Direct measurement of N₂O₅ heterogeneous uptake coefficients on ambient aerosols via an aerosol flow tube system: design, characterization and performance

An improved aerosol flow tube system coupled with a detailed box model was developed to measure N₂O₅ heterogeneous uptake coefficients (γ(N₂O₅)) on ambient aerosols directly. This system features sequential measurements of N₂O₅ concentrations at both the entrance and exit of the flow tube to ensure an accurate retrieval of N₂O₅ loss in the flow tube. Simulation and laboratory tests demonstrate that this flow tube system is able to overcome the interference from side reactions led by varying reactants (e.g., NO₂, O₃ and NO) and to improve the robustness of results with the assistance of the box model method. Factors related to γ(N₂O₅) derivation – including particle transmission efficiency, mean residence time in the flow tube and the wall loss coefficient of N₂O₅ – were extensively characterized for normal operating conditions. The measured γ(N₂O₅) on (NH₄)₂SO₄ model aerosols were in good agreement with literature values over a range of relative humidity (RH). The detection limit of γ(N₂O₅) was estimated to be 0.0016 at a low aerosol surface concentration (S_a) condition of 200 µm² cm⁻³. Given the instrument uncertainties and potential fluctuation of air mass between successive sampling modes, we estimate the overall uncertainty of γ(N₂O₅) as ranging from 16 % to 43 % for different ambient conditions. This flow tube system was then successfully deployed for field observations at an urban site of Beijing that is influenced by anthropogenic emissions. The performance in field observations demonstrates that the current setup of this system is capable of obtaining robust γ(N₂O₅) amid the switch of air mass.

1 Introduction

Dinitrogen pentoxide (N₂O₅), forming from the reaction of nitrogen dioxide (NO₂) and nitrate radicals (NO₃), acts as an important reservoir of atmospheric nitrogen. The N₂O₅ can undergo either thermal dissociation (back to NO₂ and NO₃; photolysis of NO₃ also generates NO₂) to release NO₂ or hydrolysis (both homogeneous and heterogeneous) to remove nitrogen oxides from the atmosphere (Brown and Stutz, 2012; Chang et al., 2011). Among the budgets of N₂O₅, the uptake on aerosol particles is a highly efficient pathway for the production of nitrate aerosols in some regions (Fu et al., 2020; Wang et al., 2019; H. Wang et al., 2017c; Baasandorj et al., 2017; McDuffie et al., 2019; Prabhakar et al., 2017; H. Wang et al., 2018a; Chen et al., 2020) and for the activation of chlorine via ClNO₂ formation (Bertram and Thornton, 2009; Osthoff et al., 2008; Tham et al., 2018; Thornton et al., 2010; Z. Wang et al., 2017; Riedel et al., 2012a, 2013; Gaston and Thornton, 2016; Mitroo et al., 2019). The N₂O₅ uptake coefficient (γ(N₂O₅)) is critical in determining the uptake reaction rate of N₂O₅ on aerosols in addition to aerosol surface area (S_a). It represents the fraction of collisions between gaseous N₂O₅ molecules and particle surfaces that resulted in a loss of N₂O₅. Model simulation showed that the variations in γ(N₂O₅) can significantly influence the fate of NOx, O₃ and OH radicals on a regional (Li et al., 2016; Sarwar et al., 2012; Lowe et al., 2015) and global scale (Dentener and Crutzen, 1993; Evans and Jacob, 2005; Macintyre and Evans, 2010; Murray et al., 2021). However, ambient data of direct observations of γ(N₂O₅) are still scarce. It is thereby necessary to develop an accurate piece of equipment or method to quantify this parameter on ambient aerosols.

Extensive laboratory experiments have been conducted to derive the values of γ(N₂O₅) on aerosols and to understand the mechanism of N₂O₅ uptake by means of various methods, to derive the values γ(N₂O₅) on aerosols, and various methods have been used to understand the mechanism of N₂O₅ uptake, including an aerosol flow reactor (Kane et al., 2001; Mozurkewich and Calvert, 1988; Hu and Abbatt, 1997; Thornton and Abbatt, 2005; Thornton et al., 2003; Tang et al., 2014; Bertram and Thornton, 2009; Cosman et al., 2008; Escoreia et al., 2010; Gaston et al., 2014; Folkers et al., 2003), droplet train reactor (Van Doren et al., 1990; Schweitzer et al., 1998), Knudsen flow reactor (Karagulian et al., 2006) and smog chamber (Wahner et al., 1998; Wu et al., 2020). Using these laboratory methods under controllable conditions, the γ(N₂O₅) was found to be highly variable and dependent on particle chemical composition, acidity, size and phase state as well as the presence of organic coating (Badger et al., 2006; Bertram et al., 2011; Fried et al., 1994; Griffiths et al., 2009; Gross et al., 2009; Hallquist et al., 2000; McNeill et al., 2006; Mentel et al., 1999; Riemer et al., 2003; Gaston and Thornton, 2016; Escoreia et al., 2010; Gaston et al., 2014; Thornton et al., 2003). While laboratory results have contributed to recognizing the mechanism of N₂O₅ uptake and to developing γ(N₂O₅) parameterizations (Anttila et al., 2006; Bertram and Thornton, 2009; Davis et al., 2008; Griffiths et al., 2009; Riemer et al., 2009), issues might emerge when quantitatively extended to ambient conditions due to the discrepancy between laboratory conditions and real air mass. For example, the much higher reactant and particle concentrations usually used in laboratory experiments might induce surface saturation or secondary reactions in a short time period, which may lead to the bias of the reaction rate used in ambient conditions (Thornton et al., 2003). In addition, the physicochemical properties of ambient aerosols are much more complicated than the model aerosol used in laboratory studies, which means that it is difficult for the laboratory results to accurately represent what happens on the atmospheric aerosols (Royer et al., 2021; Mitroo et al., 2019).

There have been several methods implemented for field campaigns to indirectly derive γ(N₂O₅) – these have been based on observations of ambient NO₃, N₂O₅, NO₂, O₃, ClNO₂, pNO${}_{\mathrm{3}}^{-}$ (particulate nitrate) and other auxiliary parameters and have not required special equipment to capture the decay of N₂O₅, as in the laboratory-based methods. These include the following: (1) the linear fit between N₂O₅ (NO₃) lifetime and the product of NO₂ and S_a concentration according to steady-state equations (Brown et al., 2002, 2006, 2009; Platt et al., 1984; H. Wang et al., 2017b; X. Wang et al., 2017; Tham et al., 2016; Z. Wang et al., 2017; Brown et al., 2016); (2) the analysis of the production rates of products (pNO${}_{\mathrm{3}}^{-}$ and ClNO₂) resulting from N₂O₅ uptake under a stable condition (Mielke et al., 2013; Phillips et al., 2016; H. Wang et al., 2018b); and (3) box model simulations with an iterative approach to reproducing the evolution of NO₃–N₂O₅ chemistry within each separate air mass after sunset (McDuffie et al., 2018; Wagner et al., 2013; H. Wang et al., 2020a; Yun et al., 2018). All these methods contain some specific assumptions and are only applicable in a few special cases.

To directly determine the γ(N₂O₅) on ambient aerosols, Bertram et al. (2009a) firstly designed an entrained aerosol flow reactor to adapt to low atmospheric S_a concentrations with easy operation. By switching between filtered and bypass sampling mode, the N₂O₅ concentration at the exit of the flow tube can be measured in the presence and absence of aerosols, respectively. The pseudo-first-order rate coefficients for N₂O₅ loss on aerosols is thereby derived from the ratio of measured N₂O₅ concentrations in these two modes within a duty cycle according to Eq. (1):

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

where the Δt is the mean residence time of the flow tube, and the ${\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}_{\mathrm{\Delta }t}^{\mathrm{wo}/\mathrm{particles}}$ and ${\left[{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right]}_{\mathrm{\Delta }t}^{\mathrm{w}/\mathrm{particles}}$ are the measured N₂O₅ concentrations at the exit of the flow tube in filtered and bypass mode, respectively. Assuming the gas-phase diffusion effect is negligible for atmospheric particles and low reaction probability (γ<0.1) (Fuchs and Sutugin, 1970), γ(N₂O₅) can then be calculated from Eq. (2):

$$\begin{array}{}\text{(2)}& \mathit{\gamma }\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)={\displaystyle \frac{\mathrm{4}\times k_{\mathrm{aerosols}}}{c\times S_{\mathrm{a}}}}.\end{array}$$

This method was deployed to measure γ(N₂O₅) on ambient particles during two field campaigns (Bertram et al., 2009b; Riedel et al., 2012b) and on aerosols generated in the laboratory (Ahern et al., 2018). While values of γ(N₂O₅) were determined to be robust in laboratory experiments, most of the data would be dropped under ambient conditions due to the variations of wall loss coefficients (dominated by RH), fresh NO emission, N₂O₅ regeneration and flow pattern inside the flow tube. Based on the above measurement system, W. Wang et al. (2018) added NO_x, O₃ and S_a measurements upon exit of the flow tube and introduced an iterative box model to minimize the potential influences from changing air mass and non-linear responses of interference reactions. With the assumption of the equilibrium between NO₃ and N₂O₅, the box model runs backwards and forwards iteratively to obtain the N₂O₅ loss rate constant in the absence ($k_{\mathrm{het}}^{\mathrm{wo}/\mathrm{particles}}$) and presence ($k_{\mathrm{het}}^{\mathrm{w}/\mathrm{particles}}$) of aerosols, respectively. The difference between these two parameters can finally derive the γ(N₂O₅) according to Eq. (3), assuming the wall loss effect stays consistent.

$$\begin{array}{}\text{(3)}& \mathit{\gamma }\left({\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}\right)={\displaystyle \frac{\mathrm{4}(k_{\mathrm{het}}^{\mathrm{w}/\mathrm{particles}}-k_{\mathrm{het}}^{\mathrm{wo}/\mathrm{particles}})}{c\times S_{\mathrm{a}}}}\end{array}$$

This iterative approach was demonstrated to be able to buffer against certain fluctuations of air mass and to measure γ(N₂O₅) in the polluted atmosphere (Yu et al., 2020).

Until now, only a few direct measurements of γ(N₂O₅) on ambient aerosols have been conducted during field campaigns (Bertram et al., 2009b; Riedel et al., 2012b; Yu et al., 2020). Despite being combined with datasets from indirect approaches (e.g., steady-state approximations), it is still challenging to characterize the temporal and spatial distributions of γ(N₂O₅) on ambient aerosols. To better investigate the reactive uptake of N₂O₅ on aerosols in different environments, we develop an aerosol flow tube system with newly designed gas circuit and data acquisition procedures to quantify γ(N₂O₅) on ambient aerosols. In the following sections, the setup of this system and laboratory characterizations for each part are described in detail. Procedures of acquiring and processing data are compared to previous methods and discussed with attention to potential uncertainties. Laboratory tests on model aerosols and field observations are presented to demonstrate the system's performance under varying ambient conditions.

2 The aerosol flow tube system

A schematic of the aerosol flow tube system is shown in Fig. 1. The ambient air enters the system from the sampling manifold, mixes with the gaseous N₂O₅ source in a Y-tee and flows to the aerosol flow tube and detection instruments, as indicated by the arrows in the figure. The design of the sampling module and aerosol flow tube in this work follows previous work for measuring γ(N₂O₅) on ambient aerosols (e.g., Bertram et al., 2009aThe major improvements of this system in comparison to previous work are the continuous monitoring of NOx and O₃ concentrations before the inlet of the flow tube (after the sample air is mixed with the N₂O₅ source) and the sequential measurements of N₂O₅ concentrations at both the inlet and the exit of the flow tube within a duty cycle. To achieve the programmed cyclic measurement of these key parameters, we adopted a new design of Y-tee, with a static mixer inside and cyclic measurement setup.

Figure 1 Overall schematic of aerosol flow tube system. The arrows alongside the tube show the flow directions. The black arrows indicate the flow directions consistent during the measurements, green arrows indicate the flow directions active in measuring the exit N₂O₅ and blue arrows indicate the flow directions active in measuring the inlet N₂O₅.

2.1 Sampling manifold

The sampling tube is made of aluminum tubing that is 50 cm long with a half inch outside diameter (OD), with a curve tip (10 cm radius of curvature) turning the inlet straight down in order to avoid precipitation. The ambient air is then passed through a three-way, stainless-base solenoid ball valve, which is controlled by a time relay either to allow the air to flow directly into a following Y-tee (filter bypass mode) or to divert the air to a HEPA (high-efficiency particulate air filter, Whatman) to remove particles (filter inline mode). The HEPA can retain particles at a high efficiency (>99.9 %), with low pressure drop and RH difference between filter inline and bypass mode.

2.2 Gaseous N₂O₅ generation

A homemade, temperature-controlled gas generator is used to generate gaseous N₂O₅ in situ via the reaction of O₃ with NO₂ (Reaction R1) and the subsequent reaction of produced NO₃ with NO₂ (Reaction R2).

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

NO₂ is delivered from a compressed gas cylinder (20 ppmv in N₂ diluent gas, Jinghao Corp.). O₃ is generated from the photolysis of O₂ in compressed, ultra-pure, synthetic zero air at 254 nm, using a commercial mercury lamp (UVP, the USA) fixed inside the generator. The produced O₃ is then mixed with NO₂ in a Teflon chamber for about 2 min under the temperature of 15 ^∘C, stabilized by a Peltier cooler controlled by a proportion–integration–differentiation algorithm. A PFA tube with polyethylene foam was used to transmit the synthesized N₂O₅ to the sampling stream and to minimize the influence of ambient temperature variations on the N₂O₅ level. The flow rates of NO₂ (20 sccm) and of zero air (80 sccm) are controlled separately by mass flow controller at a total of 100 sccm. By changing the flow rate ratio between NO₂ and zero air, the generator can produce N₂O₅ concentrations varying from 1 to 6 ppbv (after dilution in zero air at a sampling flow rate of 4.5 slpm). Under the typical measurement condition, an excess of NO₂ concentration is applied to shift the equilibrium towards N₂O₅ production (Reaction R2) and to suppress the NO₃ concentration to less than 30 pptv, which is expected to decrease the uncertainty of varying NO₃ reactivity (NO, VOCs (volatile organic compounds) and heterogeneous loss). The resultant initial N₂O₅ concentration was 4.0 ppbv at the inlet of the aerosol flow tube, together with around 50 ppbv of NO₂ and 15 ppbv of O₃. A stability test on the N₂O₅ source showed that the variation was within 1 % for a 24 h continuous operation, with the ambient temperature ranging from 0 to 15 ^∘C.

2.3 Aerosol flow tube

Air flow enters and exits the flow tube via two identical conical diffuser caps at a diffuser angle of 45^∘. A 35 cm × 14 cm inner diameter (ID) cylindrical tube is mounted in the middle of the two caps, flanged with screws and nitrile rubber O-rings. All sections of this aerosol flow tube are made of stainless steel, with an electro-polished and FEP-coated inside. The exterior of the flow tube is insulated with aluminum-coated polyethylene foam, 3 cm thick, to minimize thermal eddy fluctuations of ambient temperature. The mechanic design of this flow tube follows that used in Bertram et al. (2009a), with different length and diffuser angles particularly designed for our typical flow rate. Under the typical flow rate of 2.1 slpm in the flow tube, the axial velocity in the cylindrical tube section is 0.23 cm s⁻¹, which produces a Reynolds number (Re) of 22, well below the threshold of laminar flow (Re<2100).

In front of the flow tube, the synthesized N₂O₅ source is introduced perpendicular to the ambient air sampling stream, and the mixture then enters a stainless-steel Y-tee for further mixing. The inner surface of the Y-tee is electro-polished and coated with SilcoNert 2000 (Silotek Corp.), a technique commonly applied in the semiconductor industry, to maintain the transmission efficiency of particles and to minimize the loss of N₂O₅ in the meantime. A 10 cm-long, stainless-steel static mixer is mounted inside the Y-tee in order to swirl the flow and therefore to facilitate the mixing between the sampling stream and the N₂O₅ source in a relatively short distance. The presence of the static mixer in front of the inlet also helps to improve the flow expansion after entering the flow tube by minimizing the recirculation zone, which decreases the wall loss of N₂O₅ and particles (Huang et al., 2017). After passing through the static mixer, the mixture of ambient air and N₂O₅ source is split into two flows at the same flow rate, one of which straightly enters the aerosol flow tube, while the other one is diverted to measurements of NO_x, O₃ and N₂O₅. We measured the concentrations of NO_x, O₃, N₂O₅ and S_a at both the exits of the Y-tee under a typical flow rate for three repeated experiments (Fig. 2). Similar gaseous concentrations and particle distributions at both exits of the Y-tee demonstrate that the N₂O₅ source has been well mixed with the sampling flow.

Figure 2 (a) The concentrations of N₂O₅, NO₂ and O₃ in the mixture of the N₂O₅ source and sampling aerosols measured at each exit of the Y-tee; (b) the size distribution of S_a concentration in the mixture of the N₂O₅ gas source and sampling aerosols measured at each exit of the Y-tee.

2.4 Detection instruments

Instruments used in this system are listed in Table 1. A portable cavity-enhanced absorption spectrometer (CEAS) is used to measure N₂O₅ concentrations (H. Wang et al., 2017a) at both the inlet and exit of the aerosol flow tube by automatically switching the flow directions (see details in Sect. 2.5). Briefly, the N₂O₅ is thermally decomposed to NO₃ by heating up to 130 ^∘C and then quantified according to the extinction coefficient caused by NO₃ absorption in the wavelength window (from 640 to 680 nm). A Teflon polytetrafluoroethylene (PTFE) membrane is placed in front of the CEAS to remove particles; this will be replaced with a new one every 2 h by a self-designed membrane auto-changer. Laboratory tests have been conducted to quantify the transmission efficiency of N₂O₅ over the membrane (92±3 %), of the sampling tube of CEAS (99.7 %) and of the inside of CEAS (93.6 %). The use of a filter upstream of the CEAS and the procedures of membrane changing have been successfully applied in many field campaigns to measure ambient N₂O₅ (Brown et al., 2016; Kennedy et al., 2011; H. Wang et al., 2017a, b, 2018a). The loss of N₂O₅ on the membrane filter, the sampling tube and the detection chamber inside the CEAS was corrected according to transmission efficiency. The detection limit of N₂O₅ was determined to be 2.7 pptv (1σ, 60 s), with the measurement uncertainty of 19 %. The CEAS has been successfully applied to measure ambient N₂O₅ concentrations in several field campaigns and laboratory studies (Chen et al., 2020; H. Wang et al., 2020a, 2017b, 2018b, 2020b; Wang et al., 2022).

Table 1 Performance of related instruments incorporated in the flow tube system.

^a Photolytic conversion to NO through blue light before detection. ^b Gas chromatography equipped with a mass spectrometer and a flame ionization detector.

At the inlet of flow tube, NO_x concentration is measured via a chemiluminescence method, equipped with a blue-light photolytic converter (Thermo, Model 42i), and O₃ concentration is also measured via a chemiluminescence method by adding excessive NO (Teledyne API, Model T265). Both NO_x and O₃ concentrations are averaged to a one-minute time resolution. The size distribution of the particle number density is measured at the exit of the flow tube using a scanning mobility particle sizer (SMPS, TSI 3776), which determines the total S_a concentration covering the range of 13–730 nm. According to our previous field measurements (Chen et al., 2020), particles larger than this range usually contributed less than 5 % of the total S_a; this is included in the uncertainty analysis (see Sect. 5). A cycle of size scanning is set to around 5 min, and the derived S_a concentration is then interpolated into 1 min for further calculation. Aerosols pass through a Nafion tubing (MD-700) before entering into the SMPS to reduce RH to less than 30 %. The dry-state S_a is therefore corrected to wet state by the RH inside the flow tube for particle hygroscopicity. The growth factor, $f\left(\text{RH}\right)=\mathrm{1}+\mathrm{8.77}\times (\text{RH}/\mathrm{100}{)}^{\mathrm{9.74}}$, used for correction is valid only when RH is within the range of 30 %–90 % (Liu et al., 2013). The RH and temperature of flow are continuously measured by commercial sensors, both before entering and after leaving the flow tube (Rotronic, Model HC2A-S). The averages of the values obtained at both locations are used to represent the RH and temperature inside the flow tube. In addition, ambient volatile organic compounds (VOCs) are measured in situ alongside the aerosol flow tube system using an online gas chromatograph mass spectrometer coupled with a flame ionization detector (GCMS-FID) to derive the NO₃ reactivity to VOCs ($k_{{\mathrm{NO}}_{\mathrm{3}}-\mathrm{VOCs}}$) in the flow tube.

2.5 Procedures of data acquisition

The N₂O₅ concentration is acquired at both the inlet and exit of the flow tube within a duty cycle via a CEAS instrument, which is different from that only at the exit of the flow tube in previous studies (Bertram et al., 2009a; W. Wang et al., 2018). Each duty cycle consists of one HEPA inline mode for measuring k_wall of N₂O₅ and one HEPA bypass mode for retrieving the N₂O₅ loss on aerosols. The procedure that measures N₂O₅ first at the inlet of flow tube and then at the exit is executed within each mode. An exemplary case obtained during a field campaign is shown in Fig. 3 to explain this procedure. Within the HEPA inline mode, N₂O₅ data are firstly acquired at the inlet of the flow tube, and then acquisition is switched to the exit of the flow tube. The $k_{\mathrm{het}}^{\mathrm{wo}/\mathrm{particles}}$, which is the k_wall of N₂O₅, can be derived from a box model constrained by these N₂O₅ data (see Sect. 3 for the model description and data processing). The same procedures are executed in the HEPA bypass mode, except the γ(N₂O₅) is derived according to Eq. (2). Two three-way valves controlled by a time relay were implemented to realize this procedure in order to avoid the changes of flow condition in the flow tube that could have been caused. As indicated in Fig. 1, the blue arrows show the flow directions when measuring the N₂O₅ concentration at the inlet of flow tube, while the green arrows show the flow directions for the exit of flow tube. It should be noted that, during the operation, the concentrations of NO_x and O₃ are always acquired at the inlet of the flow tube and the S_a concentration always at the exit of the flow tube.

Figure 3 An exemplary case of measured N₂O₅ concentrations within a duty cycle. This case was observed on the night of 13 December 2020, with average ambient S_a of 320 µm² cm⁻³. The derived k_wall of N₂O₅ and γ(N₂O₅) was 0.0023 s⁻¹ and 0.035, respectively. The blue dots indicate N₂O₅ concentrations measured under the HEPA inline mode, either at the inlet or exit of the flow tube (denoted as texts); the respective averages (blue dots of larger size) are used for deriving k_wall (blue square). The red dots indicate N₂O₅ concentrations measured under the HEPA bypass mode, either at the inlet or exit of the flow tube; the respective averages (red dots of larger size) are used for deriving the overall rate constant of N₂O₅ loss on the wall and aerosols. The data points in gray are excluded from calculation due to unstable conditions in the flow tube.

In addition, laboratory tests were conducted to determine a suitable duration for each duty cycle. During a duty cycle, the duration for each mode should last long enough to develop a stable flow condition for particles or empty particles, while a much longer duration could decrease the measurement time resolution and lead to a large uncertainty due to the fluctuations within a long time period. We measured S_a and N₂O₅ concentrations continuously at the exit of flow tube when sampling (NH₄)₂SO₄ aerosols. As shown in Fig. 4, when our system underwent mode switches, it took about 15 min for particles to rise from none to a stable level or to decrease from a certain level to none. The periodical variation of N₂O₅ concentration was consistent with the particles. The residence time distribution (RTD) profiles (see in Sect. 4.2) also demonstrated that a pulse injection of NO₂ requires 10–15 min to be fully drained out of the flow tube, which, to some extent, supports the 15 min time required for complete mixing of N₂O₅. As a result, a typical duty cycle duration is composed of 40 min, with 20 min for each mode, which is similar to that in Bertram et al. (2009a). The N₂O₅ measurement at the exit of the flow tube in the last 5 min of each mode is able to represent valid decays of N₂O₅ under this mode and satisfies the requirements of further data processing.

Figure 4 Variations of S_a and N₂O₅ concentrations (normalized to peak values) measured at the exit of flow tube when switching the sampling mode. The phases of species concentrations in the flow tube approaching stable after a mode switch are denoted as the transition phases.

3 Box model for determination of loss rate coefficients of N₂O₅

3.1 Method description

In a previous flow tube study (Bertram et al., 2009a), large uncertainties were found in retrieving γ(N₂O₅) on ambient particles according to Eq. (1) due to the dependence of homogeneous reaction rates on sampling modes and the atmospheric variations of parameters related to NO₃–N₂O₅ chemistry (e.g., NO, NO₂, O₃, VOCs and RH). To minimize these influences, a time-dependent box model constrained by the measurement of N₂O₅ concentrations and other auxiliary parameters is applied to calculate the loss rate coefficients of N₂O₅ under the HEPA inline and bypass modes, respectively. The model is able to simulate the reactions related to budgets of NO₃–N₂O₅ chemistry in a dark condition, including Reactions (R1), (R2) and the follows:

$$\begin{array}{}\text{(R3)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\mathrm{NO}\to \mathrm{2}{\mathrm{NO}}_{\mathrm{2}},\text{(R4)}& {\displaystyle }{\mathrm{NO}}_{\mathrm{3}}+\text{VOCs}\to \text{products},\text{(R5)}& {\displaystyle }{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}+\text{aerosols or wall}\to \text{products}.\end{array}$$

The rate constants for Reactions (R1) to (R3) refer to the IUPAC database. The reaction of VOCs and NO₃ is treated as pseudo first order, with a rate constant of $k_{{\mathrm{NO}}_{\mathrm{3}}-\mathrm{VOCs}}$, which is the sum of rate constants for reactions of NO₃ with each VOC scaled by the concentration of VOCs measured by GC-FID. In this work, there are 30 kinds of measured VOCs having known reaction rate constants with NO₃ included in the model (Table A1). Due to the low time resolution of VOC measurements (1 h), the $k_{{\mathrm{NO}}_{\mathrm{3}}-\mathrm{VOCs}}$ is kept constant for each derivation of γ(N₂O₅). The suppressed NO₃ concentration is expected to attenuate the influence resulting from the uncertainty of $k_{{\mathrm{NO}}_{\mathrm{3}}-\mathrm{VOCs}}$ (see discussion in Sect. 5). The Reaction R5 represents the loss of N₂O₅ only on the wall in the HEPA inline mode or on both the wall and particles in the HEPA bypass mode. The rate constant of Reaction (R5) is also treated as pseudo first order, and it is adjustable among different runs.

The same procedures of data screening and model operation are applied to both the sampling and bypass modes, as shown in Fig. 5. For example, in the HEPA inline mode, the average of NO concentrations less than 6 ppbv and the variations of less than 10 % of N₂O₅ measured at the inlet of the flow tube should be validated prior to the following model operation. Under the typical concentrations of the N₂O₅ source we used in this flow tube system, the exit concentration of N₂O₅ is detected to be under the triple-detection limit, with initial NO large than 6 ppbv according to our laboratory tests. In ambient conditions, a high level of NO is usually also accompanied by rapid variations due to fresh emission, which disturbs the decay of N₂O₅ in the flow tube and leads to a large uncertainty in deriving its loss rate coefficient. Excluding the cases in which N₂O₅ measured at the inlet of flow tube varies by more 10 % can further minimize the uncertainty of the N₂O₅ loss rate coefficient resulting from the rapid change of NO₃ reactants (NO, VOCs). If the measured data within the duration of a sampling mode satisfy the criteria for data screening, as described above, then based on these data, the model can simulate the reactions starting from the entrance of flow tube and lasting for 156 s (mean residence time). The initial concentrations of [NO]_t=0, [NO₂]_t=0, [O₃]_t=0 and [N₂O₅]_t=0 are the averages of the last-five-minute values measured at the inlet of the flow tube. The RH and temperature are constrained by the mean values during this sampling mode. By tuning the loss rate coefficient of N₂O₅ ($k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$) in the way of a binary search, we optimized an appropriate $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ to ensure that the N₂O₅ concentration output from the simulation is consistent with the last-five-minute average of N₂O₅ concentrations measured at the exit of the flow tube within 1 pptv. As a result, this derived $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ (a.k.a. $k_{\mathrm{het}}^{\mathrm{wo}/\mathrm{particles}}$) is expected to be the k_wall of N₂O₅. The same procedures as above are then applied to the data obtained in the HEPA bypass mode, except that the derived $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ (a.k.a. $k_{\mathrm{het}}^{\mathrm{w}/\mathrm{particles}}$) contains the loss rate coefficients of N₂O₅ on both the wall and the particles. It should be noted that the above calculation for the obtained data is only valid under the variation of RH that is below 2 % within a duty cycle, and the k_wall of N₂O₅ can then be reasonably assumed to be constant between two successive sampling modes. Therefore, the γ(N₂O₅) can be retrieved by means of Eq. (3), where the last-five-minute average of the S_a concentrations in the HEPA bypass mode is used.

Figure 5 Flow diagram of γ(N₂O₅) derivation through the box model method.

3.2 Evaluation of the box model method

The box model method is introduced to our flow tube system to overcome the influence of homogeneous reactions and variations of air mass on γ(N₂O₅) retrieval. A series of scenarios was provided to evaluate the performance of the box model method by means of both simulations and laboratory experiments. We allow NO, NO₂ and O₃ in the mixture of sampling air at the entrance of the flow tube to vary within a reasonable range in order to develop the scenarios of different gradients of NO concentrations and NO₃ production rates (PNO₃). The levels of PNO₃ were adjusted by NO₂ and O₃ concentrations (O₃ ranging from 10 to 80 ppbv and NO₂ ranging from 50 to 160 ppbv) under a temperature of 283 K and RH of 30 %. In simulation studies, the exit concentration of N₂O₅ would be obtained from the simulated N₂O₅ evolutions with and without particles in the flow tube. To corroborate the results estimated by simulations, laboratory tests were performed on (NH₄)₂SO₄ aerosols to measure the exit concentration of N₂O₅ under varying NO concentrations. The γ(N₂O₅) on particles are then calculated according to Eqs. (1) and (2) or by the box model method described above.

As shown in Fig. 6a, the exit concentration method (γ(N₂O₅) exit conc., derived directly by Eqs. 1–2) underestimates γ(N₂O₅), and the extent of underestimation increases with PNO₃ levels in simulation tests. Similarly, the exit concentration method underestimates γ(N₂O₅) by 50 %–60 %, with PNO₃ of 1.0 ppbv h⁻¹ in the laboratory tests (Fig. 6b). It is noted that the γ(N₂O₅) was determined by the box model method to be around 0.01 over the NO range of 0–6 ppbv, which agrees well, within uncertainty, with previous laboratory observation of γ(N₂O₅) on (NH₄)₂SO₄ aerosols (Badger et al., 2006; Hallquist et al., 2003; Kane et al., 2001). The cause of γ(N₂O₅) exit conc. underestimation is mainly due to the in situ N₂O₅ production in the flow tube. With a continuous production of NO₃ via the reaction of NO₂ and O₃ and the rapid heterogeneous loss of N₂O₅ in the flow tube, the equilibrium between NO₃ and N₂O₅ always shifts to the production of N₂O₅ and masks he actual amount of N₂O₅ removal. In the HEPA bypass mode, the N₂O₅ consumes faster than in the other mode due to the addition of particles, which further facilitates the N₂O₅ formation through the equilibrium. Previous studies also found similar impacts from N₂O₅ production on retrieving γ(N₂O₅) in the aerosol flow tube (Bertram et al., 2009a; W. Wang et al., 2018). However, the discrepancy of γ(N₂O₅) derived by these two methods is much less dependent on the NO concentration, at least within the prescribed range, due to the relatively small ratio of ${\mathrm{NO}}_{\mathrm{3}}/{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}$ in the N₂O₅ source. The absence of a dependence between NO concentration and γ(N₂O₅) also indicates that this aerosol flow tube system can buffer against NO within the range of 0–6 ppbv under typical operating conditions. However, this is not always the case when there is a rapid fluctuation of NO in a real atmosphere, which might lead to intractable uncertainty and is therefore excluded from further analysis according to the criteria of data screening.

Figure 6 Simulated and laboratory tests on the performance of the box model method and exit concentration method for γ(N₂O₅) derivation. (a) The ratios of given γ(N₂O₅) (γ(N₂O₅) true) over exit concentration-derived γ(N₂O₅) (γ(N₂O₅) exit conc.) determined from simulated scenarios. The γ(N₂O₅) derived by the box model method is exactly the same as γ(N₂O₅) true. The ratios vary with NO concentration, and the lines are color coded by PNO₃ values. Both NO concentration and PNO₃ represent the values at the entrance of the aerosol flow tube. (b) γ(N₂O₅) measurements on laboratory-generated (NH₄)₂SO₄ aerosols under different gradients of NO with a constant RH of 50 % and PNO₃ typically generated from our N₂O₅ source. The red line shows the γ(N₂O₅) derived by the box model method, and the gray line shows the γ(N₂O₅) derived by the exit concentration method. The NO concentrations are measured at the entrance of the aerosol flow tube.

In comparison to the work by Bertram et al. (2009a) and W. Wang et al. (2018), the combination of the above box model method and the improved flow tube system in this study has made progress in the following aspects. First, the dynamic quantification of k_wall of N₂O₅ within each duty cycle based on the constraint of sequentially measured N₂O₅ sources is helpful to provide accurate data for both k_wall and γ(N₂O₅) retrieval. The k_wall in ambient conditions could deviate from the results of laboratory tests (Fig. B1) due to temperature variations and particle adsorption, which leads to large uncertainty when calculating γ(N₂O₅) without the frequent determination of k_wall. While the k_wall was also determined frequently in the flow tube of W. Wang et al. (2018), the N₂O₅ source they used for k_wall and γ(N₂O₅) retrieval is an assumed stable value instead of an observed one. Second, in this work, the concentrations of initial NO, NO₂, O₃ and N₂O₅ at the entrance of the flow tube and the exit N₂O₅ are obtained through programmed cyclic measurements, which can reduce the uncertainties by adding the model constraints. It is different from the iterative box model used in W. Wang et al. (2018), as we enable a straightforward simulation of NO₃-N₂O₅ chemistry occurring in the flow tube instead of estimating the initial NO₂ and O₃, with an assumed NO profile and stable N₂O₅ source based on backward simulations. In ambient conditions, the initial N₂O₅ concentration can be largely influenced by air mass conditions (especially NO concentration and temperature). Figure B2a presents a box whisker plot of N₂O₅ and NO concentrations at the flow tube entrance during a field campaign, which shows a much larger variation of N₂O₅ than in laboratory conditions (<1 %). As a result, the box model would underestimate γ(N₂O₅) by using a fixed initial N₂O₅ concentration under certain circumstances (Fig. B2b). Third, we simulate the NO₃–N₂O₅ relationship via specific reactions rather than by approximating it in equilibrium and introducing the equilibrium coefficient (K_eq) into the calculation. Calculating NO₃ or N₂O₅ concentrations by means of K_eq could induce a large bias (up to 90 %) under the high aerosol loading and low temperature (Chen et al., 2022).

4 Laboratory characterizations

4.1 Particle transmission efficiency

The transmission efficiency of particles in the sampling module and flow tube are estimated respectively in Fig. 7. In the laboratory, pure ammonia nitrate ((NH₄)₂SO₄) aerosols were generated from an atomizer loaded with 0.1 M (NH₄)₂SO₄ solution. The RH and concentration of the produced aerosol flow were conditioned in a glass bottle (∼2 L) by introducing a humidified dilution flow of ultrahigh-purity N₂. As a result, aerosols in different concentrations (1000–4500 µm² cm⁻³) and under a range of RH (20 %–70 %) were applied to test the transmission efficiency. Figure 7a shows that the loss of total S_a concentrations in the sampling module and flow tube are 8±1 % and 10±2 % on average, respectively. We found that the fraction of particle loss is mainly caused by particles smaller than 100 nm. This is most likely due to the turbulence generated by the static mixer and the recirculation in the flow tube. Large particles are prone to stay within the main flow direction, whereas small particles readily adsorb on the walls by the entrainment of turbulence or recirculation. In addition, the particle distribution measured at the exit of the flow tube with the HEPA inline (gray line in Fig. 7a) demonstrated its capability of removing almost all particles (>99.5 %) at the typical flow rate. The same transmission efficiency as that on laboratory-generated aerosols was also found on ambient aerosols (Fig. 7b). The results we obtained from the above particle transmission experiments are similar to the findings of Bertram et al. (2009a).

Figure 7 (a) Particle transmission determined by sampling laboratory-generated (NH₄)₂SO₄ aerosols. Aerosols at different concentrations and RH levels are used in experiments, and the size distributions of S_a concentrations are normalized to the peak values. The normalized size distributions of S_a concentrations measured before the sampling inlet (green line), at the inlet of the flow tube with the HEPA bypass (red line) and at the bottom of the flow tube with the HEPA bypass (blue line) are shown respectively. Under the HEPA inline mode, the S_a concentration was almost zero at the bottom of flow tube (gray line). The shadows indicate the standard deviations of the normalized S_a concentrations for all experiments. (b) Particle transmission determined by sampling ambient particles.

4.2 Residence time in the flow tube

The method of residence time distribution (RTD) was applied to estimate the average reaction time of the gas species in the flow tube (residence time). In comparison to ideal plug flow, the RTD method can better describe the actual behavior of the flow in practice and determine the mean residence time more accurately (Danckwerts, 1953). Several studies have also used this RTD method to determine the residence time in the flow tube (Huang et al., 2017; W. Wang et al., 2018; Lambe et al., 2011).

The RTD profiles were obtained by introducing a two-second pulse of NO₂ gas diluted in N₂ into the flow tube under RH less than 1 %. NO₂ is relatively inert against the flow tube wall coated with FEP and was measured at the exit of the flow tube by a CEAS (Li et al., 2021) at a high time resolution (2 Hz). A three-way solenoid valve combined with a time relay was implemented to control the pulse in order to avoid the disturbance of the flow condition by the injection. Experiments were performed under typical operation. The mean residence time (t_ave) can be derived from each RTD profile according to Eq. (4):

$$\begin{array}{}\text{(4)}& t_{\mathrm{ave}}={\displaystyle \frac{{\sum }_{i=\mathrm{0}}{C}_i\times t_i}{{\sum }_{i=\mathrm{0}}{C}_i}},\end{array}$$

where the C_i is the concentration of the NO₂ recorded at the time step t_i. From the RTD profiles of NO₂ injection experiments in Fig. 8, the determined t_ave was 156±3 s. This value is 19 % less than the space time (τ_space, flow tube volume divided by operation flow rate, 192.6 s). It has also been found that the assumption of ideal plug flow overestimated the residence time in previous flow tube experiments (Lambe et al., 2011; Huang et al., 2017; W. Wang et al., 2018), which could lead to the underestimation of the derived $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$. The residence time of the current setup is designed for investigating γ(N₂O₅) in typical episode days with medium to high aerosol loadings (a S_a concentration usually larger than 500 µm² cm⁻³) in polluted regions. As shown in Sect. 5, the detection limit of this system is $\mathrm{6.4}\times {\mathrm{10}}^{-\mathrm{4}}$ with S_a of 500 µm² cm⁻³, which is well below most of the previous ambient γ(N₂O₅) results ranging from $\mathrm{1}\times {\mathrm{10}}^{-\mathrm{3}}$ to >0.1 in polluted regions of China (H. Wang et al., 2020a; X. Wang et al., 2017; Z. Wang et al., 2017; Xia et al., 2019). The residence time determined in this work is also slightly higher than the 149 s reported in a previous work focused on investigating γ(N₂O₅) in polluted regions (W. Wang et al., 2018). In addition, the residence time for this flow tube can be extended to over 300 s to satisfy the γ(N₂O₅) measurement requirements under low S_a by reducing the flow rate of air passing through, which is controlled by an extra pump.

Figure 8 Residence time distribution derived by sampling NO₂ gas. Red solid line indicates the measured RTD profiles. The calculated RTD of ideal laminar flow (without dispersions) and the Taylor dispersion model fitted to measurements are shown as a blue dashed line and dot-dash line, respectively.

Two theoretical RTDs were calculated – namely, ideal laminar flow and Taylor diffusion – besides the measured RTD, intended to reflect the fluid field inside the flow tube. The ideal laminar flow describes the flow without dispersion. The velocity profile of the ideal laminar flow is parabolic, with the fluid in the center of the tube moving the fastest. According to the following Eq. (5), the RTD of the ideal laminar flow is scaled by the integrated concentration of NO₂ and is presented as the blue dashed line in Fig. 8.

$$\begin{array}{}\text{(5)}& \left\{\begin{array}{ll}\mathrm{0},& t<\mathrm{0.5}{\mathit{\tau }}_{\mathrm{space}}\\ {\displaystyle \frac{{\mathit{\tau }}_{\mathrm{space}}^{\mathrm{2}}}{\mathrm{2}{t}^{\mathrm{3}}}},& t\ge \mathrm{0.5}{\mathit{\tau }}_{\mathrm{space}}\end{array}\right.,\end{array}$$

While the determined Re is well within the laminar flow threshold, the measured RTD occurs earlier than the theoretical laminar flow condition and exhibits a broadened distribution. The discrepancy between them indicates that the dispersions or potential secondary flows could dominate the flow regime. Instead, an improved Taylor dispersion model (shown as the gray dot-dash line in Fig. 8) is able to reproduce the measured RTD, which was previously implemented in the characterization of photooxidation flow reactors (Lambe et al., 2011). Two flow patterns with distinct effective diffusivities (0.02 and 0.51, derived from best fit) were considered in this dispersion model. An implication from the characteristics of the model is that the flow regime consists of two flow components: a direct flow path through the flow tube with less diffusion and a secondary flow path representing the recirculation in the dead zone that is induced by temperature gradient and significant diffusions (Huang et al., 2017).

4.3 N₂O₅ wall loss

Laboratory tests were conducted to quantify the k_wall of N₂O₅ under different levels of RH with the HEPA inline. As shown in Fig. 9, the k_wall of N₂O₅ gradually increases from 0.002 s⁻¹ in a dry condition to 0.006 s⁻¹ when RH is 70 %. The level of k_wall is less than the result of W. Wang et al. (2018) but higher than the result of Bertram et al. (2009a), as indicated in Table 2. In addition, the flow tube was rinsed with deionized water every week during the field campaigns to remove the build-up of particles, which might increase the hygroscopicity of the internal surface and thus the k_wall of N₂O₅ in a wet condition. Uncertainty in γ(N₂O₅) derivation that resulted from the variation of k_wall related to RH is discussed in Sect. 5.

Figure 9 The dependence of the pseudo-first-order wall loss coefficient (k_wall) on N₂O₅ in the FEP-coated aerosol flow tube.

Table 2 Summary of the k_wall of N₂O₅ for the existing aerosol flow tube deployed in field campaigns.

4.4 Demonstration of γ(N₂O₅) measurements on model particles

Measurements of γ(N₂O₅) made by the current aerosol flow tube system equipped with a box model method were performed on laboratory-generated (NH₄)₂SO₄ aerosols over a range of RH. The system was operated at room temperature of 295K with an N₂O₅ concentration of 4.0 ppbv at the entrance of flow tube. We conditioned the RH of generated aerosols by introducing dry N₂ gas dilution, which could decrease the RH level down to 10 %–55 %, starting from over 95 %, where (NH₄)₂SO₄ aerosols are expected to be in aqueous state. The resulting S_a concentrations of aerosols were around 600 µm² cm⁻³. As shown in Fig. 10, the observed γ(N₂O₅) values were below 0.01 when RH was within 40 % and significantly rose up to 0.02 with higher RH. The dependence of γ(N₂O₅) on RH and the exact values are consistent with previous laboratory results on (NH₄)₂SO₄ aerosols (Badger et al., 2006; Hallquist et al., 2003; Hu and Abbatt, 1997; Kane et al., 2001; Mozurkewich and Calvert, 1988), which shows that the setup of our instrument has good practicability. A large standard deviation of γ(N₂O₅) found at RH of 39 % is possibly due to the unstable phase transition of (NH₄)₂SO₄ particles, as its efflorescence RH is reportedly from 35 % to 48 % (Martin, 2000).

Figure 10 The dependence of γ(N₂O₅) on RH for laboratory-generated (NH₄)₂SO₄ aerosols. The red points with standard deviations represent the values measured by the current aerosol flow tube system in this work. Previously reported values are indicated in blue marks.

5 Uncertainty analysis and detection limit

The uncertainty of γ(N₂O₅) is relevant to the measurement uncertainties of each instrument and the rapid fluctuations of various parameters. As outlined before, the five-minute averages of N₂O₅ concentrations measured at the inlet and exit of the flow tube were used for calculating γ(N₂O₅) via the box model method. The potential variations within these selected time periods would therefore lead to relative errors. For example, the variations of N₂O₅ concentrations result majorly from the rapid changes of ambient NO and less from variations of VOCs, NO₂, O₃ as well as the N₂O₅ gas source itself (1 % in 24 h). A cutoff of 10 % for N₂O₅ variation was implemented to filter out the air mass that was too unstable for valid analysis according to our prescribed criteria of data screening. It consequently leads to 10 % uncertainty in the average of N₂O₅ and can translate into a deviation of 2 % in γ(N₂O₅), with the γ(N₂O₅) at 0.02, S_a at 800 µm² cm⁻³ and other parameters (shown in Table 3) representing the typical inlet values measured during the field campaign (described in Sect. 6). Similarly, cases that demonstrate over 2 % variation in RH between the HEPA inline and bypass modes are excluded from analysis owing to the significant influence of RH on k_wall of N₂O₅ in the flow tube. By assuming a consistent k_wall in successive sampling modes, the potential variations in RH could lead to uncertainty in γ(N₂O₅), from $\pm \mathrm{8}\times {\mathrm{10}}^{-\mathrm{4}}$ at RH of 20 % to $\pm \mathrm{2}\times {\mathrm{10}}^{-\mathrm{3}}$ at RH of 70 %, respectively, with the S_a at 800 µm² cm⁻³. In addition, the $k_{{\mathrm{NO}}_{\mathrm{3}}-\mathrm{VOCs}}$ is treated as constant in a duty cycle due to the limit of the time resolution of VOC measurements. A variation of ±0.01 s⁻¹ in $k_{{\mathrm{NO}}_{\mathrm{3}}-\mathrm{VOCs}}$ only induces less than ±1 % uncertainty in γ(N₂O₅) for more than 95 % of the cases obtained during the field campaign. All the impacts from inherent instrument uncertainties and variations of different parameters are thereby considered in Monte Carlo simulations to assess the overall uncertainty of γ(N₂O₅). The basic simulation is initialized, with the typical conditions measured at the inlet of the flow tube during the field campaign, and repeatedly performs the procedures of determining γ(N₂O₅) via the box model method 1000 times. In each run, all parameters were allowed to vary independently within a prescribed range. The basic simulation condition and variation ranges are presented in Table 3.

Table 3 Parameters involved in the Monte Carlo simulations.

^a Values used for initializing Monte Carlo simulations in a basic scenario. ^b Ranges within which each parameter can vary independently. ^c Determined from the case in which γ(N₂O₅) is at 0.02 and S_a is at 800 µm² cm⁻³; other parameters are shown in this table. ^d The RH and its variation can be transformed into values in k_wall of N₂O₅ via the fitting function derived from Fig. 9.

The resulting γ(N₂O₅) values from Monte Carlo simulations under the basic scenario are shown as frequency distributions in Fig. 11a. This distribution can be fitted by a Gaussian function, and the standard deviation (1σ) of Gaussian distribution is regarded as the overall uncertainty of γ(N₂O₅), which is $\pm \mathrm{9}\times {\mathrm{10}}^{-\mathrm{4}}$ (4.5 % relative to true γ(N₂O₅)). The uncertainty of S_a measurements and unmeasured particles larger than 730 nm (usually less than 5 % of the total S_a) would, together, introduce an extra 16 % uncertainty to γ(N₂O₅).

Figure 11 The uncertainty of γ(N₂O₅) determined from the Monte Carlo simulations. (a) Histogram distribution of γ(N₂O₅) generated from a Monte Carlo simulation (1000 single runs) in the basic scenario (shown in Table 3), where the overall uncertainty of γ(N₂O₅) was determined to be $\pm \mathrm{9}\times {\mathrm{10}}^{-\mathrm{4}}$; (b) dependence of the uncertainty of γ(N₂O₅) on NO, NO₂ and O₃; (c) dependence of the uncertainty of γ(N₂O₅) on RH and T; (d) dependence of the γ(N₂O₅) uncertainty on γ(N₂O₅) level.

We further found that the uncertainty of γ(N₂O₅) could be sensitive to the measurement conditions. With higher O₃, potential variations of NO and $k_{{\mathrm{NO}}_{\mathrm{3}}-\mathrm{VOCs}}$ will induce larger uncertainty of γ(N₂O₅) (Fig. 11b), as it enhances the abundance of NO₃ and N₂O₅. In comparison, the low O₃ in the basic scenario suppressed the side formation of NO₃ in the flow tube, limiting the aggravation of γ(N₂O₅) uncertainty as a result of the increase of NO and NO₂. The γ(N₂O₅) uncertainty is also positively correlated with RH and T. As discussed before, the k_wall of N₂O₅ increases with RH level, which can amplify the potential bias of k_wall at a higher RH level. The equilibrium between NO₃ and N₂O₅ shifts towards the decomposition of N₂O₅ at higher T, leading to larger uncertainty of γ(N₂O₅), caused by potential variations of NO and $k_{{\mathrm{NO}}_{\mathrm{3}}-\mathrm{VOCs}}$. The overall uncertainty of γ(N₂O₅) therefore rises to 8.2 % at the RH of 70 % and to 14.4 % at the temperature of 293 K (Fig. 11c), with NO, NO₂, O₃, γ(N₂O₅) and S_a staying the same as the basic scenario. In addition, Monte Carlo simulations were also performed for different γ(N₂O₅) values ranging from 0.01 to 0.08. The uncertainty of γ(N₂O₅) clearly decreased with the γ(N₂O₅) (Fig. 11d). A lower γ(N₂O₅) weakened the impact that N₂O₅ uptakes has on the budgets of NO₃ and N₂O₅, which causes the γ(N₂O₅) derivation to be more susceptible to the uncertainties of other parameters and then increases the uncertainty of γ(N₂O₅).

In addition, the mean residence time used in the box model method could bias the retrieved γ(N₂O₅) due to the non-normal distribution of the residence time with a discernable tail. The reactants entrained by those slower streamlines close to the wall will take a much longer time to reach the exit of the flow tube than those by the centerline. In order to evaluate the uncertainty caused by the distribution of residence time, we first performed simulations of N₂O₅ decay in the flow tube under the basic scenarios and calculated the exit N₂O₅ concentration according to the probability distribution function derived from the RTD profile. Then, the γ(N₂O₅) can be retrieved from the box model method running for the duration of the mean residence time, constrained by this calculated exit N₂O₅ concentration. The result shows that the use of mean residence time produces a 32 % underestimation of γ(N₂O₅) in the basic scenario. The extent of underestimation is most sensitive to the level of γ(N₂O₅) and RH. In short, when taking all the factors and their corresponding varying ranges discussed above into consideration, the overall uncertainty of γ(N₂O₅) determined from Monte Carlo simulations is in the range of 16 %–43 %. To directly compare with previous studies, at 0.03 γ(N₂O₅) with 1000 µm² cm⁻³ S_a, the uncertainty is calculated to be 19 %, which is lower than the ∼24 % in Bertram et al. (2009a) and than the range of 37 %–40 % in W. Wang et al. (2018).

In order to determine the detection limit of the current aerosol tube system, the continuous blank measurements in zero air were performed with settled operation procedures. Within each duty cycle (40 min), one k_wall of N₂O₅ and one γ(N₂O₅) can be derived in a pair. In total, we obtained 56 sets of results. The detection limit of $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ on aerosols is $\mathrm{2.1}\times {\mathrm{10}}^{-\mathrm{5}}$ s⁻¹, derived from 1σ of the Gaussian function fitted to this distribution. It is equivalent to 0.0016 for the detection limit of γ(N₂O₅), with a low S_a condition of 200 µm² cm⁻³ (Fig. 12a), and 0.00064 for the detection limit of γ(N₂O₅), with a moderate S_a condition of 500 µm² cm⁻³ (Fig. 12b). This result indicates that the flow tube system is capable of quantifying γ(N₂O₅) for most cases, even under a low aerosol-loading environment.

Figure 12 The γ(N₂O₅) derived from blank measurements in a histogram distribution plot. The γ(N₂O₅) was calculated from $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ by means of Eq. (2) with S_a of (a) 200 µm² cm⁻³ and (b) 500 µm² cm⁻³, respectively, under the temperature of 293 K. The Gaussian function is fitted to the distribution and plotted in a black line. The 1σ from the Gaussian fit is regarded as the detection limit.

6 Performance in the field campaign

The aerosol flow tube system was successfully deployed to measure γ(N₂O₅) on ambient aerosols in Beijing, lasting for 20 d during December 2020. The sampling site was at the campus of Peking University, which is located in the city center of Beijing, surrounded by major roads with heavy traffic. Therefore, this site represents an area with a large amount of fresh emissions of NO_x and other anthropogenic sources. The system was mounted on the top floor of a building about 15 m in height above the ground. The sampling manifold was placed in open air, and the ambient aerosols could directly enter the inlet of the manifold without additional sampling tubes. During the period of measurement, the averages of ambient temperature, RH, NO, NO₂, O₃ and S_a were 273±3 K, 25±12 %, 23±36 ppbv, 23±12 ppbv, 16±15 ppbv and 409±249 µm² cm⁻³, respectively. The NO and S_a levels could vary by 2 orders of magnitude due to the periodical switch between clean air mass from the north and pollutants accumulated by local emissions.

A total of 99 valid γ(N₂O₅) values were determined from the measurements based on the criteria of data screening described in Sect. 3.1. We found that γ(N₂O₅) was 0.042±0.026, on average, with a median of 0.035, ranging from 0.0045 to 0.12 (Fig. 13). These results are comparable to that previously determined in the north of China using various different methods (H. Wang et al., 2017b, 2018b; X. Wang et al., 2017; Z. Wang et al., 2017; Xia et al., 2019; Yu et al., 2020). The k_wall of N₂O₅ corresponding to valid γ(N₂O₅) measurements was rather stable at an average of 0.0021±0.0007 s⁻¹, which was consistent with the values determined at similar RH levels in the laboratory tests. It somehow reflected the robustness of the status of the flow tube system and the derived results.

Figure 13 The histogram distribution of measured γ(N₂O₅) for valid cases.

In the current system, the N₂O₅ concentrations measured at both the entrance and exit of the flow tube are sensitive to the NO fluctuations within the timescale of one sampling mode, which can induce large uncertainty in calculating γ(N₂O₅). With our stringent criteria of data screening, the cases of drastic NO fluctuations were excluded from the analysis. Hence, the majority of valid γ(N₂O₅) for this campaign were obtained during the periods of the NO below 2 ppbv, when the clean air mass was dominant at this urban site. Meanwhile, the S_a concentrations within clean episodes were lower than during other periods, with an average of 159 µm² cm⁻³. The derived $k_{{\mathrm{N}}_{\mathrm{2}}{\mathrm{O}}_{\mathrm{5}}}$ ranged from $\mathrm{2.1}\times {\mathrm{10}}^{-\mathrm{5}}$ to $\mathrm{1.6}\times {\mathrm{10}}^{-\mathrm{3}}$ s⁻¹, well above the detection limit, which demonstrated the robustness of results, even subject to low ambient S_a conditions. In order to improve the applicability of γ(N₂O₅) measurements, future development is suggested to give priority to removing NO (at least the fluctuation of NO) in the sampling system before the entrance of the flow tube without the cost of particle transmission efficiency.

7 Summary and conclusion

We report the new development of an aerosol flow tube system coupled with a detailed box model to derive γ(N₂O₅) on ambient aerosols directly. The unique feature of this system is that the sequential N₂O₅ measurement at both ends of the flow tube was applied to improve the accuracy in quantifying γ(N₂O₅) by taking it as a constraint for the box model to reproduce the decay of introduced N₂O₅ gas sources in the flow tube. With the consideration of detailed chemistry related to N₂O₅, the proposed approach was testified to refrain from the interference of side reactions (induced by the additional N₂O₅ generation), NO titration in the flow tube and variations of air masses between successive sampling modes.

A series of laboratory tests were performed to characterize factors affecting γ(N₂O₅) derivation and to demonstrate the system's applicability to (NH₄)₂SO₄ aerosols. The uncertainties associated with the instruments used in the system and potential fluctuations of various parameters were thoroughly discussed in the uncertainty analysis, and we estimated the overall uncertainty of γ(N₂O₅) to be 16 %–43 %, which is subject to NO, NO₂, O₃, meteorological parameters, residence time and the γ(N₂O₅) value itself. The detection limit of γ(N₂O₅) was quantified to be 0.0016 at the aerosol surface concentration (S_a) of 200 µm² cm⁻³. We deployed this system for field observations of γ(N₂O₅) at an urban site in Beijing, where strong anthropogenic emissions and frequent switches of air mass were encountered. The obtained γ(N₂O₅) was comparable to previously reported values in northern China and demonstrated the robustness of this system during low NO episodes. Further investigations by the introduced approach on N₂O₅-heterogeneous chemistry for both laboratory-generated and ambient particles are also available.

Appendix A: Measured VOCs used to calculate NO₃ reactivity in the box model method

A total of 59 kinds of VOCs were measured by GC-FID-MS in this work, half of which had known rate constants that can be used to parameterize the reaction of NO₃ with VOCs (mainly composed of alkenes and aromatics) in γ(N₂O₅) retrieval by the box model method (see also Sect. 3). Their rate constants were obtained from MCM331 or IUPAC, and the values at 298 K are listed in Table A1.

Table A1 VOCs used to calculate NO₃ reactivity ($k_{{\mathrm{NO}}_{\mathrm{3}}}$) in the box model method.

Note: ^a MCM; ^b IUPAC.

Appendix B: Evaluations of box model method by ambient data

Figure B1 The derived dependence of N₂O₅ wall loss on RH under laboratory conditions (red dots) and in field measurements (blue square).

Figure B2 (a) The box whisker of N₂O₅ source and NO measured before the entrance; (b) the intercomparison of derived N₂O₅ uptake coefficients by using a fixed initial N₂O₅ and a dynamic measured N₂O₅ at the flow tube entrance in the iterative box model.