Supplement of Simulation of SOA formation from the photooxidation of monoalkylbenzenes in the presence of aqueous aerosols containing electrolytes under various NOx levels

The formation of secondary organic aerosols (SOAs) from the photooxidation of three monoalkylbenzenes (toluene, ethylbenzene, and n-propylbenzene) in the presence of inorganic seeds (SO4-NH4-H2O system) under varying NOx levels has been simulated using the Unified Partitioning-Aerosol Phase Reaction (UNIPAR) model. The evolution of the volatility10 reactivity distribution (mass-base stoichiometric coefficient, αi) of oxygenated products, which were created by the nearexplicit gas kinetic mechanism, was integrated with the model using the parameters linked to the concentrations of HO2 and RO2 radicals. This dynamic distribution was applied to estimate the model parameters related to the thermodynamic constants of the products in multiple phases (e.g., the gas phase, organic phase, and inorganic phase) and the reaction rate constants in the aerosol phase. The SOA mass was predicted through the partitioning and aerosol chemistry processes of the oxygenated 15 products in both the organic phase and aqueous solution containing electrolytes, with the assumption of organic-inorganic phase separation. The prediction of the time series SOA mass (12-hr), against the aerosol data obtained from an outdoor photochemical smog chamber, was improved by the dynamic αi set compared to the prediction using the fixed αi set. Overall, the effect of an aqueous phase containing electrolytes on SOA yields was more important than that of the NOx level under our simulated conditions or the utilization of the age-driven αi set. Regardless of the NOx conditions, the SOA yields for the three 20 aromatics were significantly higher in the presence of wet electrolytic seeds than those obtained with dry seeds or no seed. When increasing the NOx level, the fraction of organic matter (OM) produced by aqueous reactions to the total OM increased due to the increased formation of relatively volatile organic nitrates and peroxyacyl nitrate like products. The predicted partitioning mass fraction increased as the alkyl chain length increases but the organic mass produced via aerosol phase reactions decreased due to the increased activity coefficient of the organic compounds containing longer alkyl chains. Overall, 25 the lower mass-base SOA yield was seen in the longer alkyl-substituted benzene in both the presence and absence of inorganic seeded aerosols. However, the difference of mole-base SOA yields of three monoalkylbenzenes becomes small because the highly reactive organic species (i.e., glyoxal) mainly originates from ring opening products without alkyl side chain. UNIPAR predicted the conversion of hydrophilic, acidic sulfur species to non-electrolytic dialkyl-organosulfate (diOS) in the aerosol. Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2018-963 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 26 October 2018 c © Author(s) 2018. CC BY 4.0 License.

The mass-based stoichiometric coefficient ( ) of species, i, was constructed, as shown in Eq. S1, to calculate the gas-phase concentration (µg m -3 of air) of each lumping species, i.
Section S3. Estimation of the atomic oxygen-to-carbon ratio ( : ) and molecular weight

( ) for each lumping species
We assume that the model parameters (i.e., atomic oxygen-to-carbon ratio ( : ), molecular weight ( ), and hydrogen bonding ( ) parameter) related to the thermodynamic equilibrium process of a lumping group (see Section S4) linearly change as a function of NOx levels, which range from HC/NOx=2 (high NOx level (H-NOx)) to HC/NOx=14 (the low NOx level (L-NOx)).
For example, the calculation of the : is exemplified in the following part in this Section. Based on the simulations from the near-explicit gas kinetic model under the same metrological condition (6/19/2015), four sets of : are carried out under four conditions: Since the change of the : of the lumping species, i, is due to the evolution of the gas-phase products, which is governed by the αi, the dynamic : set can be simply estimated by comprising the : ℎ and : ℎ ℎ using the aging scale, ′( ), as shown in Eq.
S4 (same method in Eq. 2 in the manuscript).
dynamic : = (1 − ′( )) · : ℎ + ( ′( )) · : ℎ ℎ (S4) The calculation of dynamic and dynamic is also treated with the similar method used for the dynamic : . dynamic : , , and sets are applied to estimate the activity coefficient of the organics in the inorganic (in) phase, as shown in Eq. 4 in the manuscript.

Section S4. Activity coefficient of organic species in the aqueous solutions containing electrolytes
In the UNIAPR model, the formation of aromatic SOA is simulated with the assumption of organic-inorganic phase separation. To predict the partitioning of organic species on both the organic phase and the inorganic phase, the key model parameters are , and , , respectively (described in Section 3.2 of the main manuscript). In order to predict , , the calculation of the activity coefficient ( , ) of organic species in the inorganic phase (aqueous phase containing electrolytes) is necessary.
In our study, , was semi-empirically predicted by a polynomial equation, which was fit the theoretical , of various organic compounds to relative humidity ( The theoretical , was determined at the maximum solubility of organic species in the electrolytic aqueous phase (SO4 2--NH4 + -H2O system) using the Aerosol Inorganic-Organic Mixtures Functional Groups Activity Coefficients (AIOMFAC) (Zuend et al., 2011).
AIOMFAC was run for the estimation of , of 20 model compounds with diverse , : , and under varying inorganic phase compositions (FS and hygroscopicity linked to RH).
The oligomeric products form in aqueous phase, but they deposit to the organic phase due to their poor solubility in inorganic phase. However, some hydrophilic oligomers can dissolve in both organic and inorganic phases. For example, glyoxal-origin oligomers might be hydrophilic and partially soluble in inorganic phase. Hence, the trace amount of glyoxaloligomer (MW = 290 g/mol and O:C = 1 with mole fraction = 0.01) was included in inorganic phase as seen in Table S4. In Figure S1, the , predicted by AIOMFAC was plotted to that predicted by the polynomial equation (Eq. 4 in the manuscript) along with the one-to-one line for 20 organic species (Table S4). : , , and range from 0.14 to 1.2, 58.00 to 204.18, 0.0 to 3.2, respectively. FS ranges from 0.34 to 1.0 and RH ranges from 0.1 to 0.8.   Table S4.

Section S5. Derivation of the model equations used to predict the organic mass
The gas-organic phase partitioning coefficient ( , , m 3 μg −1 ) and the gas-inorganic phase partitioning coefficient ( , , m 3 μg −1 ) of each species are obtained from Eq. 3 in the manuscript. The concentrations ( , , , , and , : μg m −3 of air) of each lumping species in the gas (g), organic aerosol (or), and inorganic (in) phases can be derived from the Eqs. S6, S7, and S8, respectively. The partitioning and aerosol-phase reactions in the multiphase system (g, or, and in phase) can be kinetically represented as shown in Fig. S2.
where the subscript i represents the lumping species, i. , is the total organics concentration in multiple phases (i.e., , = , + , + , ). and are the mass concentration (μg m −3 of air) of the total organic matter and the total inorganic aerosol, respectively.
The formation of organic matter (Δ ) through aerosol-phase reactions are described by two processes: (1) the oligomerization in or phase and (2) the oligomerization in in phase (i.e., acid-catalyzed reaction). The two reactions are described based on the secondorder kinetic self-dimerization as shown in Eqs. S9 and S10. is fulfilled by the bracketed terms, 10 3 and 10 3 , respectively. MWi is the molecular weight of species, i. OMT is the total organic matter (OM) concentration (μg m -3 ). and are the densities (g cm -3 ) of the or phase aerosol and in phase aerosol.
Based on the mass balance, Δ is same as the consumed total concentrations of lumping species (sum up of , i of each lumping species, i) as shown in the following equation.
Thus, the following equations can be applied to kinetically express partitioning and in-particle chemistry processes of the lumping species.
Section S9. Simulation of SOA mass against chamber data obtained under various NOx levels, aerosol acidity, and humidity (dry and wet inorganic seed aerosol) Figure S7: Time profiles of measured and modeled SOA mass concentrations for toluene (Tol: a-e), ethylbenzene (EB: f-h), and n-propylbenzene (PB: i-k) SOA under various NOx levels in the presence/absence of inorganic seeded aerosol. The red, green, and blue colors indicate experiments with sulfuric acid seed, without inorganic seed, and with ammonium sulfate seed, respectively. SA denotes the direct-SA injection experiment. "wet" or "dry" in the figure denotes the physical state of the inorganic seed. Solid, dashed, and dotted lines denote total OM (OMT), the OM from partitioning only (OMP), and the OM from the aerosol-phase reactions (OMAR), respectively. The uncertainty associated with experimentally measured OM is 9 %, which is estimated from the uncertainties of measured OC and correction of particle wall loss. The experimental conditions are available in Table 1 in the manuscript.
Section S10. Uncertainties in UNIPAR predicted SOA mass for major model parameters Figure S8: Prediction of model uncertainty (simulated SOA mass deviated from the reference SOA mass) due to the variation of major model parameters. The simulations employ the experiment performed on 06/14/2018 (Exp. Tol9 in Table 1 in the manuscript). The estimated errors associated with vapor pressure ( ), enthalpy of vaporization ( ), activity coefficients of the organics in the inorganic phase ( , ) and oligomerization reaction rate constants in the inorganic phase ( , ) were predicted with increasing/decreasing the , , , , and , by factors of 1.5, 1.1, 2, and 2, respectively.