for “Model-measurement comparison of functional group abundance in α -pinene and 1,3,5-trimethylbenzene secondary organic aerosol formation”

Abstract. Secondary organic aerosol (SOA) formed by α-pinene and 1,3,5-trimethylbenzene photooxidation under different NOx regimes is simulated using the Master Chemical Mechanism v3.2 (MCM) coupled with an absorptive gas–particle partitioning module. Vapor pressures for individual compounds are estimated with the SIMPOL.1 group contribution model for determining apportionment of reaction products to each phase. We apply chemoinformatic tools to harvest functional group (FG) composition from the simulations and estimate their contributions to the overall oxygen to carbon ratio. Furthermore, we compare FG abundances in simulated SOA to measurements of FGs reported in previous chamber studies using Fourier transform infrared spectroscopy. These simulations qualitatively capture the dynamics of FG composition of SOA formed from both α-pinene and 1,3,5-trimethylbenzene in low-NOx conditions, especially in the first hours after start of photooxidation. Higher discrepancies are found after several hours of simulation; the nature of these discrepancies indicates sources of uncertainty or types of reactions in the condensed or gas phase missing from current model implementation. Higher discrepancies are found in the case of α-pinene photooxidation under different NOx concentration regimes, which are reasoned through the domination by a few polyfunctional compounds that disproportionately impact the simulated FG abundance in the aerosol phase. This manuscript illustrates the usefulness of FG analysis to complement existing methods for model–measurement evaluation.

We first revisit the relationship among equilibrium vapor pressure p of a substance i in a mixture, its pure component vapor pressure (possibly over sub-cooled liquid) p 0 , and its activity a of solution. The vapor and aerosol solution phase chemical potentials can be written as a sum of their standard chemical potentials µ 0 and µ * and their ideal (and non-ideal, in the case of liquid) mixing contributions to the partial molar Gibbs free energy (Denbigh, 1981;Seinfeld and Pandis, 2006): At equilibrium, the chemical potential of substance i in the two phases are equal, µ (vap.) i = µ (soln.) i ; the equilibrium constant K is given by the relation between equations A1 and A2: Using a pure component reference (as opposed to infinite dilution) for all species, K i = p 0 L,i . With activity of substance i defined as a i = ζ i x i , the equality in equation A3 is commonly written as: The pure component and equilibrium vapor pressures are equivalent to their mass concentrations C 0 and C (g) , respectively at a given temperature by the ideal gas law (Chen et al., 2011;Donahue et al., 20 2012): The saturation concentration C * (Donahue et al., 2006) is also a widely used metric for characterizing the volatility of a mixture; it is the reciprocal of the venerable G/P partition coefficient K p (Pankow, 1994(Pankow, , 2011: The mass fraction of i in the particle phase (with respect to the total organic aerosol mass) can be expressed according to its molar abundance n, mole fraction x, and molecular weight MW , and the mean molecular weight MW defined for the set of compounds M in the mixture: By substitution of equation A7 into A4-A6, C * i can be related to C 0 i : For a pure component solution, C * i = C 0 i . At equilibrium with a solution mixture, the gas phase concentration is related to saturation concentrations C 0 i and C * i through equations A4-A6: C * is a useful construct to represent volatility of aggregated mixtures when its composition is not well-defined (Donahue et al., 2006;Grieshop et al., 2009;Chen et al., 2011), and we use this for specifying initial concentrations of a generic organic aerosol mixture (Appendix B). For subsequent G/P partitioning calculations, we follow the approach of Donahue et al. (2012) and use C 0 according to molecular specificity provided by the MCMv3.2 mechanism.

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Considering the dynamics of condensation and evaporation, mass transfer of individual compounds from the bulk vapor phase (at concentration C (g) i,∞ ) to a monodisperse particle population of size D p is driven by the concentration gradient with respect to the equilibrium vapor concentration at the aerosol surface, and the surface characteristics for exchange to take place (Fuchs and Sutugin, 1971;Seinfeld and Pandis, 2006;Chen et al., 2011): We assume activity coefficients ζ i and mass accommodations α i of unity, and a diffusivity of D i = 5×10 −6 m 2 s −1 for all molecules (Chen et al., 2011). One notable difference with Chen et al. (2011) is that we run this model as a batch reactor rather than a continuously-stirred flow tank reactor, in 50 accordance with the operation of experimental chambers of the reference studies used in this work.
Given our assumption of monodisperse particles and fixed particle number N p (no particle losses; negligible coagulation for the duration of our simulations), we estimate the size D p of particles (which includes the seed, if applicable, and condensed organic matter) at each timestep to satisfy the following condition, assuming SOA density of ρ p = 1.5 g cm −3 (Kostenidou et al., 2007): Values for these parameters are discussed in Appendix B.

Appendix B: Initial and fixed conditions
In addition to precursor, NO x , and oxidant concentrations specified in Table 1, we initialize gasphase concentrations to small, non-zero values (C tioning from x i = 1 to x i 1 immediately following initial condensation. The use of an organic seed aerosol (C OA,init ) to initiate G/P partitioning alleviates such problems and accounts for the effects of homogeneous and heterogeneous nucleation (Flagan and Seinfeld,70 1988; Seinfeld and Pandis, 2006;Fan et al., 2013, e.g.,) of organic aerosol not included in our model. Initial aerosol concentrations are specified to be in equilibrium with the specified gas-phase concentrations for a given C OA,init (according to equations A6 and A8 with ζ i = 1): This leads to the introduction of negligible mass of MCM compounds into the system, but pro- all compounds in the MCM mechanism; we assume the existence of an inactive medium (C solvent ) which comprises this difference:

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C solvent does not participate in G/P partitioning or reactions, and is not reported with the SOA formed.
The initial and subsequent mole fractions are calculated in the presence of this virtual medium: M , in combination with this inactive medium, comprises the complete set of molecule types M in the system (Appendix A).

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A value of C OA,init = 1 µg m −3 is assumed in all of our simulations, which leads to initial values of i C (p) i < 5 × 10 −4 µg m −3 . Therefore, C solvent ∼ C OA,init and the organic aerosol phase affecting G/P partitioning is effectively C OA = C solvent + C SOA ≈ C OA,init + C SOA . For use in both equations B1 and B2 we assume a mean molecular weight of MW = MW solvent = 200 g mol −1 , which is in the range of products estimated or identified in the condensed phase (e.g., Odum et al., 1996 (Table 1). With C OA,init = 1µg m −3 and ρ p = 1.5 g cm −3 , initial D p becomes 203 nm. For APIN-lNO x and TMB-lNO x where no seed is used, we assume 100 N p = 10 4 cm −3 and initial D p = 43 nm is calculated according to C OA,init , which corresponds to a system which condensational growth and scavenging of the smallest clusters has occured. The Kelvin effect is neglected but results are insensitive to this omission since the condensation and particle growth is rapid in these two systems. D p increases up to 350 nm over the course of the APIN-lNO x and TMB-lNO x simulations for the given C OA loadings, and up to 220 nm (including 105 seed) for APIN-hNO x and APIN-nNO x on account of the lower mass loading. Inorganic reactions (such as the production of nitric acid) in simulations involving NO x are included to maintain radical balance, but are not treated in G/P partitioning. Rate of particle growth may therefore be underestimated when condensation of such species (e.g., nitric acid) may be important compared to the growth due to the organic phase.