The gas-phase oxidation of HCs is simulated using the near-explicit gas-phase chemistry mechanism (Master Chemical Mechanism, MCM, v3.3.1) (Jenkin et al., 2012) integrated with the Morpho chemical solver (Jeffries et al., 1998). To represent the polluted urban and clean environments, the gas-phase oxidation is simulated under various NOx levels (HCppbC/NOxppb = 2–14) for given meteorological conditions (e.g., sunlight, temperature, and RH on 14 June 2018 near the summer solstice, with a clear sky in Gainesville, Florida). The resulting oxygenated products are lumped into 51 species within a 2-D set with eight levels of volatility (1–8: 10-8, 10-6, 10-5, 10-4, 10-3, 10-2, 10-1, and 1 mm Hg) and six levels of aerosol-phase reactivity (very fast: VF, fast: F, medium: M, slow: S, partitioning only: P, and multi-alcohol: MA) plus three additional reactive species (glyoxal, GLY; methylglyoxal, MGLY; and epoxydiols, IEPOX, isoprene products) with their own vapor pressure. The detailed lumping criteria and αi equations are described in Sect. S2 along with the major product structures (Tables S1–S3 in the Supplement).

To simulate age-dependent SOA formation, αi is reconstructed over time by a weighted average method using a pair of gas-phase oxidation compositions with different aging statuses: fresh composition and highly oxidized composition. The weighting factor at time = t is related to an aging scale factor (fA(t)), which is defined as 1fA(t)=log⁡HO2+RO2[HC]0, where [RO2] and [HO2] represent the concentrations (ppb) of RO2 and HO2 radicals, respectively, and [HC]0 represents the initial HC concentration (ppbC). The lower boundary of fA(t) (t = fresh) to determine the fresh αi set is equal to -7.2 at HC/NOx = 2 (high NOx levels) and -3.7 at HC/NOx = 14 (low NOx levels) for all three HCs. The upper boundary of fA(t) (t = highly aged) to determine the highly aged αi set is equal to -5.2 and -2.9 under the same high and low NOx levels, respectively. Both the fresh αi and highly aged αi are functions of HC/NOx. fA(t) is further converted into a fractional aging scale (fA′(t) ) ranging from 0 (fresh composition) to 1 (highly aged composition) using a weight average method fA′(t)=fA(highlyaged)-fA(t)fA(highlyaged)-fA(fresh) at each NOx level. Then, αi is dynamically reconstructed based on fA′(t) under varying NOx conditions. 2αi=1-fA′(t)freshαi+fA′(t)highlyagedαi The molecular structures, including O : Ci, MW (MWi), and hydrogen bonding (HBi) parameters, of each species (i) are also dynamically represented by a similar method, as shown in Sects. S3 and S4.

The partitioning coefficient (KP) from the gas (g) phase to the organic (or) phase (Kor,i, m3 µg-1) and from the g phase to the inorganic (in) phase (Kin,i, m3 µg-1) of each species is estimated using the following gas–particle absorption model (Pankow, 1994). Kor,i=7.501RT109MWorγor,ipl,ioand3Kin,i=7.501RT109MWinγin,ipl,io, where R represents the gas constant (8.314 J mol-1 K-1). T represents the ambient temperature (K). MWor and MWin represent the average MW (g mol-1) of organic and inorganic aerosols, respectively. pl,io represents the subcooled liquid vapor pressure (mm Hg) of a species, i. In the organic phase, we assume that the activity coefficient (γor,i) of a species (i) is unity (Jang and Kamens, 1998). In the inorganic phase, γin,i is semi-empirically predicted by a regression equation, which was fit the theoretical activity coefficients of various organic compounds to RH, fractional sulfate (FS), and molecular structures (i.e., MWi, O : Ci, and HBi). FS is a numerical indicator for inorganic compositions related to aerosol acidity FS=SO42-SO42-+NH4+, where [SO42-] and [NH4+] are the concentration of the total sulfate and the total ammonium, respectively). The theoretical activity coefficients were estimated at a given humidity and an aerosol composition through a thermodynamic model (Aerosol Inorganic-Organic Mixtures Functional Groups Activity Coefficients, AIOMFAC) (Zuend et al., 2011). γin,i=4e0.035⋅MWi-2.704⋅ln⁡O:Ci-1.121⋅HBi-0.330⋅FS-0.022⋅(100⋅RH) The statistical information for Eq. (4) is shown in Sect. S4 and Fig. S1 in the Supplement. The resulting Kor,i and Kin,i are employed to calculate the concentration (µg m-3) of the lumping species in multiple phases (Cg,i, Cor,i, Cin,i, and CT,i=Cg,i+Cor,i+Cin,i).

Schell et al. (2001) developed a partitioning model to predict SOA formation. This model was reconstructed by Cao and Jang (2010) to include OM formed via aerosol-phase reactions (OMAR,i) for a species (i), which is estimated in Sect. 3.3. OM formed during the partitioning process (OMP) is estimated by utilizing the mass balance shown in the following equation. OMP=∑ijCT,i-OMAR,i-Cg,i*5Cor,iMWi∑ijCor,i′MWi+OMAR,iMWoli,i+OM0 Cg,i* (1/Kor,i) is the effective saturation concentration and OM0 represents the concentration (mol m-3) of the preexisting OM. MWoli,i represents the average MW of oligomeric products. Equation (5) is solved via iterations using the globally converging Newton–Raphson method (Press et al., 1992).

The formation of OMAR,i is processed in both the organic and inorganic phases: oligomerization in the organic phase to form OMAR,or,i and oligomerization in the inorganic phase to form OMAR,in,i based on the assumption of a self-dimerization reaction (i.e., second-order reaction) (Odian, 2004) for organic compounds in media. Oligomerization in an aqueous phase can be accelerated under acidic environment (Jang et al., 2002). The oligomerization rate constants (L mol-1 s-1) in the organic phase and inorganic phase are ko,i and kAC,i, respectively, and the kinetic equations for oligomerizations are written as follows. 6dCor,idt=-ko,iC′or,i2MWiOMTρor1037dCin,idt=-kAC,iC′in,i2MWiMinρin103 The bracketed terms in the equations indicate the conversion factors from aerosol-based concentrations (Cor,i′ and Cin,i′: mol L-1) into air-based concentrations (µg m-3). The detailed derivations are shown in Sect. S5 and are illustrated in Fig. S2. ρor and ρin represent the density of the aerosol of organic and inorganic aerosol. ρor was experimentally determined (EB4 in Table 1) to be 1.38 g cm-3, which was similar to the reported value of 1.4 g cm-3 for aromatic SOA (Nakao et al., 2011; Chen et al., 2017; Ng et al., 2007). ρin is obtained from a regression equation through the extended aerosol inorganic model (E-AIM) (Clegg et al., 1998). Due to atmospheric diurnal patterns (high RH at nighttime to low humidity during daytime), it is likely that the RH changes would be based on inorganic aerosol ERH. UNIPAR internally predicts the ERH using the equation derived by Colberg et al. (2003).

kAC,i in Eq. (7) is estimated based on a semiempirical model developed by Jang et al. (2005) as a function of species reactivity (Ri), protonation equilibrium constant (pKBH+i), excess acidity (X), water activity (aw), and proton concentration ([H+]), which are estimated by the E-AIM. 8kAC,i=100.96Ri+0.0005pKBH+i+0.96⋅X+log⁡awH+-2.56 In the organic phase, ko,i is estimated by excluding the X and aw [H+] terms. The formed OMAR can be calculated as a sum of OMAR,or,i and OMAR,or,i for each species assuming that OMAR is irreversibly formed and nonvolatile (Kleindienst et al., 2006; Cao and Jang, 2010).

In the presence of aqueous acidic sulfate, UNIPAR predicts the formation of diOS ([diOS]model) to compute the change in aerosol hygroscopicity and acidity. At each time step, free electrolytic sulfate ([SO42-]free), which is the sulfate that is unassociated with ammonium ([NH4+]), is represented as ([SO42-] - 0.5 [NH4+]). [SO42-]free is then applied to the semiempirical equation tested previously for several SOA systems (Im et al., 2014; Beardsley and Jang, 2016) to predict [diOS]model, as described below: 9[diOS]modelSO42-free=1-11+fdiOSNdiOSSO42-free, where fdiOS represents the diOS conversion factor introduced by Im et al. (2014), which was semi-empirically determined to be 0.071 in this study. NdiOS represents the numeric parameter for scaling lumping groups based on the effectiveness of the chemical species to form diOS. For example, the diOS scale factor is 1 for each alcohol and aldehyde group and 2 for each epoxide group (see Tables S1–S3 for functional groups). Then, NdiOS is summed at each time step and applied to Eq. (9).

The variables, which include HC consumption (ΔHC), [HO2], [RO2], HC/NOx, RH, temperature, and the inorganic concentration (i.e., Δ[SO42-] and Δ[NH4+]), were input to the UNIPAR model every 6 min (Δt=6 min).

As reported in former studies, the kinetic mechanism tends to underestimate the decay of aromatic HCs because of the low prediction of OH radicals (Johnson et al., 2005; Bloss et al., 2005). In this study, the addition of artificial OH radicals varies with the HC/NOx ratio by fitting the predicted decay of HCs using the kinetic mechanism in the experimental measurements. The time profiles of the decays of the three HCs are shown in Fig. S3 (Sect. S6). When the NOx level is very low, the maximum additional OH radical production rate for monoalkylbenzenes is 2×108 molecules cm3 s-1, which is less than 4×108 (Bloss et al., 2005) but similar to the value reported by Im et al. (2014). When HC/NOx < 3, no addition of artificial OH radicals is needed for the chamber simulation of the decay of monoalkylbenzenes. For the make-up OH production rate constants of all three HCs under varying NOx, the mathematical weighting equation is written below: dynamicmakeupOHrate=e0.6×HC/NOxe0.6×HC/NOx+5010×2.0×108moleculescm3s-1. In our model, we assume that the oxidation of products progresses in the gas phase. Lambe et al. (2012) reported that the transition point of n-C10 SOAs from a functionalization-dominant regime to a fragmentation-dominant regime is approximately 3 d (photochemical equivalent age under an atmospheric OH exposure of 1.5×106 molecules cm-3). Under this criterion, we exclude the aging of nonvolatile aerosol products (OMAR). However, the oxidation of aerosol products for longer periods of time may decrease the volatility (George and Abbatt, 2010; Jimenez et al., 2009).

Figure 2 illustrates the evolution of the volatility–reactivity-based distribution of the mass-based stoichiometric coefficient (αi) of toluene at the two different NOx levels (HC/NOx = 2.9 and 10.5). Collectively, most αi values at both NOx levels tend to decline as the reaction time lapses (Fig. 2a vs. Fig. 2b; Fig. 2c vs. Fig. 2d) since the evolution of some semivolatile organic compounds (SVOCs) forms very volatile molecules (i.e., CO2, formic acid, and formaldehyde). For example, the αi values of highly reactive carbonyls with high volatility (GLY and MGLY in Table S1 of Sect. S7) are high under the fresh condition and significantly decline as the system ages, because they undergo fast photolysis under sunlight (George et al., 2015; Henry and Donahue, 2012). Consequently, the decay of these highly reactive species leads to the decrease in the production of OMAR. The high NOx level delays the oxidation of gas-phase products. Similar trends in the αi set can be found for ethylbenzene and n-propylbenzene, as shown in Sect. S7 (Tables. S2 and S3, Figs. S4 and S5). The αi of highly reactive species (e.g., GLY, 8VF, 3M, and 5S) decreases by increasing the NOx level due to the suppression of the HOx cycle via the reaction of NO2 with OH radicals. As seen in Fig. 2d, some medium reactivity species – i.e., 2-methyl-4-oxo-3-nitro-2-butenoic acid (3M), 2-methyl-4-oxo-2-butenoic acid (6M), and acetyl-3-oxopropanoate (7M) – start to form as NOx decreases.

In Fig. 3, the comparison between the simulations of SOA formation from toluene oxidation is based on two different αi-reconstruction strategies: dynamic αi and fixed αi. A clear improvement in the prediction of SOA formation is demonstrated when comparing the SOA mass using dynamic αi to that using fixed αi. The aged SOA growth from the three systems (i.e., low NOx level, Fig. 3a and d; moderate NOx level, Fig. 3b and e; and high NOx level with an inorganic seed, Fig. 3c and f) is even smaller than that predicted with the less-aged αi set, which is obtained when precursors being consumed make up half of the total simulated consumption. Our model simulation against the chamber data suggests that while aging may alter aerosol compositions (Fig. 2), it does not always increase SOA yields. Traditionally, the SOA mass has been predicted using fixed thermodynamic parameters (i.e., Kp and αi), which is inadequate when reflecting upon practical scenarios, where oxygenated product distributions vary dynamically with oxidation.

In the model, aerosol acidity was expressed using a fractional free sulfate (FFS), which is defined as FFS = ([SO42-] - 0.5[NH4+])/[SO42-]. Humidity can influence both aerosol acidity and LWC, which are the model parameters in UNIPAR. Thus, UNIPAR has the capability to decouple the effect of aerosol acidity and humidity, as shown in Fig. 4 for toluene SOA. The impact of aerosol acidity and humidity on the yields of SOAs derived from ethylbenzene and n-propylbenzene is illustrated in Fig. S6 (Sect. S8). The dramatic difference in SOA yields appears between the RH above ERH and the RH below ERH. The LWC disappears below ERH, and there are no aqueous reactions. For example, the observed SOA yield of ethylbenzene with effloresced AS was significantly smaller than that with wet AS: 11 % (EB8 in Table 1) vs. 30 % (EB9 in Table 1). Kamens et al. (2011) and Liu et al. (2018) reported a significantly lower yield of toluene SOA for dry AS-seeded aerosols compared with its wet counterpart. The partitioning of polar carbonaceous products increases with increasing LWC and, thus, aqueous reactions. In the presence of wet aerosols, SOA yields gradually increase with increasing FFS (increasing acidity) at a given RH due to acid-catalyzed oligomerization. The oxygenated products of toluene are relatively more polar than those of ethylbenzene or propylbenzene and positively attributed to the increase in OMAR.

Compared to isoprene SOAs reported by Beardsley and Jang (2016), the impacts of humidity and acidity on the SOA yields of monoalkylbenzenes in this study are relatively weaker above the ERH (Fig. 4), except for the highly acidic conditions under high humidity. In this study, aromatic SOA mass is attributed to a few highly reactive species, such as GLY. Other aromatic oxidation products partitioned in the aerosol phase have moderate solubility and they are slow to react in the aqueous phase. Isoprene products are more hygroscopic than aromatic products and even mixable with an aqueous phase containing electrolytes. The reactions of medium reactivity polar products that formed during isoprene oxidation can be accelerated by an acid catalyst with higher sensitivities to acidity and humidity.

Figure 5 illustrates the time profiles of the predicted concentrations of diOS ([diOS]model) and protons ([H+]) with the measured concentrations of diOS ([diOS]exp), [NH4+], and [SO42-] for different aromatic HCs under given experimental conditions (Fig. 5a–c). For the three SA-seeded SOA experiments, the fractions of diOS to the total sulfate amount are 0.09, 0.15, and 0.06 for toluene (Exp. Tol8, HC/NOx = 2.9, FS changing from 0.64 to 0.39), ethylbenzene (Exp. EB7, HC/NOx = 12.3, FS changing from 0.82 to 0.46), and n-propylbenzene (Exp. PB5, HC/NOx = 14.4, FS changing from 0.76 to 0.38), respectively. The [diOS]model reasonably agrees with [diOS]exp. The aerosols in Exp. Tol8 and Exp. PB5 show the cessation in diOS formation at approximately 10:00 EST since they became effloresced due to the neutralization of SA with ammonia under the reduction in humidity during the daytime. The diOS fraction in Exp. EB7, which contained wet acidic aerosols, was higher than those in Exp. Tol8 and Exp. PB5, indicating that the acidic condition was favorable for the formation of diOS (Surratt et al., 2010; Lin et al., 2013).

Beardsley and Jang (2016) reported that the diOS fraction for isoprene SOAs was 0.26 (HC/NOx = 32.5, FS changing from 0.69 to 0.47), which was more than that for toluene SOAs, indicating that the oxidation products of isoprene may contain more reactive species to form diOS. For example, IEPOX products in isoprene SOAs are known to be reactive to SA (Budisulistiorini et al., 2017). Additionally, isoprene aerosol products are mixable with aqueous solutions containing electrolytes, and they can more effectively form diOS compared to the aromatic products in liquid–liquid phase separation.

To estimate the potential upper boundary of the concentration of diOS ([diOS]max) in monoalkylbenzene SOA, the aerosol composition was predicted by the model in the presence of SA aerosols (without neutralization with ammonia) under the given experimental conditions shown in Fig. 5. The resulting diOS fractions were 0.29 (OM-to-sulfate mass ratio (OM : sulf) = 1.4), 0.25 (OM : sulf = 1.4), and 0.12 (OM : sulf = 0.7) for toluene, ethylbenzene, and n-propylbenzene, respectively. The aerosol acidity of the ambient aerosol is generally lower than ammonium hydrogen sulfate (AHS), and, thus, the diOS fraction in ambient air would be much lower than the estimated upper boundary. Figure 5 suggests that the change in both aerosol acidity and hygroscopicity by the formation of non-electrolytic sulfate is important to predict SOA mass.

Figure 6 shows the impact of NOx on the three aromatic SOAs in this study by producing SOAs at two different NOx levels in the presence and absence of SO2. Overall, regardless of the inorganic seed conditions, both the chamber observation and model simulation suggest that increasing the NOx level leads to the decreased formation of SOAs. This trend in the absence of inorganic seed aerosols has also been observed multiple times (Li et al., 2015; Ng et al., 2007; Song et al., 2005). By increasing [NOx], the path of an RO2 radical progresses to the formation of organonitrate and peroxyacyl nitrate (PAN) products, which are less reactive to aerosol-phase reactions. They are relatively volatile and, thus, insignificantly attributed to partitioning SOA mass.

For example, the SOA yields under the low NOx level (HC(ppbC)/NOx(ppb) = 9.1–14.8, Table 1) in the presence of SO2, with a similar degree of ammonia titration (i.e., similar FS values by the end of the experiments), were higher than those without seeded aerosols: 42 % for toluene (Exp. Tol1, FS = 0.44), 26 % for ethylbenzene (Exp. EB1, FS = 0.37), and 66 % for propylbenzene (Exp. PB1, FS = 0.43). The impact of aerosol acidity was even greater for SOAs produced under a high NOx level (HC(ppbC)/NOx(ppb) = 2.8–5.0): 65 % for toluene (Exp. Tol3, FS = 0.43), 146 % for ethylbenzene (Exp. EB5, FS = 0.39), and 77 % for propylbenzene (Exp. PB3, FS = 0.40). SOA formation under high-NOx conditions is generally more sensitive to aerosol acidity compared to that at low NOx levels (Fig. 6a–c vs. Fig. 6d–f). The fractions of medium reactivity products are relatively high in high NOx levels, and their reactions in aerosol phase can be accelerated by an acid catalyst. Figure S7 (Sect. S9) also illustrates the simulation of SOA mass against chamber data under varying humidity, NOx levels, and aerosol acidity (Table 1).

Figure 7 illustrates the sensitivity of the SOA mass simulated at relatively low concentration of HCs (20 ppb) (panel i) for three monoalkylbenzenes to important variables – i.e., humidity (Ai vs. Bi for AHS and Ci vs. Di for AS), temperature (Ai vs. Ei for AHS and Fi vs. Gi without inorganic aerosol), aerosol acidity (Ai vs. Ci at RH = 45 % and Bi vs. Di at RH = 65 %), and NOx levels (Ai vs. Hi with AHS-seeded aerosols and Fi vs. Ii without inorganic-seeded aerosols). The most drastic change appears by changing the temperature from 298 K (Ai) to 273 K (Ei). The SOA yield is known to increase by 20 %–150 %, which results from a 10 K decrease in temperature (Sheehan and Bowman, 2001). For all SOAs, noticeable changes are shown between the absence (Fi) and presence (Ai) of wet inorganic seeds, while a minor change appears between wet AHS (Ai) and wet AS (Ci). Within the wet acidic aerosols (Ai vs. Bi and Ci vs. Di), the effect of RH is insignificant in our simulation, as discussed in Sect. 4.2. Although the impact of NOx (Ai vs. Hi and Fi vs. Ii) is less than that of temperature and inorganic seeds, SOA yields are still significantly altered, as discussed in Sect. 4.4.

The panel ii series in Fig. 7 illustrates SOA growth curves under various conditions shown in panel i. Overall, the simulated SOA yields (slopes) increase with a decreased alkyl chain length (toluene > ethylbenzene > n-propylbenzene), which is consistent with our chamber observations (Table 1). Although the decrease in the vapor pressure of products benefits the increases in OMP as the alkyl chain length increases, the increase in the activity coefficient of the organic products containing longer alkyl chains in aqueous phase is unfavorable to the formation of OMAR via aqueous reactions. However, the difference of mole-based SOA yields of three monoalkylbenzenes becomes small because the highly reactive organic species (i.e., glyoxal), which are produced through ring opening reactions without an alkyl side chain, are significantly attributed to OMAR. Fig. 7ii confirms that the effect of an aqueous phase containing electrolytes on SOA yields is more critical than that of the NOx level under our simulated conditions.

To determine the model sensitivity to these parameters, simulations (Exp. Tol9 in Table 1) were performed by increasing/decreasing vapor pressure (Vp), the enthalpy of vaporization (Hvap), γin,i, and kAC,i by factors of 1.5, 1.1, 2, and 2, respectively. The corresponding changes in the SOA mass are -7.2 %/6.8 %, -1.9 %/1.7 %, -8.8 %/4.7 %, and 2.5 %/-3.5 %, respectively. The change in SOA mass from the reference for each simulation is shown in Fig. S8 (Sect. S10).

The uncertainty associated with the group contribution method used for Vp estimation is a factor of 1.45 (Zhao et al., 1999). Hvap has a reported error of 2.6 % (Kolska et al., 2005). γin,i is estimated as a function of O : C, MW, RH, and FS (Eq.  ). kAC,i is semi-empirically calculated based on [H+], LWC, and species reactivity (Eq. 8). The E-AIM is performed to estimate the LWC, which is reliable and based on a broadly used water activity dataset (Zhang et al., 2000). Yet, the inorganic thermodynamic models including E-AIM performed inadequately in the prediction of [H+] under low-RH and ammonia-rich conditions (FS < 0.55) (Li and Jang, 2012).

Although most identified toluene products have been included, such as methyl-cyclohexene (3S), 2-methyl-5-nitrophenol (5P), 2-methyl-benzoquinone (6S), 2-methyl-4-oxo-2-butenoic acid (6M), o-cresol (7P), 3-hydroxy-1,3-propandial (7VF), 3-methyl-2(5H)-furanone (8P), MGLY, and GLY (Forstner et al., 1997; Jang and Kamens, 2001; Sato et al., 2007; Gomez Alvarez et al., 2007; Huang et al., 2016), a large number of toluene oxidation mechanisms and involved products remain unstudied. A similar trend can be found in ethylbenzene and propylbenzene. Evidently, the addition of artificial OH radicals in the gas-phase simulation suggests missing mechanisms in the MCM v3.3.1 or an improper branching ratio of reactions. Additionally, the diverse reactions of the RO2 radicals might be oversimplified in the gas-phase simulation by employing surrogate coefficients.

In the model, non-electrolytic diOS was predicted and applied to the prediction of LWC and [H+], which subsequently affect aerosol growth via aqueous reactions. Typically, the monoalkyl sulfate is identified as a product of the esterification of SA with reactive species (Hettiyadura et al., 2015; J. Li et al., 2016; Estillore et al., 2016; Chen et al., 2018). It is possible that monoalkyl sulfates can influence LWC and aerosol acidity differently from sulfuric acid, although they are strongly acidic and hygroscopic. Although Noziere et al. (2010) reported that OS could be produced by the reactions of GLY and sulfate radicals in the presence of aqueous AS under UV light, the amounts of formed monoalkyl OS and their influence on aerosol hygroscopicity are still not clear.

Some other factors in recent investigations, such as organic vapor wall loss and aerosol viscosity, have not been accounted for by the UNIPAR model. The loss of organic vapor to the Teflon chamber wall can compete with the gas–particle partitioning process and the reactions in both the gas phase and aerosol phase to initiate a negative bias in the experimental measurements (Zhang et al., 2014; Mcvay et al., 2014). The modeling of the gas–wall process of semivolatile organic compounds can improve the prediction of SOA mass in regional scales. In addition, an increased aerosol viscosity via aging could modify the diffusivity of the partitioned organic molecules (Abramson et al., 2013) and the reaction rate constant for oligomerization in the aerosol phase.