Experiments (see Table ) were conducted in the Caltech dual chamber facility using a 21 m3 Teflon chamber. Prior to each experiment, the chamber was flushed with dry, purified air for 24 h. For humid experiments, the chamber was humidified prior to all injections. Ultrapure water (18 MΩ, Millipore Milli-Q) at 25 ∘C was recirculated through a Nafion membrane humidifier (FC200, Permapure LLC) while purified air flowed through the humidifier and into the chamber. First, isoprene (99 % purity) or methacrolein (95 % purity) was injected into a glass bulb using a gas-tight syringe and was carried by a flow of dry nitrogen into the chamber.

Second, methyl nitrite (CH3ONO) was injected into the chamber. CH3ONO was synthesized using the technique described in and and was stored in liquid nitrogen. Prior to each experiment, an evacuated glass bulb was filled with CH3ONO to the desired pressure, as measured by a capacitance manometer (MKS Baratron^™). This bulb was then backfilled with nitrogen and flushed into the chamber. The bulb pressure was used to calculate the CH3ONO mixing ratio in the chamber (see Table ). After CH3ONO was injected, pulses of purified air were added to the chamber to enhance mixing. Once the chamber was adequately mixed, NO (501 ppm in N2, Scott Specialty Gases) or NO2 (488 ppm in N2, Scott Specialty Gases) was injected into the chamber through a calibrated mass flow controller. Again the chamber was mixed by pulses of purified air.

Seed particles were generated from an atomizer using 0.06 M (NH4)2SO4 seed solution. The seed aerosol was directed through a soft X-ray neutralizer (TSI Model 3088) prior to injection into the chamber to ensure a consistent initial particle charge distribution for all experiments. For humid experiments, the seed aerosol was directed through a wet-wall denuder after exiting the neutralizer in order to ensure the particles were deliquesced. After seed injection, mixing air was turned on for 1 min to enhance mixing. The seed aerosol particle number concentration had an approximately lognormal diameter distribution centered on average ∼100 nm.

After injecting all gas-phase precursors and seed aerosol, photooxidation was delayed by 1 h for experiments with no initial seed aerosol and 4 h for experiments with initial seed aerosol. The rate of particle wall deposition was measured for each experiment during this 4 h delay. Although NO2 was not intentionally added for the LV pathway experiments, a modest NO2 signal was observed to form during the 4 h delay and is reported in Table . This “NO2” signal may be NO2 itself or an interference in the NOx monitor from an NOy compound (e.g., known interferences include organic nitrates, nitrous acid, and CH3ONO). The small signal of NO2, or a different NOy compound, is not expected to influence the results given the significantly larger initial NO levels (Table ). When NO2 or CH3ONO were injected into the chamber, an NO signal was observed on the NOx monitor. As the NOx monitor has few interferences for NO, a small fraction of NO was likely formed from NO2 or CH3ONO photolysis in the Teflon injection lines. Thus, the slight increase in NO with the NO2 and CH3ONO injection was assumed and reported to be initial NO (Table ).

The Caltech chamber uses ultraviolet (UV) broadband lights with the main emission peak centered at ∼350 nm. Only 10 % of full light capacity (jNO210%=4×10-4 s-1) was used for these experiments because CH3ONO photolyzes rapidly, and the lower light intensity minimizes chamber temperature increases (∼0.4 ∘C on average) caused by the UV lights. In all experiments, OH was produced by the photolysis of CH3ONO as shown in the following reactions: R1CH3ONO+hν→CH3O+NO,R2CH3O+O2→CH2O+HO2,R3HO2+NO→OH+NO2. Relative to other OH precursors, CH3ONO has a low Henry's law constant (15 M atm-1, calculated by theory) . During experiments with high relative humidity (RH), unlike other OH precursors, CH3ONO is not expected to enhance OH production in the particle phase beyond atmospherically relevant levels.

Temperature and RH were measured using a Vaisala HMM211 probe. NO and NO2 were monitored using a Teledyne NOx analyzer (T200). Because the Teledyne NOx monitor detects CH3ONO, organic nitrates, and other NOy compounds as NO2, only initial NO2 measurements can be constrained with this instrument. For some experiments, NO2 was also monitored using a luminol NO2 and acyl peroxynitrate analyzer developed by Fitz Aerometric Technologies. This instrument separates NO2 via chromatography at room temperature using a deactivated DB-5 column. NO2 then reacts with luminol to produce a chemiluminescence response . The NO2 measured by the luminol NO2 and acyl peroxynitrate analyzer compares reasonably well with the simulated NO2 from the kinetic model (Fig. S3 in the Supplement).

A gas chromatograph with a flame ionization detector (GC-FID; HP 6890N, column HP-Plot-Q) was used to measure the decay of isoprene and methacrolein. The GC-FID was calibrated with ∼50–60 ppm of isoprene or methacrolein generated from analytical standards (Aldrich 95 %–99 % purity) and cross-calibrated by Fourier transform infrared absorption (FT-IR) spectroscopy (pathlength 19 cm) using the absorption cross sections measured by Pacific Northwest National Laboratory (PNNL) for isoprene or methacrolein . Linearity in the GC-FID calibration was determined to an error of ∼1 % across a factor of 150 in dilution.

Aerosol organic and inorganic composition was recorded in situ using a high-resolution time-of-flight aerosol mass spectrometer (HR-AMS; Aerodyne Research, Inc.). The HR-AMS switched every 1 min between the high-resolution W mode and the lower-resolution, higher-sensitivity V mode. The data were analyzed with Igor Pro (Wave Metrics, Inc.), utilizing the Squirrel 1.56D and PIKA 1.15D analysis toolkits (from http://cires1.colorado.edu/jimenez-group/ToFAMSResources/ToFSoftware/index.html, last access: 14 April 2017). In-line filter runs conducted prior to each experiment were used to correct for air interferences . Bulk SOA elemental composition was calculated following the methods and recommendations of and .

Aerosol volume and number concentration were monitored using a differential mobility analyzer (DMA; TSI 3081 column) coupled with a condensation particle counter (CPC; TSI 3010), which measures all particles with a diameter between 20 and 800 nm. The voltage scan used by the DMA was 1 min hold at 15 V, 4 min increase to 9850 V, 1 min hold at 9850 V, and 0.5 min decrease back to 15 V. Only the up-scan data were used for the analysis. The longer up-scan and hold times used here, compared to previous studies (e.g., and ), reduced biases caused by mixing in the CPC. Such CPC mixing biases particularly impact the measurement of large particles, which are important in SOA yield experiments as they contribute significantly to the total SOA volume.

The DMA data analysis includes an improved data inversion and a correction for particle mixing in the condensation particle counter, which influences the CPC response time . The inversion technique is applicable only to particles ≤600 nm. Particle concentration between 600 and 800 nm was calculated assuming a nonlinear least squares lognormal fit applied to particles from 400 to 600 nm. For experiments with no initial seed aerosol, the inversion inconsistently determined the presence of particles beyond 400 nm. Such large particles are unlikely to be the result of nucleation and more likely to represent an artifact of the inversion; thus, only particles <400 nm were used in the analysis of these experiments. Corrections to the DMA data for coagulation and particle wall loss are addressed in Sect. .

Isoprene oxidation products were measured using a CF3O- chemical ionization mass spectrometer (CIMS), which utilizes a custom-modified triple quadrupole mass analyzer (Varian 1200) . CF3O- interacts with a gas-phase compound (A) to form a complex that is detected at the molecular weight of A+85 or, in some cases, to fragment. Various fragmentation products can form as explained in previous work (e.g., ; ; ). In this work, the CIMS results are only used to identify the presence of highly functionalized organic nitrates and not for quantification, so only signals from the complex (i.e., A⋅CF3O-) and not from fragmentation are reported.

Past studies reporting particle wall deposition coefficients apply the measured particle number decay rate in each size bin to produce a wall deposition coefficient, (β(Dp,t)), that is a function of particle size (Dp) . Because larger seed particle number and surface area concentrations were used in these experiments, corrections to β(Dp,t) that account for coagulation are needed . The current work uses an approach similar to that of and with updates to account for electrostatic charges on the chamber walls as described by . To reduce the experimental uncertainty associated with these processes, particle wall deposition was calculated during each experiment. This approach accounted for the day-to-day fluctuations in particle coagulation processes, chamber wall charging, and chamber mixing. We summarize these approaches and describe any changes required for this analysis in Sect. S2 of the Supplement.

Four particle wall loss experiments were performed under dry conditions (RH <10 %) at varying seed surface areas as controls to verify the technique used to correct for particle wall loss, particle coagulation, and electrostatic charges on the chamber walls. These particle wall deposition experiments were performed by injecting ammonium sulfate seed into the chamber, as described in Sect. . Mixing air was added, and the ammonium sulfate seed aerosol was monitored in the dark chamber for at least 14 h. These controls confirmed that the wall loss correction calculated over the first 3.5 h could be extrapolated for an additional 10 h. Beyond 10 h, the wall loss correction was more uncertain, so only results from the first 10 h of each experiment are reported. The percent change between the aerosol volume over 10 h and the aerosol volume at the start of the control experiment was between +4 % and -6 % for all dry control experiments (Fig. ).

The results of these control experiments verified the robustness of the correction technique and provided an estimate for the uncertainty. The reported uncertainty for the particle wall deposition correction is +4 % and -6 % of the corrected aerosol volume at the start of photooxidation. Experiments with larger seed aerosol volumes exhibit larger uncertainty in the reported SOA yield. However, such experiments are necessary despite the extra uncertainty, as larger seed surface areas minimize low biases in SOA yields due to vapor wall deposition of low-volatility compounds . For experiments with no initial seed aerosol, particle wall loss corrections were applied assuming the particles coagulated and deposited similarly to the lowest aerosol loading control experiment (C1). No uncertainty for the particle wall deposition correction was added to these experiments because the uncertainty derived here is applicable only to experiments with initial seed aerosol.

In experiments C1–C4, D1–D9, and M1–M8, electrostatic charges on the chamber walls were inferred to be present. After these experiments were completed, new Teflon chambers were acquired with negligible electrostatic charges on the chamber walls likely due to their smaller volume (18 m3). Three additional new experiments (D10, D11, and M9) were completed using one of these new Teflon chambers to confirm that we had accurately corrected for the chamber wall charging effects. For the LV pathway experiments (Sect. ), results for the new experiments were quite similar and within uncertainties of the old experiments. The new 2MGA pathway experiment produced slightly lower SOA yields than the old experiments but not necessarily because of the chamber wall charging corrections as described in Sect. .

Five control experiments were also performed under humid conditions. The DMA cannot measure hydrated particles owing to arcing in the DMA column at high RH. Thus, a Nafion dryer was used to dry particles before measurement. For the coagulation correction, the volume of the hydrated seed was calculated based on the dry DMA particle measurement, the RH in the chamber, and the hygroscopic growth curve for ammonium sulfate measured by . The percent change for the aerosol volume was higher and less consistent in the humid control experiments than in the dry control experiments. Also, the optimized value of the electric field (E‾) was higher in many of the humid experiments than in the dry experiments (Sect. S2, Table S3). Increased humidity is expected to decrease the electrostatic charges on the chamber walls (e.g., ), but the inferred E‾ suggests the opposite. Possibly, the humidifying process enhanced the electrostatic charges on the chamber walls or nitric acid, which is enhanced in the particle phase in the humid experiments under high-NOx conditions, impacts the coagulation or particle wall loss processes.

The aerosol mass spectrometer (AMS) data confirm that during the humid experiments, nitric acid partitioned to the particle phase and that organic aerosol was produced during photooxidation for all experiments. Nevertheless, the particle wall loss corrected volume measured by the DMA decayed below zero during photooxidation in the humid experiments. Potentially, this DMA volume decay suggests that nitric acid present in the particle phase changes the particle coagulation or wall loss characteristics. Even if we understood the impact of nitric acid on the particle coagulation or wall loss corrections, assessing how much of the particle growth is due to nitric acid versus organics would be difficult with the DMA, which measures only total aerosol volume and not composition. Further chamber characterization is required in order to assess isoprene SOA yields measured by the DMA from humid experiments under high-NOx conditions. Thus, in this work, only the AMS results will be discussed for the humid experiments and SOA yields are only reported for experiments performed under dry conditions (Table ). None of the dry experiments exhibited the odd behavior observed in the humid experiments, and the AMS results confirm that under dry conditions minimal nitric acid partitioned to the aerosols (Fig. S10). For the dry experiments, the uncertainties are characterized well by the dry control experiments presented in Fig. .

The SOA mass yields from isoprene for all LV pathway experiments (i.e., experiments targeting low-volatility compounds) are shown in Figs.  and . To convert aerosol volume measured by the DMA to aerosol mass, a density of 1.4 g cm-3 was assumed, consistent with past work . The kinetic mechanism suggests that in all experiments targeting the LV pathway, the formation of HMML was <0.12 ppb even in experiments performed under cold conditions (13 ∘C). The AMS results also confirm that 2-MGA and its oligomers are not present in the LV pathway experiments (Sect. ). Thus, the kinetic mechanism and AMS results verify that the experimental design correctly separates the two chemical regimes and 2-MGA is not substantially adding to the aerosol mass in the LV pathway experiments.

Aerosol growth in the absence of seed aerosols was not observed in the LV pathway experiments (Fig. ). As expected, SOA formed from gas–particle partitioning in the LV pathway exhibited a large dependence on seed surface area (Fig. ). Without sufficient seed aerosol, low-volatility nitrates partition primarily to the chamber walls, and the resulting SOA yields are biased low. With the addition of inorganic seed aerosol like ammonium sulfate, vapor species are expected to partition more to particles relative to the chamber wall . The gas-particle equilibrium is not expected to be dependent on the concentration of inorganic seed aerosol but instead is dependent on the concentration of organic aerosol. Depending on the saturation mass concentration (C∗), as the concentration of organic aerosol rises, vapors are present more in the particle phase relative to the gas phase . C∗ and the fraction of a compound expected to be in the particle phase (FP) were estimated for a variety of organic nitrates and dinitrates in MCM v3.3.1 at 13, 26, and 32 ∘C (Table S2).

Similar to previous studies (e.g., ), at a certain point increased seed surface area no longer substantially impacts the SOA yield (i.e., Fig.  after 2500 µm2 cm-3). This point will heavily depend on the system and the saturation mass concentration (C∗) of the SOA precursors. As shown in Table S2, the isoprene SOA precursors are mostly classified as IVOCs and SVOCs . Reaching a point where most of the vapors are in particles relative to the chamber wall is expected for IVOCs and SVOCs, which have moderate vapor wall losses in Teflon chambers especially under dry conditions .

As expected the isoprene dihydroxy dinitrates had the lowest C∗ values and high FP at all temperatures. Based on the kinetic model, even assuming all of the isoprene dihydroxy dinitrates exist in the particle phase, the SOA formed would be much less than that detected in this study (Fig. S4). This is likely caused by too low of a production of the isoprene dihydroxy dinitrates and/or the importance of other SOA precursors. There are many additional compounds largely produced from hydroxy aldehyde oxidation or alkoxy [1,5]-H shifts (Fig. ) with FP at 26 ∘C between 0.05 and 0.4 (Table S2). The vapor pressures may be overpredicted for these specific compounds, but past studies suggest that in general, vapor pressure estimation methods like underpredict rather than overpredict vapor pressure . From the C∗ calculations (Table S2), none of the multifunctional organic nitrates are expected to be appreciably in the particle phase. However, in a recent study, detected many multifunctional organic nitrates in aerosols in the ambient atmosphere, which has lower organic aerosol concentrations than chamber studies. Possibly, MCM underpredicts the formation of these IVOC and SVOC products (Fig. S4), such that even if only a fraction exists in the particle phase relative to the gas phase, an appreciable mass of aerosol still forms and/or these results suggest that volatility is not the only driver for aerosol formation from the LV pathway. All of the multifunctional nitrates here with estimated FP at 26 ∘C between 0.05 and 0.4 have at least one hydroxy or aldehyde group (Table S2). Alcohols and aldehydes are well known to combine in particles to produce hemiacetals, whose vapor pressure is significantly lower than that of the initial reactants . Several past studies have confirmed that NOx in general, but not necessarily linearly, decreases the volatility of isoprene SOA . This decrease in volatility is likely due to accretion reactions. Whether the accretion reactions from hemiacetal formation versus those from 2MGA oligomerization are responsible for the decrease in volatility is yet unknown.

Differences in the SOA yield at 10 h of photooxidation by varying temperatures (13–32 ∘C) lie within the experimental uncertainty. SOA forms earlier (i.e. with less isoprene reacted) at 13 ∘C than at 26 or 32 ∘C at comparable seed surface areas. This is consistent with the C∗ values estimated in Table S2 and the above explanation demonstrating the likelihood of accretion reactions. Vapors that are only moderately in the particle phase at 26 ∘C (e.g., FP=0.05–0.4) will exist more appreciably in the particle phase at 13 ∘C (e.g., FP=0.2–0.8). From the above discussion, we expect that many of these compounds are SOA precursors not based only on their volatility but also on their potential to react in the particle phase to form lower-volatility products such as hemiacetals. Thus, if accretion reactions are the main factor, reducing temperature is expected to increase the rate of SOA production but not necessarily to impact the overall SOA yield.

have also measured isoprene SOA formation under high-NOx conditions at varying temperatures. Under the high-NOx conditions of their study, SOA is produced from both the 2MGA and LV pathways combined. Similarly to our study, do not find appreciable differences for temperatures from 27 to 40 ∘C. Contrary, to our work, found that reducing the temperature to 5 ∘C increases the SOA yield by a factor of 4. Unfortunately, there are no experiments between 5 ∘C and 27 ∘C to determine whether this shift is exponential or linear, so direct comparison of our results at 13 ∘C is difficult. Under the high-NOx conditions used by , at colder temperatures MPAN will be more stable and so more HMML will form, which produces more SOA. Under this mixed regime, determining how much of the SOA increase is due to the LV versus the 2MGA pathway for direct comparison to this study is difficult. Additionally, start with significantly more isoprene than in our experiment, which enhances the concentration of organic aerosol, which will increase the fraction of a compound in the particle phase relative to the gas phase.

While vapor wall losses of LV compounds are expected to increase at colder temperatures , the organic nitrate yields are also expected to be enhanced under colder temperatures . Thus, the effects of these two temperature-dependent processes might cancel each other out. The increase in organic nitrate yield is expected to be moderate. For example, a ∼30 % increase from 32 to 13 ∘C is estimated for the yield of isoprene hydroxy nitrates . The loss of vapors to the walls could be much higher at colder temperatures, but this is hard to constrain as vapor wall deposition is dependent on the compound itself and the chamber used. The chamber used by (90 m3) is larger than our chamber (21 m3). Vapor wall losses are expected to be lower in larger chambers, which have a lower chamber surface-area-to-volume ratio . Significant seed aerosol is added into our chamber to reduce the influence of vapor wall deposition, but vapor wall deposition could certainly explain some of the differences at cold temperatures between our results and those from .

Consistent with past work (e.g., ), aerosol from the LV pathway is produced only after most of the isoprene is consumed, implying that aerosol from the LV pathway largely forms from later-generation chemistry (Fig. ). As shown in Fig. 4, generally, SOA formation begins earlier (i.e., with less isoprene reacted) in experiments with larger seed aerosol. This is consistent with vapors partitioning more to particles relative to the chamber wall when seed aerosol is enhanced. The extent to which later-generation products are oxidized (i.e., the degree of oxidation) impacts the SOA yield as demonstrated by the varying slope (i.e., SOA yield) during each experiment in Fig. . We tested the OH/isoprene ratio on the SOA yield. Experiment D7 was performed with 40 ppb of isoprene compared to 55–60 ppb used in the other experiments, while the OH precursor concentration was kept constant. The kinetic model predicts that the production of important gas-phase SOA precursors from the LV pathway (e.g., isoprene dihydroxy dinitrates), when corrected for total isoprene reacted, is similar in experiment D7 to the other experiments (Fig. S4). The empirical results are consistent with these predictions. Although a lower isoprene loading decreases the competition of isoprene with OH, other compounds also react with OH quickly (e.g., NO). Under the conditions used in this study, differences in isoprene loading are not expected to greatly influence the isoprene SOA mass yield. However, detailed kinetic modeling of past experimental conditions would be necessary to understand how the degree of oxidation of later-generation products in this study compares to other studies.

In summary, the results (Fig. ) suggest that one of the most important metrics for understanding the variability in SOA production from the LV pathway in various chamber experiments may be the initial seed surface area, instead of temperature or OH/isoprene ratio. Other parameters such as humidity and seed composition may also be important for SOA yields but were not tested in this study. Future experiments examining SOA yields should report the initial seed surface area and use a sufficient seed loading to reduce the impact of vapor wall deposition.

The SOA mass yields from methacrolein for all 2MGA pathway experiments (i.e., experiments targeting 2MGA and its oligomers) are shown in Figs.  and . Results from past experiments have already demonstrated that fluctuations in the NO2/NO ratio impact SOA formation through the production of MPAN. In this work, the NO2/NO ratio is kept as consistent as possible to isolate other influences on SOA production. The kinetic model suggests that the conditions for each experiment produce a consistent level of HMML (Fig. S4). Interestingly, because the experimental conditions heavily favored MPAN formation, the level of OH available to react with MPAN became the limiting reactant for aerosol formation in each experiment.

Contrary to the LV pathway, SOA in the 2MGA pathway experiments does not require seed particles to form. The process of SOA formation from these two pathways is very different. Lactone SOA precursors may polymerize in the presence of organics and water, which possibly explains why SOA from the 2MGA pathway readily forms particles without significant seed surface area, whereas in the LV pathway experiments volatility-based SOA formation results in aerosol yields that are particularly impacted by vapor partitioning. For the 2MGA pathway experiments, even though SOA formation occurred without initial seed aerosol, larger initial seed loadings still enhanced the SOA yield (Fig. ). Possibly, similar to the LV pathway, larger seed surface areas limit vapor wall loss of HMML or its oligomerization partners. Alternatively, the presence of higher ammonium sulfate seed aerosol may also increase organosulfate formation, which could impact SOA composition and yield.

Temperature was varied between 13 and 32 ∘C. The NO2/NO ratio used in this work was sufficiently high such that this temperature change did not greatly influence MPAN or HMML formation (Fig. S4). Thus, these experiments only test whether aerosol properties and SOA yields are affected by temperature, as MPAN thermal decomposition is minimized. At the high NO2/NO ratios used in this work, temperature does not impact SOA mass yield beyond given uncertainties (Fig. ). Based on known gas-phase chemistry, past studies (e.g., ) with more moderate NO2/NO ratios than that used in this work are expected to measure an enhanced SOA yield under colder temperatures due to a reduction in MPAN thermal decomposition and thereby an increase in HMML formation.

HMML, based on volatility alone, would exist mostly in the gas phase, but because HMML is very reactive (e.g., oligomerization or reaction with inorganic ions in the particle phase), HMML quickly produces aerosol . Based on HMML production simulated by the kinetic mechanism under the conditions used in these experiments, ∼0.21 SOA mass yield from methacrolein is expected purely from the mass contained in HMML (molecular weight = 102 g mol-1, Fig. S4). At first, the molecular weight of HMML itself is used because this is the mass of the majority of the oligomer monomers. This represents about half of the SOA mass yield (∼0.5) measured from the experiment performed with the highest seed surface area. The rest of the aerosol is likely comprised of inorganic or organic compounds that react with HMML in the particle phase. For example, inorganic compounds such as water, nitrate, and sulfate can react with HMML through ring-opening reactions to produce total methacrolein SOA mass yields of ∼0.25, ∼0.34, and ∼0.41, respectively (Fig. ). Additionally, HMML can react with 2-MGA and other organic compounds through oligomerization processes (e.g., ; ; ). Some of these organic oligomerization reactions bring into the particle phase additional organic compounds (e.g., organic acids) that ordinarily would exist primarily in the gas phase (Fig. ). The details of these particle-phase reactions are further discussed in Sect. .

In general, there is much greater variability in the SOA mass yields measured from the 2MGA pathway than the LV pathway. The additional variability is only partially explained by the initial seed surface area (Fig. ). Because the SOA yield is larger for experiments in which less methacrolein is oxidized (Figs.  and b), potentially, the extent of methacrolein oxidization contributes to this variability. The kinetic model suggests that the formation of gas-phase HMML is similar for all of the experiments (Fig. S4), but potentially slight variations in the NO2/NO ratio and/or OH particularly near the end of each experiment are not well captured by the model. The kinetic model used here only simulates gas-phase oxidation. Chemistry occurring on surfaces such as the chamber walls or in the particle phase may be especially important for capturing the variability in the 2MGA pathway experiments. Considering that the 2MGA pathway experiments are very susceptible to small differences in chamber conditions, regional and global models should parameterize SOA formation from the 2MGA pathway through gas-phase formation of HMML and subsequent particle-phase reactions.

Numerous nitrates and dinitrates are detected in the gas phase by the CF3O- CIMS (i.e., compounds highlighted in blue boxes in Fig. ). Many of these nitrates have been identified in previous studies (e.g., ). Yields for the low-volatility later-generation nitrates are either highly uncertain or unknown. Quantification is difficult for these low-volatility compounds due to high losses to sampling lines or chamber walls and lack of available standards. One study, , was able to quantify the yield of dinitrates from the first-generation isoprene hydroxy nitrate standards. Assuming a sensitivity similar to the isoprene hydroxy nitrate standards, measured a dinitrate yield of 0.03–0.04 from OH-initiated oxidation of the δ-1-hydroxy,4-nitrate isomer.

Although most past studies have focused on dihydroxy dinitrates as the main contributor to isoprene high-NO SOA, other low-volatility nitrates are likely also important. In Fig. , the CIMS signals for the other low-volatility nitrates are comparable or larger than the dihydroxy dinitrate signal. The relative sensitivities for these compounds are unknown, but these results suggest that detection and quantification of all low-volatility dinitrates and nitrates is important. The peroxy radical formed from OH-initiated oxidation of an isoprene hydroxy nitrate can undergo a 1,5 or 1,6 α-hydroxy H shift to form a number of low-volatility nitrates that would occur in the ambient atmosphere . The NO concentrations are too high in these experiments for such shifts to occur. However, similarly, certain isomers of the alkoxy radical, formed from OH-initiated oxidation of a isoprene hydroxy nitrate, can undergo a 1,5 α-hydroxy H shift to form a dihydroxy carbonyl nitrate detected by the CIMS at m/z (-) 264 (Fig.  and ). Additionally, various low-volatility nitrates in the gas phase are detected, which are potentially oxidation products from the δ-isoprene hydroxy alkoxy radical as depicted in Fig. .

Many multifunctional isoprene-derived organic nitrates have been detected in ambient aerosol . Although these low-volatility nitrates and dinitrates have low molar yields from isoprene OH-initiated oxidation, their mass is substantially larger than isoprene and so their contribution to the isoprene SOA mass yield is significant. The nitrate yield from straight-chain hydrocarbons is reasonably well understood, but few experimental measurements of the nitrate yield from highly oxidized compounds exist . Further measurements of the yield of these low-volatility nitrates and dinitrates in the gas phase will be crucial for a better understanding of isoprene SOA formation under high-NO conditions.

determined that inorganic aerosol such as ammonium nitrate or ammonium sulfate causes an interference on the AMS for the CO2+ ion signal. Although this interference is small for ammonium sulfate aerosol (<1 %, ), a correction may be needed for experiments with high initial seed aerosol loadings. Here organic signals from the AMS rise when ammonium sulfate seed is injected into the chamber. We expect that this is due to the same interferences described in and not due to contamination in ammonium sulfate solution or atomization technique. The background organic signal caused by the ammonium sulfate is subtracted from the overall results to produce Figs.  , , and .

The AMS spectra from the LV pathway confirm that SOA formed from the LV pathway is not dominated by 2-MGA and its oligomers (cyan and red bars in Figs.  and S11). This is an important confirmation that isoprene SOA formed from the 2MGA and LV pathways are distinct. A small yield of isoprene epoxydiol (IEPOX) is produced from OH-initiated oxidation of isoprene hydroxy nitrates , and IEPOX SOA can be formed when particle liquid water is present . NO levels remained high (>100 ppb) throughout all LV pathway experiments (Fig. S3), ensuring that the RO2 fate in these experiments was always RO2+NO. AMS fragments associated with IEPOX, which were identified by , are slightly enhanced under humid conditions in the LV pathway experiments (Fig. ). Some examples of organonitrate fragments (CxHyNOz+) are highlighted in Fig. . Some of these organonitrate fragments are enhanced under humid conditions (e.g., CH3NO+). In general, the AMS spectra are similar between all LV pathway conditions (i.e. varied humidity – Fig. ; varied temperature – Fig. S11).

Prominent peaks in the AMS spectra from the 2MGA pathway clearly indicate that under dry conditions aerosol is comprised of various oligomerization products as mechanistically summarized in Fig. . These oligomerization processes include 2-MGA oligomerization with HMML (cyan bars in Fig. a) and, possibly, esterification of 2-MGA with carboxylic acids including formic, acetic, and pyruvic acids (red bars in Fig. a), which yield products that have been detected in numerous studies . Based on the AMS spectra, 2-MGA oligomerization appears to be more dominant without the presence of ammonium sulfate seed aerosol (Fig. S13). Varying temperature from 13 to 32 ∘C does not appear to substantially change the extent of 2-MGA oligomerization (Fig. S14).

Past studies have determined that HMML reaction with 2-MGA to form oligomers decreases under humid conditions, while HMML ring-opening reactions with water and inorganic ions to form organic nitrates and organic sulfates increase . Consistent with these past studies, the 2-MGA oligomer fragments on the AMS (cyan and red) are no longer prominent signals for all humid experiments (Figs.  and S12). 2-MGA oligomer fragments are not substantially different at 47 %, 67 %, or 81 % RH, suggesting that the HMML oligomerization processes are impeded as soon as aerosol particles become deliquesced. Because isoprene is mostly emitted in regions with relatively high humidity, in the ambient atmosphere, HMML will more likely react with water and inorganic ions than undergo the various organic oligomerization reactions summarized in Fig. .

Based on the DMA measurements when assuming the same density, the SOA mass produced from the 2MGA pathway experiments is ∼2 times higher in magnitude than that from the LV pathway experiments (Figs.  and ). However, the AMS results (Fig. ) suggest that the SOA mass produced from the 2MGA pathway experiments is ≥8 times larger than that from the LV pathway experiments. This implies that the collection efficiency (CE) and/or the ionization efficiency of the AMS is quite different between these two regimes. Because the AMS is significantly more sensitive to aerosol formed from the 2MGA pathway, and not to SOA formed from the LV pathway, even ambient organic aerosol measurements have the potential to be impacted. Understanding whether the AMS is systematically underestimating organic aerosol from organic nitrates and dinitrates in general, or if this is only relevant to the isoprene system is crucial as the AMS is used throughout the world to quantify organic aerosol. Moreover, ambient measurements over the isoprene-rich southeastern United States of particulate organic nitrates measured by the AMS are a factor of ∼5 lower than those measured by the thermal dissociation laser-induced fluorescence instrument (TD-LIF) . The relative CE differences between the LV and 2MGA pathways in this study and these field campaign results suggest that further AMS calibration of organic nitrates is necessary.

In this work, a CE of 0.5 is assumed for both regimes consistent with past work . The exact CE is not relevant as no mass yields are reported here from the AMS. determined that the CE could be estimated based on the f44/f57 ratio. The f44/f57 ratio for all experiments (2MGA and LV) is ≥6, which is where the CE vs. f44/f57 curve plateaus at 0.2. Thus, the CE vs. f44/f57 relationship developed by is not able to explain the large difference in AMS sensitivity between aerosol formed from the LV and 2MGA pathways.

SOA mass yields reported from past environmental chamber studies of OH-initiated oxidation of isoprene under high-NOx conditions vary over the range of 0.001–0.41 , suggesting isoprene SOA yields are highly dependent on chamber conditions . In Table , past reported SOA mass yields are summarized along with the chamber conditions for both isoprene and methacrolein OH-initiated oxidation under high-NOx conditions. Only experiments that explicitly measure an SOA mass yield are listed in Table . Overall, our results suggest that the initial seed surface area has the greatest impact on SOA yield. Unfortunately, the initial seed surface area was not commonly reported in past studies. The closest metric is aerosol volume, which can roughly be used to understand differences.

As shown in Table , the range for isoprene SOA yields under high-NOx conditions even from the two most recent studies at comparable temperatures spans over an order of magnitude (0.004 at ∼21 ∘C for , and 0.1 at 27 ∘C for ). Our results are most consistent with those of . As shown in Table , a variety of NOx regimes (i.e., non-consistent NO2/NO ratios) are all labeled as high-NOx in these past studies. Each study likely produces SOA in varying degrees from the LV and 2MGA pathways, which greatly complicates direct comparison between these past studies. By varying a large number of conditions and completely separating SOA production between the 2MGA and LV pathways, our results lend insight into the variation in these past experiments.

Many of the past SOA yield measurements were performed with no seed aerosol. Consistent with past results, when no seed aerosol was injected into the chamber (experiments D1 and M1), the SOA mass yield for the LV pathway (0 from isoprene) and 2MGA pathway (0.1 from methacrolein) were quite low. Past experiments performed with no seed aerosol only measured SOA from the 2MGA pathway, which is highly dependent on the NO2/NO ratio , which varied greatly between these past studies. , who measured high SOA yields (0.1 at 27 ∘C) in unseeded experiments, are the exception. Possibly, the larger chamber volume (90 m3) used by compared to most studies listed in Table  reduced vapor wall losses and contributed to the enhanced SOA yield. However, other chamber characteristics might also be important because measured quite low isoprene SOA yields (0.007–0.03) using a chamber larger than the one used in the study.

While the zero or low seed aerosol loading experiments in this study generally compare well with the past, SOA yields measured here using higher initial seed surface areas are substantially greater than most studies, especially for the LV pathway. The SOA yield from the LV pathway is ∼0.15 in this study, while past isoprene SOA yields are largely ≤0.07 with the exception of studies optimizing for high RO2+NO2 reactions or mixed regimes – RO2+HO2/NO . The SOA yield from the LV pathway in this work is even larger than the SOA yield from (0.1 at 27 ∘C), which includes SOA from both the LV and 2MGA pathways. Possibly the larger chamber volume used by reduces vapor wall losses but not to the extent that enhanced seed surface area does in this work. The higher yields measured in this study are not unexpected given that recent publications have recognized the importance of using high initial seed surface areas when measuring SOA yields to reduce the impact of vapor wall deposition (e.g., ; ). The methacrolein SOA yields measured in this study from the 2MGA pathway are comparable to those measured by but larger than those measured by .

measured low isoprene (0.001–0.01) and methacrolein (0.005–0.042) SOA mass yields and proposed that these lower yields were due to using xenon arc lamps as a light source, which are more representative of natural sunlight than the UV lamps used here and in most other studies. also used xenon arc lamps and reported low yields. However, both of these studies used chambers with moderate to low chamber volumes (27–4.2 m3) unlike the chamber used by and low levels of initial seed aerosol (0–16 µm3 cm-3) unlike this work, which could also cause this low bias. Additionally, the stainless steel chamber used by may have higher vapor wall losses than the Teflon chambers used in other studies. Further work is necessary to understand how vapor wall losses compare across different types of environmental chambers.

As discussed by , isoprene SOA forms mostly from oxidation of second and later-generation products e.g.,. Towards the end of the experiment, SOA continues to grows even when isoprene is no longer reacting (e.g., the characteristic hook in Fig. ). Differences in the level of oxidation of second and later-generation products could also explain some of the discrepancies between our results and past results. The isoprene SOA mass yields from the LV pathway are particularly sensitive to the extent of oxidation. More studies measuring the gas-phase yields and formation processes of low-volatility nitrates and dinitrates will be critical for further understanding isoprene SOA.

Many of the previous studies listed in Table  report the VOC/NO ratio when comparing experiments. A more useful metric is understanding the RO2 fate and RO2 lifetime. Simply injecting NO and/or NO2 and reporting the initial concentrations are not sufficient to confirm that SOA was dominantly produced from the RO2+NO channel or in the case of HMML formation from the RO2+NO2 channel. For example, if NO decreases to zero before the end of the experiment, SOA has formed in a mixed regime; RO2+NO reactions dominate in the beginning and RO2+HO2 reactions dominate at the end. If large initial VOC loadings are used in the beginning of the experiment without comparable increases in NO, RO2+RO2 reactions may become dominant.

Experiments here are specifically designed to test two different RO2 fates, and the kinetic mechanism is used to confirm the fate of the RO2. In the LV pathway experiments, high NO levels are maintained such that NO2/NO ratio remains <1.5 throughout the entire experiment, and RO2 dominantly and consistently across the experiments reacts with NO. In the 2MGA pathway experiments, high NO2 levels are used such that the acyl radical derived from methacrolein dominantly and consistently across experiments reacts with NO2. By controlling for the RO2 fate, the effects of temperature, seed surface area, and relative humidity on SOA formation become easier to resolve. The design of future experiments should optimize and report the RO2 fate for which the experiment was designed, in addition to key reaction parameters such as seed surface area, rather than simply reporting an initial VOC/NO ratio.

This work was not only designed to independently study SOA formation from the two high-NOx regimes (the 2MGA and LV pathways) but also to suggest alternative methods for parameterizing isoprene SOA under high-NOx conditions in regional and global models. Because obtaining constant NO2/NO ratios similar to the ambient atmosphere is near impossible for a chamber study (e.g., temporal variation in Fig. S3), creating isoprene SOA parameterizations based on NO2/NO ratio that realistically extrapolate to the ambient atmosphere is not realistic. Instead, this work highlights a potential alternative. Aerosol from the 2MGA pathway could be incorporated directly from gas-phase HMML formation, and aerosol from the LV pathway could be included either from the formation of surrogate compounds such as isoprene dihydroxy dinitrates or with a volatility basis set scheme. By treating the SOA from these two independent regimes separately, this study sets up the experimental basis for such an approach.

In this study, direct comparison of the results from the 2MGA and LV pathways is difficult due to the difference in the extent of oxidation between the two regimes caused by the use of different VOC precursors and the variation in OH levels (Table ). Thus, the kinetic model is used here to estimate the contribution of each pathway to the total under consistent oxidant levels. A detailed global modeling study is needed to precisely capture the contribution of the LV versus the 2MGA pathways toward SOA formation from isoprene OH-initiated oxidation under high-NOx conditions. However, in order to demonstrate the significance of the new isoprene SOA yield from the LV pathway measured in this work, we roughly approximate the contribution of each pathway under typical atmospheric conditions. We use the same kinetic mechanism described in Sect.  but hold the following constant: RH = 70 %; T = 298 K; NO2 = 0.3 ppb; NO = 0.05 ppb; isoprene = 5 ppb; OH =1.5×106 molec. cm-3; CO = 135 ppb; O3 = 37 ppb; and HO2 = 25 ppt . Then gas-phase HMML and the gas-phase dinitrate SOA precursors are simulated as done for the experimental results in Fig. S4.

To estimate the aerosol contribution from the LV pathway, we assume that SOA production from the LV pathway scales with the production of isoprene dihydroxy dinitrates. Organic aerosol concentrations are higher in chamber experiments than the ambient atmosphere. By using low levels of VOC precursors compared to previous studies, this study attempts to reduce the organic aerosol concentrations to produce results more relevant to the ambient atmosphere. However, due to limitations in the DMA sensitivity, reducing the organic aerosol concentrations further to ambient levels is not possible. The ratio of the measured SOA yield (Fig. ) versus the simulated gas-phase dihydroxy dinitrate SOA precursor yield (Fig. S4) is about 5. FP is decreased by a factor of 2 for the dihydroxy dinitrates when COA is reduced from ∼25 µg cm-3 in the chamber to ∼4 µg cm-3 measured in the southeast US . Thus, we multiply the dihydroxy dinitrate SOA precursors by 2.5 and we convert to mass by multiplying by the molecular weight of dihydroxy dinitrate. MCM v3.3.1 assumes a nitrate yield of 0.087–0.104 from NO reacting with the peroxy radical derived from OH+isoprene hydroxy nitrate. Low-volatility nitrates such as dihydroxy hydroperoxy nitrates form when HO2 reacts with the peroxy radical derived from OH+isoprene hydroxy nitrate. Such products would not form in the chamber conditions used in this work, where NO levels remained above 100 ppb, but would form in the ambient atmosphere. Considering these low-volatility species from mixed chemical regimes would further increase the SOA mass generated from the LV pathway.

For the 2MGA pathway, we convert to mass by multiplying gas-phase HMML by the molecular weight of 2-MGA (120 g mol-1), 2-MGA nitrate (165 g mol-1), and 2-MGA sulfate (200 g mol-1), which are the expected condensed-phase products under the high humidity levels in the atmosphere. Laboratory studies confirm that 2-MGA forms under humid conditions and some of the 2-MGA partitions to the gas phase as expected based on its volatility . For simplicity, we assume most of the HMML forms 2-MGA nitrate and 2-MGA sulfate but acknowledge that further experimental and modeling studies are needed to fully understand HMML and 2-MGA aqueous phase chemistry.

Then based on the gas-phase SOA precursor distribution from the kinetic model and assumptions above, under typical atmospheric conditions the fraction of the total SOA mass from isoprene OH-initiated oxidation under high-NOx conditions is ∼0.7 from the LV pathway and ∼0.3 from the 2MGA pathway. This assumes that the dihydroxy dinitrates are valid surrogates for the isoprene SOA. Considering that many multifunctional isoprene-derived organic nitrates have been detected in ambient aerosol , all SOA precursors in Table S2 with FP>0.05 at 26 ∘C are combined and converted to mass. Extrapolating these to ambient organic aerosol concentrations is more difficult because these compounds are more likely to exist in the particle phase because of accretion reactions and not volatility. When these products are assumed to exist entirely in the particle phase and no factor is applied to correct for differences in organic aerosol concentration or for these products only representing about one-third of the isoprene SOA yield measured in this study (Fig. S4), the LV pathway is estimated to contribute to ∼0.6 of the SOA formed under high-NOx conditions.

Thus, based on the simple calculations summarized above, the LV pathway may produce moderately more SOA mass than the 2MGA pathway in the atmosphere and consequently deserves equal attention. The conditions chosen here represent average atmospheric conditions around noon as measured during the Southern Oxidant and Aerosol Study (SOAS) field campaign, which occurred in the isoprene-rich southeastern United States . A more complete assessment using global and regional modeling is needed to more definitively determine the fraction of SOA formed via the LV versus 2MGA pathways as location, time of day, season, ambient aerosol concentration, and composition, etc. will all impact the amount of SOA formed from each pathway. Additional studies addressing organic nitrate hydrolysis and aerosol acidity are also necessary to fully understand the relative impact of the two pathways on SOA formation. Additionally, the kinetic model used in this work only estimates gas-phase potential SOA precursors. Future analysis using a more complex model that explicitly simulates both the gas and particle phases would be useful for extrapolating the SOA yields measured here to the ambient atmosphere, which typically has lower organic aerosol concentrations than chamber experiments. This would need to be combined with additional analysis of the chemical constituents in the particle phase. From past work demonstrating that isoprene-derived SOA under high-NOx conditions is lower in volatility than that derived under low-NOx conditions and the C∗ values estimated in this work (Table S2), accretion reactions appear to be important even in the LV pathway experiments. The degree to which accretion reactions occur in the LV pathway experiments to form even lower-volatility products is quite uncertain and will greatly impact future analysis on how best to extrapolate isoprene SOA yields measured in chambers to the ambient atmosphere.