Influence of seed aerosol surface area and oxidation rate on vapor wall deposition and SOA mass yields : a case study with α-pinene ozonolysis

Laboratory chambers, invaluable in atmospheric chemistry and aerosol formation studies, are subject to particle and vapor wall deposition, processes that need to be accounted for in order to accurately determine secondary organic aerosol (SOA) mass yields. Although particle wall deposition is reasonably well understood and usually accounted for, vapor wall deposition is less so. The effects of vapor wall deposition on SOA mass yields in chamber experiments can be constrained experimentally by increasing the seed aerosol surface area to promote the preferential condensation of SOA-forming vapors onto seed aerosol. Here, we study the influence of seed aerosol surface area and oxidation rate on SOA formation in α-pinene ozonolysis. The observations are analyzed using a coupled vapor–particle dynamics model to interpret the roles of gas–particle partitioning (quasi-equilibrium vs. kinetically limited SOA growth) and α-pinene oxidation rate in influencing vapor wall deposition. We find that the SOA growth rate and mass yields are independent of seed surface area within the range of seed surface area concentrations used in this study. This behavior arises when the condensation of SOA-forming vapors is dominated by quasi-equilibrium growth. Faster α-pinene oxidation rates and higher SOA mass yields are observed at increasing O3 concentrations for the same initial α-pinene concentration. When the α-pinene oxidation rate increases relative to vapor wall deposition, rapidly produced SOA-forming oxidation products condense more readily onto seed aerosol particles, resulting in higher SOA mass yields. Our results indicate that the extent to which vapor wall deposition affects SOA mass yields depends on the particular volatility organic compound system and can be mitigated through the use of excess oxidant concentrations.

SOA formation in α-pinene ozonolysis. The observations are analyzed using a coupled 23 vapor-particle dynamics model to interpret the roles of gas-particle partitioning (quasi-24 equilibrium vs. kinetically-limited SOA growth) and α-pinene oxidation rate in 25 influencing vapor wall deposition. We find that the SOA growth rate and mass yields are 26 independent of seed surface area within the range of seed surface area concentrations 27 used in this study. This behavior arises when the condensation of SOA-forming vapors is 28 dominated by quasi-equilibrium growth. Faster α-pinene oxidation rates and higher SOA 29 mass yields are observed at increasing O 3 concentrations for the same initial α-pinene 30 concentration. When the α-pinene oxidation rate increases relative to vapor wall 31 deposition, rapidly produced SOA-forming oxidation products condense more readily 32 onto seed aerosol particles, resulting in higher SOA mass yields. Our results indicate that 33 the extent to which vapor wall deposition affects SOA mass yields depends on the 34

Introduction 37
Secondary organic aerosol (SOA), formed from the oxidation of volatile and 38 intermediate volatility organic compounds (VOCs and IVOCs), contributes a significant 39 fraction of the global organic aerosol burden (Kanakidou et al., 2005;Hallquist et al., 40 2009;Tsigaridis et al., 2014). SOA formation studies, which are typically conducted in 41 laboratory chambers in the presence of seed aerosol particles, provide fundamental data 42 that can be used to predict the rate of atmospheric SOA formation. An essential 43 parameter of interest in laboratory chamber studies is the SOA mass yield (Y), which is 44 defined as the ratio of mass concentration of SOA formed to mass concentration of parent 45 hydrocarbon reacted ((ΔHC), Y = ΔM o /ΔHC (Odum et al., 1996;Odum et al., 1997a;46 Odum et al., 1997b)). The measured SOA mass yields can subsequently be applied in 47 atmospheric models to predict regional and global organic aerosol burdens. In order to 48 obtain accurate SOA mass yields from the evolving aerosol size distribution in chamber 49 experiments, the loss of both particles and vapors to the chamber walls needs to be 50 accurately accounted for (Crump and Seinfeld, 1981;McMurry and Grosjean, 1985;51 McMurry and Rader, 1985;Cocker et al., 2001a;Weitkamp et al., 2007;Pierce et al., 52 2008;Hildebrandt et al., 2009;Loza et al., 2010;Matsunaga and Ziemann, 2010;Loza et 53 al., 2012;Kokkola et al., 2014;McVay et al., 2014;Yeh and Ziemann, 2014;Zhang et 54 al., 2014;Yeh and Ziemann, 2015;Zhang et al., 2015a;La et al., 2016). 55 The mechanisms by which particles in chambers deposit on chamber walls are 56 reasonably well understood. Particles are transported to the boundary layer on the 57 chamber walls via diffusion, gravitational settling, and electrostatic forces (Crump and 58 Seinfeld, 1981;McMurry and Grosjean, 1985;McMurry and Rader, 1985;Pierce et al., 59 2008). The rate at which particles are transported to the edge of the boundary layer is 60 dictated primarily by mixing conditions in the chamber. An effective approach for 61 characterizing particle wall loss involves measuring the size-dependent wall loss rates of 62 polydisperse inert seed aerosol (e.g. ammonium sulfate particles) injected into the 63 chamber during seed-only experiments (Keywood et al., 2004;Pierce et al., 2008). The particles is kinetically limited (i.e., the timescale for gas-particle equilibrium is 95 competitive with or greater than the timescale for reaction and vapor-wall deposition). In 96 addition to the seed aerosol surface area, VOC oxidation rate may also play an important 97 role in the effect of vapor wall loss on SOA formation. Ng et al. (2007) showed that the 98 SOA mass yields from m-xylene photooxidation are dependent on the oxidation rate, with 99 higher OH concentrations (hence faster oxidation rates) resulting in higher SOA mass 100 yields. It was suggested that the "oxidation rate effect" could arise as a result of 101 competition between growing particles and chamber walls for condensable VOC 102 oxidation products . However, McVay et al. (2016) reported similar SOA 103 growth at low and high OH concentrations in α-pinene photooxidation. Taken together, 104 these studies show the importance of understanding how gas-particle partitioning and 105 VOC oxidation rate impact vapor-wall deposition and SOA mass yields in laboratory 106 chamber experiments. 107 In this study, we examine the influence of seed aerosol surface area and oxidation 108 rate on SOA formation in α-pinene ozonolysis chamber experiments. α-pinene is the most 109 abundant monoterpene, with global emissions estimated to be ~66 Tg yr -1 (Guenther et 110 al., 2012). Ozonolysis is the major atmospheric oxidation pathway of α-pinene, and is 111 estimated to account for reaction of ~46 % of emitted α-pinene 112 Capouet et al., 2008). α-pinene ozonolysis, a major source of atmospheric SOA on both 113 regional and global scales (Kanakidou et al., 2005;Hallquist et al., 2009;Carlton et al., 114 2010;Pye et al., 2010), has been the subject of numerous studies (Hoffmann et al., 1997;115 Griffin et al., 1999;Cocker et al., 2001b;Gao et al., 2004;Presto et al., 2005;Presto and 116 Donahue, 2006;Pathak et al., 2007a;Pathak et al., 2007b;Song et al., 2007;Shilling et 117 al., 2008;Henry et al., 2012;Ehn et al., 2014;Kristensen et al., 2014;Zhang et al., 118 2015b). Here, we measure the α-pinene SOA mass yield as a function of seed aerosol 119 surface area concentration (0 to 3000 µm 2 cm -3 ) and O 3 mixing ratio (100 vs. 500 ppb). 120 These results are analyzed using a coupled vapor-particle dynamics model to evaluate the 121 roles of gas-particle partitioning and VOC oxidation rate in influencing vapor-wall 122 deposition effects on the measured SOA mass yields. 123

Particle wall deposition correction 171
Particle wall deposition needs to be accounted for to determine the SOA mass 172 concentration in the chamber. Two limiting assumptions have traditionally been made 173 regarding interactions between particles deposited on the chamber walls and suspended 174 vapors when accounting for particle wall loss in the computation of SOA mass yields 175 (Weitkamp et al., 2007;Hildebrandt et al., 2009;Loza et al., 2012;. 176 The first case assumes that particles deposited on the walls cease to interact with 177 suspended vapors, and therefore the SOA mass present on these deposited particles does 178 not change after deposition (Loza et al., 2012;. Adding the SOA mass 179 present on these deposited particles to that present on the suspended particles provides a 180 lower bound of the total SOA mass concentration. In the second case, it is assumed that 181 particles deposited on the walls continue to interact with suspended vapors as if these 182 particles had remained suspended, and therefore the SOA mass present on these 183 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 4 April 2016 c Author(s) 2016. CC-BY 3.0 License. deposited particles increases at the same rate as those suspended (Hildebrandt et al., 184 2009;Weitkamp et al., 2007). Thus, this case provides an upper bound of the total SOA 185 mass concentration due to the additional uptake of suspended vapors to wall-deposited 186 particles. However, it must be kept in mind that the calculated SOA mass concentration 187 can be underestimated even in the upper bound case since the calculation accounts 188 neither for differences in the vapor-particle and vapor-wall interaction and transport 189 timescales nor for the significantly larger amount of absorbing mass of the chamber walls 190 (relative to the deposited particles) for suspended vapors (McVay et al., 2014;Zhang et 191 al., 2014;McVay et al., 2016). 192 In this study, we calculate SOA mass yields using the lower bound of the total 193 SOA mass concentration obtained from SMPS measurements, which has been described 194 in detail previously (Loza et al., 2012), and will be reviewed briefly here. For each 195 particle size bin i at each time increment Δt, the particle number distribution deposited on 196 the wall (n w,i,j ) is: 197 (1) 198 where n s,i,j is the suspended particle number distribution in particle size bin i at time step 199 j, Δt is the difference between time step j and time step j + 1, and β i is the size-dependent 200 first-order exponential wall loss rate obtained from seed-only experiments. The particle 201 wall loss corrected number distribution (n total,i,j ) is obtained from the sum of the particle 202 number distribution of deposited particles (n w,i,j ) and suspended particles (n s,i,j ): 203 Assuming spherical particles, the particle wall loss corrected volume concentration 205 (V total,j ) is: 206 where m is the number of particle size bins, D p,i+ and D p,i-are the upper and lower limits 208 for size bin i, respectively, and D p,i is the median particle diameter for size bin i. The term 209 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 4 April 2016 c Author(s) 2016. CC-BY 3.0 License. D p,i ln10 is needed to convert from a lognormal distribution. Figures S1-S4 and Table S1  210 show results from the particle wall loss correction. To calculate the SOA mass 211 concentration (ΔM o,j ), the SOA density (ρ org ) is multiplied by the difference of the 212 particle wall loss corrected volume concentration (V total,j ) and the initial seed volume 213 concentration (V seed ): 214 The measured densities of the α-pinene SOA are 1.39 and 1.37 g cm -3 for the 100 and 500 216 ppb O 3 experiments, respectively, and are within the range (i.e., 1.19 to 1.52 g cm -3 ) 217 reported in previous α-pinene ozonolysis studies (Bahreini et al., 2005;Kostenidou et al., 218 2007;Song et al., 2007;Shilling et al., 2009). 219 3. Vapor-particle dynamics model 220 A coupled vapor-particle dynamics model is used to evaluate the influence of seed 221 aerosol surface area and oxidation rate on SOA formation in the α-pinene ozonolysis 222 chamber experiments. This model is similar to that used in McVay et al. (2014), and will 223 be briefly described here. Parameters from the experimental data (temperature, pressure, 224 initial α-pinene concentration) are used as model inputs. The initial size distribution is set 225 to that measured by the SMPS, with the exception of the two nucleation experiments. 226 Because nucleation is not explicitly simulated, an approximation is used in which the 227 smallest diameter bin is initialized with the total number of particles measured at the end 228 of the experiment (see Table S1). In each simulation, the decay of α-pinene, the 229 consumption of O 3 , the SOA mass concentration, and the SOA mass yield are calculated 230 throughout the duration of the experiment. We assume a linear injection rate of O 3 based 231 on the time required to inject the desired O 3 concentration. For example, O 3 is injected at 232 a rate of 500/54.25 ppb min -1 for the first 54.25 min during the 500 ppb O 3 experiments. 233 O 3 simultaneously decays by reaction with α-pinene at a rate constant of 9.4 × 10 -17 cm 3 234 molec. -1 s -1 (Saunders et al., 2003). The O 3 +α-pinene reaction is assumed to occur in a 235 well-mixed chamber and produces 5 classes of first-generation products, which are 236 grouped according to mass saturation concentrations, similar to the volatility basis set 237 (Donahue et al., 2006): >10 3 (assumed to be completely volatile), 10 2 , 10, 1 and 0.1 µg 238 m -3 . Branching ratios between these products are optimized to fit the experimental data. 239 These branching ratios cannot be compared directly to previously reported VBS 240 parameters for α-pinene ozonolysis (e.g., Henry et al. (2012)) since VBS parameters are 241 typically mass-based, while the branching ratios in the model are mole-based. 242 Furthermore, the branching ratios here account for the influence of vapor wall deposition, 243 while typical VBS parameters do not. We assume that these 5 classes of products have 244 molecular weights 168,184,192,200 and 216 g mole -1 based on the group contribution 245 method (Donahue et al., 2011). The first-generation products are assumed not to undergo 246 further reaction with O 3 upon formation. 247 The aerosol dynamics in the chamber obey the aerosol general dynamic equation 248 (Seinfeld and Pandis, 2006): 249 Coagulation is not considered, since an alternative version of the model including 251 coagulation showed no change in the predicted α-pinene ozonolysis SOA mass 252 concentrations in simulations with and without coagulation. The change in particle 253 number distribution due to particle wall loss is: 254 where, as noted in section 2.2, β j (D p ) is the size-dependent first-order wall loss rate 256 coefficient obtained from fitting seed-only experiments. The rate at which vapor 257 condenses onto a spherical aerosol particle is: 258 where G i is the concentration of gas-phase species i, G i eq is the saturation concentration 260 of gas-phase species i, D i is the gas-phase molecular diffusivity (assumed to be 3 × 10 -6 261 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. where α p is the vapor-particle mass accommodation coefficient, and Kn is the Knudsen 265 number, Kn = 2λ AB /D p . The vapor-particle mass accommodation coefficient accounts for 266 any resistance to vapor molecule uptake at the particle surface (e.g. surface 267 accommodation and particle-phase diffusion limitations). λ AB is the mean free path of the 268 gas-phase species, which is: 269 where R is the ideal gas constant, T is the temperature, and M i is the molecular weight of 271 diffusing gas-phase molecule i. For each particle size bin, Eqs. 7-9 are used to compute 272 the flux of each gas-phase species to and from an aerosol particle, scaled by the particle 273 number concentration in the size bin. The net rate of change for each gas-phase species 274 due to evaporation or condensation is obtained from the total flux summed over all the 275 particle size bins. 276 G i eq varies for each particle size bin because it depends on the mass concentration 277 of species i and the total organic mass concentration in the size bin: 278 where A i is the concentration of species i in the particle phase, C i * is the saturation 280 The oxidation products of α-pinene ozonolysis are assumed to be subject to 285 vapor-wall deposition, which is simulated using a first-order wall-loss coefficient 286 (McMurry and Grosjean, 1985): 287 where A/V is the surface area-to-volume ratio of the chamber (estimated to be 2.5 m -1 ), 289 α wall is the vapor-wall mass accommodation coefficient, and k e is the eddy diffusion 290 coefficient that describes mixing conditions in the chamber. Based on the measured size-291 dependent particle wall loss rates (method is described in ), k e is 292 estimated to be 0.03 s -1 for the GTEC chamber. Vapor-wall deposition is assumed to be 293 reversible, and the rate constant of vapor desorption from the chamber walls is: 294 where C w is the equivalent organic mass concentration in the wall (designated to treat 296 gas-wall partitioning in terms of gas-particle partitioning theory and not necessarily 297 representative of a physical layer of organic concentration on the wall (Matsunaga and 298 Ziemann, 2010)), K w is the gas-wall partitioning coefficient, M w is the effective molecular 299 weight of the wall material, γ w is the activity coefficient of the species in the wall layer, 300 M p is the average molecular weight of organic species in the particle, and γ p is the activity 301 coefficient of the species in the particle. For simplicity, we assume that M w = M p and γ w = 302 γ p . C w is set to 10 mg m -3 based on previous inferences by Matsunaga and Ziemann 303 (2010). Sensitivity studies (not shown) show no change in model predictions when 304 varying C w above C w = 0.1 mg m -3 . 305 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 4 April 2016 c Author(s) 2016. CC-BY 3.0 License.
In the initial version of the model, after all the α-pinene is consumed, vapor wall 306 deposition was assumed to continue to deplete the gas-phase oxidation products and 307 aerosol mass evaporates to maintain gas-particle equilibrium. SOA evaporation was not 308 observed experimentally (i.e., the SOA mass concentration does not decrease 309 significantly over time after peak SOA growth has been achieved in these chamber 310 experiments (Fig. 2)). In order to represent these observations in the model, a first-order, 311 particle-phase reaction is introduced by which aerosol species are converted into non-312 volatile absorbing organic mass with a timescale of τ olig . This mechanism (which is not 313 included in the model used in McVay et al. (2014)) is similar to that used by the 314 sequential equilibrium partitioning model, in which aerosol is converted from an 315 absorbing to non-absorbing, non-volatile phase in order to explain the inhibited diffusion 316 and evaporation observed in α-pinene ozonolysis SOA (Cappa and Wilson, 2011). 317 Although we assume here that the converted non-volatile aerosol mass still participates in 318 partitioning, either mechanism invokes a particle-phase process to retard SOA 319 evaporation. 320 Model parameters α w , α p , τ olig and the branching ratios between the oxidation 321 products are optimized to best-fit the predictions with the experimental observations. 322 Specifically, model predictions are compared to experimental data: SOA mass 323 concentration vs. reaction time, α-pinene concentration vs. reaction time, and O 3 324 concentration vs. reaction time. Figure S6 compares reaction profiles of measured and 325 modeled O 3 and α-pinene concentrations for the base model case. Sensitivity tests were 326 also performed on each model parameter, shown in Figs. S7-S10. Table 2 summarizes the 327 parameters used. While the optimized parameters provide a good fit to the data, we 328 caution that the parameters are interconnected, and other fits may also be possible. We 329 are confident that our conclusions derived using these parameters are robust. 330 4. Results 331 Figure 1 shows the size-dependent particle wall deposition coefficients inferred 332 from seed-only deposition experiments. The initial total AS seed surface area 333 concentration in the low AS-seed only and high AS-seed only experiments (which are 334 conducted using 0.015 M AS and 0.05 M AS solutions, respectively) are similar to those used in the α-pinene ozonolysis experiments (i.e., ~1000 and ~3000 µm 2 cm -3 , 336 respectively). While there are differences in the particle wall deposition coefficients from 337 the low and high AS-seed only experiments, this difference is likely the result of 338 uncertainties arising from the low particle number concentrations for the larger particles 339 in the low AS-seed only experiment. As shown in Fig. 1, both sets of particle wall 340 deposition coefficients generally fall within the range of those measured in routine 341 monthly AS-seed only experiments conducted in the chamber. 342 The particle wall deposition corrected number concentration data provide a test of 343 the appropriateness of the particle wall deposition correction. This is because the 344 corrected number concentration should level off at a constant value (i.e., the initial 345 particle number concentration), assuming no significant coagulation, when particle wall 346 deposition is properly accounted for since the wall-deposited particle number distribution 347 is added to the suspended particle number distribution during particle wall loss 348 correction. We account for particle wall deposition in nucleation and low AS experiments 349 using deposition coefficients determined from the low AS-seed only experiments, while 350 particle deposition in high AS experiments are accounted for using coefficients 351 determined from the high AS-seed only experiments. Figures S1 and S2 show the particle 352 wall deposition-corrected aerosol number and volume concentrations. Over all 353 experiments, the particle wall deposition-corrected final particle number concentration 354 (i.e., at the end of the reaction) is 9 to 17 % less than the initial particle number 355 concentration for the low AS and high AS experiments (Table S1), respectively, 356 indicating that the particle wall deposition-corrected volume concentrations are slightly 357 underestimated. It is currently unclear why the particle wall deposition-corrected final 358 particle number concentrations are somewhat smaller than the initial particle number 359 concentrations, though this could be due to variations in particle wall deposition rates in 360 the AS-seed only and α-pinene ozonolysis experiments. As a sensitivity test, we used the 361 average of the low AS-seed only and high AS-seed only particle wall deposition 362 coefficients to account for particle wall deposition in all the experiments (Figs. S3 and 363 S4). While there is a negligible difference in the particle wall deposition corrected 364 volume concentrations (Figs. S3 and S4 vs. Figs. S1 and S2), a larger spread (1 to 22 %) 365 exists in the difference between the initial and final particle number concentrations when the average particle wall deposition coefficients are used (Table S1). Therefore, all 367 subsequent nucleation and low AS data presented here are particle wall deposition-368 corrected using coefficients determined from the low AS-seed only experiments, and all 369 high AS data are corrected using particle wall deposition coefficients determined from 370 the high AS-seed only experiments. 371 α-pinene reacted (Ng et al., 2006)) for the 100 and 500 ppb O 3 experiments. Only SOA 386 growth data up to SOA peak concentrations are shown. SOA growth essentially stops 387 once all the α-pinene has reacted. This is expected, as α-pinene has only one double 388 bond; the first step of α-pinene ozonolysis is rate-limiting and the first-generation 389 products are condensable (Ng et al., 2006;Chan et al., 2007). high AS-seed only particle wall loss coefficients are used to account for particle wall loss 409 in all the experiments (Fig. S5). The enhancement of SOA mass yields at higher O 3 410 concentrations and the lack of a SOA mass yield dependence on AS seed surface area 411 (within the range of AS seed surface area concentration used in this study) will be 412 discussed further in Section 5. 413 The α-pinene ozonolysis SOA mass yields obtained in this study are compared to 414 those reported in previous studies in Fig. 5. Table S2 lists the experimental conditions 415 employed in these studies. To facilitate comparison between the different studies, all the 416 SOA mass yield and concentration data (including this study) are adjusted to an organic 417 density of 1.0 g cm -3 . As shown in Fig. 5, the SOA mass yields obtained at peak SOA 418 growth in this study are generally consistent with those of previous studies where the 419 chamber was operated in batch mode (that in this study). 420 The competition between the condensation of SOA-forming vapor to aerosol 421 particles vs. to chamber walls is investigated using the coupled vapor-particle dynamics 422 model described in Section 3. As noted earlier, optimal model values for α p , α w , τ olig and 423 the branching ratios between the oxidation products were determined for the 100 and 500 424 ppb O 3 experiments by comparing the observed and best-fit time-dependent SOA, α-425 pinene, and O 3 concentrations profiles (Figs. S6-S10). Sensitivity tests were performed for each parameter to establish that the set of optimal model values provide the best 427 overall agreement with time-dependent SOA formation profiles observed for all 428 experiments (Figs. S7-S10). Predictions from the coupled vapor-particle dynamics model 429 show that the optimal parameters are: α w = 10 -6 , α p = 1, τ olig = 4 h, branching ratios = 0.57, 430 0.35, 0.04, 0.015 and 0.025 for oxidation products with vapor pressures >10 3 , 10 2 , 10, 1 431 and 0.1 µg m -3 , respectively. The best-fit α w = 10 -6 ( Fig. S7) corresponds to a first-order 432 vapor-wall deposition rate constant (k wall,on ) of 10 -4 s -1 . This k wall,on value is comparable to 433 that reported by Matsunaga and Ziemann (2010) for a 8.2 m 3 chamber. 434 unseeded experiments is most pronounced at low aerosol loadings . 459

Discussion
We note that the concentrations of α-pinene reacted and SOA mass loadings obtained in 460 this study are significantly larger than those reported by Pathak et al. (2007b). Therefore, 461 it is possible that due to the relatively large concentrations of α-pinene reacted in this 462 study, substantial concentrations of gas-phase oxidation products are generated, which 463 results in rapid partitioning into the particle phase even in the absence of seed aerosol. 464 This is evident from the large increase in the particle number concentration during the 465 early stages of the unseeded 100 and 500 ppb O 3 experiments, where the particle number 466 concentration increased to ~8000 and ~10000 particles/cm 3 during the first 45 min of the 467 100 and 500 ppb O 3 experiments, respectively ( Fig. S1a and S2a). Thus, the SOA growth 468 rates are not controlled by the presence of AS seed in this study. 469 Figure 4 shows that for both initial O 3 mixing ratios used, the time-dependent 470 SOA mass yield is similar at any given AS seed surface area (see also Table 1). The 471 absence of a SOA growth dependence on the AS seed surface area is similar to 472 observations reported by McVay et al. (2016) for the α-pinene photooxidation (OH-473 driven chemistry) system, but differ from those reported by  for the 474 toluene photooxidation system in which the SOA mass yield increased with the surface 475 area concentration of seed aerosol. 476 The best-fit α p = 1 (Fig. S8) suggests the absence of significant limitations to 477 vapor-particle mass transfer in the present α-pinene ozonolysis study, and that SOA 478 formation is governed by quasi-equilibrium growth (McVay et al., 2014), which occurs 479 when SOA-forming vapors are produced at a rate that is significantly slower than that 480 required to establish gas-particle equilibrium (Shiraiwa and Seinfeld, 2012;Zhang et al., 481 2012). Moreover, the characteristic timescale to establish gas-particle equilibrium is less 482 than those for reaction and vapor-wall deposition. When the vapor and particle phases 483 maintain equilibrium, gas-particle equilibrium is controlled by the amount of organic 484 matter in the VOC system. As a result, the rate of condensation of SOA-forming vapors 485 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. is independent of the seed aerosol surface area (McVay et al., 2014). The best-fit α p = 1 is 486 within the approximate range of α p coefficients determined from α-pinene ozonolysis 487 SOA thermodenuder studies (α p = 0.1) (Saleh et al., 2013) and α-pinene photooxidation 488 chamber studies (α p = 0.1 or 1) (McVay et al., 2016). Notably, this result differs markedly 489 from that for toluene photooxidation , where α p was determined to be 490 0.001, and for which, since the SOA mass yield was strongly dependent on the seed 491 aerosol surface area, the condensation of SOA-forming vapors onto seed aerosol particles 492 was kinetically limited (McVay et al., 2014). Kinetically-limited SOA growth occurs 493 when the timescale for gas-particle equilibrium is competitive with or exceeds the 494 timescale for reaction and vapor wall deposition, and may reflect imperfect 495 accommodation of gas-phase organics to the particle phase. The markedly different 496 behavior of the α-pinene and toluene SOA systems could be due to differences in SOA 497 volatility and aerosol physical phase state (McVay et al., 2016). 498

Oxidation rate effect 499
At higher O 3 concentrations, the α-pinene oxidation rate increases, leading to 500 higher SOA mass yields (the "oxidation rate effect"). This behavior was previously 501 observed by Ng et al. (2007) for the m-xylene photooxidation system, for which the 502 oxidation rate effect was attributed to the loss of semi-volatile condensable products to 503 chamber walls in competition with condensation onto seed particles to form SOA. 504 SOA formation from α-pinene ozonolysis is presumed to be driven by a range of 505 semi-and low-volatility first-generation products arising from reaction of O 3 with the 506 single C=C double bond (Ng et al., 2006). These products are subject to two competing 507 routes: condensation to particles to form SOA or deposition on the chamber walls. Each 508 process can be represented in terms of a first-order rate constant: k wall,on and k particle,on (s -1 ). 509 The rate of vapor-wall deposition of condensable species A is then k wall,on × [A] (molec 510 cm -3 s -1 ) and the rate of condensation onto particles is k particle,on × [A] (molec cm -3 s -1 ). 511 Increasing the rate of reaction increases the concentration of [A], but the relative rates of 512 vapor-wall deposition and condensation onto particles will remain the same. In general, 513 however, both vapor-wall deposition and vapor-particle condensation are reversible 514 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. processes (McVay et al., 2014;. The first-order rate constant for 515 evaporation from the wall can be represented as (Matsunaga and Ziemann, 2010): 516 where C i * is the saturation concentration and C w is the assumed equivalent wall organic 518 concentration. The rate of evaporation from particles is: 519 where C aer is the organic aerosol concentration (C aer = A k +M init ). 521 The difference between C aer and C w is the key to explaining the oxidation rate 522 effect. At the beginning of the experiment, C aer is very small because the inorganic seeds 523 are essentially non-absorbing. Therefore, k particle,off is large, and the net SOA growth is 524 small. In contrast, C w is considered to be substantial (on the order of 10 mg m -3 ) and to be 525 essentially constant throughout the experiment (Matsunaga and Ziemann, 2010;McVay 526 et al., 2014;. Model predictions are insensitive to the value of C w 527 since, in any event, C w is significantly larger than C aer . Therefore, 528 k wall,off is small at the beginning of the experiment and the net vapor wall loss rate is fast. 529 As C aer increases, the net SOA condensation rate increases relative to the net vapor wall 530 loss rate. When the reaction rate increases corresponding to higher O 3 concentrations, C aer 531 grows more quickly because more condensable species are available to form SOA, and 532 the net condensation rate increases more rapidly. Therefore, the observed oxidation rate 533 effect is due to vapor wall deposition, and arises because vapor-particle and vapor-wall 534 condensation are essentially reversible processes. This explanation is consistent with 535 simulations varying the O 3 concentration in which all species are non-volatile (i.e., do not 536 evaporate from the particles or the wall). In this case, no oxidation rate effect is observed 537 as the O 3 concentration increases. The growth curves for different O 3 concentrations 538 overlap, and the same yield is obtained regardless of O 3 concentration (Fig. S11). 539 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. used, the oxidation rate effect will persist to higher O 3 concentrations (i.e., > 500 ppb O 3 ) 555 ( Fig S13). With a faster injection rate, 500 ppb O 3 is injected before all of the α-pinene 556 has reacted. Continuing to inject O 3 to a higher concentration (i.e., 750 ppb) will cause α-557 pinene to decay faster and SOA to grow faster than when the O 3 injection stops at 500 558 ppb. The oxidation rate effect is then apparent at higher O 3 concentrations. If, instead of 559 using an injection rate of O 3 , simulations are run using fixed initial O 3 (not possible 560 experimentally), the rate effect persists to even higher O 3 concentrations. The relative 561 increase in yield with increasing O 3 concentrations slows at very high O 3 concentrations 562 because the rate of reaction becomes substantially faster than the vapor wall deposition 563 rate, and there is less marginal effect to increasing the reaction rate. 564

Interplay of the seed aerosol surface area effect and the oxidation rate effect 565
In this study, we observe an oxidation rate effect but not a seed aerosol surface 566 area effect. In , a seed aerosol surface area effect was observed, but 567 the variation of the oxidation rate was not studied. A key aspect of vapor wall deposition 568 is the potential interplay between the seed aerosol surface area effect and the oxidation 569 rate effect. To examine this interplay in the α-pinene ozonolysis system, simulations were 570 carried out by varying the seed aerosol surface area and the O 3 concentration 571 simultaneously, while using the branching ratios, oligomerization rate, and vapor wall 572 deposition rate parameters obtained in the present study. The initial α-pinene 573 concentration was set to 50 ppb, and a fixed O 3 concentration was used in place of a 574 linear injection. α p was varied at 0.001, 0.01, and 1 in these simulations. Figure 6 shows 575 the SOA mass yield at peak SOA growth as a function of both the seed aerosol surface 576 area and O 3 concentration for α p = 1, 0.01, and 0.001. For α p = 1, the oxidation rate 577 dominates: SOA mass yield increases significantly as O 3 concentration increases while 578 the seed aerosol surface area has a negligible effect. For α p = 0.01, both effects can be 579 observed in different regions: at low O 3 concentrations and high seed aerosol surface 580 areas, the oxidation rate effect dominates; at low seed aerosol surface areas and high O 3 581 concentrations, the seed surface area dominates. At low seed aerosol surface areas and 582 low O 3 concentrations, both effects are present. For α p = 0.001, the seed aerosol surface 583 area effect dominates except at very high seed aerosol surface areas. These observations 584 show that the presence of an oxidation rate effect and/or seed aerosol surface area effect 585 depends on a complex interplay of factors, such as α p , the rate of hydrocarbon oxidation, 586 and the amount of seed surface area present. 587

Implications 588
In this study, we systematically examine the roles of gas-particle partitioning and 589 VOC oxidation rate in the presence of vapor-wall deposition in α-pinene ozonolysis. We 590 show that despite the presence of vapor-wall deposition, SOA mass yields at peak SOA 591 growth remain approximately constant regardless the seed aerosol surface area (within 592 the range of AS seed surface area concentration used in this study). This observation is 593 consistent with SOA formation in the α-pinene ozonolysis system being governed by 594 quasi-equilibrium growth, for which there are no substantial limitations to vapor-particle 595 mass transfer. This result was demonstrated in a previous modeling study which showed 596 that increasing the seed-to-chamber surface area ratio will lead to increased SOA growth 597 only in cases in which the condensation of SOA-forming vapors onto seed aerosol 598 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 4 April 2016 c Author(s) 2016. CC-BY 3.0 License. particles is kinetically limited as a result of imperfect accommodation of gas-phase 599 organics to the particle phase (McVay et al., 2014). 600 An important implication of this study is that diverting vapor-wall deposition in 601 chamber studies via the addition of ever-increasing quantities of seed aerosol particles is 602 not effective in VOC systems for which SOA formation is governed by quasi-equilibrium 603 growth. This study also underscores the importance of accounting for particle wall 604 deposition appropriately in chamber studies, to avoid erroneous conclusions regarding the 605 role of gas-particle partitioning (quasi-equilibrium vs. kinetically-limited SOA growth) in 606 influencing vapor wall loss in the VOC system. 607 We note that the present study shows that the SOA mass yield is independent of 608 seed aerosol surface area concentration for values ranging from 0 to ~3000 µm 2 cm -3 . 609 This corresponds to a seed-to-chamber surface area ratio of 0 to ~1 × 10 -3 , which is 610 substantially smaller than the range used by  to study the influence of 611 vapor-wall deposition on toluene photooxidation SOA formation in the Caltech chamber 612 (i.e., 0 to ~5 × 10 -3 ). It is possible that a SOA mass yield dependence on the seed surface 613 area may have become more apparent had a larger range of seed aerosol surface area (i.e., 614 > 3000 µm 2 cm -3 ), and hence a larger range of seed-to-chamber surface area ratio, been 615 used here. One consideration is that coagulation may become increasingly important, and 616 will need to be accounted for, when higher seed aerosol number concentrations (relative 617 to those used in this study) are used (Seinfeld and Pandis, 2006;Pierce et al., 2008). A 618 detailed analysis of the effect of seed aerosol surface area concentrations > 3000 µm 2 cm -619 3 on α-pinene ozonolysis SOA mass yields will be the subject of forthcoming work. 620 Higher SOA mass yields at peak SOA growth are observed in the present study 621 when O 3 is increased from 100 to 500 ppb. This is because α-pinene is oxidized more 622 quickly, which leads to gas-phase oxidation products being formed more rapidly, and 623 consequently partitioning more quickly onto AS seed aerosol particles before they are 624 lost to the chamber walls. Therefore, the oxidation rate effect (i.e., higher SOA mass 625 yields as a result of faster hydrocarbon oxidation rates) is a consequence of vapor-wall 626 deposition. An important implication of this study is that SOA mass yields can be 627 affected by vapor-wall deposition in VOC systems that are not characterized by slow 628 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 4 April 2016 c Author(s) 2016. CC-BY 3.0 License. mass accommodation of gas-phase organics to the particle phase . 629 Thus, this work demonstrates that the effect of vapor-wall deposition on SOA mass yields 630 can be mitigated through the use of excess oxidant concentrations. It should be noted that 631 the α-pinene ozonolysis SOA mass yields (absolute values) increased by 5 to 9 % when 632 O 3 is increased from 100 to 500 ppb (for an initial α-pinene concentration of ~50 ppb), 633 where SOA formation is governed by quasi-equilibrium growth. In the absence of vapor-634 wall deposition, SOA mass yields are predicted by the model used here to approximately 635 double from those observed experimentally. In contrast,  showed that 636 the presence of vapor-wall deposition led to underestimation of SOA formation by factors 637 as much as four in the toluene photooxidation system, where the condensation of SOA-638 forming vapors onto seed aerosol is kinetically limited. Taken together, these results 639 indicate that the magnitude by which vapor-wall deposition affects SOA mass yields 640 depends on the extent to which the VOC system is governed by kinetically-limited SOA 641 condensational growth. 642 Given these observations of how gas-particle partitioning can influence the 643 magnitude by which vapor-wall deposition affects SOA mass yields, an overriding 644 question is: what controls the gas-particle partitioning behavior of SOA formed in 645 different VOC systems? α p describes the overall mass transfer of vapor molecules into the 646 particle phase (McVay et al., 2014;. Thus, α p affects the vapor-647 particle equilibrium timescale, which, depending on the extent to which it is competitive 648 with the timescales for reaction and vapor-wall deposition, determines whether SOA 649 formation is governed by kinetically-limited or quasi-equilibrium growth. Markedly 650 different α p values could arise from the physical phase state of the SOA formed. As 651 discussed by McVay et al. (2014McVay et al. ( , 2016, if the SOA formed exists in a semi-solid state 652 (Vaden et al., 2010;Virtanen et al., 2010;Cappa and Wilson, 2011;Vaden et al., 2011;653 Virtanen et al., 2011;Kuwata and Martin, 2012;Perraud et al., 2012;Saukko et al., 2012;654 Abramson et al., 2013;Renbaum-Wolff et al., 2013), a low value of α p might be expected 655 owing to retarded surface accommodation and particle-phase diffusion (Zaveri et al., 656 2014). Quantification of α p is challenging experimentally, and reported α p values for the 657 same system can vary by several orders of magnitude (Grieshop et al., 2007;Stanier et 658 al., 2007;Vaden et al., 2011;Miles et al., 2012;Saleh et al., 2013). Therefore, α p of SOA formed in different VOC systems need to be better constrained through a combination of 660 experimental and modeling efforts. 661 The SOA mass yield from the ozonolysis of monoterpenes in the GEOS-CHEM 662 chemical transport model (19 % at 10 µg m -3 ) is currently based on that measured in α-663 pinene ozonolysis studies by Shilling et al. (2008) (Pye et al., 2010). Shilling et al. (2008) 664 measured these SOA mass yields in a teflon chamber operated in continuous-flow mode, 665 as opposed to batch mode, which is how experiments in the present study and most of 666 those shown in Fig. 5 and Table S2 were conducted. While it is not possible to directly 667 compare our results with those of Shilling et al. (2008) due to differences in SOA mass 668 concentrations, the SOA mass concentrations and yields measured in the current study 669 are generally consistent with those of previous batch chamber studies. The SOA mass 670 yields at ~10 µg m -3 SOA mass concentration measured by Shilling et al. (2008) are 671 generally higher than those measured in chambers operated in batch mode (Griffin et al., 672 1999;Cocker et al., 2001b;Presto et al., 2005;Presto and Donahue, 2006;Pathak et al., 673 2007b) (Fig. 5). One possible explanation for the higher SOA mass yields in the 674 continuous-flow, steady state, mode is that the SOA-forming vapors are in equilibrium 675 with the organic mass present on the chamber walls and seed aerosol, hence minimizing 676 the irreversible loss of SOA-forming vapors to the chamber walls (Shilling et al., 2008). 677 However, the extent to which SOA mass yields obtained in a continuous-flow reactor are 678 influenced by vapor wall loss is unclear. Using a continuous-flow reactor, Ehn et al. 679 (2014) observed α-pinene ozonolysis SOA mass yields to increase with increasing seed 680 aerosol surface area but required α p = 1 to fit the observed SOA growth. The observed 681 vapor-wall deposition rate constant in their continuous-flow reactor (0.011 s -1 ) is two 682 orders of magnitude larger than that of the GTEC chamber (10 -4 s -1 ). The estimated 683 timescales for gas-particle and gas-wall partitioning are also approximately equal in their 684 continuous-flow reactor. This indicates that SOA condensational growth is kinetically 685 limited in their continuous-flow reactor even at α p = 1 (Ehn et al., 2014;McVay et al., 686 2014), which suggests that SOA mass yields measured in their continuous-flow reactor 687 may be significantly affected by vapor-wall deposition. 688 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. reported SOA mass yields 10 to 30 % higher than those previously reported by Fry et al. 692 (2009Fry et al. 692 ( , 2014. In addition to differences in the experimental conditions of the two studies, 693 Boyd et al. (2015) hypothesized that the higher SOA mass yields could also be a result of 694 the higher NO 3 concentrations used in their study (which led to faster β-pinene oxidation 695 rates) compared to those used by Fry et al. (2009Fry et al. ( , 2014. The oxidation rate effect was 696 also observed in the m-xylene photooxidation system, where Ng et al. (2007) showed that 697 the SOA mass yields were dependent on the m-xylene oxidation rate, with higher OH 698 concentrations (and hence faster oxidation rates) resulting in higher SOA mass yields 699 Together, these studies show that faster hydrocarbon oxidation rates can alleviate the 700 effects of vapor-wall deposition on SOA mass yields in different VOC systems. 701 This gives rise to the question: should chamber SOA experiments on different 702 VOC systems be performed under as rapid oxidation conditions as possible (i.e., large 703 oxidant concentrations) to reduce the effects of vapor-wall deposition? A recent study by 704 McVay et al. (2016) reported similar SOA growth under low and high OH levels for α-705 pinene photooxidation. The authors hypothesized that the autoxidation mechanism likely 706 becomes a more important pathway at low OH levels (Crounse et al., 2013), and thus 707 contributes substantially to SOA growth. Therefore, it is possible that certain reaction 708 pathways and mechanisms (which are important in the atmosphere) are biased when 709 unusually high levels of oxidants are used in chamber experiments (e.g. autoxidation). 710 Thus, this underscores the need to design chamber experiments that simultaneously 711 mitigate the magnitude of vapor-wall deposition while ensuring that reaction conditions, 712 and consequently reaction pathways and oxidation products, are atmospherically relevant.   Initially absorbing organic material in seed aerosol 0.01 µg m -3 P Pressure 1 × 10 5 Pa T Temperature 298 K ρ seed Density of inorganic seed 1700 kg m -3 ρ org Density of organic material on seed particle 1300 kg m -3 1062 chamber. The symbols are the SOA mass yields at peak SOA growth obtained from 1096 the experimental data. The y-axis error bars represent the uncertainty in the SOA mass 1097 yield at peak SOA growth, which originates from the α-pinene injection and the aerosol 1098 volume concentration measured by the SMPS at peak SOA growth (one standard 1099 deviation).  and (c) have different SOA mass yield ranges. Simulations were carried out using the 1117 branching ratios, oligomerization rate, and vapor wall deposition rate parameters obtained 1118 in this study. The initial α-pinene concentration was set to 50 ppb, and a fixed O 3 1119 concentration was used in place of a linear injection. 1120 Atmos. Chem. Phys. Discuss., doi:10.5194/acp-2016-269, 2016 Manuscript under review for journal Atmos. Chem. Phys. Published: 4 April 2016 c Author(s) 2016. CC-BY 3.0 License.