The LWC in particles makes up a great percentage under humid conditions (as shown in Fig. 1). To calculate the yield of SOA, the LWC has to be excluded. On the other hand, since LWC was only measured at the end of the reaction, to obtain the time evolution of SOA concentrations we needed to deduct LWC during the whole reaction period. The value of LWC depends on chemical components of particles and environmental conditions (temperature and humidity). The volume growth factor (VGF) was used to estimate the contributions of LWC in particles, which was defined by Engelhart et al. (2011) as the ratio of the particle volume at humid air to the particle volume at dry air. Assuming that all the particles are spheres and have the same growth factor, the VGF is equal to the growth factor (GF) cubed as VGF=VhydratedVdried=DhydratedDdried3=GF3. Vhydrated and Vdried indicate the total measured volumes of hydrated or dried particles, respectively. Dhydrated and Ddried are the diameter of hydrated or dried particles, respectively, calculated from their volumes.

VGF is determined to be 1.28 (GF = 1.09, RH = 78 %) for the particles from toluene-NO2 irradiations, 1.18 (GF = 1.06, RH = 79 %) from isoprene-NO2 irradiations, 1.40 (GF = 1.12, RH = 77 %) from isoprene-H2O2 irradiations, and 1.30 (GF = 1.09, RH = 88 %) from isoprene-O3 reaction systems. There have been many studies about the growth factor of SOA. Aklilu and Mozurkewich (2004) gave a GF range of 1.05–1.12 for atmospheric organic particles (79 % RH). Stroud et al. (2004) predicted a GF of 1.1 for the organic aerosols from toluene-NO-isopropyl nitrite irradiations at 79 % RH. Prenni et al. (2007) reported the GF of 1.065±0.02 at 85 % RH for SOA formed from toluene. Jimenez et al. (2009) obtained GF =1.057±0.02 at 95 % RH for SOA from isoprene. In general, our results of GF are in good agreement with previous estimates, indicating that the LWC measured by our modified SMPS is reliable.

We assumed that the VGF did not change during the reaction course. Thus, the LWC from toluene and isoprene under humid conditions can be determined by VGF. Figure 2 shows that in touene-NO2 irradiations, the mass concentrations of SOA at 81 % RH are much larger than those at 10 % RH, with a ratio of maximum mass concentration of SOA at 81 % RH to that at 10 % being 2.2. However, in isoprene-NO2 irradiations, the mass concentrations of SOA at 80 % RH are much lower than those at 7 % RH, with the ratio of maximum mass concentration of SOA being 0.57, which is almost the same as that from isoprene-O3 reactions (the ratio is 0.45). For isoprene-H2O2 irradiations, the mass concentrations of SOA from humid conditions are generally larger than those under dry conditions. Nevertheless, the maximum mass concentration of SOA from humid conditions is 177.9 µgm-3 (the ratio is 1.01), which is close to that from dry conditions.

The mass yield of SOA generally increases with time. The maximum yields during the experimental course were used for the following discussion. The mean maximum yields of SOA from toluene were obtained to be 5.58±0.76 % (dry) and 8.97±0.84 % (humid), respectively (Fig. 3). Our results are within the range obtained by other investigators (Kamens et al., 2011; Odum et al., 1997; Ng et al., 2007). Previous studies (Kamens et al., 2011; Zhou et al., 2011; Jia and Xu 2014; Wang et al., 2016) mainly ascribed the positive effect of RH on SOA yields from aromatics to LWC, which can enhance the formation of SOA by aqueous reactions, such as reactive uptake of glyoxal in aerosol water. Our yields of SOA from toluene are smaller than those from Ng et al. (2007) (around 11 % at 4 % RH) and Hildebrandt et al. (2009) (11–17 % at 21 % RH), which is probably due to the additional and excessive OH radical sources (HONO or H2O2) used in their experiments. In addition, the temperature in this study is higher than the previous studies, which may be another reason accounting for the lower SOA yields in this work.

A negative effect of RH on SOA yields was observed in the systems of isoprene-NO2-hν and isoprene-O3. The mean maximum yields from isoprene-NO2 irradiations are reduced from 3.14±0.35 % (dry) to 1.19±0.38 % (humid) (Fig. 3). This negative RH effect is in good agreement with the corresponding results from Zhang et al. (2011) and Lewandowski et al. (2015). The yields of SOA from our isoprene-O3 reactions are 3.00 % (dry) and 1.40 % (humid), which are quite close to the results from the isoprene-NO2 system, while RH has a very weak effect on the SOA yields from isoprene-H2O2 irradiations in our study. The maximum yields of SOA were determined to be 7.7 % (dry) and 7.8 % (humid) from photooxidation of isoprene-H2O2, which are in good agreement with the results (around 8 %) of isoprene-H2O2 irradiations under dry conditions from Clark et al. (2016). A similar yield (7 %) of SOA from photooxidation of isoprene-NOx-H2O2 was also obtained in the results from Nguyen et al. (2011b). Based on the experimental conditions in Nguyen et al. (2011b), we estimated that for their reaction system over 99 % of isoprene was oxidized by OH and the remaining 1 % by O3 by using simulations based on the MCM. Thus, the reaction system by Nguyen et al. (2011b) can be considered to be closer to the isoprene-H2O2 system. In addition, some other previous studies (Gaston et al., 2014; Riedel et al., 2015; Zhang et al., 2018) showed that RH had a negative effect on the formation of SOA from isoprene-OH systems due to an acid dilution effect. In these studies, acidic sulfate seed particles were used and the acid-catalyzed effect was very obvious. Thus, higher RH can reduce the acidity of the seed particles by particle water. In our study acidic seed particles were from a little amount of H2SO4 formed from the gas-phase reaction of SO2 and OH. It was estimated that the mass concentration of H2SO4 particles was less than 1 µgm-3. When liquid water content increased from 1 µgm-3 to the maximum 54 µgm-3 under humid conditions, the pH value was estimated to be in the range of 2 to 3.7, indicating that the pH variation was small in our experimental conditions. Therefore, compared with previous studies, the acid dilution effect was not remarkable in our work. These results show that high RH can reduce the maximum yields of SOA from the reaction channel of isoprene with O3 (O3 channel) and that RH has little effect on the maximum yields from the reaction channel of isoprene with OH (OH channel) without sufficiently high mass concentrations of acid particles. Thus, it shows that the ozonolysis of isoprene is probably a key pathway influencing SOA formation in isoprene-NO2 irradiations in our experimental conditions, which will be further discussed in a later section.

In our isoprene-NO2 irradiations, based on the MCM simulation (Exp. 25), the amount of isoprene oxidized by OH, O3, and NO3 is 59, 25, and 16 % at the end of reactions, respectively. There are cross-reactions when NO2 and O3 are both present. Thus, we cannot deduce SOA contribution simply by initial ratios of isoprene oxidized by OH and O3. Since SOA is mainly formed by the secondary or later generation products, we can evaluate the contribution of reaction pathways to the formation of SOA in terms of SOA precursors from different channels. As described previously, SCIs can be taken as the SOA precursors from the O3 channel, while IEPOX, MPAN, HMML, and MAE can be used as SOA precursors from the OH channel. The MCM simulations show that the total yield of SCIs was dominant as compared to OH channel precursors such as IEPOX, MPAN, HMML, and MAE. The former accounts for 70 % of total concentrations (ppb) of SOA precursors, and the latter (IEPOX + MPAN + HMML + MAE) 30 % at the end of reaction in isoprene-NO2 irradiations. Therefore, even though 59 % of isoprene was consumed by OH and only 25 % by O3, the formation of SOA in isoprene-NO2 was mainly from the O3 channel. For these three oxidation channels, RH has little effect on SOA yields from OH channel oxidization. Previous studies have shown that humidity has little effect on SOA formation from NO3 oxidation of alkenes (Bonn and Moorgat, 2002; Fry et al., 2009; Boyd et al., 2015). Thus, only the O3 channel is greatly influenced by RH. The maximum possibility is that the O3 channel can produce SCIs that can be consumed by water. Thus, although most of the isoprene was oxidized by OH and the SOA yield from the OH channel was over 2 (5) times greater than that from the O3 channel under dry (humid) conditions, the O3 channel was still a major pathway influenced by water vapor in the isoprene-NO2 system, which will be discussed in the following section.

Figure 5a and b show the typical infrared spectra of SOA from the irradiations of toluene under both dry and humid conditions. The prominent features on SOA spectra are the board hydrogen bonded O–H stretching, the carbonyl C = O stretching, the organic nitrate (ONO2) bands, the C–OH bands of alcohols or polyalcohol. The bands all greatly increase by over 2 times as RH increases from 10 to 81 %. These changes in band strength with RH are quite similar to the changes in the SOA mass yield with RH.

To further reveal the chemical properties of the increased products formed from humid conditions, the SOA sample from humid conditions was evaporated. First, we found that the IR spectrum of SOA almost did not change after being heated at 100 ∘C for 15 min. Then the sample was further evaporated at 110 ∘C for 15 min. After the evaporation at 110 ∘C, the major absorption bands were considerably changed. As a result, the spectrum is almost the same as the spectrum of SOA collected under dry conditions (Fig. 5c). The major reduced absorptions are from the O–H and C–OH bands (Fig. 5d). These bands are assigned to hydrates of glyoxal and other water-soluble compounds in SOA (Volkamer et al., 2009; Lim et al., 2010; Kamens et al., 2011; Jia and Xu, 2014; Wang et al., 2016). Therefore, alcohols (such as hydrates) are considered major contributors to toluene SOA under humid conditions.

LWC is an important factor that can greatly influence the contribution of SOA from aqueous reactions. The maximum LWC was measured to be about 44 µgm-3 from humid toleuene-NO2 irradiations. To determine the role of LWC in SOA formation, extra LWC was introduced into the reaction system by adding 10 µgm-3 of NaCl particles. The initial LWC was determined to be 30 µgm-3, and maximum LWC was 74 µgm-3 during 6 h of reaction. The SOA mass concentration was obtained by subtracting the mass concentrations of NaCl, NaNO3, and LWC from total mass concentration of particles. Compared with the experiment without NaCl, the SOA mass concentrations increased by 16 % in the experiment with NaCl, and all the bands assigned to O–H, C = O, and C–OH were enhanced by 50, 29, and 35 %, respectively (Fig. 5e). This demonstrates that the increase in LWC can greatly enhance the formation of SOA from hydration of glyoxal. Therefore, it is concluded from our study that the formation of SOA from toluene is controlled by LWC under humid conditions, and that most SOA is formed by aqueous reactions in touene-NO2 irradiations.

The spectra of SOA from the irradiations of isoprene-NO2 are characterized by the high abundance of C = O and ONO2 groups (Fig. 6). There are three bands assigned to different kinds of C–O or C–O–O groups in the region of 927–1243 cm-1 under dry conditions (Pretsch et al., 2009). These bands are indicators of alcohols and polymeric structures (Czoschke et al., 2003). Thus, oligomers and organic nitrates are dominant species in SOA. Under humid conditions, the absorption intensities of the bands (O–H, C = O, ONO2, C–O, or C–O-O) are all reduced by 2 times. The tert-nitrate can hydrolyze in particle water by the replacement of ONO2 with the -O–H group (Liu et al., 2012). Because such replacement hardly changes the vapor pressure of corresponding species (Pankow and Asher, 2008), newly formed alcohols should remain in the aerosol phase. We also did extra experiments to test the hydrolysis of organic nitrates. After the SOA sample from dry isoprene-NO2 irradiation was exposed to humid air (90 % RH) for 1 h, we did not find any apparent change in the ONO2 group. Meanwhile, the peak height ratios of ONO2 / O–H from SOA are almost the same under dry and humid conditions. Thus, the hydrolysis of nitrates is not the major reason for the decrease in particle-phase organic nitrates. It also indicates that aerosol phase oligomers can hardly be influenced by RH. Then, high RH likely inhibited the formation of particle-phase organics by reducing the oligomerizations in the gas phase (e.g., SCI-derived oligomers).

RH generally enhances SOA formation by the aqueous reactions. Similarly, the aqueous reactions also exist in isoprene-NO2 irradiations. However, the maximum LWC from humid isoprene-NO2 irradiations was measured to be 8 µgm-3 at the end of reaction, which is much smaller as compared to 44 µgm-3 in toluene irradiations. Taking glyoxal as an example, although the maximum concentrations of glyoxal were simulated to be 39 ppb in isoprene-NO2 irradiations, which is only 60 % of its maximum concentration of 65 ppb from toluene irradiations, due to the limitation of LWC, the SOA from the aqueous reactions was significantly reduced in isoprene-NO2 irradiations. To further confirm the role of LWC, we did an additional experiment with NaCl seeds (initial LWC of 30 µgm-3) in isoprene-NO2 irradiations. The results show that the absorptions of the bands from O–H and C–OH increase by 20 to 30 % as compared to those without additional LWC (Fig. 6). It is true that increasing LWC can indeed enhance SOA formation in isoprene-NO2 irradiations; however, the absorptions of C = O, ONO2, and C–O from dry conditions are still 2 times larger than those from the experiment with extra LWC. This demonstrates that the increase in SOA through aqueous reactions is far less than the decrease due to H2O-related reactions under humid conditions. Thus, high water vapor can probably inhibit some key processes responsible for SOA formation from isoprene-NO2 irradiations, which will be discussed in the following contents.

To determine which process responds to the decrease in SOA under humid conditions from isoprene-NO2 irradiations, IR spectra of SOA from the OH and O3 channels were studied, respectively. Since isoprene is the chain unit of terpenes, the abundance of functional groups in oxidation products from isoprene and terpenes is expected to be close. O–H-containing products from terpene are 10 times more enriched from the OH channel oxidation than from the O3 one (Calogirou et al., 1999). Our extra experiments show the similar characteristics of IR spectra of SOA from both isoprene and α-pinene (figure not shown). The peak height ratio of O–H / C = O is 0.24 in the SOA from the α-pinene-O3 system, while it is as high as 2.19 in the SOA from the α-pinene-OH system. Here the absorption ratio of O–H to C = O was used to examine the difference between the O3 and OH oxidation channels.

The IR spectra of SOA from the isoprene-H2O2 system are characterized by strong absorptions of both hydrogen bonded O–H and C–OH and by weak absorption of C = O under both dry and humid conditions (Fig. 7, top), with the peak height ratios of O–H / C = O being 1.63 (dry) and 1.45 (humid), which strongly supports the claim that alcohols or polyalcohols are major components of SOA from isoprene-H2O2 irradiations. Under humid conditions, the peak at 1090 cm-1 assigned to the C–O–C group from esters is slightly decreased, while the band at around 3200 cm-1 from O–H absorption is broadened as compared to the dry condition. It indicates that esters (e.g., oligomers) decrease while the compounds containing O–H increase under humid conditions. Nevertheless, the relative abundances of O–H, C = O, and C–OH groups are almost the same between dry and humid conditions, which shows a weak effect of RH on SOA from isoprene-H2O2 irradiations as compared to isoprene-NO2 irradiations. In the OH channel, isoprene can be oxidized to form RO2 (ISOPO2). If there is no NO, ISOPO2 will be further oxidized to isoprene epoxydiols (IEPOX) by OH and HO2 radicals. IEPOX are key intermediates of SOA in isoprene-OH reactions (Surratt et al., 2010). Under dry conditions, IEPOX can be adsorbed on H2SO4 seeds to form polyalcohols (e.g., 2-methyltetrols) through acid-catalyzed heterogeneous reactions, which can further form oligomers by esterification (Lin et al., 2012). Under humid conditions, IEPOX can be absorbed into particle water to produce polyalcohols (Nguyen et al., 2014). In addition, the decrease in the C–O–C group indicates that the formation of oligomers is inhibited by the abundance of particle water as discussed in Sect. 3.2, which is in agreement with the result of Lin et al.  (2014). Because polyalcohols (dominant) and IEPOX-derived oligomers are all in the aerosol phase, the total mass concentration of SOA does not change much under humid conditions in isoprene-H2O2 irradiations. In other words, RH does not change the partition of IEPOX in our experimental conditions. This is consistent with the result of Riva et al. (2016) that water has a weaker impact on IEPOX-derived SOA yield.

In the isoprene-O3 systems, if the bands from ONO2 are excluded, both the shape and band intensities of IR spectra of SOA are quite similar to those of SOA from isoprene-NO2 irradiations. All the bands assigned to O–H, C = O, and C–O are reduced by over 2 times under humid conditions (bottom panel of Fig. 7). The ratios of O–H / C = O are 0.36 (0.44) under dry (humid) conditions. The results are consistent with our expectation that lower ratios of O–H / C = O should be in SOA from the ozonolysis of isoprene. Since OH radicals were well removed in our experiments, SCIs became the key intermediates of SOA. The C–O–O group is an indicator of the participation of SCIs in SOA from the ozonolysis of isoprene. The C–O–O group is very apparent under dry conditions, which decreases by 60 % under humid condition. Oligomer products in SOA have been found to be formed by the reactions of n (n= 1–10) SCIs with RO2 in the ozonolysis of small enol ethers and trans-3-hexene (Sadezky et al., 2008; Zhao et al., 2015). Thus, SCI-derived oligomers are also deduced to be the key components in SOA from the O3 channel of isoprene. The model-simulated results show that when RH increases from 10 to 88 %, the consumption of SCIs by water increases from 13 to 58 %, while the SCI-derived oligomers decrease from 87 to 42 %. The reaction products of SCIs with H2O have relatively high vapor pressures as compared to oligomers, so they are mainly in the gas phase. Therefore, humid conditions can reduce the SOA formed by SCI-related reactions in the isoprene-O3 systems.

In isoprene-NO2 irradiations, the ratios of O–H / C = O are 0.35 (0.36) under dry (humid) conditions, which are almost the same as the corresponding values in isoprene-O3 but totally different from the values in isoprene-H2O2. The yields IR spectra (ratios of O–H / C = O) and the influence of RH on SOA production from the isoprene-O3 system is almost the same as those from isoprene-NO2 irradiations. In isoprene-NO2 irradiations, even though 60 % of isoprene was oxidized by OH, because of the presence of NO, most of the ISOPO2 from oxidation of OH could be quickly consumed by NO to form MPAN (around 15 ppb under both dry and humid conditions) and other products, leading to the decrease in IEPOX from 224.0 ppb (in isoprene-H2O2) to 41.2 ppb (in isoprene-NO2). The yield of MACR is generally greater in isoprene-NO2 irradiations and isoprene-O3 systems than that in isoprene-H2O2 irradiations. MACR can react to form MPAN in the presence of NO2, which can be oxidized by OH to form SOA precursors of epoxides (e.g., HMML, MAE), such as in the Nguyen et al. (2011b) work. Epoxides can further be oxidized to produce 2-MG and related oligomers (Surratt et al., 2010; Lin et al., 2013; Nguyen et al., 2015). 2-MG-derived oligomers can be enhanced under lower RH (Zhang et al., 2011). Both the results from Nguyen et al. (2014) and MCM simulations further show that if there are enough OH radicals, most MPAN can be further oxidized by OH to produce epoxides. However, since there were no extra OH sources in our systems, MCM simulations show that only 12 % (24 %) of MPAN under dry (humid) conditions was oxidized by OH to produce HMML and MAE. The maximum concentrations of HMML and MAE were only 6.8 and 2.7 ppb under dry conditions (Fig. 13), which is too small to explain the yields of SOA in isoprene-NO2 irradiations. If we simply assume that the concentrations of SOA were proportional to the IEPOX concentration as in isoprene-H2O2 irradiations, over 70 % of SOA should come from IEPOX in dry or humid isoprene-NO2 irradiations. However, the IR spectra of SOA from dry or humid isoprene-NO2 are totally different from those in isoprene-H2O2 irradiations. In contrast, they are similar to those from the isoprene-O3 system. Thus, IEPOX is not the major contributor to SOA in isoprene-NO2 systems. On the other hand, similar to the isoprene-O3 system, SCI-related reactions in the isoprene-NO2 system were probably key pathways.

There are 16 kinds of SCIs produced in isoprene-NO2 irradiations based on MCM v3.3.1 simulation, in which CH2OO (CH2O2, with a yield of 50.1 %), MACROO (C4H6O2, 18.3 %), MVKOO (C4H6O2, 12.2 %), MGLOO (C3H4O3, 11.3 %), and GLYOO (C2H2O3, 2.6 %) account for 95 % of total SCIs. To explain that these SCIs exist in SOA as base units of CH2O2, C4H6O2, C3H4O3, and C2H2O3, a wide set of other base units (OH, CO, NO2, ONO2, CH2, CH2O, and COO) are also included for KMD analysis. The ratio of oligomers with a given base unit to total mass is defined to characterize the contribution of different base units to SOA. It should be pointed out that large uncertainties exist in the estimate of relative contributions of different units because of the poor quantification performance using ESI-MS techniques. Due to the cross containing of units in oligomer molecules, the sum of the ratios is larger than 100 %. The oligomers with the same base unit (M-[base unit]n, n=0,1,2,3…) that contains at least three compounds are considered one class of oligomers. The results show that only the ratios of oligomers with the base units of CH2O2, C4H6O2, C3H4O3, and C2H2O3 are proportional to the yields of corresponding SCIs from the isoprene-NO2 system. Figure 10 displays the correlation diagram between the ratios of oligomers (with CH2O2, C4H6O2, C3H4O3, and C2H2O3 as repeating units) to total mass and the top five SCI yields (CH2OO, MACROO, MVKOO, MGLOO, and GLYOO). It shows that the ratios linearly increase with increasing yields under both dry and humid conditions. Thus, this demonstrates that the oligomers with CH2O2, C4H6O2, C3H4O3, and C2H2O3 repeat units are from contributions of these SCIs of CH2OO, MACROO (and MVKOO), MGLOO, and GLYOO in the isoprene-NO2 system. Therefore, these five SCIs are chosen as the base units for KMD analysis, which shows that the ratios of compounds containing SCI units are reduced by 45 % on average as RH increases from 7 to 85 %. This is also in good agreement with MCM simulation of decrease in SCI-derived oligomers by 44 % and with the decrease in intensity of peroxide C–O–O absorption in FTIR (Fig. 6). In addition, the KMD analysis is also used to determine the components of oligomers in SOA from isoprene-H2O2. All the above base units are tested, and the results show that CH2O-containing oligomers are the major products in SOA, and the chain lengths of oligomers are much shorter than those from isoprene-NO2. The maximum repeat unit number of n is less than 3 in most families of oligomers in SOA from isoprene-H2O2. By contrast, the maximum value of n is larger than 5 in oligomer families of SOA from isoprene-NO2. This indicates that SCIs incline to produce long chain oligomers.

It has been considered that the CH2OO radical can serve as an oligomer unit in SOA from the ozonolysis of ethylene (Sakamoto et al., 2013). CH2OO has the highest yield (50.1 %) of all the SCIs from isoprene. The KMD analysis shows that the masses of CH2OO-containing oligomers account for 46.2 % (29.4 %) of the total mass on the MS under dry (humid) conditions. Figure 11 displays the selected mass spectra of oligomers with CH2OO as chain units and their corresponding KMD plots under dry and humid conditions, which shows that both the length of oligomer chains and the number of oligomers are greatly reduced under humid conditions. The number of oligomers under humid conditions is reduced by 64 % as compared to dry conditions. Another feature of CH2OO-based oligomers is that the sizes of their end groups are larger than 300 (C14–C17), which probably come from other oligomers formed during reactions. This indicates that most CH2OO-based oligomers are formed in the particle phase.

Figure 12 shows the mass spectra and KMD plot of oligomers with C4H6O2 (MACROO and MVKOO) as base units. The KMD analysis results show that the ratio of C4H6O2--based oligomers to total compounds is 39.7 % (17.2 %) under dry (humid) conditions. In addition to CH2OO, MACROO and MVKOO based oligomers have the second highest contribution to SOA among all the SCIs. Similar to CH2OO, the maximum number of chain units is 6 in oligomers from C4H6O2. However, the size of end groups is much smaller than that from CH2OO. The most frequent end group is C3H6O2 as shown in Fig. 12. Based on the Chemspider database and MCM simulation, we deduced that C3H6O2 is from hydroxyacetone (ACETOL), which is the most abundant carbonyl-containing products in the isoprene-NO2 reaction system. The maximum concentration of ACETOL is over 90 ppb based on our experimental conditions. C2H2O3 is deduced to be glyoxylic acid that is one of products from isoprene irradiation. SCIs can react with carbonyl and alcohol products (e.g., ACETOL), RO2, and H2O (Calvert et al., 2000; Chao et al., 2015; Tobias and Ziemann, 2001). However, different from the isoprene-O3 system, MCM simulations show that most RO2 is consumed by NO in isoprene-NO2 irradiations. Thus carbonyl and alcohol products become the major initiators of SCI oligomerizations.

An addition of a C–O–O group can change the vapor pressure of oligomers (containing n SCI units) by a factor of 2.5×10-3 (Pankow and Asher, 2008). The vapor pressures of SCI-derived oligomers (e.g., C3H3O2–[C4H6OO]n) are estimated to be less than 10-7 atm (n≥2) and 10-12 atm (n≥4). The compounds can self-nucleate as their vapor pressures are less than 10-9 atm (Kamens et al., 1999). It indicates that the initial particles in the O3 oxidation channel of isoprene are formed by the self-nucleation of oligomers (n≥4). The oligomers with n≥2 probably further condensed on these particles. Thus, MACROO- or MVKOO-based oligomers can be formed in the gas phase (e.g., Reactions R1 and R2). With the increase in chain units, these oligomers can either self-nucleate or further oligomerize in the aerosol phase.

It is worth noticing that the yield of CH3OC3H3OO (C4H6O3) is only 1.4 % based on the MCM simulation. However, the contribution of C4H6O3 to oligomers is as high as 25.3 % (9.0 %) under dry (humid) conditions (Table 2). Thus, C4H6O3 is not totally from CH3OC3H3OO. 2-MG usually serves as molecular tracers for isoprene SOA (Kleindienst et al., 2007). As reported by Zhang et al. (2011) and Nguyen et al. (2011b), C4H6O3 was the repeated unit of 2-MG's corresponding oligomers in SOA from isoprene-NOx irradiations. Lin et al. (2013) reported that C4H6O3 was from MAE in MACR-NOx irradiations. Thus, C4H6O3 is probably formed from dehydration of 2-MG and MAE in oligomers. Considering the low yield of MAE in our system, we considered that most C4H6O3-based oligomers are probably contributed by 2-MG in our work. The ratios of CH2OO, MACROO, and MVKOO based oligomers are almost 2 times larger than that from 2-MG under both dry and humid conditions. Thus, even though the ratio of C4H6O3-based oligomers was decreased by 65 % as RH increased from 7 to 85 %, 2-MG derived oligomers would not be the major reason for the decrease in SOA yield from isoprene-NO2 irradiations. In addition to C4H6O3, CH2 and CH2O based oligomeric compounds also have high ratios in isoprene-NO2 systems, which have been also reported as the most prominent units in SOA products from the ozonolysis of isoprene in the Nguyen et al. (2010) study under dry conditions. However, different from SCI based oligomers, the ratios of CH2 and CH2O based oligomers decreased by 18 and 14 % as RH increased from 7 to 85 %, respectively. Thus, the reduction of SCI based oligomers is the major reason for the decrease in SOA yields from isoprene-NO2 photooxidations.

It is noted that the wall loss of semi-volatile organic compounds (SVOCs) can lead to the underestimation of the yield of SOA (Matsunaga and Ziemann, 2010; Loza et al., 2010; Zhang et al., 2014; Yeh and Ziemann, 2015; Ye et al., 2016; Palm et al., 2016; Krechmer et al., 2016; La et al., 2016; Nah et al., 2017). Since SCI-derived oligomers are the major products of SOA from isoprene-NO2 irradiations, a question arises about which process is dominant for the reduction of SOA production under humid condition, wall loss of SCI related oligomers (in gas phase), or the reaction between SCI and H2O. The MCM simulation shows that SCIs are so reactive that most of them are consumed by reactions before they are lost to the wall (Fig. 14). The percentage of the SCIs consumed by H2O was increased from 6 to 46 % as RH increased from 5 to 85 % due to the extremely high concentration of gas H2O. The removal of SCIs by H2O (85 % RH) can lead to a decrease in SCI-derived oligomers by 43 % as compared to 5 % RH. The result is comparable with the decrease in SOA yields of 62 % from isoprene-NO2 irradiations. Meanwhile, as discussed in the previous section, the vapor pressures of SCI-derived oligomers were so low that they were ready to condense on particles. The upper limit of the wall loss rate constant of 4.8×10-4 s-1 for SVOC was calculated from the equation given by McMurry and Grosjean (1985), while the condensation rate constant of SVOC to the particles was calculated to be over 0.65 s-1 in our study based on the equation from La et al. (2016). This indicates that the condensation rate of gas-phase oligomers to particles is much faster than that to the wall. Therefore, the reactions between SCIs and H2O rather than the wall loss of SVOC are the major cause of the decrease in SOA formation from isoprene-NO2 irradiations in this work.

To quantify the RH effect of SOA and relatively possible contribution of SCI-derived oligomers from isoprene-NO2 irradiations, the reactions of SCIs with formic acid, glyoxylic acid, and ACETOL were added into MCM, in which the reaction of SCIs with formic acid does not form oligomers. Simulations show that the total mass concentration of oligomers from these reactions was 558.4 (271.2) µgm-3 at 7 % (80 %) RH, and the mass concentrations from other SOA precursors IEPOX, MPAN, HMML, and MAE were 182.8 (167.0), 27.4 (28.9), 28.1 (27.4), and 11.2 (10.9) µgm-3 at 7 % (80 %) RH (Fig. 13). It is obvious that the mass concentrations of SCI-derived oligomers reduced by 51 % as RH increased from 7 to 80 %, while the concentrations of other precursors had little change under different RH conditions. Thus, SCI-derived oligomers should have a great potential for formation of SOA, compared to other precursors.

Our results clearly show that the different effects of RH on SOA yields originate from the oxidation channels (Fig. 15). Both the OH and O3 channels can well explain the differences in results of isoprene-NO2 irradiations from the Zhang et al. (2011) and Nguyen et al. (2011b) studies. In the Zhang et al. (2011) study, there were no additional OH radical sources in their systems. Thus, the SOA was mainly from the O3 channel. Similar to our isoprene-O3 systems, a negative effect of humidity on SOA yield was observed in their work. In the Nguyen et al. (2011b) work, due to sufficient OH radical source, over 99 % of isoprene was oxidized by OH, and SCI concentrations were very low. Even though high NOx was used, most MPAN could be further oxidized by OH to produce epoxides. Therefore, SOA was mainly from the OH channel in Nguyen et al. (2011b)'s work. This is why the yield of SOA in their work was not influenced by RH. Our results obviously show that SOA is formed by reactive uptake of SOA precursors (e.g., IEPOX) in the OH channel, and by the condensation of SCI-derived oligomers in the O3 channel. In the presence of NO2, the formation of SOA is also controlled by the SCI-related reactions without extra OH sources. However, the SCI-related reactions (SCI-derived oligomers) can be inhibited by high water vapor. In previous studies, SOA was usually modeled based on the vapor pressures of SVOC, which only considers the effect of temperature. Our study strongly suggests that RH is also a key factor in SOA formation.