An in situ flow tube system for direct measurement of N₂O₅ heterogeneous uptake coefficients in polluted environments

The heterogeneous reactivity of dinitrogen pentoxide (N₂O₅) on ambient aerosols plays a key role in the atmospheric fate of NO_x and formation of secondary pollutants. To better understand the reactive uptake of N₂O₅ on complex ambient aerosols, an in situ experimental approach to direct measurement of N₂O₅ uptake coefficient (γN₂O₅) was developed for application in environments with high, variable ambient precursors. The method utilizes an aerosol flow tube reactor coupled with an iterative chemical box model to derive γN₂O₅ from the depletion of synthetically generated N₂O₅ when mixed with ambient aerosols. Laboratory tests and model simulations were performed to characterize the system and the factors affecting γN₂O₅, including mean residence time, wall loss variability with relative humidity (RH), and N₂O₅ formation and titration with high levels of NO, NO_x, and O₃. The overall uncertainty was estimated to be 37 %–40 % at γN₂O₅ of 0.03 for RH varying from 20 % to 70 %. The results indicate that this flow tube coupled with the iterative model method could be buffered to NO concentrations below 8 ppbv and against air mass fluctuations switching between aerosol and non-aerosol modes. The system was then deployed in the field to test its applicability under conditions of high ambient NO₂ and O₃ and fresh NO emission. The results demonstrate that the iterative model improved the accuracy of γN₂O₅ calculations in polluted environments and thus support the further field deployment of the system to study the impacts of heterogeneous N₂O₅ reactivity on photochemistry and aerosol formation.

1 Introduction

Dinitrogen pentoxide (N₂O₅) is a nocturnal reactive intermediate in the atmospheric oxidation of nitrogen oxides (NO_x), which plays an important role in atmospheric photochemistry and the production of secondary pollutants (e.g., Chang et al., 2011). N₂O₅ is formed from the reaction of nitrogen dioxide (NO₂) and nitrate radical (NO₃). Because NO₃ is photolytically unstable, it (and therefore N₂O₅) only accumulates under dark conditions (i.e., at night). The heterogeneous reactions of N₂O₅ on aerosols have been recognized as a major sink for NO_x, affecting the atmospheric lifetime of NO_x and the formation of ozone and other secondary pollutants (e.g., Brown et al., 2007; Wang et al., 2016). The heterogeneous N₂O₅ loss rate on aerosols (k_aerosols) depends on the uptake coefficient of N₂O₅ (γN₂O₅) and the available aerosol surface area, and can be expressed using Eq. (1) when the gas-phase diffusion effect is negligible (Fuchs and Sutugin, 1971; Tang et al., 2014).

$$\begin{array}{}\text{(1)}& {\displaystyle }{k}_{\mathrm{aerosols}}={\displaystyle \frac{\mathrm{1}}{\mathrm{4}}}{c}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}{S}_{\mathrm{a}}\mathit{\gamma }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}},\end{array}$$

where c${}_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ (m s⁻¹) is the mean molecular speed of N₂O₅ and S_a (m² m⁻³) is the aerosol surface area concentration. γN₂O₅ is the reaction probability of a N₂O₅ molecule colliding with the aerosol surface, resulting in net removal via reactions on aerosols. Because γN₂O₅ is a critical parameter for determining N₂O₅ uptake on aerosols, it is necessary to develop reliable methods to measure it.

γN₂O₅ has typically been determined in the laboratory using different types of flow tubes and reactors to measure the decay rate of N₂O₅ in the presence of pure inorganic and organic aerosols or mixed aerosols under different conditions (e.g., Thornton et al., 2003; Tang et al., 2017, and references cited therein). The γN₂O₅ has been shown to be highly dependent on aerosol composition, temperature, and relative humidity; different parameterizations of varying degrees of complexity have thus been proposed to relate γN₂O₅ to aerosol composition (Anttila et al., 2006; Bertram and Thornton, 2009; Davis et al., 2008; Evans and Jacob, 2005; Riemer et al., 2009). In ambient conditions, several methods have been developed to derive γN₂O₅ directly from atmospheric concentrations of N₂O₅. Brown et al. (2007) utilized steady-state approximation of NO₃ and N₂O₅ to derive γN₂O₅ based on the correlation of inverse N₂O₅ steady-state lifetime with NO₂ concentration and aerosol surface area; Phillips et al. (2016) assumed a conserved air mass and used the production rates of ${\mathrm{NO}}_{\mathrm{3}}^{-}$ and ClNO₂ to derive γN₂O₅; and Wagner et al. (2013) applied an iterative chemical box model to derive the appropriate γN₂O₅ to match the predicted N₂O₅ concentration to the measured values with the assumption of the reaction time starting at sunset and with no interception of other NO_x emissions.

Bertram et al. (2009a) introduced an approach to directly measure γN₂O₅ on ambient aerosols by utilizing an entrained aerosol flow reactor coupled with a chemical ionization mass spectrometer (CIMS). By switching sampling between filtered and unfiltered ambient air, the reactivity of N₂O₅ was determined based on a comparison of the pseudo-first-order loss rate of N₂O₅ in ambient air with and without aerosols. The loss rate of N₂O₅ to aerosols (k_aerosols) could be derived from the concentration ratio at the exit of the flow reactor, with the assumption that the wall loss of N₂O₅ is constant in the successive two measurements and that all losses are first order (Bertram et al., 2009a):

$$\begin{array}{}\text{(2)}& k_{\mathrm{aerosols}}=-{\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta }t}}\ln \left({\displaystyle \frac{[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}{]}_{\mathrm{\Delta }t}^{\mathrm{w}/\mathrm{aerosols}}}{[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}{]}_{\mathrm{\Delta }t}^{\mathrm{wo}/\mathrm{aerosols}}}}\right),\end{array}$$

where Δt is the mean residence time in the flow tube reactor and [N₂O₅]_Δt is the N₂O₅ concentration measured at the exit of the flow reactor in the two modes (i.e., the presence and absence of aerosols). This flow tube apparatus was deployed at two urban sites in Boulder and one coastal site in La Jolla to measure γN₂O₅ on ambient aerosols (Bertram et al., 2009b; Riedel et al., 2012). They found that the fluctuation of relative humidity (RH) and NO₃ reactivity (mainly dominated by NO) could lead to great uncertainty in measured γN₂O₅, and they therefore applied some screening criteria, including only data with a RH fluctuation of less than 2 % and NO concentration lower than 750 pptv. This constraint resulted in about 20 % of the data being used for further analysis. It was necessary to adopt these criteria because only first-order loss is considered in the flow tube reactor and other reactions involving ambient NO, NO₂, and O₃ are not. The latter treatment is suitable when ambient concentrations are low and the air mass is relatively stable, but it may be problematic in polluted environments with high fresh NO_x emissions, high O₃ concentrations, and rapidly changing air mass.

Figure 1 Schematic diagram of the aerosol flow tube system.

Several recent studies have revealed active N₂O₅ heterogeneous processes on aerosols at polluted sites and its significant impacts on photochemistry and secondary aerosol formation due to abundant NO_x, O₃, and aerosols (e.g., Li et al., 2016; Tham et al., 2016; Wang et al., 2016; X. Wang et al., 2017; Z. Wang et al., 2017; Yun et al., 2018). The γN₂O₅ derived from ambient concentration measurements showed different characteristics and dependence compared to previous measurements in relatively clean environments (Morgan et al., 2015; Z. Wang et al., 2017). To better understand the reactive uptake of N₂O₅ on complex ambient aerosols, a flow tube reactor approach was developed for direct N₂O₅ reactivity measurement under highly polluted conditions. In the following sections, we describe in detail the method used for determining the N₂O₅ uptake coefficient with an iterative box model and discuss the factors affecting the system's performance and uncertainty. Laboratory tests and field deployment of the method are presented to demonstrate its application under conditions with high ambient concentrations of NO₂ and O₃ and fresh NO emission.

2 Methodology

2.1 Flow tube reactor

The flow tube system consists of an N₂O₅ generation part, a sample inlet with aerosol filter manifold, a flow tube reactor, and detection instruments. A schematic diagram of the experimental apparatus is given in Fig. 1. The sample inlet with an aerosol filter manifold is made of 1∕4 in. outer diameter (OD) stainless-steel tubing. By switching two stainless-steel ball valves, ambient air can be introduced directly into the flow tube or through a PTFE membrane (Pall Life Sciences) to remove aerosols. The flow tube is a Teflon-coated stainless-steel tube, 120 cm in length with an internal diameter of 12.5 cm. The ambient or filtered air enters and exits the flow tube via 10 cm deep 60^∘ tapered end caps. The total flow rate through the flow tube is 4.6 standard liter per minute (SLPM) and includes 120 standard cubic centimeter per minute (SCCM) of N₂O₅ flow, which is introduced through an orthogonal entry to minimize the entrance length of the injected flow. The air pressure in the flow tube reactor is around 730 torr. The adopted flow rate and pressure give a Reynolds number of 55 (i.e., laminar flow) in the flow tube reactor. At the exit of the flow tube reactor, several detection instruments are used to measure the concentrations of N₂O₅, O₃, NO_x, and aerosol surface area.

2.2 Generation of N₂O₅

N₂O₅ is generated in situ from the reaction of O₃ with excess NO₂ at room temperature via Reactions (R1) and (R2), which has been used in many previous lab and field measurements (e.g., Bertram et al., 2009a).

$$\begin{array}{}\text{(R1)}& {\displaystyle }& {\displaystyle }{\mathrm{O}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{2}}\to {\mathrm{NO}}_{\mathrm{3}}+{\mathrm{O}}_{\mathrm{2}}\text{(R2)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+{\mathrm{NO}}_{\mathrm{2}}+\mathrm{M}\leftrightarrow {\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+\mathrm{M}\end{array}$$

In this study, ozone was generated from O₂ photolysis with a mercury lamp in a commercial calibrator (model 4010, Sabio Instrument Inc.). One hundred SCCM of produced O₃ flow was mixed with 20 SCCM of NO₂ (10 ppmv balanced in N₂; Arkonic, USA) in a Teflon reaction chamber (volume = 68 cm³) for about 28 s prior to injection into the flow tube reactor. Under conditions of excessive NO₂, the system was expected to shift the R2 equilibrium towards N₂O₅. Concentrations of synthesized N₂O₅ were calculated from observed changes in NO₂ (before and after addition of O₃), and the N₂O₅ content had also been inter-validated with a cavity ring-down spectrometer (CRDS) in our previous studies (Wang et al., 2016). Prior to the N₂O₅ generation, the system was purged with dry zero air and NO₂ for at least 2 h, to minimize the water content level and stabilize the NO₂ source. This system was shown to be able to produce N₂O₅ concentrations from 1 to 10 ppbv (after dilution in the flow tube). In a typical experiment used in the present study, the input of the N₂O₅ source to the top of the flow tube contained 4.3 ppbv of N₂O₅, together with 106 ppbv of O₃ and 57 ppbv of NO₂. The stability of the synthetic-N₂O₅ source was tested continuously for 8 h, and the variation of the signal was within ±2 % in each hour. More detailed description of the N₂O₅ generation can be found in Wang et al. (2016).

2.3 Detection instruments

At the exit of the flow tube reactor, O₃ was measured by a UV photometric analyzer (Thermo, Model 49i) and NO₂ was measured by a chemiluminescence NO_x analyzer (Thermo, Model 42i) equipped with a blue-light photolytic converter (BLC). The aerosol number concentration and size distribution (10 nm to 10 µm) were measured by a wide-range particle spectrometer (WPS, model 1000XP, MSP Corporation, USA) to determine the aerosol surface area. The uncertainty of the aerosol surface area measurement was 20 %–30 % (Z. Wang et al., 2017; Tham et al., 2018). The transmission of aerosols in the flow tube was evaluated using laboratory-generated (NH₄)₂SO₄ particles. The passing efficiency was around 50 % for particles with a size of 20 nm and more than 90 % for particles larger than 100 nm. The total surface area loss in the flow tube was around 10 %–25 %. The N₂O₅ and ClNO₂ concentrations were quantified by an iodide-adduct chemical ionization mass spectrometer (CIMS; THS Instrument, Atlanta). The CIMS has been deployed in several field campaigns, and the setup and operation have been previously described (Tham et al., 2016; Wang et al., 2016; X. Wang et al., 2017; Z. Wang et al., 2017). Briefly, the primary ion I⁻ was generated from ionization of CH₃I diluted in N₂ flow through a ²¹⁰Po source. The N₂O₅ and ClNO₂ were detected as ion clusters of I(N₂O₅)⁻ and I(ClNO₂)⁻ at 235 and 208 m∕z by the quadrupole mass spectrometer. Because of the higher pipeline resistance in the flow tube reactor compared to ambient measurement, a smaller orifice with a 0.0135 in diameter was utilized in the CIMS inlet to reduce the sample flow, and another orifice was added before the scroll pump to keep the pressure in the ionization reaction chamber at 50 torr. The corresponding sample flow was 0.4 SLPM. The detection limit of the instrument was estimated to be 2 pptv (1 min averaged data), and the uncertainty of the CIMS measurement was estimated as ±25 % (Tham et al., 2016). The ambient volatile organic compounds (VOCs) were determined using an online gas chromatograph (GC) coupled with a flame ionization detector (FID) and a mass spectrometer (MS). The VOC concentrations were used to determine the $k_{{\mathrm{NO}}_{\mathrm{3}}\text{-VOC}}$ in the aerosol flow tube system, which was treated as constant during the short time period of flow tube measurement. The ambient NO level was measured by another chemiluminescence NO_x analyzer (Thermo, Model 42i) equipped with a molybdenum converter.

3 Determination of residence time

The mean residence time that represents the average reaction time of the gases in the flow tube reactor is an essential parameter in calculation of the reactive uptake coefficient. In a previous flow reactor studies (e.g., Thornton et al., 2003), the average residence time has usually been calculated from the flow rate and flow tube volume assuming an ideal laminar flow. To determine the mean residence time for non-ideal flow more accurately, the residence time distribution (RTD) method introduced by Danckwerts (1953) was used in the present study. The RTD method involves introduction of an inert tracer species into the reactor and detection of its transient concentration leaving the reactor outlet, and it has been widely used in previous lab studies to characterize the mixing and flow behavior of non-ideal aerosol flow reactors (e.g., Lambe et al., 2011).

Pulse injection of highly concentrated ClNO₂ was used in the present study to measure the RTD and hence determine the mean residence time. ClNO₂ is an inert gas within the dark Teflon-coated flow tube reactor and can be measured by CIMS with high time resolution (>1 Hz). ClNO₂ was synthesized in situ via passing the N₂O₅ through a NaCl slurry in the Teflon tubing reactor (Wang et al., 2016). The pulse injection was controlled by a solenoid valve. At t=0 s, 120 SCCM (the same flow as N₂O₅ injection during the uptake measurement) of ClNO₂ was directly injected into the flow tube reactor; at t=2 s, the solenoid valve switched and the ClNO₂ flow was passed through a charcoal filter to provide zero gas into the flow tube reactor. The RTD function E(t) is defined by the following equation:

$$\begin{array}{}\text{(3)}& E\left(t\right)={\displaystyle \frac{C_{\left(t\right)}}{{\int }_{\mathrm{0}}^{\mathrm{\infty }}{C}_{\left(t\right)}\mathrm{d}t}},\end{array}$$

where C_(t) represents the ClNO₂ concentration measured at time t. Then the mean residence time can be calculated as follows:

$$\begin{array}{}\text{(4)}& \mathrm{\Delta }t=\underset{\mathrm{0}}{\overset{\mathrm{\infty }}{\int }}tE\left(t\right)\mathrm{d}t.\end{array}$$

The measurement result of the residence time test is shown in Fig. 2. With a flow rate of 4.6 SLPM in the flow tube reactor, the mean residence time determined from the RTD method was 149±2 s. In comparison, the residence time calculated using the flow rate and reactor volume gives a value of 159±5 s, which is 6.7 % higher than that given by the RTD method, and could lead to underestimation of the rate constant. The RTD function in Fig. 2 is clearly different from the ideal laminar flow reactor. Bertram et al. (2009a) have suggested that the determined rate constant would be underestimated by up to 25 % due to non-ideal plug flow conditions. More discussion of the uncertainty in γN₂O₅ calculation associated with residence time distribution is presented in Sect. 5.

Figure 2 The measured residence time distribution of the injected ClNO₂ in the flow tube reactor. The blue line represents the fitted residence time distribution of the ClNO₂ pulse injection experiment. The pink line represents the expected residence time distribution of an ideal laminar flow reactor without diffusion.

4 Iterative box model for determination of loss rate and uptake coefficient

As described previously, the reactivity of N₂O₅ can be investigated using the aerosol modulation by comparing the loss rate of generated N₂O₅ in the flow tube reactor with and without ambient aerosols. Previous studies (e.g., Bertram et al., 2009a) utilized the exit-concentration ratio of N₂O₅ to obtain the N₂O₅ loss rate on aerosols. However, air mass changes lead to different NO₃ loss rates and production rates over a short time period (i.e., a typical sampling cycle for about 1 h), and high background NO₂ and O₃ in the ambient air would affect the exit N₂O₅ concentration and hence bias the measurement of loss rate and uptake coefficient from the flow tube experiments. To minimize the potential influences of high levels of ambient pollutants and rapidly changing air mass, a time-dependent box model constrained by the real measurement data was used in the present study to directly calculate the N₂O₅ loss rate in both aerosol and non-aerosol mode, considering multiple reactions describing the production and loss of NO₃ and N₂O₅ (Reactions R1–R6) under ambient conditions.

$$\begin{array}{ll}\text{(R3)}& {\displaystyle }& {\displaystyle }{\mathrm{O}}_{\mathrm{3}}+\mathrm{NO}\to {\mathrm{NO}}_{\mathrm{2}}+{\mathrm{O}}_{\mathrm{2}};k_{\mathrm{3}}\text{(R4)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{NO}\to \mathrm{2}{\mathrm{NO}}_{\mathrm{2}};k_{{\mathrm{NO}}_{\mathrm{3}}\text{-NO}}\text{(R5)}& {\displaystyle }& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{VOC}\to \mathrm{products};k_{{\mathrm{NO}}_{\mathrm{3}}\text{-VOC}}{\displaystyle }& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+\mathrm{aerosols}/\mathrm{wall}\to \mathrm{products};\\ \text{(R6)}& {\displaystyle }& {\displaystyle }{k}_{\mathrm{het}}=k_{\mathrm{wall}}+k_{\mathrm{aerosols}}\end{array}$$

The rate constants for Reactions (R1) to (R4) recommended by the National Aeronautics and Space Administration–Jet Propulsion Laboratory (Sander et al., 2009) were used. The loss rate coefficient $k_{{\mathrm{NO}}_{\mathrm{3}}\text{-VOC}}$ from NO₃ reactions with VOCs (Reaction R5) was determined by ambient measured VOC concentrations and rate coefficients from Atkinson and Arey (2003). The N₂O₅ heterogeneous loss rate coefficient k_het (Reaction R6) including heterogeneous loss on both aerosol and reactor surfaces was the only adjustable parameter, while other parameters such as N₂O₅, NO, NO₂, and O₃ concentration were constrained by concurrent measurements. The model simulated the reactions starting from the entrance of the reactor after mixing the ambient air sample and synthetic-N₂O₅ source. The initial concentrations of [NO₂]_t=0 and [O₃]_t=0 were calculated from the ambient measured levels of NO₂ and O₃ and those from the N₂O₅ source. Given the constraint of measured parameters at the entrance of the flow tube reactor – including [NO]_t=0, [NO₂]_t=0, [O₃]_t=0, [N₂O₅]_t=0, [VOCs]_t=0, temperature, and pressure – these reactions could be integrated in time (performed in Matlab with the Kinetic PreProcessor using a Radau5.integrator) (Damian et al., 2002) to obtain the exit concentrations of NO₂, O₃, and N₂O₅. The calculated concentrations were then compared with the measured concentrations at the exit of the flow tube reactor, and the N₂O₅ loss rate coefficient was tuned until the N₂O₅ concentration predicted by the box model agreed with the measured N₂O₅ concentration, [N₂O₅]_Δt. Assuming that k_wall are constant between successive flow tube experiments with and without aerosols, the loss rate coefficient on aerosols surfaces can be determined from the differences between two modes: $k_{\mathrm{aerosols}}=k_{\mathrm{het}}^{\mathrm{w}/\mathrm{aerosols}}-k_{\mathrm{het}}^{\mathrm{wo}/\mathrm{aerosols}}$. Then the uptake coefficient of N₂O₅ on aerosol surfaces (γN₂O₅) can be calculated by the following equation:

$$\begin{array}{}\text{(5)}& {\displaystyle }\mathit{\gamma }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}=\mathrm{4}\left(k_{\mathrm{het}}^{\mathrm{w}/\mathrm{aerosols}}-k_{\mathrm{het}}^{\mathrm{wo}/\mathrm{aerosols}}\right)/\left(c{S}_{\mathrm{a}}\right).\end{array}$$

In circumstances without concurrent ambient measurement of NO₂ and O₃ and when accurate measurements are only available at the flow tube outlet, as in the present study, an iterative box model including both backward and forward simulation is needed. Following the method suggested by Wagner et al. (2013), the relevant reactions can be integrated backward starting with the measured concentrations at the exit of the reactor (t=Δt) to obtain the initial concentrations. As the cycle between NO₃ and N₂O₅ is fast and quickly established in high-NO_x conditions, the NO₃ and N₂O₅ are considered as one singular N₂O₅^∗ species by assuming NO₃ and N₂O₅ are in equilibrium (Brown et al., 2003). Doing this also makes backward reaction simulation possible by avoiding unstable equilibrium in the box model. The NO at the entrance of the flow tube could react quickly with O₃ and NO₃, with a short lifetime of a few seconds, resulting in near-zero concentration at the exit of the flow tube. To initialize the simulation, a time-dependent NO concentration in the flow tube must be derived. An approximate [NO] profile can be estimated from a forward simulation with inputs of measured initial NO, N₂O₅, guessed k_het, and estimated initial NO₂ and O₃ concentrations from the following equations. The measured initial NO data used 3 min earlier data as input data considering the mean residence time of 150 s.

$$\begin{array}{}\text{(6)}& {\displaystyle }& {\displaystyle }[{\mathrm{NO}}_{\mathrm{2}}{]}_{\mathrm{0}}=[{\mathrm{NO}}_{\mathrm{2}}{]}_{\mathrm{\Delta }t}\times e^{\mathrm{\Delta }t{k}_{\mathrm{1}}[{\mathrm{O}}_{\mathrm{3}}{]}_{\mathrm{\Delta }t}}[\mathrm{NO}{]}_{\mathrm{0}}\text{(7)}& {\displaystyle }& {\displaystyle }[{\mathrm{O}}_{\mathrm{3}}{]}_{\mathrm{0}}=[{\mathrm{O}}_{\mathrm{3}}{]}_{\mathrm{\Delta }t}\times e^{\mathrm{\Delta }t{k}_{\mathrm{1}}[{\mathrm{NO}}_{\mathrm{2}}{]}_{\mathrm{\Delta }t}}+[\mathrm{NO}{]}_{\mathrm{0}}\text{(8)}& {\displaystyle }& {\displaystyle }{\left[\mathrm{NO}\right]}_t=[\mathrm{NO}{]}_{\mathrm{0}}\times e^{-t\left(k_{\mathrm{3}}{\left[{\mathrm{O}}_{\mathrm{3}}\right]}_{\mathrm{0}}+\frac{k_{\mathrm{4}}{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}_{\mathrm{0}}}{K_{\mathrm{eq}}{\left[{\mathrm{NO}}_{\mathrm{2}}\right]}_{\mathrm{0}}}\right)}\end{array}$$

The estimated [NO] profile was then constrained in the backward model simulation – together with inputs of measured concentrations of N₂O₅, NO₂, and O₃ at the exit of the flow tube reactor and the initially guessed k_het – to derive the initial mixing ratios. The box model was run forward and backward iteratively with updated values and adjusted k_het until simulated N₂O₅ concentration matched the measurement at the exit of the flow tube reactor. The agreement of simulated NO₂ and O₃ concentrations with measurements was also used as a check to validate the model calculation. Thus, the uptake coefficient of N₂O₅ was determined from Eq. (5). An example of the iterative box model calculation is shown in Fig. 3.

Figure 3 An example of the iterative box model simulation to derive k_het from the measured concentrations of NO₂, O₃, and N₂O₅ at the exit of the flow tube reactor. The concentration profiles obtained from the simulation in 10 iterations are shown for (a) O₃, (b) NO₂, (c) N₂O₅, and (d) NO. In the upper part of (e), the adjusted N₂O₅ loss rate is shown for each iteration. The lower part of (e) shows the concentration differences between the model simulation and measurements of N₂O₅, O₃, and NO₂ at the exit of the reactor for each iteration. (f) shows the comparison between measured initial concentrations from laboratory test and predicted initial concentrations from the iterative model.

For some conditions, the iterative box model returns a negative N₂O₅ loss rate coefficient. This non-physical result might result from much larger fluctuations of $k_{{\mathrm{NO}}_{\mathrm{3}}}$ or k_wall in the system during each measurement cycle. When k_aerosol is small due to the low S_a or insignificant uptake, the $k_{{\mathrm{NO}}_{\mathrm{3}}}$ or k_wall may dominate the N₂O₅ loss in flow tube reactor, and the fluctuations of $k_{{\mathrm{NO}}_{\mathrm{3}}}$ or k_wall due to the air mass or temperature/RH changes would bias the k_aerosol determination and lead to large uncertainty or negative values. This situation often occurred under conditions of fresh NO emission; more discussion of the influence of NO is presented in Sect. 6.

5 Laboratory test and overall uncertainty

Laboratory tests of N₂O₅ uptake on (NH₄)₂SO₄ aerosols were also performed with different NO, NO₂, and O₃ conditions, and the uptake coefficients were determined from the iterative box model analysis described above with input of measured concentrations. The determined uptake coefficient ranged from 0.018 to 0.026 (Table S1 in the Supplement), which are similar to previous laboratory study results with (NH₄)₂SO₄ aerosols (Davis et al., 2008). The consistency also can serve as a validation of the applicability of the introduced system and method. In addition, we also compared the measured initial concentration of NO₂ and O₃ during the lab tests with that predicted from the iterative model (Fig. 3f). The NO₂ concentration matched well between model prediction and measurement, while O₃ was a little lower from the model simulation, which might be due to the wall loss or other loss ways of O₃ in the flow tube reactor.

In the present work, the determination of k_aerosols is independent of the magnitude of k_wall, but the stability of k_wall is critical for the accurate retrieval of k_aerosols. k_wall depends on RH, and the variability in RH on the timescale of the measurement can introduce additional uncertainty (Bertram et al., 2009a). Laboratory experimental tests have been conducted to investigate the variability of k_wall with RH in the current flow tube system. k_wall can be determined from the previously described iterative model with the measurement of N₂O₅ loss through the flow tube in a zero air flow in the absence of aerosols. As shown in Fig. 4, k_wall has a strong positive relationship with RH and increases with RH, especially when RH is higher than 50 %. The consistent k_wall at each RH condition with different initial N₂O₅ concentrations suggests that k_wall in the current system is relatively stable under different chemical conditions but varies as a function of RH.

The sample air exiting the flow reactor was continuously measured by a RH probe, and the results showed that the RH variation between the aerosol presence and absence modes was within 1 % more than 80 % of the time during the ambient measurement cases. This result would translate into an uncertainty of ($\pm \mathrm{0.15}\times {\mathrm{10}}^{-\mathrm{3}}$) to ($\pm \mathrm{2.4}\times {\mathrm{10}}^{-\mathrm{3}}$) in γN₂O₅ with RH of 20 % to 70 %, respectively, and a S_a of 1000 µm² cm⁻³. To minimize the magnitude of the variability in k_wall, the wall of the reactor was coated with Teflon PFA, and the flow tube reactor was cleaned daily with distilled water. Ultrasonic baths were also utilized after a 1-week period of ambient measurement to remove aerosol buildup from the wall of the flow tube reactor.

Figure 4 Relative humidity dependence of the wall loss rate coefficient (k_wall) of N₂O₅ in the flow reactor.

Table 1 Parameters varied in the Monte Carlo simulations.

^a 1σ standard deviation for the varied parameters. ^b The k_wall is calculated from RH, using the relation fitting equation in Fig. 4. ^c The variation of k_wall is calculated as RH varied 1 %.

Figure 5 The partial uncertainty in γN₂O₅ determination associated with k_wall changes, VOC variation, and the variation of different parameters during the measurement cycles derived from Monte Carlo simulations for three individual sets with 400 simulations at (a) RH =40 % and (b) different RH values. In these three data sets, the condition was set as follows: surface area =1000 µm² cm⁻³, reaction time =150 s, initial O₃=80 ppbv, initial NO₂=50 ppbv, initial NO =2 ppbv, initial N₂O₅=5 ppbv, temp =25 ^∘C, and $k_{{\mathrm{NO}}_{\mathrm{3}}\text{-VOC}}=\mathrm{0.01}$ s⁻¹.

In addition to k_wall being affected by RH, uncertainty in k_aerosols determination can also result from N₂O₅ source variability, NO₃ reactivity with VOCs, and precision as well as accuracy associated with the measurement of all parameters. The long measurement cycle may also bring about uncertainty due to variation in concentrations in two operation modes. As described in Sect. 2.2, the stability of the N₂O₅ generation source was within ±2 % over an hour. In the present study, online VOCs were measured with a time resolution of 1 h. A ±0.01 s⁻¹ variation of $k_{{\mathrm{NO}}_{\mathrm{3}}\text{-VOC}}$ would lead to a single-point uncertainty in γN₂O₅ of $\pm \mathrm{0.4}\times {\mathrm{10}}^{-\mathrm{3}}$ for S_a = 1000 µm² cm⁻³. NO reacts at a faster rate with NO₃, having a larger impact on the γN₂O₅ calculation compared to VOCs. With a constrained real-time NO concentration, the iterative model can buffer against small NO changes. Stability of NO, NO₂, O₃, and N₂O₅ for a period of at least 5 min for each mode is required to ensure that the flow tube reactor measurement and iterative model yield reasonable results. The measurement precision and variation of these species during each cycle might also introduce uncertainty in the iterative model calculation.

The uncertainty in the γN₂O₅ determination associated with k_wall changes, VOC variation, and the variation of the different parameters during the measurement cycles was estimated with a Monte Carlo approach, as described in Groß et al. (2014), by assessing the uncertainty from individual key parameters (shown in Table 1) in the calculation model. γN₂O₅ was found to be most sensitive to RH, which was closely related to k_wall as discussed before. Figure 5a shows the partial uncertainty of γN₂O₅ derived from Monte Carlo simulations with RH at 40 %. The single-point uncertainty in γN₂O₅ was estimated to be $\pm \mathrm{4.1}\times {\mathrm{10}}^{-\mathrm{3}}$ for γN₂O₅ around 0.03 and $\pm \mathrm{3.6}\times {\mathrm{10}}^{-\mathrm{3}}$ for γN₂O₅ around 0.01, with RH of 40 %. The uncertainty increased with RH and would be 9 % to 17 % at γN₂O₅ around 0.03 for RH ranging from 20 % to 70 % (Fig. 5b).

Sensitivity tests with the iterative model calculation were performed to evaluate the uncertainty associated with measurement accuracy of N₂O₅ and VOCs, by varying the input N₂O₅ concentrations and $k_{{\mathrm{NO}}_{\mathrm{3}}\text{-VOC}}$ in both modes. It is found that the N₂O₅ measurement uncertainty of 25 % (Tham et al., 2016; Z. Wang et al., 2017) would translate into an uncertainty of 12 % in the γN₂O₅ (shown in the Supplement). The VOC measurement uncertainty, however, has negligible influence on γN₂O₅ calculation. In a previous flow tube method introduced by Bertram et al. (2009a), the homogeneous reaction was expected to be independent of the aerosol and non-aerosol modes and was thus able to be canceled out in the calculation. Only strong atmospheric variation in VOC in a short time period would influence the N₂O₅ uptake measurement. The uncertainty introduced by the aerosol surface area measurement including aerosol loss influence would be propagated to an uncertainty in the γN₂O₅ calculation of 30 %.

As mentioned in Sect. 3, the use of mean residence time rather than RTD function by assuming an ideal reactor and ignoring diffusion and dispersion processes would also introduce uncertainties. In order to evaluate the magnitude of this bias, we performed a simplified test by comparing a first-order loss rate from mean residence time with a residence time distribution range. Briefly, the mean concentration of N₂O₅ at the exit of the reactor could be expressed by

$$\begin{array}{}\text{(9)}& \left[\stackrel{\mathrm{‾}}{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}\right]=\underset{\mathrm{0}}{\overset{\mathrm{\infty }}{\int }}{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}_t{E}_t\mathrm{d}t=\underset{\mathrm{0}}{\overset{\mathrm{\infty }}{\int }}{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}_{\mathrm{0}}{e}^{-kt}{E}_t\mathrm{d}t,\end{array}$$

where [N₂O₅]_t is the average concentration exit from the reactor between t and t+dt, E(t) is the residence time distribution function, and k is the first-order loss rate coefficient of N₂O₅. The results showed that the first-order loss rate calculated from the distribution function was higher than that with a mean residence time and was about 5 % or 16 % higher when the ratio of $\frac{{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}_t}{{\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}_{\mathrm{0}}}$ was 0.6 or 0.2 in the flow tube system, respectively. When all of these factors are incorporated, the estimated total uncertainty is propagated to be 37 % to 40 % at γN₂O₅ around 0.03 with 1000 µm² cm⁻³ S_a for RH ranging from 20 % to 70 %.

6 Demonstration of γN₂O₅ measurements under polluted conditions

In polluted environments, high concentrations of NO₂, O₃, or NO in ambient air would affect the determination of the N₂O₅ loss rate and uptake coefficient in the flow tube experiments. To investigate the effect of multiple reactions of these species in polluted conditions, a series of tests with different conditions were simulated to compare the derived loss rate and uptake coefficient with and without consideration of N₂O₅ regeneration and NO titration in the flow tube system. Using the forward box model described in Sect. 4, the process in the flow tube reactor was simulated with an assumed fixed S_a of 1000 µm² cm⁻³, γN₂O₅ of 0.03, k_wall of 0.004 s⁻¹, and $k_{{\mathrm{NO}}_{\mathrm{3}}\text{-VOC}}$ of 0.01 s⁻¹. Various conditions were simulated with different O₃, NO₂, and NO levels introduced into the flow tube, and the resulting concentrations of N₂O₅, NO₂, and O₃ at the exit of the reactors with and without aerosols modes were obtained. The loss rate and uptake coefficients of N₂O₅ were then calculated using the simple exit-concentration ratio approach (Eq. 2) and time-dependent iterative box model, respectively. The difference in γN₂O₅ obtained from these two methods reflects the effect of N₂O₅ regeneration and NO titration on uptake coefficient determination.

Figure 6 The influence of multiple reactions resulting from high ambient NO₂ and O₃ levels under different ambient NO₂ levels from 0 to 40 ppbv. The colors indicate the NO₃ production rate (pNO₃) at the entrance of the flow tube reactor after mixing with 106 ppbv of O₃ and 57 ppbv of NO₂ from the N₂O₅ source.

Figure 7 (a) Simulation results of NO titration effect on γN₂O₅. The γN₂O₅ ratio represents (γN₂O₅ from the iterative model) ∕ (γN₂O₅ from the method of ignoring multiple reactions). Initial NO and initial N₂O₅ represent the respective initial concentrations of NO and N₂O₅ in the flow tube reactor. The lines represent the simulation result, and the cubes represent the lab test result. (b) k_het calculated via the iterative model in laboratory experiments with constant RH of 21 %, different initial N₂O₅, and varied NO additions.

Figure 6 shows the simulation results for the derived uptake coefficients regarding the effect of N₂O₅ formation in the flow tube reactor, with O₃ varying in the range of 0–100 ppbv and NO₂ in the range of 0–40 ppbv without NO presence in the ambient air. The N₂O₅ source input was fixed at 4.3 ppbv, as measured in the laboratory, together with 106 ppbv of O₃ and 57 ppbv of NO₂ from the N₂O₅ source. The N₂O₅ regeneration effect on γN₂O₅ calculation was significant when O₃ and NO_x levels in the ambient air were high. For example, at NO₂=40 ppbv and O₃=100 ppbv, which may frequently be encountered in city cluster regions in China, neglecting N₂O₅ formation in the flow tube would result in underestimating γN₂O₅ by 42 %.

To demonstrate the influence of NO titration, simulation tests were performed with NO varying from 0 to 8 ppbv. Because the reaction rate of NO with NO₃ is 2 orders of magnitude faster than that of NO with O₃, the initial N₂O₅ level would affect the NO titration process. We performed the simulation with different initial N₂O₅ concentrations injected into the flow tube reactor. As the green line in Fig. 7a indicates, the calculated γN₂O₅ will be greatly underestimated when NO concentration increases, up to 55 % at a NO level of 8 ppbv with an initial N₂O₅ level of 3 ppbv compared to a NO level of 0. During the laboratory experiments, two initial N₂O₅ conditions with the input of an additional 5 ppbv of NO were also tested. The determined γN₂O₅ from the iterative model simulation and exit-concentration method was compared and is shown as cubes in Fig. 7a. The model results lie within the uncertainty range of the measurements, further cross-validating the NO influences and the model simulation. Figure 7a also shows that a lower initial N₂O₅ leads to a larger underestimation of γN₂O₅ in the presence of NO. It is not desirable to use N₂O₅ concentrations above 5 ppbv to minimize the NO effect, because of other potential artifacts associated with working at high concentration (Thornton et al., 2003).

To explore which NO level would leave an extremely low N₂O₅ concentration in the exit of the reactor and make N₂O₅ loss rate measurement impossible, a series of experiments in clean air with additional NO was conducted in the laboratory to investigate NO titration effects and the performance of the iterative model in buffering against high NO. As shown in Fig. 7b, the derived k_het showed consistent results for zero NO and NO <6 ppbv conditions when RH and other parameters were unchanged. With higher NO addition and a lower initial N₂O₅ level, the calculated k_het, however, could be underestimated due to greater uncertainty when NO₃ and N₂O₅ were insufficient to titrate with NO. Figure 7b also shows that the introduced box model method could buffer against NO below 8 ppbv with an initial N₂O₅ level of 4.3 ppbv. For future development, an activated-carbon scrubber in the inlet to reduce the gas-phase interferers (NO, NO₂, O₃, VOCs) but transmit aerosols could be a complementary approach to apply the flow tube system coupled with iterative box model analysis to even more polluted conditions.

In summary, the simulation and laboratory results demonstrate that neglecting the formation and titration reactions in a flow tube reactor will result in underestimating γN₂O₅. To reduce the NO titration effect, a relatively high level of N₂O₅ (but less than 5 ppbv) should be introduced to the flow tube reactor. Consideration of the multiple reactions in the iterative model is sufficiently robust to encourage further development to improve the accuracy of γN₂O₅ calculations.

7 Ambient measurement

During winter 2017, the flow tube system was deployed to measure the N₂O₅ uptake coefficient at a sub-urban site in Heshan, Guangdong, in southern China. The sampling time for each mode with and without ambient aerosols lasted for at least 15 min to ensure 5 min stable data at the exit for subsequent modeling analysis. The measured 5 min average concentrations of initial NO and exit N₂O₅, NO₂, and O₃ were used as the inputs in the iterative box model to derive k_het and γN₂O₅. Most measurements were conducted during the daytime to avoid interruption of nighttime ambient N₂O₅, and daytime N₂O₅ levels could be neglected. The average ambient temperature, RH, NO, NO₂, and O₃ during the field campaign were 23 ^∘C, 51 %, 3.2 ppbv, 23 ppbv, and 32 ppbv, respectively. As discussed previously, changes in RH and temperature can influence the stability of k_wall and N₂O₅–NO₃ equilibrium, and thus upset γN₂O₅ measurement. In the cases where γN₂O₅ measurement was affected by extreme fluctuations in NO (above 8 ppbv), temperature and RH (fluctuation >2 %) were discarded from the analysis.

In addition to the iterative box model approach, we also used the exit-concentration ratio approach (cf. Eq. 2) to calculate the γN₂O₅. Figure 8 exhibits the comparison of γN₂O₅ obtained using these two methods. Fifteen out of 51 measurements occurred under relatively “clean and stable” conditions (defined as ambient NO <1 ppbv, fluctuation of NO <0.3 ppbv, NO₃ production rate <0.8 ppbv min⁻¹, and fluctuation of NO₂ and O₃ <4 ppbv), and the corresponding values of γN₂O₅ from the two methods show good correlation, with an average ratio of 1.34, which is consistent with our previous simulation results that the exit-concentration ratio approach could underestimate γN₂O₅ mainly due to N₂O₅ regeneration reaction. For conditions with higher precursor concentrations and fluctuations, a larger discrepancy between γN₂O₅ from two methods was found (see Fig. 8). As described previously, greater uncertainty in the exit-concentration ratio approach could result from multiple reactions and air mass changes. The fluctuations of NO, NO₂, and O₃ could greatly affect the exit N₂O₅ concentration ratio. For example, a lower NO level and higher NO₂ and O₃ levels in the aerosol mode relative to the non-aerosol mode would result in a higher exit N₂O₅ concentration ratio, which would lead to underestimation of γN₂O₅ and even negative values (see Fig. 8 and Supplement). As even a 1 ppbv fluctuation of NO concentration could largely affect the exit N₂O₅ concentration, it would result in significant uncertainty for the exit-concentration ratio approach. When NO concentration is much higher, for example in the aerosol-existing mode, the measured N₂O₅ concentration is lower due to NO titration; thus the uptake coefficient is overestimated when only the end concentration ratio of N₂O₅ in two modes is compared.

Figure 8 Comparison of γN₂O₅ determined from the exit-concentration ratio approach and the iterative model approach for all available data measured in the Heshan campaign. The blue points represent the data obtained under “clean and stable condition”, while green points are data obtained from other condition. The “clean and stable condition” is defined as follows: ambient NO <1 ppbv, the change of NO <0.3 ppbv, the NO₃ production rate <0.8 ppbv min⁻¹, and the change of NO₂ and O₃ <4 ppbv. The error bar represents the uncertainty calculated by the Monte Carlo approach under the measurement condition.

Figure 9 Two sample cases are shown. In the upper panel, the blue and light brown dots represent 1 min ambient O₃ and NO₂ data, respectively. In the middle panel, the brown dots represent 1 min ambient NO data. In the lower panel, the pink dots represent 1 min average of N₂O₅ concentration normalized to the initial N₂O₅ concentration in the flow tube reactor. The calculated total N₂O₅ loss rate derived from the iterative model with 5 min average input data (the blue bar) is also shown for each cycle.

Two example cases with large air mass changes are shown in Fig. 9. In Fig. 9a, a case with high and fluctuating NO emission was observed on the night of 21 March 2017, with average ambient concentrations of NO of 6 ppbv, NO₂ of 27 ppbv, O₃ of 2 ppbv, and S_a of 1880 µm² cm⁻³. γN₂O₅ was determined to be 0.028 from the iterative model approach, and a higher γN₂O₅ value of 0.036 was obtained from the exit-concentration ratio approach. The overestimated γN₂O₅ from the exit-concentration ratio approach could be explained by the increased NO level (∼1.5 ppbv) in the aerosol mode. For comparison, another two periods of data points in the 21 March case (Fig. 9a) with different NO levels were also selected to derive the k_het, and the results showed good consistency (0.0136–0.0140 s⁻¹) (Fig. S2 in the Supplement), also demonstrating the applicability of the iterative model in buffering against fluctuating NO. In Fig. 9b, another case with fluctuating NO₂ and O₃ levels was observed on 26 March 2017, and the NO₂ level was about 5 ppbv higher, but the O₃ level was about 11 ppbv lower in aerosol mode. With S_a of 681 µm² cm⁻³, γN₂O₅ was determined to be 0.020 from the iterative model approach and a much lower value of 0.008 from the exit-concentration ratio approach. The consideration of multiple reactions in the iterative model approach was able to buffer against small fluctuations of precursors in switching between aerosol and non-aerosol modes. The results demonstrated the applicability of the iterative model approach to directly measuring the N₂O₅ heterogeneous uptake coefficient under conditions of high NO₂ and O₃ and fresh NO emission.

8 Summary and conclusion

An in situ experimental approach for direct measurement of N₂O₅ heterogeneous reactivity in a polluted environment was developed and introduced in the present study. The method uses an aerosol flow tube reactor combined with an iterative box model, to determine the heterogeneous loss rate of synthesized N₂O₅ on ambient aerosols with consideration of multiple reactions affecting N₂O₅ in the flow tube. A series of laboratory and model simulations were conducted to test the applicability of the system under different conditions. The overall γN₂O₅ uncertainty from the variations of parameters during two operation modes and uncertainties associated with measurements of gaseous and aerosol species was propagated to be 37 %–40 % at γN₂O₅ around 0.03 with S_a of 1000 µm² cm⁻³ and RH ranging from 20 % to 70 %. Field deployment of this system at a polluted suburban site in southern China demonstrated the applicability of the introduced method in measuring N₂O₅ uptake coefficients in polluted environments with high ambient levels of O₃, NO, and NO₂ and rapid air mass changes. Both field results and simulation tests demonstrate that neglecting multiple reactions within the flow tube reactor leads to underestimating γN₂O₅ values. The introduced approach could also be used to investigate the heterogeneous reactivity of other trace gases on ambient aerosols in polluted environments.