocatalysts may be important (Saliba et al., 2014).

Using an average daytime maximum for [NO₂], j(NO₂) and aerosol surface area measurements for a non-haze period in May–June in 2018 in Beijing, of 50 ppb, 1 × 10⁻² s⁻¹ and 2.5 × 10⁻³ m² m⁻³ (of which a maximum of 0.3 % was assumed to be TiO₂, though this could be higher in dust impacted events, Schleicher et al., 2010) respectively, a production rate of HONO of 1.70 × 10⁵ molec. cm⁻³ s⁻¹ (∼ 24.8 ppt h⁻¹) has been estimated using the maximum reactive uptake coefficient measured in this work, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}=$ (1.26 ± 0.17) × 10⁻⁴. The average RH in Beijing during summertime is significantly higher than the range of RH used in the TiO₂ aerosol experiments. In previous work (Gustafsson et al., 2006), the NO₂ reactive uptake coefficient decreased for relative humidities above those studied here, and hence the HONO production calculated under the conditions in Beijing may represent an upper limit. The lamp used to illuminate the TiO₂ aerosols in these experiments gives rise to j(NO₂)= (6.43 ± 0.3) × 10⁻³ s⁻¹, and so ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ has been scaled by a factor of 1.55 to match the noon j(NO₂) measured in May–June 2018 in Beijing (10⁻² s⁻¹), to take into account the relatively small difference in experimental and atmospheric photon flux for Beijing. The HONO production rate estimated here for noontime summer (May–June 2018) in Beijing (∼ 25 ppt h⁻¹) is similar to the value for the maximum production of HONO from urban humic acid aerosol surfaces in Europe, 17 ppt h⁻¹ at 20 ppb NO₂ reported by Stemmler et al. (2007). For comparison, the net gaseous production rate of HONO at noon in May–June (2018) Beijing was determined from the measured rate of gas-phase production and losses:

$$\begin{array}{}\text{(13)}& \begin{array}{rl}& P_{\mathrm{HONO}}=k_{\mathrm{OH}+\mathrm{NO}}\left[\mathrm{OH}\right]\left[\mathrm{NO}\right]-\\ & (j\left(\mathrm{HONO}\right)\times \left[\mathrm{HONO}\right]+k_{\mathrm{OH}+\mathrm{HONO}}\left[\mathrm{OH}\right]\left[\mathrm{HONO}\right]),\end{array}\end{array}$$

where $k_{\mathrm{OH}+\mathrm{NO}}=$ 3.3 × 10⁻¹¹ cm³ molec.⁻¹ s⁻¹ (Atkinson et al., 2004), k_OH+HONO = 6 × 10⁻¹² cm³ molec.⁻¹ s⁻¹ (Atkinson et al., 2004) and j(HONO) = 1 × 10⁻² s⁻¹ for an average maximum noontime OH concentration of 8 × 10⁶ molec. cm⁻³ (Whalley et al., 2021), NO concentration of 1.45 ppb (Whalley et al., 2021) and HONO concentration of 0.8 ppb (Whalley et al., 2021).

The net gas-phase production of HONO from Eq. (13) was calculated to be −3.8 ppb h⁻¹ (a net loss) as expected due to HONO loss by photolysis peaking at solar noon, suggesting the production of HONO heterogeneously from TiO₂ and NO₂ (∼ 25 ppt h⁻¹) would have little effect on the overall HONO budget for Beijing summertime at noon.

4.2 Production of HONO from photolysis of mixed dust/nitrate aerosols

Particulate nitrate photolysis could be an important source of HONO in oceanic environments, for example the Atlantic Ocean, where both dust aerosols from the Sahara and high concentrations of mixed nitrate aerosols from sea spray are present, despite low NO₂ concentrations (Hanisch and Crowley, 2003; Ye et al., 2017b). From the particulate nitrate photolysis experiments in the absence of NO₂ conducted here, a $j{\left(p{\mathrm{NO}}_{\mathrm{3}}\right)}_{\mathrm{N}}=$ (4.73 ± 1.01) × 10⁻⁵ s⁻¹ was determined in the presence of the TiO₂ photocatalysts (Sect. 3.4). Using the experimental j(pNO₃), scaled to typical ambient light levels, and a mean noon concentration of nitrate aerosols of 400 ppt measured at Cabo Verde (Reed et al., 2017), taken as an example marine boundary layer environment with a high concentration of mineral dust aerosols, a rate of HONO production from particulate nitrate at Cabo Verde was calculated as 4.65 × 10⁵ molec. cm⁻³ s⁻¹ (68 ppt h⁻¹). We note that this value would be ∼ 50 times smaller for pure nitrate aerosols. The missing rate of HONO production, i.e. not taken into account by the gas-phase production and loss, P_other, from the Cabo Verde RHaMBLe campaign, can be calculated using the observed HONO concentration, [HONO], and the known gas-phase routes for HONO production and loss:

$$\begin{array}{}\text{(14)}& \begin{array}{rl}& P_{\mathrm{other}}=\left(\right[\mathrm{HONO}\left]\right(j\left(\mathrm{HONO}\right)+k_{\mathrm{OH}+\mathrm{HONO}}\left[\mathrm{OH}\right]\left)\right)\\ & -\left(k_{\mathrm{OH}+\mathrm{NO}}\left[\mathrm{OH}\right]\left[\mathrm{NO}\right]\right)),\end{array}\end{array}$$

where $k_{\mathrm{OH}+\mathrm{NO}}=$ 3.3 × 10⁻¹¹ cm³ molec.⁻¹ s⁻¹ (Atkinson et al., 2004), $k_{\mathrm{OH}+\mathrm{HONO}}=\mathrm{6}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ molec.⁻¹ s⁻¹ (Atkinson et al., 2004) and j(HONO) = 2 × 10⁻³ s⁻¹ for average maximum measured concentrations of 1 × 10⁷ molec. cm⁻³ for OH (Whalley et al., 2010), 5.41 × 10⁷ molec. cm⁻³ for NO (Whalley et al., 2010) and 1.23 × 10⁸ molec. cm⁻³ for HONO (Whalley et al., 2010).

Using Eq. (14) this missing HONO production rate for Cabo Verde was 34.6 ppt h⁻¹, which is within a factor of 2 of the rate of HONO production (68 ppt h⁻¹) calculated from nitrate photolysis using our experimental HONO production data for mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ aerosols. These results provide further evidence that particulate nitrate photolysis in the presence of photocatalytic compounds such as TiO₂ found in dust could be significant in closing the HONO budget for this environment (Whalley et al., 2010; Reed et al., 2017; Ye et al., 2017a).

5 Conclusions

The experimental production of HONO from both illuminated TiO₂ aerosols in the presence of NO₂ and from mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ aerosols in the absence of NO₂ was observed, with the HONO concentrations measured using photo-fragmentation laser-induced fluorescence spectroscopy. Using experimental data, the reactive uptake of NO₂ onto the TiO₂ aerosol surface to produce HONO, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, was determined for NO₂ mixing ratios ranging from 34 to 400 ppb, with a maximum ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$ value of (1.26 ± 0.17) × 10⁻⁴ for single-component TiO₂ aerosols observed at 51 ppb NO₂ and for a lamp photon flux of (1.63 ± 0.09) × 10¹⁶ photons cm⁻² s⁻¹ (integrated between 290 and 400 nm). The measured reactive uptake coefficient, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, showed an increase and then a subsequent decrease as a function of NO₂ mixing ratio, peaking at 51 ± 5 ppb. Box modelling studies supported a mechanism involving two NO₂ molecules on the aerosol surface per HONO molecule generated, providing evidence for the formation of a surface-bound NO₂ dimer intermediate. The exact mechanism for HONO formation, for example the step(s) which is accelerated in the presence of light, remains unclear, although previous studies would suggest the process occurs via the isomerisation of the symmetric N₂O₄ dimer to give trans-ONO-NO₂, either via cis-ONO-NO₂ or directly, suggested to be more reactive with water than the symmetric dimer (Finlayson-Pitts et al., 2003; Ramazan et al., 2004; Ramazan et al., 2006; de Jesus Madeiros and Pimentel, 2011; Liu and Goddard, 2012; Murdachaew et al., 2013; Varner et al., 2014). Investigations into the RH dependence of the HONO production mechanism on TiO₂ aerosols showed a peak in production between ∼ 25 %–30 % RH, with lower HONO production at higher NO₂ mixing ratios observed for all RHs tested. The increase in HONO production with increasing RH can be attributed to a higher concentration of H₂O on the surface increasing its availability for the hydrolysis reaction to give HONO, whereas a decrease in HONO production after RH ∼ 30 % could be due to the increased water surface concentration inhibiting the adsorption of NO₂. Using the laboratory reactive uptake coefficient for HONO production, ${\mathit{\gamma }}_{{\mathrm{NO}}_{\mathrm{2}}\to \mathrm{HONO}}$, the rate of production of HONO from illuminated aerosols in Beijing in summer for typical NO₂ mixing ratios and aerosol surface areas was found to be similar to that estimated previously for the production of HONO from urban humic acid aerosol surfaces in Europe.

In the absence of NO₂, significant HONO production from 50:50 mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ aerosols was measured. Using the experimental HONO concentrations observed, a rate of HONO production from nitrate photolysis was calculated, which was then scaled to the ambient conditions encountered at the Cape Verde Atmospheric Observatory in the tropical marine boundary layer. A HONO production rate of 68 ppt h⁻¹ for the mixed $\mathrm{nitrate}/{\mathrm{TiO}}_{\mathrm{2}}$ aerosol was found for CVAO conditions, similar in magnitude to the missing HONO production rate that had been calculated previously in order to bring modelled HONO concentrations into line with field-measured values at CVAO. These results provide further evidence that aerosol particulate nitrate photolysis may be significant as a source of HONO, and hence NO_x, in the remote marine boundary layer, where mixed aerosols containing nitrate and a photocatalytic species such as TiO₂, as found in dust, are present.

However, the production of HONO from pure, deliquesced ammonium nitrate aerosols alone could not be definitively confirmed over the range of conditions used in our experiments, suggesting that another component within the aerosol is necessary for HONO production. Future work should be directed towards studying pure nitrate aerosols over a wider range of conditions, for example varying the aerosol pH, and also adding other chemical species into the aerosol which may promote HONO production.