Mass accommodation and gas–particle partitioning in secondary organic aerosols: dependence on diffusivity, volatility, particle-phase reactions, and penetration depth

Mass accommodation is an essential process for gas–particle partitioning of organic compounds in secondary organic aerosols (SOA). The mass accommodation coefficient is commonly described as the probability of a gas molecule colliding with the surface to enter the particle phase. It is often applied, however, without specifying if and how deep a molecule has to penetrate beneath the surface to be regarded as being incorporated into the condensed phase (adsorption vs. absorption). While this aspect is usually not critical for liquid particles with rapid surface–bulk exchange, it can be important for viscous semi-solid or glassy solid particles to distinguish and resolve the kinetics of accommodation at the surface, transfer across the gas–particle interface, and further transport into the particle bulk. For this purpose, we introduce a novel parameter: an effective mass accommodation coefficient αeff that depends on penetration depth and is a function of surface accommodation coefficient, volatility, bulk diffusivity, and particlephase reaction rate coefficient. Application of αeff in the traditional Fuchs–Sutugin approximation of mass-transport kinetics at the gas–particle interface yields SOA partitioning results that are consistent with a detailed kinetic multilayer model (kinetic multilayer model of gas–particle interactions in aerosols and clouds, KM-GAP; Shiraiwa et al., 2012) and two-film model solutions (Model for Simulating Aerosol Interactions and Chemistry, MOSAIC; Zaveri et al., 2014) but deviate substantially from earlier modeling approaches not considering the influence of penetration depth and related parameters. For highly viscous or semi-solid particles, we show that the effective mass accommodation coefficient remains similar to the surface accommodation coefficient in the case of low-volatility compounds, whereas it can decrease by several orders of magnitude in the case of semi-volatile compounds. Such effects can explain apparent inconsistencies between earlier studies deriving mass accommodation coefficients from experimental data or from molecular dynamics simulations. Our findings challenge the approach of traditional SOA models using the Fuchs–Sutugin approximation of mass transfer kinetics with a fixed mass accommodation coefficient, regardless of particle phase state and penetration depth. The effective mass accommodation coefficient introduced in this study provides an efficient new way of accounting for the influence of volatility, diffusivity, and particle-phase reactions on SOA partitioning in process models as well as in regional and global air quality models. While kinetic limitations may not be critical for partitioning into liquid SOA particles in the planetary boundary layer (PBL), the effects are likely important for amorphous semi-solid or glassy SOA in the free and upper troposphere (FT–UT) as well as in the PBL at low relative humidity and low temperature. Published by Copernicus Publications on behalf of the European Geosciences Union. 1566 M. Shiraiwa and U. Pöschl: Effective mass accommodation and gas–particle partitioning


Abstract. 11
Mass accommodation is an essential process for gas-particle partitioning of organic compounds in 12 secondary organic aerosols (SOA). The mass accommodation coefficient is commonly described 13 as the probability of a gas molecule colliding with the surface to enter the particle phase. It is often 14 applied, however, without specifying if and how deep a molecule has to penetrate beneath the 15 surface to be regarded as incorporated into the condensed phase (adsorption vs. absorption). While 16 this aspect is usually not critical for liquid particles with rapid surface-bulk exchange, it can be 17 important for viscous semisolid or glassy solid particles to distinguish and resolve the kinetics of 18 accommodation at the surface, transfer across the gas-particle interface, and further transport into 19 the particle bulk. 20 For this purpose, we introduce a novel parameter: an effective mass accommodation coefficient 21 aeff that depends on penetration depth and is a function of surface accommodation coefficient, 22 volatility, bulk diffusivity, and particle-phase reaction rate coefficient. Application of aeff in the 23 traditional Fuchs-Sutugin approximation of mass-transport kinetics at the gas-particle interface For highly viscous or semisolid particles, we show that the effective mass accommodation 29 coefficient remains similar to the surface accommodation coefficient in case of low-volatile 30 compounds, whereas it can decrease by several orders of magnitude in case of semi-volatile 31 compounds. Such effects can explain apparent inconsistencies between earlier studies deriving 32 mass accommodation coefficients from experimental data or from molecular dynamics 33

simulations. 34
Our findings challenge the approach of traditional SOA models using the Fuchs-Sutugin 35 approximation of mass transfer kinetics with a fixed mass accommodation coefficient regardless 36 of particle phase state and penetration depth. The effective mass accommodation coefficient 37 introduced in this study provides an efficient new way of accounting for the influence of volatility, 38 diffusivity, and particle-phase reactions on SOA partitioning in process models as well as in 39 regional and global air quality models. 40 41 https://doi.org/10.5194/acp-2020-536 Preprint. Discussion started: 7 July 2020 c Author(s) 2020. CC BY 4.0 License.

Introduction. 42
Secondary organic aerosols (SOA) are major constituents of atmospheric particulate 43 matter, affecting air quality, climate, and public health (Jimenez et  oxidants such as ozone and OH radicals lead to the formation and growth of SOA (Kroll and 47 Seinfeld, 2008). The oxidation of VOC forms a myriad of semi-volatile (SVOC) and low volatility 48 organic compounds (LVOC) that can condense on pre-existing particles (Ziemann and Atkinson,49 2012) or contribute to nucleation and new particle formation (Tröstl et al., 2016). The evolution of 50 SOA is a complex multi-step process that involves chemical reactions and mass trnsport in the gas 51 phase, at the particle surface and in the particle bulk, but the interplay of these processes and the 52 rate-limiting steps in SOA formation have not yet been fully resolved/elucidated (Shiraiwa et al., 53 2014). 54 Traditionally, SOA particles were assumed to be homogeneous and well-mixed quasi-55 liquid droplets (Pankow, 1994). As demonstrated by recent atmospheric measurements and 56 laboratory experiments, they can adopt glassy solid or amorphous semi-solid phase states,  The formation and properties of SOA are large sources of uncertainty in the current 69 understanding of global air quality, climate change, and public health. The development of SOA 70 models is among the most challenging problems in atmospheric chemistry (Tsigaridis et al., 2014). 71 In most current air quality, atmospheric chemistry and climate models, the limiting step of SOA 72 https://doi.org/10.5194/acp-2020-536 Preprint. Discussion started: 7 July 2020 c Author(s) 2020. CC BY 4.0 License. condensed phase (adsorption vs. absorption). This aspect is usually not critical for liquid droplets 133 with rapid surface-bulk exchange, fast bulk diffusion, and swift equilibration between the 134 condensed phase and the surrounding gas phase. For viscous or solid particles, however, it can be 135 essential to distinguish and resolve the kinetics of surface and bulk processes, including 136 accommodation at the surface, transfer across the gas-particle interface, and further transport into 137 the particle bulk (Kolb et al., 2010;Pöschl et al., 2007;. 138 Building on the PRA kinetic model framework (Pöschl et al., 2007)  Here w (cm s -1 ) is the mean thermal velocity of the organic compound in the gas phase, 5 (cm 2 145 s -1 ) is its diffusivity in the condensed phase, ! (g cm -3 ) is the particle density, and x (cm) is the 146 penetration depth. The scaling factor 10 -12 (g cm -3 )/(µg m -3 ) allows for inserting C 0 in the 147 commonly used units of µg m -3 ; it can be omitted when C 0 is inserted in g cm -3 or when all 148 quantities are inserted with standard SI units (cgs or mks system of units). 149 The surface accommodation coefficient as, which corresponds to a(0) with the penetration 150 depth of 0, is the probability for a gas molecule Z colliding with the surface not to be immediately 151 scattered back to the gas phase but to be accommodated at the surface for period longer than the 152 duration of an elastic scattering process (Pöschl et al., 2007). Various equivalent, similar or closely 153  Using the two-film theory of mass transfer between gas and particle phase, Zaveri et al. 174 (2014) showed that the effects of a concentration gradient in the particle can be represented by a 175 thin film adjacent to the surface with the following thickness or effective penetration depth for 176 non-reactive partitioning and reactive uptake, respectively: 177 9:: = ! / 5 (non-reactive partitioning) (6) 178 9:: = ! ( ) 8 ; where Q is the ratio of the average particle-phase concentration to the surface concentration at 180 steady state and is a dimensionless diffusion-reaction parameter (Seinfeld and Pandis, 2016): 181 Note that A is the ratio of the particle radius to the so-called reacto-diffusive length, (Db/kb) 0.5 , 184 representing the characteristic depth to which a species can penetrate while reacting in the particle 185 bulk (Pöschl et al., 2007;Worsnop et al., 2002). 186 By inserting 9:: in equation (5), we obtain an effective mass accommodation coefficient 187 that accounts for the influence of penetration depth and its dependence on the diffusivity and 188 reactivity of the investigated chemical species in the particle:

213
For liquid particles with fast surface-bulk exchange and bulk diffusion (Db = 10 -7 cm 2 s -1 ), 214 a(x) remains close to as = a(0) = 1, and all models yield the same result of fast mass transfer from 215 the gas to particle phase and equilibration within one second. For semi-solid particles with Db = 216 10 -15 cm 2 s -1 , however, the temporal evolution of the SVOC gas-phase and particle-phase According to KM-GAP (black line), the initial uptake of SVOC by the semisolid particle 220 phase is as fast as approximated by F-S with a = ass = aZ(d) = 3´10 -2 corresponding to a 221 penetration depth of only one molecular length (monolayer) below the particle surface. After one 222 second, however, the KM-GAP uptake is limited by bulk diffusion and slows down substantially. 223 After about one hour, KM-GAP converges with the F-S approximation using a = aeff = a(rp/5) = 224 8´10 -4 . Notably, the F-S approximation with aeff is identical to the MOSAIC approximation,

225
although the latter is based on different rate equations using a unity mass accommodation 226 coefficient like KM-GAP (as = 1) and a two-film approach of bulk diffusion .  volatility are more strongly affected by particle phase state and diffusivity is that they are more 271 likely to desorb back to the gas phase when diffusion into the bulk is slow. Compounds with lower 272 volatility exhibit much lower desorption rates and are less likely to re-evaporate even if their 273 diffusion into the bulk is slow. On the other hand, the influence of particle phase state and 274 diffusivity increases with particle size because longer pathways of diffusion are required for 275 effective accommodation, penetration, and absorption of gas molecules into larger particles as 276 illustrated in Figures 3c and 3d. 277 The theoretically predicted influence of volatility on effective mass accommodation is 278 consistent with a recent experimental study of a-pinene SOA reporting that the observed mass 279 accommodation coefficients decreased from ~1 for low-volatile compounds to ~0.3 for semi-280 and diffusivity, which can lead to a substantial decrease of aeff relative to as in semi-solid particles.

300
With regard to the dependence of aeff on C 0 , mixing effects and non-ideality may lead to deviations 301 between C 0 and C* (Zuend and Seinfeld, 2012), which should be taken into account in further 302 investigations of mass accommodation and its influence on the formation and growth of SOA 303

particles. 304
On the other hand, high reactivity can compensate the influence of low diffusivity and mass 305 transport limitations in the particle phase, keeping aeff close to as. In case of non-reactive 306 partitioning, the effective penetration depth used to calculate aeff is one fifth of the particle radius, i.e., 9:: / ! = 0.2 (Eq. 6). In case of reactive uptake, however, 9:: decreases with increasing 308 reactivity and with decreasing diffusivity according to Eqs. (7) to (9). Figure 5a illustrates how the 309 effective penetration depth normalized by particle radius, 9:: / ! , decreases with increasing first-310 order bulk reaction rate coefficient, kb, and with decreasing diffusion coefficient, Db. The reduced 311 effective penetration depths at high kb and low Db reflect that reactive uptake by semisolid particles 312 proceeds mainly through chemical reaction near the surface (Shiraiwa et al., 2013a). Figure 5b  313 illustrates how aeff depends on volatility and diffusivity for reactive uptake with as = 1 and a first-  We suggest that aeff and its dependence on penetration depth and related parameters should 331 be applied and considered when the F-S approximation is used to investigate and simulate gas-332 particle interactions in viscous or semi-solid organic aerosols. The simple parameterization can be 333 incorporated into regional and global models for a more realistic representation of SOA processes 334 in the atmosphere, which seems particularly important with regard to the ubiquity of amorphous 335 semi-solid or glassy particles predicted for the free troposphere as well as planetary boundary layer 336 air at low relative humidity and low temperature (Maclean et al., 2017;Shiraiwa et al., 2017). 337 In the analysis and interpretation of SOA chamber and laboratory experiments, aeff 338 provides a simply way of accounting for the potential impact of volatility, diffusivity, and particle 339 phase state on the kinetics of gas-particle partitioning for analysis and interpretation of chamber 340 experiments. In particular, it may help to address and resolve apparent inconsistencies between the 341 definitions and parameter values of mass accommodation coefficients that are derived from 342 experimental data and from molecular dynamics simulations. 343 At short timescales, however, aeff is not sufficient to properly describe the kinetics of gas- compounds Z (as = 1, w = 2´10 4 cm s -1 ) with liquid, semi-solid, or solid aerosol particles (r p = 1 383 g cm -3 ) depending on pure compound volatility, C 0 , particle bulk diffusivity, Db (corresponding to 384 viscosity, h), and particle radius, rp: aeff calculated as a function of Db for C 0 = 10 -5 to 10 5 µg m -3 385 with rp = 100 nm (a); aeff calculated as a function of C 0 and Db with rp = 100 nm (b) and 10 µm 386 (d); aeff calculated as a function of particle radius for Db =10 -15 cm 2 s -1 and different levels of   Figure A1 illustrates the applied kinetic multi-layer model framework, in which the 420 structure and composition of a particle are described by a sorption layer (s), a quasi-static surface 421 layer (ss), multiple bulk layers (b), and any volatile, semi-volatile, or low-volatile chemical species 422 (Z) that can undergo gas-particle partitioning and transport between the different layers and  The first-order rate coefficients of adsorption and desorption are given by ka = αs w / 4 and kd = 453 1/td, respectively, where w (cm s -1 ) is the mean thermal velocity of Z in the gas phase and td is the  In analogy, the first-order rate coefficient kbx,ss can be estimated based on the Fick's first law of 467 diffusion, considering that a molecule Z at penetration depth x in the bulk needs to travel a distance 468 of x -d to move into the quasi-static surface layer (Fig. A1) where C 0 (µg m -3 ) is the pure compound saturation mass concentration, C g and C P (µg m -3 ) are the 476 gas-phase and particle-phase mass concentrations of the compound Z, respectively, and COA (µg where M is the molar mass of compound Z. [Z]g,eq is the equilibrium (saturation) number 481 concentration of Z in the gas phase.
[Z]g,eq can be calculated using the saturation vapor pressure p: 482 [Z]g,eq = p NA / (R T) where NA is the Avogadro number, R is the gas constant, and T is the 483 temperature.
[Z]b,eq corresponds to the ratio between the number concentration of Z in the particle 484 phase (per m 3 of air) to the particle volume concentration (m 3 per m 3 of air), which can be 485 expressed using CZ PM and COA with the particle density rP (g cm -3 ):