Volatile oxidation products and secondary organosiloxane aerosol from D₅ + OH at varying OH exposures

Siloxanes are composed of silicon, oxygen, and alkyl groups and are emitted from consumer chemicals. Despite being entirely anthropogenic, siloxanes are being detected in remote regions and are ubiquitous in indoor and urban environments. Decamethylcyclopentasiloxane (D₅) is one of the most common cyclic congeners, and smog chamber and oxidation flow reactor (OFR) experiments have found D₅ + OH to form secondary organosiloxane aerosol (SOSiA). However, there is uncertainty about the reaction products and the reported SOSiA mass yields (Y_SOSiA) appear inconsistent. To quantify small volatile oxidation products (VOPs) and to consolidate the Y_SOSiA in the literature, we performed experiments using a potential aerosol mass OFR while varying D₅ concentration, humidity, and OH exposure (OH_exp). We use a proton transfer reaction time-of-flight mass spectrometer to quantify D₅, HCHO, and HCOOH and to detect other VOPs, which we tentatively identify as siloxanols and siloxanyl formates. We determine molar yields of HCHO and HCOOH between 52 %–211 % and 45 %–127 %, respectively. With particle size distributions measured with a scanning mobility particle sizer, we find Y_SOSiA to be < 10 % at OH_exp < 1.3 × 10¹¹ s cm⁻³ and ∼ 20 % at OH_exp, corresponding to that of the lifetime of D₅ at atmospheric OH concentrations. We also find that Y_SOSiA is dependent on both organic aerosol mass loading and OH_exp. We use a kinetic box model of SOSiA formation and oxidative aging to explain the Y_SOSiA values found in this study and the literature. The model uses a volatility basis set (VBS) of the primary oxidation products as well as an aging rate coefficient in the gas phase, k_age,gas, of $\mathrm{2.2}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ s⁻¹ and an effective aging rate coefficient in the particle phase, k_age,particle, of 2.0 × 10⁻¹² cm³ s⁻¹. The combination of a primary VBS and OH-dependent oxidative aging predicts SOSiA formation much better than a standard-VBS parameterization that does not consider aging (root mean square error = 42.6 vs. 96.5). In the model, multi-generational aging of SOSiA products occurred predominantly in the particle phase. The need for an aging-dependent parameterization to accurately model SOSiA formation shows that concepts developed for secondary organic aerosol precursors, which can form low-volatile products at low OH_exp, do not necessarily apply to D₅ + OH. The resulting yields of HCHO and HCOOH and the parameterization of Y_SOSiA may be used in larger-scale models to assess the implications of siloxanes for air quality.

1 Introduction

Organosiloxanes are molecules composed of silicon–oxygen bonds with alkyl groups on the silicons and encompass linear and cyclic species, some of which have vapor pressures on par with volatile organic compounds (VOCs). Siloxanes are entirely anthropogenic pollutants (Rücker and Kümmerer, 2015) commonly used in consumer and industrial chemical products (Seltzer et al., 2021a; Gkatzelis et al., 2021) and their emissions are projected to increase in the coming decades (Tansel and Surita, 2017). Decamethylcyclopentasiloxane (D₅, C₁₀H₃₀O₅Si₅), where “D” refers to silicon center atoms bonded to two oxygens, is a ubiquitous cyclosiloxane in the ambient environment.

Siloxanes have been detected in the indoor environment (Tang et al., 2015; Tran and Kannan, 2015; Arata et al., 2021; Katz et al., 2021; Kaikiti et al., 2022; Wang et al., 2022), near landfills (Schweigkofler and Niessner, 1999), and near sewage treatment sites (Lee et al., 2014; Horii et al., 2019). Siloxanes are also found in outdoor urban air (Xiang et al., 2021), and organosilicon compounds have been found in varying amounts in ambient particulates in China (Lu et al., 2019; Cheng et al., 2021; Meng et al., 2021; Song et al., 2022; Xu et al., 2022) and the United States (Milani et al., 2021).

Siloxanes are suspected to be environmentally persistent or emitted continuously to appear as such (Howard and Muir, 2010; Xiang et al., 2021), while other studies have found that methyl siloxanes would be removed on timescales of days to weeks (Graiver et al., 2003; Whelan and Kim, 2021). Reaction rate coefficients of D₅ with atmospheric oxidants have been reported, and Atkinson (1991) found D₅ to be effectively unreactive with atmospheric concentrations of O₃ ($k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{O}\mathrm{3}}$ < $\mathrm{3}\times {\mathrm{10}}^{-\mathrm{20}}$ cm³ s⁻¹) and NO₃ radicals ($k_{{\mathrm{D}}_{\mathrm{5}}+{\mathrm{NO}}_{\mathrm{3}}}$ < 3 × 10⁻¹⁶ cm³ s⁻¹) at ∼ 298 K. While D₅ is reactive with OH and Cl, Alton and Browne (2020) calculated that the removal of D₅ by Cl radicals would only be a few percent of that by OH radicals at typical ambient oxidant concentrations.

Atkinson (1991), Safron et al. (2015), Xiao et al. (2015), Kim and Xu (2017), and Alton and Browne (2020) have measured $k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}$ at ∼ 298 K to be 1.55 × 10⁻¹², 2.6 × 10⁻¹², 2.46 × 10⁻¹², 1.46 × 10⁻¹², and $\mathrm{2.1}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ s⁻¹, respectively. These measurements are summarized in Table S1 in the Supplement. Xiao et al. (2015) derived $k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}$ computationally as 2.90 × 10⁻¹² cm³ s⁻¹. In this paper, we use $k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}=$ 2.0 × 10⁻¹² cm³ s⁻¹, which is a rounded average of the empirically determined rate coefficients. This $k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}$ corresponds to a D₅ atmospheric lifetime of about 4 d via removal by OH, assuming a daily average OH concentration ([OH]_avg) of 1.5 × 10⁶ cm⁻³.

D₅ is expected to suppress O₃ formation in urban environments. Carter et al. (1993) performed a series of chamber experiments mimicking urban air conditions and found that D₅ siloxane would inhibit ozone formation by suppressing the OH radical. In contrast, formaldehyde (HCHO) is known to contribute to O₃ formation (Derwent et al., 1996). Fu et al. (2020) predicted the formation of HCHO as a product of D₅+ OH in low-NO / HO₂ conditions using quantum chemical calculations and kinetics modeling, but an experimental yield of HCHO from D₅+ OH has not been reported. Atkinson (1991) proposed HCHO as a product of the siloxane alkoxyl radical (RO) pathway, assuming an analogous mechanism to that of VOCs. Sommerlade et al. (1993) suggested that HCHO may arise from siloxane RO decomposition and from ROOH rearrangement in the presence of acids and H₂O. Alton and Browne (2022) predicted HCHO as a product of RO₂ rearrangement in the case of D₃ siloxane. Because HCHO is a secondary product, the O₃ formation potential of D₅ may differ between at a source and at downwind locations.

Formic acid (HCOOH) is a common acid catalyst in the atmosphere (Hazra et al., 2014) and a particle-nucleating species (Yu, 2000). Studies have identified some HCOOH sources in the atmosphere (Millet et al., 2015; Franco et al., 2021); however, HCOOH is suspected to have unidentified anthropogenic sources in the troposphere (Millet et al., 2015; Chen et al., 2021) as some urban sources remain unaccounted for (Le Breton et al., 2012; Yuan et al., 2015). Chandramouli and Kamens (2001) proposed that the RO₂ initially formed from D₅+ OH makes a siloxanyl formate (D₄T(OCHO), where “T” refers to a silicon center bonded to three oxygens) that reacts with H₂O to form a siloxanol (D₄T(OH)) and HCOOH. However, we are unaware of experimental HCOOH yields reported for D₅ + OH.

Whelan et al. (2004) used known siloxane chemistry in a partitioning model to assess the atmospheric fate of siloxanes and found that silanols are the predominant oxidation products. These silanols are generally water soluble and either removed from the atmosphere via wet deposition or undergo a pH-dependent process of hydrolysis, forming smaller and smaller silanols (Whelan et al., 2004). Eventually, the small silanols are converted to SiO₂, H₂O, and CO₂ through photolytic reactions in water or biological processes in soil (Spivack et al., 1997; Stevens, 1998; Graiver et al., 2003).

The intermediate products between D₅ and those small silanols are less studied, and the OH-oxidation rate coefficients of these intermediates have not been reported. Sommerlade et al. (1993) and Alton and Browne (2022) used mass spectrometry to study the gaseous products of D₅ oxidation in chambers, while Fu et al. (2020) used quantum chemistry modeling. These studies found that gaseous intermediates are composed of a variety of alcohols, aldehydes, esters, and hydroperoxides. Given that such volatile oxidation products (VOPs) in experiments with higher OH_exp are likely to undergo multiple oxidation steps, there is a need to address their subsequent oxidation rate coefficients. Moreover, while the formation of HCHO and HCOOH has been predicted in mechanisms, it has not been quantified.

Secondary aerosol mass yield (Y, Eq. 1) is defined as the ratio of produced aerosol mass (Δm(SOSiA)) to reacted precursor mass (Δm(D₅)), which we adopt here for secondary organosiloxane aerosol (SOSiA). Reports about secondary aerosol formation from D₅ siloxane seem conflicting, with some experiments reporting much higher Y_SOSiA than others. For instance, Wu and Johnston (2017) and Janechek et al. (2019) saw maximum Y_SOSiA of 23 % and 50 %, respectively, in their photo-oxidation chamber and oxidation flow reactor (OFR) experiments, albeit at different OH exposures (OH_exp). Charan et al. (2022) found a Y_SOSiA of 158 % with their OFR at an OH_exp of 3.2 × 10¹² s cm⁻³. Avery et al. (2023) reported a wide range of Y_SOSiA values (2 %–146 %) from their OFR experiments.

$$\begin{array}{}\text{(1)}& Y_{\mathrm{SOSiA}}={\displaystyle \frac{\mathrm{\Delta }m\left(\mathrm{SOSiA}\right)}{\mathrm{\Delta }m\left({\mathrm{D}}_{\mathrm{5}}\right)}}\end{array}$$

In contrast, Charan et al. (2022) reported almost negligible Y_SOSiA (< 5 %) from their chamber studies where [OH] was on the order of ∼ 10⁶ cm⁻³, which is closer to [OH] found in ambient conditions (Peng and Jimenez, 2020). Han et al. (2022) conducted OFR experiments and found that Y_SOSiA would be 2 % at [OH] of 4.6×10⁸ cm⁻³ or OH_exp of 5.5 × 10¹⁰ s cm⁻³. The variation of Y_SOSiA reported in the literature suggests that oxidation conditions need to be considered to accurately parameterize Y_SOSiA, especially given that D₅ is being considered in air-quality models as a part of volatile chemical product inventories (Pennington et al., 2021; Seltzer et al., 2021a, b).

In this study, we aim to assess the OH oxidation of D₅ by determining the rate coefficients of secondary reactions of VOPs with OH (i.e., chemical aging) and providing a first quantification of HCHO and HCOOH yields. We also measure Y_SOSiA under diverse OH_exp and [D₅]₀ conditions. Lastly, we develop parameterizations of SOSiA yield using a kinetic model with a chemical aging reaction scheme to reconcile the reported Y_SOSiA from D₅+ OH in the literature and for use in air-quality models.

2 Method and materials

2.1 Experiments

The Aerodyne Research (Billerica, MA, USA) potential aerosol mass OFR (PAM-OFR) (Kang et al., 2007) has a volume of 13.3 L and is made of chromated aluminum (Xu and Collins, 2021). We operated the PAM-OFR in OFR185 mode (Peng and Jimenez, 2020), where 185 nm lamps that also emit 254 nm light (GPH436T5VH, LightSources, Orange, CT, USA) generate OH and O₃ with injected H₂O vapor from a Nafion humidifier (FC-100-80-6MKK, Perma Pure, Lakewood, NJ, USA). There were two of these 185 nm lamps placed across from each other in clear fused quartz sleeves. The 185 nm lamps were wrapped with covers at even intervals to reduce the UV intensity so that 90 % of the lamp surface was covered. We operated the PAM-OFR at residence times (τ_res) of 120 and 180 s with flow rates of 6.65 and 4.43 L min⁻¹, respectively. Additional details about the experiment setup are summarized in Fig. S1 and Sect. S1.

We use the D₅ siloxane trace measured from the proton transfer reaction mass spectrometer (PTR-MS) to calculate OH_exp with Eq. (2), where $k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}=$ 2.0 × 10⁻¹² cm³ s⁻¹. [D₅]₀ and [D₅]_final are the D₅ concentrations before and after the exposure to OH.

$$\begin{array}{}\text{(2)}& {\mathrm{OH}}_{\exp }=-{\displaystyle \frac{\mathrm{1}}{k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}}}\times \ln \left({\displaystyle \frac{{\left[{\mathrm{D}}_{\mathrm{5}}\right]}_{\mathrm{final}}}{{\left[{\mathrm{D}}_{\mathrm{5}}\right]}_{\mathrm{0}}}}\right)\end{array}$$

Prior to experiments, we checked the background particle and D₅ concentrations with the scanning mobility particle sizer (SMPS) and PTR-MS. In all experiments, the background particle number concentrations were < 10 cm⁻³, and the background [D₅] values were below the limit of detection (3σ=80 ppt). Then, we injected D₅ with a syringe pump while monitoring the PTR-MS, with major ions at $m/z$ 371 and $m/z$ 355. We performed the experiments with a target [D₅]₀ of 50, 100, or 200 ppb. With these target [D₅]₀ values, we get external OH reactivities (OHR_ext) of 2.5–9.8 s⁻¹ at 298.15 K and 1 atm, where OHR_ext is the reactivity caused by the injection of D₅ into the PAM-OFR (Peng and Jimenez, 2020). With these OHR_ext values, we reduce the risk of OH suppression and VOCs photolysis (Peng and Jimenez, 2020).

When the D₅ trace stabilized near the target [D₅]₀, we began the experiment by turning the UV lamps in the PAM-OFR on at either 2.4 or 8.0 V. We waited 30 min for the UV lamps to stabilize and for the PAM-OFR walls to equilibrate with gaseous species. The Y_SOSiA values (Eq. 1) were calculated using the average SOSiA mass concentration from four SMPS cycles following that 30 min. We obtained Δm(D₅) as the difference between [D₅]₀ and [D₅]_final. At the end of an experiment, we turned off the UV lamps to check the D₅ trace return.

To clean the PAM-OFR between experiments, we stopped the syringe pump and removed the syringe from the glass bulb while keeping the humid airflow in the PAM-OFR. We turned on the PAM-OFR UV lamps and connected the outlet directly to the exhaust, until D₅ and particle number concentrations were below the limit of detection. We used Igor Pro 9 (WaveMetrics, Portland, OR, USA) for data post-processing and visualization.

2.2 Instrumentation

2.2.1 PTR-MS

To measure D₅ and VOPs, we used a PTR-MS (PTR-TOF 1000, IONICON Analytik, Innsbruck, Austria) equipped with the extended volatility range (EVR) option (Piel et al., 2021), where the wetted inlet components and the drift tube are passivated with a silicon coating. The PTR-MS also had an ion transfer lens between the drift tube and time-of-flight mass spectrometer (Jordan et al., 2009). An internal permeation source (PerMaSCal) emitted a steady stream of 1,3-diiodobenzene into the mass spectrometer for mass calibration scale adjustments. Additional PTR-MS details are in Sect. S1.

To reduce H₂O clusters at high humidities, we operated the PTR-MS at 137 Td (U_drift=600 V; Td is the Townsend unit where 1 Td = 10⁻¹⁷ V cm²) for quantification. The drift tube pressure and temperature were set to 2.30 mbar and 80 ^∘C. For the reagent ion source, we set the U_s, U_so, and H₂O flow rate to 150 V, 80 V, and 6.00 sccm respectively. The ion source hollow-cathode discharge current was set to 5.0 mA. The PTR-MS drift tube was 9.6 cm long, and at 137 Td the [H₂O]H⁺ reaction time (Δt) was 94 µs (de Gouw et al., 2003). We calculate the primary reagent ion signal, [H₂O]H⁺, by multiplying the signal of its isotope, [H${}_{\mathrm{2}}^{\mathrm{18}}$O]H⁺, by 500.

We use the PTR-MS data for the quantification of D₅ ($m/z$ 371), HCHO ($m/z$ 31), and HCOOH ($m/z$ 47), where the primary reagent ion counts were normalized to 10⁶ counts per second (ncps). For D₅, we used a calibration gas cylinder (Apel-Riemer Environmental, Miami, FL, USA) containing D₅ to calibrate the PTR-MS. We also calculate the normalized measurement sensitivity (ncps ppb⁻¹) of D₅, HCHO, and HCOOH using Eq. (3) adapted from de Gouw and Warneke (2007). I_(VOC)H+ and $I_{\left({\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right)\mathrm{H}+}$ are the ion counts of the protonated VOCs and the reagent ion, respectively. Additional details on the mass spectra interpretation and quantification are in Sects. S1.5 and S3.

$$\begin{array}{}\text{(3)}& \mathrm{Sensitivity}={\displaystyle \frac{\frac{I_{\left(\mathrm{VOC}\right){\mathrm{H}}^{+}}}{I_{\left({\mathrm{H}}_{\mathrm{2}}\mathrm{O}\right){\mathrm{H}}^{+}}}\times {\mathrm{10}}^{\mathrm{6}}}{\left[\mathrm{VOC}\right]}}\end{array}$$

We tested the instrument sensitivity response with humidity by keeping the species concentrations constant while changing the sample air humidity. The sensitivity of D₅ at $m/z$ 371 was not heavily affected by humidity at 137 Td, and we did not correct for humidity in the D₅ quantification (Fig. S5). On the other hand, HCHO and HCOOH sensitivities varied with humidity, and we corrected their sensitivities as detailed in Sect. S3. Prior to experiments, we tuned the micro-channel plate (MCP) to prevent signal bias against higher-mass ions (Müller et al., 2014). We adjusted the MCP voltage in steps to increase the signal strength at $m/z$ 331, a diiodobenzene ion, until the relative signal increase was < 20 %.

2.2.2 Scanning mobility particle sizer

An SMPS 3938 (TSI, Shoreview, MN, USA) equipped with an impactor (0.0508 cm) measured the particle mobility diameter size distribution between diameters of 14.3 and 723.4 nm. The SMPS consisted of a model 3082 electrostatic classifier, a model 3081A differential mobility analyzer (DMA), a model 3088 soft X-ray neutralizer, and a model 3756 ultrafine condensation particle counter. We set the SMPS sheath flow at 3.0 L min⁻¹ and the aerosol flow rate at 0.3 L min⁻¹, and the DMA voltage ranged from 10.6 to 9921.4 V. The SMPS scanned for 150 s, followed by a 5 s retrace and 10 s purge while recording on a 3 min cycle. We referred to the manufacturer's recommendations when deciding these SMPS settings (TSI Inc., 2012), and a sample particle size distribution from experiment 12 (Table 1) is shown in Fig. S4.

Table 1 Summary of SOSiA mass yields (Y_SOSiA) with aerosol sampling line corrections assuming ρ_SOSiA= 1.07 g cm⁻³ for all experiments. [H₂O] is the molar mixing ratio of H₂O in air. For C_OA and [D₅] the errors are the standard deviation of the data points averaged, while for Y_SOSiA they are calculated with error propagation. For reference, at 25 ^∘C and 1 atm, 1 ppb of D₅ is ∼ 15 µ g m⁻³ and 1 d equivalent of OH_exp is ∼ 1.3 × 10¹¹ s cm⁻³ at a daily [OH]_avg of 1.5 × 10⁶ cm⁻³.

For the Y_SOSiA calculations, we convert the SMPS integrated particle volumes into mass using a SOSiA mass density (ρ_SOSiA) of 1.07 g cm⁻³ for all experiments. We obtained this ρ_SOSiA from PAM-OFR experiments separate from the ones described here, where we weighed the masses of SOSiA collected on filters and obtained particle volumes with the SMPS. Additional details on ρ_SOSiA are available in Sect. S2.

2.3 Volatility distribution parameterization

Janechek et al. (2019) and Charan et al. (2022) fitted their Y_SOSiA data to the Odum two-product model (Odum et al., 1996), and we follow the same methodology for comparison with the literature (Sect. S4). Similarly, we fit the standard volatility basis set (VBS) parameters α (Donahue et al., 2006) in Eq. (4) to the measured Δm(SOSiA) using the measured Δm(D₅), where α_i is the product mass yield for volatility bin i.

$$\begin{array}{}\text{(4)}& \mathrm{\Delta }m\left(\mathrm{SOSiA}\right)=\mathrm{\Delta }m\left({\mathrm{D}}_{\mathrm{5}}\right)\times \sum _{i=\mathrm{1}}^n{\displaystyle \frac{{\mathit{\alpha }}_i}{\mathrm{1}+\frac{C_i^{\ast }}{C_{\mathrm{OA}}}}}\end{array}$$

In the experiments, the organosiloxane aerosol mass loading (C_OA) was equivalent to the SOSiA mass concentrations. As the produced aerosol mass in the experiments ranged from 3.7 to 965.7 µg m⁻³, we use six logarithmically spaced effective saturation mass concentration (C^*) bins ranging from 0.1 to 10 000 µg m⁻³ at 298.15 K to cover the low- and high-volatility products. For reference, D₅ liquid has a vapor pressure of 20.4 Pa at 298.15 K or $C^{*}=\mathrm{3.05}\times$ 10⁶ µg m⁻³ (Lei et al., 2010). Since the experiments had slight variations in temperature, we correct for temperature impacts on C^* between experiments using the Clausius–Clapeyron equation and an enthalpy of vaporization of 60 kJ mol⁻¹, which is that of D₅ siloxane (Lei et al., 2010).

As the experiments were performed for a range of OH_exp, the products between experiments may have varied due to multi-generational aging (Zhao et al., 2015). To account for aging and parameterize Y_SOSiA as a function of OH_exp, we also analyze the yield data using a kinetic box model with four chemical reactions (Reactions R1–R3) written in MATLAB (MathWorks, Natick, MA, USA).

$$\begin{array}{}\text{(R1)}& {\displaystyle }\begin{array}{rl}{D}_{\mathrm{5}}& +\mathrm{OH}\to \sum {\mathit{\alpha }}_i\times \mathrm{prod}\left(i\right)\\ & \left(k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}=\mathrm{2.0}\times {\mathrm{10}}^{-\mathrm{12}}{\mathrm{cm}}^{\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}\right)\end{array}\text{(R2)}& {\displaystyle }\begin{array}{rl}(\mathrm{1}-f_i)& \times \mathrm{prod}\left(i\right)+\mathrm{OH}\to (\mathrm{1}-f_i)\\ & \times \mathrm{prod}(i-\mathrm{1})\left(k_{\mathrm{age},\mathrm{gas}},i=\mathrm{2},\mathrm{\dots },\mathrm{6}\right)\end{array}\text{(R3)}& {\displaystyle }\begin{array}{rl}{f}_i& \times \mathrm{prod}\left(i\right)+\mathrm{OH}\to f_i\times \mathrm{prod}(i-\mathrm{1})\\ & \left(k_{\mathrm{age},\mathrm{particle}},i=\mathrm{2},\mathrm{\dots },\mathrm{6}\right)\end{array}\end{array}$$

Reaction (R1) describes the initial oxidation of D₅ and immediate formation of products of varying volatility. Here, prod(i) refers to the sum of products (gas + particle) in volatility bin i, which are formed with a molar branching ratio α_i. We assume that prod(i) values have the same molecular weights (g mol⁻¹) as D₅, and so the α_i values are equivalent to the product mass yields at OH_exp→0. In the model, a fraction f_i of each oxidation product partitions instantaneously from the gas phase to the particle phase according to absorptive partitioning theory (Donahue et al., 2006) (Eq. 5).

$$\begin{array}{}\text{(5)}& f_i=\left({\displaystyle \frac{\mathrm{1}}{\mathrm{1}+\frac{C_i^{\ast }}{C_{\mathrm{OA}}}}}\right)\end{array}$$

Reactions (R2) and (R3) describe how OH_exp causes volatility to decrease (Robinson et al., 2007). This decrease in volatility via “bin hopping” (Sommers et al., 2022) occurs at a rate proportional to the chemical aging rate coefficient for the gas-phase (k_age,gas, cm³ s⁻¹) and an effective aging rate coefficient for the particle-phase species (k_age,particle, cm³ s⁻¹). Here we assume that products in the lowest-volatility bin (i=1) cannot be removed from that bin and that the highest-volatility bin (i=6) does not receive product with aging. The [OH] values are set by dividing the experimental OH_exp from Eq. (2) by the PAM-OFR residence times.

We use k_age,gas and k_age,particle as aggregate chemical aging rate coefficients, not specific to any species or volatility bin. Studies on chamber experiments (Robinson et al., 2007) and ambient measurements (Sommers et al., 2022) have applied chemical aging only to the gas phase as heterogeneous aging is slower. However, studies have found that the high oxidant concentrations in OFRs would appreciably oxidize organic aerosol (OA) within experiment timescales (Kessler et al., 2012; Kroll et al., 2015). To accommodate OH uptake to the bulk phase, we include particle-phase aging that also decreases the volatility of particle-phase products. The timescales and atmospheric relevance of heterogeneous oxidation in OFRs are areas of ongoing research (Zhao et al., 2019; Peng and Jimenez, 2020), but for now we opt to fit chemical aging rate coefficients for each phase. Note that surface and bulk accommodation processes are not explicitly resolved in the kinetic model and k_age,particle acts on the concentrations of particle-phase products per unit gas volume (Sect. S1.6).

We fit k_age,gas, k_age,particle, and α_iin the aging-VBS model to the experimental SOSiA mass using the Monte Carlo genetic algorithm (MCGA) (Berkemeier et al., 2017). We obtain a best model fit and a fit ensemble consisting of 1059 parameter sets for which the model's root mean square error (RMSE) is below the threshold of 50. We find this ensemble to estimate the parametric uncertainty associated with the model fit (Berkemeier et al., 2021).

We use the OFR chemistry template with KinSim (Peng and Jimenez, 2020) to estimate the RO₂ fates and expect the fates to have been uniform across the experiments (Sect. S5). Although there are uncertainties in the RO₂ reaction rate coefficients for siloxanes, we expect that the variation in Y_SOSiA is not driven by RO₂ fate in these experiments. We also report the condensational sink and condensation lifetimes (Palm et al., 2016) calculated using the particle size distributions in Sect. S1.3.

3 Results and discussion

3.1 Volatile organic products (VOPs)

3.1.1 Siloxanol and formate ester trends

In Fig. 1, the PTR-MS signals before and after D₅ is oxidized are displayed relative to the protonated D₅ ion at $m/z$ 371 on the y axis. We perform this scaling because the isotopologues of the product fragment ions overlap with the isotopologues of D₅. Thus, changes in signal intensity are caused by both product formation and D₅ oxidation. We choose to normalize the spectra at $m/z$ 371 because we assume that no product ion peaks overlap with the [D₅]H⁺ signal at $m/z$ 371. While this scaling makes the product peaks appear larger, the changes in the mass spectrum are also qualitatively highlighted. For example, D₅ loses a methyl group during the PTR, which forms a large signal at $m/z$ 355. The isotopologues of the -CH₄ fragment of [D₅]H⁺ overlap with fragments of VOPs. By scaling the mass spectrum with the ratio of [D₅]H⁺ signal before and after oxidation, the signal of the VOPs is separated from that of remaining D₅.

Figure 1 Example PTR-MS mass spectra from experiment 12 and proposed VOP ions. For visualization, the signal intensities before (black) and after (gray) oxidation are shown relative to the maximum signal intensity of the [D₅]H⁺ ion at $m/z$ 371, which is set to 1. The multifunctional species (blue, pink) are expected to be formed through multiple steps of OH oxidation. The red and pink areas in the inset each refer to the enhancement in signal attributed to D₄T(OH) and D₃T₂(OH)₂ over that of the -CH₄ fragment of [D₅]H⁺ and isotope signals, respectively.

Using the mass spectra and species reported by Alton and Browne (2022), we attribute the indicated ions in Fig. 1 to siloxanol (D₄T(OH)), siloxanediol (D₃T₂(OH)₂), siloxanyl formate (D₄T(OCHO)), and siloxanolyl formate (D₃T₂(OH)(OCHO)). Here, D and T refer to silicon centers bonded to two and three oxygen atoms, respectively. The multifunctional VOPs are reported to arise from multiple steps of oxidation (Alton and Browne, 2022). The red and pink shaded areas in the inset of Fig. 1 refer to the enhancement in signal over that of the -CH₄ fragment of [D₅]H⁺, which we attribute to the -H₂O fragments of [D₄T(OH)]H⁺ and [D₃T₂(OH)₂]H⁺, respectively. We use the masses of the -H₂O fragments of the protonated siloxanols as large alcohols dissociate during the PTR (Brown et al., 2010). We also attribute the ions in the blue- and yellow-dotted boxes to the -H₂O fragments of [D₃T₂(OH)(OCHO)]H⁺ and [D₄T(OCHO)]H⁺.

As we did not have calibration standards to quantify these VOPs, we calculate the molar yields of the VOPs relative to that of protonated D₅ siloxane at $m/z$ 371 to study the trends of siloxane VOPs (Fig. 2). For each VOP, we choose a characteristic peak in the mass spectrum and calculate the change in signal due to VOP formation (Sect. S1.5). Then, we calculate the ratios of the changes in the VOP and D₅ signals to get the relative molar yields (Y_rel,VOPi). In the right-side panels for each VOP in Fig. 2, the Y_rel,VOPi decreases with increasing OH_exp (x axes). This decrease in VOP signal is consistent with these gaseous products undergoing further oxidation or increased gas–particle partitioning due to higher C_OA at higher OH_exp. We use the colors to highlight the functional groups on the D₅ backbone.

Figure 2 Relative molar yields of VOPs as a function of OH_exp and D₅ consumed: (a1, a2) D₄T(OCHO), (b1, b2) D₃T₂(OH)(OCHO), (c1, c2) D₃T₂(OH)₂, and (d1, d2) D₄T(OH). The colors correspond to the attributed mass ions and molecular structures shown at the top. We did not have a calibration for the suspected VOPs, so the y axes are relative molar yields (ncps $/$ ncps) calculated with the change in signal attributed to each VOP and that of D₅ at $m/z$ 371. The relative molar yields decrease with OH_exp, which is used to fit their OH-oxidation rate coefficients and γ_i (black lines).

In the left-side panels for each VOP in Fig. 2, the relative signals of the VOPs (y axes) decrease with increasing OH_exp (color scale). Then, assuming that [OH] is constant throughout the PAM-OFR, that D₅+ OH is the rate-limiting step in VOP formation, and that removal via gas–particle partitioning is negligible (Alton and Browne, 2022), we can consider a simplified D₅+ OH chemical mechanism, Reactions (R4) and (R5).

$$\begin{array}{}\text{(R4)}& {\displaystyle }{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}\to \sum {\mathit{\gamma }}_i{\mathrm{VOP}}_i\left(k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}=\mathrm{2.0}\times {\mathrm{10}}^{-\mathrm{12}}{\mathrm{cm}}^{\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}\right)\text{(R5)}& {\displaystyle }{\mathrm{VOP}}_i+\mathrm{OH}\to \left(k_{\mathrm{VOP}i+\mathrm{OH}}\right)\end{array}$$

In Reaction (R4), γ_i is the relative molar yield of a given VOP_i found by extrapolating $Y_{\mathrm{rel},{\mathrm{VOP}}_i}$ (y axes in Fig. 2) to OH_exp→0. With ordinary differential equations (Eqs. 6 and 7) from these reactions and experimental inputs, we fit γ_i and the VOP_i+ OH rate coefficient (k_VOPi+OH, cm³ s⁻¹). The fits are shown as black lines in the right-side panels of each VOP in Fig. 2.

$$\begin{array}{}\text{(6)}& {\displaystyle \frac{d\left[{\mathrm{D}}_{\mathrm{5}}\right]}{\mathrm{d}t}}=-k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}\left[{\mathrm{D}}_{\mathrm{5}}\right]\left[\mathrm{OH}\right]\text{(7)}& {\displaystyle }\begin{array}{rl}{\displaystyle \frac{d\left[{\mathrm{VOP}}_i\right]}{\mathrm{d}t}}& ={\mathit{\gamma }}_{\mathrm{i}}{k}_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}\left[{\mathrm{D}}_{\mathrm{5}}\right]\left[\mathrm{OH}\right]\\ & -k_{\mathrm{VOP}i+\mathrm{OH}}\left[{\mathrm{VOP}}_i\right]\left[\mathrm{OH}\right]\end{array}\end{array}$$

The fitted k_VOPi+OH values for each VOP are on the order of ∼ 10⁻¹² cm³ s⁻¹ (Table S7) but faster than $k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}$, which suggests that these VOPs have atmospheric lifetimes shorter than that of D₅. Alton and Browne (2022) have estimated these VOPs to be volatile with quantitative structure–activity relationship models. However, there are uncertainties in those models, and the VOPs may have lower-saturation mass concentrations than expected. Moreover, the chemical mechanism might be more complex than the one outlined with simple Reactions (R4) and (R5). Consequently, we present these k_VOPi+OH values as estimates for secondary chemistry in this simplified reaction scheme, and future work using quantitative measurements should improve the calculated lifetimes of these intermediate D₅+ OH products in the atmosphere.

3.1.2 Formaldehyde (HCHO) yields

As shown in Table S8 and Fig. 3, the experimental molar yields of HCHO (Y_HCHO, ΔHCHO/ΔD₅ in ppb ppb⁻¹) exceed 100 % at low OH_exp and decrease with higher OH_exp. We attribute the decreasing Y_HCHO with increasing OH_exp to HCHO removal by OH in the PAM-OFR. HCHO has a lifetime of 0.91 d at [OH]_avg= 1.5×10⁶ cm⁻³ (Atkinson et al., 2006) or 78 s at [OH] = 1.5×10⁹ cm⁻³. In such high-[OH] conditions, some HCHO is oxidized while being produced, which is consistent with the decreasing Y_HCHO with increasing OH_exp (Fig. 3a). However, HCHO formation likely occurs over multiple oxidation steps (Fu et al., 2020), and how VOP + OH branches to produce HCHO and the rate coefficients for those reactions are not experimentally constrained.

Figure 3 Experimental molar yields of selected VOPs: (a) HCHO and (b) HCOOH as functions of OH_exp. The blue shaded area in (b) is the range of Y_HCOOH (< 10 %) measured by Friedman and Farmer (2018) with monoterpenes under low-RH and low-NO_x conditions. The pink shaded area refers to Y_HCOOH from isoprene + OH chamber experiments (Link et al., 2020) at lower OH_exp.

Consequently, we implement a simplified mechanism (Reactions R6–R8) where D₅+ OH produces a representative VOP (VOP_rep) and yields HCHO at each oxidation step. The subsequent VOP_rep+ OH reactions share the same rate coefficient as D₅+ OH and produce HCHO with the same yield (γ_HCHO). This γ_HCHO is the cumulative molar yield of HCHO or the molar yield of HCHO as OH_exp→0. This γ_HCHO is also used to correlate satellite column retrievals of HCHO with VOC emissions (Millet et al., 2006) where an empirical value can be used to constrain uncertainty.

$$\begin{array}{}\text{(R6)}& {\displaystyle }\begin{array}{rl}& {\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}\to {\mathrm{VOP}}_{\mathrm{rep}}+{\mathit{\gamma }}_{\mathrm{HCHO}}\mathrm{HCHO}\\ & \left(k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}=\mathrm{2.0}\times {\mathrm{10}}^{-\mathrm{12}}{\mathrm{cm}}^{\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}\right)\end{array}\text{(R7)}& {\displaystyle }{\mathrm{VOP}}_{\mathrm{rep}}+\mathrm{OH}\to {\mathrm{VOP}}_{\mathrm{rep}}+{\mathit{\gamma }}_{\mathrm{HCHO}}\mathrm{HCHO}\left(k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}\right)\text{(R8)}& {\displaystyle }\begin{array}{rl}& \mathrm{HCHO}+\mathrm{OH}\to \left(k_{\mathrm{HCHO}+\mathrm{OH}}=\mathrm{8.5}\right.\\ & \left.\times {\mathrm{10}}^{-\mathrm{12}}{\mathrm{cm}}^{\mathrm{3}}{\mathrm{s}}^{-\mathrm{1}}\right)\end{array}\end{array}$$

We fit γ_HCHO to be 223 % (black line in Fig. 3a), assuming a constant [OH] in the PAM-OFR and that HCHO removal via partitioning or reactive uptake is negligible. This γ_HCHO is consistent with the modeled yields of those for VOCs used by Millet et al. (2006), who used γ_HCHO from chemical models ranging from 60 %–230 % for a variety of VOCs. Thus, D₅ has a comparable γ_HCHO to that of isoprene or aromatic VOCs. An improved mechanism and additional rate coefficients are needed to accurately model HCHO formation.

Fu et al. (2020) proposed a mechanism for D₃ siloxane where high Y_HCHO is produced under low-NO / HO₂ conditions. In that mechanism, RO₂ rearrangement and RO H shift is fast, and HCHO is produced at each rearrangement step. The γ_HCHO exceeding 100 % in these D₅ experiments is consistent with HCHO production over multiple rapid oxidation steps. The results we report suggest that a similar HCHO production mechanism exists for D₅.

Mao et al. (2009) found that models under-predicted tropospheric HCHO during their aircraft campaign studying Asian pollution outflows into the Pacific Ocean. This discrepancy between the measurements and calculations was pronounced near the surface and up to 2 km. They proposed that there is some missing OH reactivity and that the unaccounted species would be reactive with OH and yield HCHO when oxidized. Based on the D₅ experiments present here, the inclusion of siloxane species may reduce the HCHO formation gap; Coggon et al. (2021) already noted that including volatile chemical products in their model would increase HCHO production.

The large formation of HCHO may entail D₅ siloxane contributing to O₃ formation, albeit indirectly. We were unable to observe O₃ enhancement due to the high concentrations of O₃ produced from the PAM-OFR internal chemistry itself and the lack of NO_x. Given that $k_{{\mathrm{D}}_{\mathrm{5}}+\mathrm{OH}}$ is relatively slow compared to that of other common anthropogenic VOCs, we suspect that the oxidation of D₅ will occur downwind of urban sources in low-NO_x conditions or in cases of air stagnation. Whether D₅ has a net positive or negative effect on O₃ formation in these VOC / NO_x scenarios needs to be assessed with models. To get a rough estimate of O₃ production, we consider a case where 20 ppt of D₅ reacts with OH to form 40 ppt of HCHO, which also fully reacts. This D₅ concentration is within the range reported by Coggon et al. (2018) in ambient urban air. The molar maximum incremental reactivity of HCHO under high-NO_x conditions is ∼ 20 % (Carter et al., 1995), which makes HCHO a prominent precursor for tropospheric O₃. By multiplying the maximum incremental reactivity with the HCHO reacted with OH, we can estimate an O₃ formation potential of 8 ppt from D₅ in urban air.

Figure 4 Application of standard-VBS and aging-VBS models to experimental data. (a) Y_SOSiA as a function of C_OA, where the Y_SOSiA appears to be correlated with OH_exp. The standard-VBS model is shown in blue, and the aging-VBS model is shown with OH_exp (color scale) as it is a kinetic model. (b) VBS product mass yields for each volatility bin. For the aging-VBS model, the values are those of the first-generation products. (c) Comparison of SOSiA mass concentrations and (d) comparison of Y_SOSiA between the aging-VBS and standard-VBS models against measurements. The error bars indicate the minimum and maximum values from the parameter fit ensemble. The aging-VBS model shows a lower RMSE and higher R².

3.1.3 Formic acid (HCOOH) yields

We find molar yields of HCOOH (Y_HCOOH, ΔHCOOH/ΔD₅ ppb ppb⁻¹) between 45 %–127 %, as shown in Fig. 3b, although a trend with OH_exp is not obvious (Fig. 3b). We assume HCOOH loss via OH oxidation to be minor given the rate coefficient of $k_{\mathrm{HCOOH}+\mathrm{OH}}=$ 4.5 × 10⁻¹³ cm³ s⁻¹ at 298.15 K (Atkinson et al., 2006), which corresponds to 17 d of OH_exp at [OH]_avg= 1.5 × 10⁶ cm⁻³ or an OH-oxidation lifetime of 440 s in our highest-OH_exp experiment. In addition to D₄T(OCHO) hydrolysis, HCOOH may have been produced by heterogeneous reactions of HCHO at the surface of the SOSiA or the OFR walls in these humid experiments. In the atmosphere, HCOOH is presumed to form heterogeneously from HCHO and methanediol (HOCH₂OH) in the presence of wet particles (Franco et al., 2021).

The Y_HCOOH values from D₅+ OH we report are higher than the values from isoprene + OH (Link et al., 2020) or monoterpene + OH reported by Friedman and Farmer (2018), who quantified the Y_HCOOH of seven monoterpenes at varying OH_exp without NO_x. The range of Y_HCOOH values from these references is shown as shaded areas in Fig. 3b. The Y_HCOOH from D₅ is on par with the humid isoprene ozonolysis cases reported by Link et al. (2020). Friedman and Farmer (2018) also used a PAM-OFR, but with 254 nm UV lamps in dry conditions (∼ 1 % RH), and Link et al. (2020) used a reaction chamber, which limits a direct comparison with our results. Nevertheless, Friedman and Farmer (2018) found Y_HCOOH of 0.64 %–8.5 % at OH_exp= 2.0 × 10¹¹ s cm⁻³. Aside from the different precursor VOCs and mechanism, Friedman and Farmer (2018) may have encountered less heterogenous production of HCOOH due to the dry OFR conditions. While D₅+ OH may produce more HCOOH than isoprene + OH, the global emissions of D₅ (McLachlan et al., 2010) are about 4 orders of magnitude smaller than those of isoprene (Guenther et al., 2012). Nevertheless, the product class of siloxanes may constitute a minor atmospheric HCOOH source in urban locations, especially if emissions were to increase.

3.2 SOSiA mass yields

3.2.1 Volatility basis set parameterization

The Odum two-product model does not accurately capture the Y_SOSiA in the literature in the high C_OA range (Sect. S4), so we apply a VBS model. Figure 4a shows the fitted aerosol mass yield curve (blue line) using a standard-VBS model (Eq. 4), but the experimental Y_SOSiA (y axis) appears to depend on both C_OA (x axis) and OH_exp (color scale). To address whether accounting for the varying OH_exp in these experiments would improve the VBS model outputs, we fit the produced SOSiA mass using a standard-VBS model (Eq. 4) and a kinetic model with VBS and chemical aging rate coefficients (“aging-VBS model”, Reactions R1–R3) based on OH_exp and [D5]₀ (Table 1).

We fit k_age,gas and k_age,particle in the aging-VBS model to be $\mathrm{2.2}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ s⁻¹ and 2.0 × 10⁻¹² cm³ s⁻¹, respectively. The fitted aging-VBS model parameters are summarized in Table S11. Figure 4a also shows the aerosol mass yield curves calculated with the aging-VBS model over varying OH_exp. Since the aging-VBS model is kinetic, the Y_SOSiA values are dependent on both [D₅]₀ and OH_exp, and we calculate three yield curves using the approximate experimental [D₅]₀. The yield curves generated with the aging-VBS model are more consistent with the experiments and show how Y_SOSiA, [D₅]₀, and OH_exp are intertwined in the proposed aging mechanism.

Secondary organic aerosol (SOA) mass yield often exhibits a maximum as a function of OH_exp, after which the yield decreases due to fragmentation becoming dominant at high OH_exp (Isaacman-VanWertz et al., 2018). We do not find such a maximum in the range of OH_exp studied, which suggests that an even higher Y_SOSiA could have been found at higher OH_exp. Moreover, SOSiA is reported to be non-hygroscopic compared to SOA (Janechek et al., 2019), and we do not see an obvious relationship between the experiment humidity conditions and aerosol formation.

In both the standard and aging-VBS model fits (blue and red, respectively, in Fig. 4b), ∼ 95 % of the D₅+ OH product mass is in the gas phase at a C_OA of 10 µ g m⁻³. The high fraction of gaseous products is consistent with low Y_SOSiA in the lower-OH_exp experiments, whereas additional oxidation in the higher-OH_exp experiments leads to a shift towards products that partition into the particle phase, thus increasing Y_SOSiA. The optimized α_i values for the aging-VBS model are shown as markers in Fig. 4b. The error bars indicate the minimum and maximum values of the fitted α_i in the ensemble parameter sets, which are further expanded in Fig. S12a. The fit ensemble suggests that products from D₅+ OH must be largely volatile ($C^{*}\ge {\mathrm{10}}^{\mathrm{3}}$ µ g m⁻³) in order to reproduce the experimental SOSiA yields.

Figure 4c and d show comparisons of the standard and aging-VBS models with experimental SOSiA mass concentrations and Y_SOSiA. The error bars indicate the range of model outcomes within the fit ensemble. We see an improvement in the RMSE and R² with the aging-VBS model over the standard-VBS model, suggesting that incorporating OH_exp into the yield parameterization improves model performance. Figure 5 compares the standard-VBS model with the aging-VBS model for a range of OH_exp, showing that product volatility gradually decreases with increasing OH_exp in the aging-VBS model. The high volatility of the initial products is consistent with the lack of the rapid formation of low-volatile species, such as highly oxygenated molecules known to form SOA (Isaacman-VanWertz et al., 2018).

Figure 5 Evolution of the volatility distribution with OH_exp. The standard-VBS model parameterization (blue bars) is dominated by the $C^{*}=\mathrm{1000}$ µg m⁻³ volatility bin. In the aging-VBS model, the first-generation volatility distribution is dominated by the highest-volatility bin ($C^{*}=\mathrm{10}$ 000 µg m⁻³) but decreases with increasing OH_exp (red bars).

We find that the model is sensitive to k_age,particle, and a larger rate coefficient results in higher SOSiA formation (Fig. S11a). When fitting the model with deactivated particle-phase aging ($k_{\mathrm{age},\mathrm{particle}}=\mathrm{0}$), model-experiment RMSE is slightly increased (Fig. S11b). Thus, the fitting process provides a weak constraint on the parameter value (Fig. S12c). The numerical value of the fitted k_age,particle is physically reasonable as it corresponds to an effective uptake coefficient of OH molecules colliding with the particle surface in the range of 0.1–1 (Sect. S1.6). On the other hand, k_age,gas is very influential on the model output and tightly constraint in the ensemble of model fits around a value of $\mathrm{2}\times {\mathrm{10}}^{-\mathrm{12}}$ cm³ s⁻¹ (Fig. S12b). We hence postulate that multi-generational aging of in the gas phase is likely an important process for SOSiA formation, while particle-phase aging may only play a minor role under the investigated conditions.

Figure 6 Comparison of experiments, model results, and literature values: (a) Y_SOSiA and (b) SOSiA mass concentrations as a function of [D₅]₀ and OH_exp. The aging-VBS model is fit using experimental data from (1) this study and (2) those in the literature. SOSiA formation generally increases with [D₅]₀ and OH_exp. The aging-VBS model can capture the broad range of Y_SOSiA reported in the literature.

3.2.2 Consolidating literature Y_SOSiA

To address the variation in the literature Y_SOSiA and to generate parameters for air-quality models, we fit the parameters in the aging-VBS model with all available data in the literature and those from our experiments. Given that the literature used differing ρ_SOSiA values to calculate Y_SOSiA from SMPS data, we adjust the Y_SOSiA and C_OA reported in the literature to that of the ρ_SOSiA used here (ρ_SOSiA=1.07 g cm⁻³). Similarly, we re-calculate the OH_exp in the literature using Eq. (2) and the [D₅]₀ and [D₅]_final values.

Figure 6 shows experimental values (markers) and model outputs (contours) of Y_SOSiA (panels a1 and a2) and SOSiA mass concentrations (panels b1 and b2) as a function of [D₅]₀ and OH_exp. Figure 6a1 and b1 are generated using the aging-VBS model fit using only data from experiments presented in this study, while Fig. 6a2 and b2 show a fit including data from the literature. The aging-VBS model captures the increasing Y_SOSiA with increasing [D₅]₀ and OH_exp. At a given [D₅]₀, Y_SOSiA and the SOSiA mass concentrations increase with higher OH_exp. Figure 6a2 shows that the relatively high Y_SOSiA (>50 %) is feasible at OH_exp>10¹² s cm³. Moreover, the aging-VBS model predicts that Y_SOSiA is almost negligible (< 5 %) under atmospheric concentrations of D₅ and OH_exp.

Figure S8 shows that the aging-VBS model used here leads to a much higher correlation between modeled and experimental values for SOSiA mass concentration compared to the same analysis with a standard-VBS model (RMSE = 189 vs. 378). The better correlation suggests that the volatility distribution evolves with OH_exp and that chemical aging should be considered when evaluating the volatility distribution of SOSiA from D₅ + OH.

We note that bulk-phase chemistry is more complex than logarithmic shifts in volatility with OH_exp and is not fully captured in the proposed aging-VBS parameterization. For example, Wu and Johnston (2017), Avery et al. (2023), and Chen et al. (2023) characterized D₅+ OH SOSiA with mass spectrometry and found spectra indicative of oligomers. The formation of oligomers may reduce the bulk volatility by more than one bin and change the gas–particle equilibrium timescales (Berkemeier et al., 2020). Here, we incorporate k_age,gas and a simple bin hopping approach to illustrate that a change in the volatility distribution with OH_exp can adequately capture the Y_SOSiA variation in the literature. Future work with more sophisticated chemical models should close that gap further.

4 Conclusions and atmospheric implications

With a PAM-OFR, PTR-MS, and SMPS, we studied the formation of VOPs and SOSiA under various OH_exp conditions. Using a simplified VOP oxidation scheme (Reactions R4 and R5), we find that the VOPs of tentatively identified siloxanols and formate esters have shorter OH-oxidation lifetimes than their precursor D₅ (Table S7). In addition, we find the mass yield of HCHO of D₅ comparable to that of isoprene or aromatics (Millet et al., 2006), suggesting that D₅ siloxane is a potential O₃-contributing species in downwind scenarios. We find Y_HCOOH ranging from 45 %–127 %, which suggests that D₅+ OH is a source of atmospheric HCOOH, albeit smaller than isoprene, which is emitted in higher amounts by orders of magnitude.

An aging-VBS model incorporating OH_exp and chemical aging adequately describes gas–particle partitioning at atmospheric OH_exp and C_OA. Based on these experiments, low-NO_xY_SOSiA should be < 5 % under commonly observed atmospheric OH${}_{\exp }<\mathrm{5}\times {\mathrm{10}}^{\mathrm{11}}$ s cm⁻³ (Fig. 6a1). The first-generation products of D₅+ OH are likely volatile, but their volatility decreases with increasing OH_exp (Fig. 5). This evolution in volatility suggests that further oxidation of secondary products would reduce the volatility enough to form SOSiA. Unlike α-pinene (Isaacman-VanWertz et al., 2018) or other precursors for SOA, D₅+ OH does not appear to produce low-volatile species within a single oxidation step. Instead, additional OH_exp is needed to form aerosol, which suggests that multiple oxidation steps lead to a gradual decrease of product volatility. Hence, concepts that can be successfully applied to SOA formation may not accurately capture SOSiA formation, for which models must consider chemical aging. In the atmosphere, SOSiA from D₅+ OH may be easier to detect downwind of urban sources due to the higher OH_exp and dilution and/or removal of competing OH-reactive species.

Based on KinSim calculations (Sect. S5), we expect that the RO₂ fate is dominated by RO₂+ HO₂ and RO₂+ OH, which is consistent with the calculations performed by Avery et al. (2023). However, we note that the reaction rate coefficients of RO₂ and its subsequent products are uncertain for D₅, and we cannot directly address the atmospheric relevance of these calculated RO₂ fates at this time. To improve Y_SOSiA parameterizations for the atmosphere, there is a need to study the impact NO_x has on siloxane RO₂ chemistry, given that siloxanes are likely emitted from urban sources where [NO_x] is high. In such scenarios, RO₂+ NO_x is likely an important fate (Peng et al., 2019; Newland et al., 2021). Han et al. (2022) found that the addition of N₂O into their OFR would reduce Y_SOSiA, although the cause is unclear. However, Charan et al. (2022) did not find Y_SOSiA to change with NO_x in their chamber experiments, which is consistent with rapid RO formation across RO₂ fates. Quantifying secondary species across RO₂ fates and identifying their subsequent oxidation reactions may also be useful to adapt the D₅ oxidation mechanism into more sophisticated chemical kinetics models.

We find that the aging-VBS model is very sensitive to k_age,gas (Fig. S12), suggesting that photochemical aging in the gas phase should be considered in these models. The condensation timescale calculations suggest that the loss of low-volatile species to the wall is small (Sect. S1.3); however, these calculations assume a high mass accommodation coefficient for SOSiA and do not account for particle nucleation. Should particle nucleation be delayed or happen slowly, the gas wall loss may be higher than expected, leading to under-quantification of SOSiA. Furthermore, the aging-VBS model assumes that k_age,gas is uniform across products or that chemical aging results in a 10-fold decrease in volatility.

While the proposed model assumes that the particles are internally well mixed, the high [OH] used in OFRs may induce faster radical reactions and dimerization near the particle surface (Zhao et al., 2019), which affects particle composition and equilibrium timescales. While dimers and oligomers have been found in SOSiA (Wu and Johnston, 2017; Avery et al., 2023; Chen et al., 2023), the model currently does not account for particle-phase oligomer formation. How oligomerization in the D₅+ OH SOSiA system evolves the volatility distribution and particle properties is currently not considered in the aging-VBS model. Moreover, high degrees of oxidation should lead to fragmentation and increasing volatility (Isaacman-VanWertz et al., 2018), which is also not considered in the aging-VBS model. Hence, multiphase modeling to evaluate SOSiA chemistry and translate experimental findings to atmospheric conditions remains a direction for future research.

Appendix A: Abbreviations

COA:	organic aerosol mass loading
C*:	effective saturation mass concentration
D5:	decamethylcyclopentasiloxane
EVR:	extended volatility range
I254, I185:	flux of 254 and 185 nm photons
ncps:	normalized counts per second
NOx:	nitric oxide and nitrogen dioxide
OA:	organic aerosol
OFR:	oxidation flow reactor
OH:	hydroxyl radical
[OH]avg:	24 h average daily hydroxyl
	radical concentration
OHexp:	hydroxyl radical exposure
OHRext:	external hydroxyl radical reactivity
O3:	ozone
PAM:	potential aerosol mass
PTR:	proton transfer reaction
PTR-MS:	proton transfer reaction mass spectrometer
RH:	relative humidity
RMSE:	root mean square error
RO:	alkoxyl radical
RO2:	peroxyl radical
SMPS:	scanning mobility particle sizer
SOA:	secondary organic aerosol
SOSiA:	secondary organosiloxane aerosol
UV:	ultraviolet radiation
VBS:	volatility basis set
VOPs:	volatile oxidation products
YHCHO:	formaldehyde molar yield from D5
YHCOOH:	formic acid molar yield from D5
Yrel,VOP:	relative molar yield of VOP from D5
YSOSiA:	SOSiA mass yield from D5
γ:	molar yields extrapolated to when OHexp→0
ρSOSiA:	SOSiA aerosol mass density
τres:	residence time