Estimation of Secondary Organic Aerosol Viscosity from Explicit Modeling of Gas-Phase Oxidation of Isoprene and α -pinene

. Secondary organic aerosols (SOA) are major components of atmospheric ﬁne particulate matter, affecting climate and air quality. Mounting evidence exists that SOA can adopt glassy and viscous semisolid states, impacting formation and partitioning of SOA. In this study, we conduct explicit modeling of isoprene photooxidation and α -pinene ozonolysis and subsequent SOA formation using the GECKO-A (Generator of Explicit Chemistry and Kinetics of Organics in the Atmosphere) model. Our recently-developed parameterizations to predict glass transition temperature of organic compounds are imple- 5 mented into a box model with explicit gas-phase chemical mechanisms to simulate viscosity of SOA. The effects of chemical composition, relative humidity, mass loadings and mass accommodation on particle viscosity are investigated in comparison with measurements of SOA viscosity. The simulated viscosity of isoprene SOA agrees well with viscosity measurements as a function of relative humidity, while the model underestimates viscosity of α -pinene SOA by a few orders of magnitude. This difference may be due to missing processes in the model including gas-phase dimerization and particle-phase reactions 10 leading to the formation of high molar mass compounds that would increase particle viscosity. Additional simulations imply that kinetic limitations of bulk diffusion and reduction in mass accommodation coefﬁcient may also play a role in enhancing particle viscosity by suppressing condensation of semi-volatile compounds. The developed model is a useful tool for analysis and investigation of the interplay among gas-phase reactions, particle chemical composition and SOA phase state. RH for RH 65 Simulated viscosity values of α -pinene SOA by a few orders of magnitude than the ones simulated for isoprene SOA, which is consistent with experimental observations. Simulation results for Renbaum-Wolff’s and Grayson’s experiments within uncertainties of experimental measurements for the 40-60 % RH range. In simulations for Renbaum-Wolff’s experiments at RH > 60 %, the predicted viscosity values are about one order of magnitude lower than the measured values. Larger deviations are observed for RH < 40 %, simulated viscosities are up to four orders of magnitude viscosity are based on elemental composition without accounting for molecular structure and speciﬁc intramolecular interactions. Some organic compounds with reactive functional groups may undergo particle-phase reactions, which are not treated in our simulations. To explore these aspects, we investigate the


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Secondary organic aerosols (SOA) are ubiquitous in the atmosphere and represent a major component of fine particulate matter, affecting air quality, climate and public health (Jimenez et al., 2009;Pöschl and Shiraiwa, 2015). Due to their complexity, SOA represent a large source of uncertainty in current understanding of global climate change and air pollution (Tsigaridis et al., 2014;Ciarelli et al., 2019). Development of SOA models represents one of the most challenging and demanding problems in atmospheric chemistry (Shrivastava et al., 2017). Formation of SOA is initiated by gas-phase oxidation of biogenic and 20 anthropogenic volatile organic compounds (VOC) (Kroll and Seinfeld, 2008). Typically, multigenerational oxidation of VOC in the gas phase leads to the formation of a myriad of semi-volatile and low volatility compounds which can condense on preexisting particles (Ziemann and Atkinson, 2012;Nozière et al., 2015) or contribute to nucleation and new particle formation mixing rule for mixtures of SOA multiple components and water, the viscosity of SOA can be estimated by the T g -scaled Arrhenius plot of viscosity (DeRieux et al., 2018). This method has been successfully applied to estimate particle viscosity 60 based on elemental composition obtained from high resolution mass spectrometry (Schum et al., 2018;Ditto et al., 2019;Song et al., 2019).
In this study, the T g and viscosity prediction methods are implemented into the GECKO-A and box model. Model simulations with explicit chemical mechanisms are conducted to reproduce chamber experimental conditions for SOA generation and subsequent viscosity measurements. The effects of chemical composition and mass accommodation on SOA partitioning 65 and viscosity are also investigated. The objective of this work is to expand our understanding on the relationship and interplay among gas-phase reactions, chemical composition and viscosity of SOA.

GECKO-A
GECKO-A generates detailed gas-phase chemical oxidation schemes and the associated gas-particle mass transfers for SOA 70 formation. It produces explicit highly detailed chemical mechanisms starting from experimental data and structure-activity relationships (SARs) (Aumont et al., 2005). Implemented into a box model, these explicit chemical mechanisms simulate the oxidation of parent VOC precursors to oxidation products, their subsequent gas-phase chemistry, as well as partitioning into the particle phase based on their vapor pressures. The chemical mechanism does not account for gas-phase chemistry of species with vapor pressure below 10 −13 atm, which are assumed to be of enough low volatility to partition to the condensed phase. In 75 our simulations, species vapor pressures are estimated via the approach by Nannoolal et al. (Nannoolal et al., 2008).
The mechanism generator follows a reduction protocol optimizing the number of generated reactions and chemical species (Valorso et al., 2011). This protocol has been established to reduce the computational cost of box-model simulations. In the gas phase, isomer substitution is not allowed for position isomers when the overall yield for the product is > 5 %; otherwise only the highest-yield positional isomer is considered. For each reaction, pathways with branching ratios < 5 % are not accounted 80 for and the main reaction branches are scaled proportionally (Valorso et al., 2011). The chemical mechanism accounts for chemistry of peroxy and alkoxy radicals generated during precursors oxidation. SOA chemistry is a multi-generational process and in our simulations the generated chemical schemes follow the chemistry of reaction products up to the 5th generation.
The GECKO-A version used in this study has been recently enriched with SARs estimations of alkoxy radical decomposition and H-migration reaction rates (Vereecken and Peeters, 2009;La et al., 2016). Rate coefficients and branching ratios for gas-85 phase reactions of OH with aliphatic compounds and peroxy radicals are estimated based on recent SAR investigations (Jenkin et al., 2018a,b). Our simulations do not include autooxidation and condensed-phase chemistry, which represent limitations of GECKO-A modeling.
α-pinene and isoprene oxidation mechanisms have been investigated extensively both in model and experimental studies. Their oxidation mechanisms are well known, providing good estimations of resulting SOA composition. The SARs for both 90 α-pinene and isoprene oxidation are implemented into GECKO-A with state-of-the-art protocols estimating radical reactions and respective rate constants. The base mechanism for α-pinene photooxidation and ozonolysis include a detailed description of reactions with OH radicals (McVay et al., 2016), and branch reactions identified via quantum and theoretical chemical calculations (Peeters et al., 2001;Vereecken et al., 2007). Stabilized Criegee intermediates (SCIs) chemistry is not treated explicitly and stable products are directly assigned via a rule-base method. This scheme accounts for a direct reaction route to 95 account for pinonaldehyde formation during the reaction of SCIs with water (McVay et al., 2016). The GECKO-A isoprene oxidation scheme follows the main protocol developed by Aumont et al. (Aumont et al., 2005) and branching reactions for isoprene + OH are also considered (Paulot et al., 2009). The chemical schemes for α-pinene and isoprene oxidation are composed of 84,000 and 1,900 species, and of ∼700,000 and ∼17,000 reactions, respectively.

Box model and simulations setup 100
Each chemical mechanism is coupled to a box model representing SOA formation from α-pinene or isoprene oxidation in specific chamber experiments. The time evolution of species concentration is computed through a two-step method that explicitly solves stiff ordinary differential equations (Verwer, 1994;Verwer et al., 1996). The experimental conditions are summarized in Table 1. All laboratory experiments were performed in absence of seed particles, but the box model used in our simulations does not treat nucleation. Thus, in our simulations the first steps of nucleation are approximated by the addition of seed particles 105 with a particle radius of 5 nm and a concentration of 10 4 particles cm −3 (McVay et al., 2016). It is assumed that the density of SOA particles is 1.2 g cm −3 (Kuwata and Martin, 2012). The particle number concentration is also assumed to remain constant during simulations, while the particle radius evolves following the partitioning of organics. All simulations are conducted with a NOx mixing ratio of 3 ppt to reflect low NOx conditions of chamber and flow tube experiments. For all simulations we consider reversible gas-wall partitioning of organic species with the vapor wall loss rate of 10 −3 s −1 based on experimental 110 observations (Lim and Ziemann, 2009;McVay et al., 2016). Photolysis rates are computed using the cross-sections and the quantum yields from Aumont et al. (Aumont et al., 2005). Photolysis conditions are set to average daylight conditions of a midlatitude spring day for isoprene photooxidation simulations and to zero for α-pinene dark ozonolysis experiments, coherent with the experimental conditions. concentrations are initially set to the respective experimental values and species concentrations evolve due to gas oxidation, gas-particle partitioning, and wall deposition. SOA particles were formed under dry conditions and then SOA were exposed to 120 water vapor at different RH for viscosity measurements. For each set of simulations, the measured RH and temperature were used to constrain the simulation conditions. Note that partitioning of water is not considered in the box model as particle water uptake should be very minor under the very low RH values at which SOA particles were formed.
The box model treats the mass transfer of gaseous organic species to particles and to chamber walls. Gas-particle partitioning is assumed to follow Raoult's law at equilibrium (La et al., 2016)  organic compounds assuming ideal mixing). Gas to particle partitioning is described in the box model using the gas-particle mass transfer coefficient of a compound (k gp , in s −1 ) with the Fuchs-Sutugin approach in the transition regime as (Seinfeld and Pandis, 2016): where D g (cm 2 s −1 ) is the gas diffusivity, r p (cm) is the particle radius, N p (cm −3 ) is the particle number concentration, K n is the Knudsen number, and α is the mass accommodation coefficient. α, also termed as the bulk accommodation coefficient, represents the probability for a gas molecule colliding with surface to enter the bulk of the particle. Based on recent experiments and molecular dynamics simulations α is assumed to be unity for the base case scenario of our simulations (Liu et al., 2019;Julin et al., 2014). This approach does not account for potential kinetic limitations caused by bulk diffusion in viscous particles.

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A recent study has introduced an effective mass accommodation coefficient α eff , which effectively considers the kinetics of accommodation at the surface, transfer across the gas-particle interface, and further transport into the particle bulk (Shiraiwa and Pöschl, 2021): where α s is the surface accommodation coefficient (i.e., the probability for a gas molecule colliding with surface to adsorb on the particle surface), ω (cm s −1 ) is the mean thermal velocity of the organic compound in the gas phase, is diffusivity in the condensed phase, ρ p (g cm −3 ) is the particle density, and C 0 (µg m −3 ) is the pure compound saturation mass concentration. Application of α eff in the Fuchs-Sutugin approach (e.g., α = α eff ) yields SOA partitioning with effective consideration of kinetic limitations induced by slow bulk diffusion in viscous particles. This approach can yield consistent results with a detailed kinetic multilayer model (KM-GAP, Shiraiwa et al., 2012) and two-film model solutions (Zaveri et al.,145 2014). We implement this method to explore the effects of mass accommodation and kinetic partitioning on predicted viscosity by comparing with the base case scenario (e.g., α fixed to 1).

Viscosity prediction implementation
The glass transition temperature of an organic compound i (T g,i ) can be estimated with the following recently-developed parameterization based on its elemental composition (DeRieux et al., 2018).  (Li et al., 2020): 5.34, 31.53, -7.06, 134.96, 6.54, -34.36, and -15.35]. These parametrizations can predict T g,i with an uncertainty of about ±30 K; note that, however, in multicomponent SOA mixtures this uncertainty would be much smaller for ideal mixing conditions DeRieux et al., 2018;Li et al., 2020). The T g of a mixture of organic compounds (e.g. dry SOA) can be estimated using the Gordon-Taylor equation with a Gordon-Taylor constant (k GT ) of 1: where ω i is the mass fraction of compound i (Dette et al., 2014).

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The Gordon-Taylor equation can also be used to estimate the glass transition temperature of mixtures of organic compounds and water (T g (w org )): where w org is the mass fraction of organics, T g,w is the glass transition temperature of pure water (136 K), and k GT is the Gordon-Taylor constant which is assumed to be 2.5 Zobrist et al., 2008). The w org is calculated using the mass concentration of water (mH 2 O) and of the organics in SOA (m SOA ) as: w org = m SOA / (m SOA + mH 2 O). mH 2 O can be calculated using the Kohler theory with effective hygroscopicity parameter (κ) (Petters and Kreidenweis, 2013).
Once T g (w org ) has been computed, the viscosity (η) can be derived with the following equation based on the Vogel-Tammann-Fulcher approach (DeRieux et al., 2018): where T 0 is the Vogel temperature and D is the fragility parameter. The D value is assumed to be 10 based on previous studies DeRieux et al., 2018).
Viscosity can then be converted into bulk diffusivity using the Stokes-Einstein equation: where k is the Boltzmann constant (1.38 × 10 −23 J K −1 ), T is the temperature (K), and a is the effective molecular radius (m). This relation, however, may not be accurate for very high viscosities and needs to be corrected with the fractional Stokes-Einstein (FSE) relation (Evoy et al., 2019): where ξ is an empirical fit parameter with the value of 0.93 (Evoy et al., 2019), η c is the crossover viscosity with the value showing that lower and higher κ would lead to higher and lower viscosity, respectively.
Isoprene photooxidation in chamber experiments was conducted with very high precursor concentrations and a short reaction time such that a traditional gas-phase oxidation scheme dominates, which can be captured well in GECKO-A (Aumont et al., 2005). Note that the formation of isoprene epoxydiols (IEPOX) (Paulot et al., 2009;Bates et al., 2014) and subsequent 195 uptake of IEPOX into acidic particles followed by a series of multiphase reactions including the formation of oligomers and organosulfates (Riva et al., 2019) are found to be important in the ambient atmosphere (Wennberg et al., 2018). The uptake of IEPOX can be limited by bulk diffusion in a viscous matrix  and IEPOX-SOA is reported to have high viscosity (Riva et al., 2019). For viscosity simulations of atmospherically relevant IEPOX-derived SOA, IEPOX multiphase processes would need to be treated in future studies. are about three to four orders of magnitude lower than measurements.

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The simulated T g,org are within 255-285 K (see Table 1), which is in good agreement with a previous estimation of 278 K viscosity; for lower mass loadings, condensation of lower volatility compounds with higher T g would be dominant, resulting in higher viscosity.

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The GECKO-A box model tracks the concentrations of species both in the gas and particle phases, while retaining information on molecular properties including molar mass, O:C ratio, vapor pressure, and volatility or pure compound saturation mass concentration (C 0 ). Figure 4 shows most abundant particle-phase 500 compounds in simulated isoprene and α-pinene SOA products in the 2-dimensional volatility basis set framework of O:C ratio vs. log C 0 (Donahue et al., 2011). The markers are color-coded with T g and the marker size is scaled with particle-phase concentration in each simulation. Compounds with lower 235 volatility tend to have higher O:C ratio and higher T g , in good agreement with recent experimental and model studies (Zhang et al., 2019;Li et al., 2020). Isoprene oxidation products are found to have higher O:C ratio, while α-pinene oxidation products have lower C 0 and higher T g . Note that, dark ozonolysis experiments of α-pinene have been conducted with an OH scavenger, which may contribute to lower O:C ratios for α-pinene ozonolysis products in the absence of OH oxidation. These results are in line with higher viscosity of α-pinene SOA compared to isoprene SOA, as measured and modeled in Figs. 1 and 2.

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Our method to estimate T g of organic compounds and SOA viscosity are based on elemental composition without accounting for molecular structure and specific intramolecular interactions. Some organic compounds with reactive functional groups may undergo particle-phase reactions, which are not treated in our simulations. To explore these aspects, we investigate the autoxidation to form highly oxygenated organic molecules (HOMs) nor gas-phase dimerization reactions of peroxy radicals, which are recently found to play a significant role in SOA formation and growth (Bianchi et al., 2019). These higher molar mass compounds with very low volatility have higher T g , hence leading to higher SOA viscosity Zhang et al., 2019;Champion et al., 2019;Li et al., 2020). While the extent of effects of these processes may vary among reaction conditions applied in each experiment, the lack of treatment of these processes may be another plausible reason of lower simulated 265 viscosity compared to experimental measurements.

Effects of mass accommodation
All the above simulations were conducted with mass accommodation coefficient equal to unity. Hereby, we investigate poten-  α when RH < 40 %; for example, at 40 % RH the simulated SOA viscosity is ∼10 4 Pa s with α = 1, while it is ∼10 8 Pa s with α = α eff . This large difference stems from a stark reduction of α eff for semivolatile compounds in a glassy solid matrix, which would prevent condensation of semi-volatile compounds with relatively low T g ; α eff for low volatile compounds with higher T g remains still close to unity allowing condensation, resulting in solidification of SOA particles.
This effect is reflected on the low simulated SOA mass loading of Kidd's experiments. When α = α eff the simulated SOA  (Table 1), resulting in larger effects of mass loadings and hence mass accommodation.
As viscosity measurements were not conducted at lower RH in Kidd et al. (Kidd et al., 2014) and time evolution of SOA mass 290 concentrations and viscosity are unavailable for both studies, it is hard to fully resolve impacts of mass accommodation in this study; we intend to investigate this aspect in a follow-up study.
We applied the T g parameterizations and viscosity prediction method in the GECKO-A box model to simulate the evolution of viscosity and composition of SOA generated via α-pinene and isoprene oxidation. A range of simulations were performed 295 with experimental conditions applied for viscosity measurements in order to explore various effects such as chemical composition, relative humidity, mass loadings, and mass accommodation coefficient on SOA viscosity. Simulated viscosities are consistent with the observed RH-dependence of viscosity for α-pinene and isoprene SOA, demonstrating the robustness of our viscosity prediction method. Simulated viscosity values for isoprene SOA are in good agreement with measurements, while those for α-pinene SOA were by a few orders of magnitude lower than experimental measurements. The simulated chemical 300 composition and functional group distributions indicate that α-pinene SOA contain substantial amounts of aldehydes, ketones, and carboxylic acids. These compounds are reactive and may undergo dimerization and oligomerization reactions. In addition, GECKO-A does not treat detailed chemistry involving stabilized Criegee intermediates, autoxidation and gas-phase dimerization by peroxy radicals. These processes are known to lead to the formation of high molecular mass compounds that would increase viscosity of SOA. Moreover, the model assumes that gas-particle partitioning of organics follows Raoult's law with 305 ideal mixing conditions. The implementation of these processes are warranted in future studies for better representation of SOA chemical composition and viscosity.
Experiments were conducted to form SOA under dry conditions followed by water exposure for viscosity measurements and it was unnecessary to consider uptake of water into the condensed phase upon SOA formation. Previous studies have suggested that water vapor can significantly affect the composition of SOA. At higher RH water vapor interacts with Criegee 310 intermediates, leading to production of carboxylic acids or aldehydes and ketones via decomposition routes (Kristensen et al., 2014). Kidd et al. (Kidd et al., 2014) have reported that as the RH at which the SOA is formed increases, there is a decrease in viscosity, accompanied by an increasing contribution from carboxylic acids and a decreasing contribution from higher molecular mass products. These aspects including chemistry of Criegee intermediates and water uptake should be a subject of future studies for simulating particle viscosity under humid conditions. 315 We have also explored the effects of kinetic partitioning by accounting for reduction of mass accommodation coefficient in a semisolid or viscous phase. The simulation results suggest that kinetic limitations in the particle phase would result in a decrease in SOA mass loading and an increase in viscosity due to suppression of condensation of semi-volatile compounds. It is still challenging to accurately assess the extent of this effect on viscosity due to the lack of experimental data for comparison and to the absence of some chemical processes in our modeling method. Future experiments with simultaneous measurements 320 of chemical composition in the gas and particle phases as well as particle viscosity under different RH conditions will be enormously helpful to further improve and constrain the model. While this study simulated viscosity of pure organic particles, future studies should also investigate viscosity of inorganic-organic particles and effects of non-ideal interactions including phase separation (Zuend and Seinfeld, 2012;You et al., 2014) and gel formation (Richards et al., 2020). The developed model in this study is a useful tool for further exploration of phase state of atmospherically relevant SOA and it should also be useful 325 in refining the representation of SOA chemical evolution and phase state in regional and global air quality models.
GECKO-A and box models and provided a training on the tools. YL developed the Tg parameterizations. TG and MS wrote the manuscript with contributions from all coauthors.
Competing interests. The authors declare that they have no conflict of interest.
Data availability. The simulation data may be obtained from the corresponding author upon request.