The influences of mass loading and rapid dilution of secondary organic aerosol on particle volatility

Introduction Conclusions References Tables Figures


Introduction
Atmospheric aerosol particles have an important impact on human health (Chen et al., 2013) and climate (IPCC, 2014). Organic aerosol (OA) is a significant portion of atmospheric particulate mass, often contributing 20-90 % of the fine particle mass world- 10 wide (Saxena and Hildemann, 1996;Andreae and Crutzen, 1997), a major portion of which is secondary organic aerosol (SOA) (Zhang et al., 2005). One pathway through which SOA is formed is when products from the gas-phase oxidation of volatile organic compounds (VOCs) condense onto pre-existing particles or nucleate to form new particles. VOCs are broadly classified as being either biogenic (BVOCs) or anthropogenic 15 (AVOCs). The source of SOA varies with geographical location, with larger contributions of anthropogenic SOA in and around urban areas (Weber et al., 2007) and larger contributions of biogenic SOA in rural areas (Han et al., 2014).
An important source of biogenic SOA is the reaction of unsaturated gas-phase VOCs with O 3 . The most globally abundant BVOC compounds are isoprene (C 5 H 8 ) Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | increases, most steeply below ∼ 30 µg m −3 . Other studies have shown that the mass yield of a variety of SOA, including α-pinene + O 3 SOA, increases as C OA increases (Henry et al., 2012;Odum et al., 1996;Pathak et al., 2007). Changes to aerosol composition as a function of C OA can be explained by gas/particle partitioning in which the distribution of material between the gas and particle phases is related to the saturation 5 vapor concentration, C * , and the total OA concentration (Pankow, 1994;Odum et al., 1996) according to: where C i ,p is the concentration of compound i in the particle phase (µg m −3 ), C i ,tot is the total concentration of i in both the gas and particle phase (µg m −3 ), C * i is the sat-10 uration vapor concentration (µg m −3 ) and α i is the mass yield of compound i . When C OA is equal to C * i 50 % of compound i exists in the particle phase. Compounds are generally considered semi-volatile when their C * i are within 1-2 orders of magnitude of the concurrent C OA . According to gas/particle partitioning, as C OA increases the fraction of higher volatility compounds, which usually have a lower O/C ratio, present in 15 the condensed phase will increase. SOA growth experiments have historically been interpreted through the framework of absorptive gas/particle partitioning theory, where volatility distributions, i.e. distributions of α i as a function of C * i for some number of surrogate compounds, are derived by fitting the observed SOA formation (Odum et al., 1996;Donahue et al., 2006). Such analyses indicate that SOA is composed of a dis-20 tribution of semi-volatile compounds with volatilities greater than ∼ 10 −1 µg m −3 . However, the volatility distributions determined from fitting of growth experiments have been mostly unable to describe the reverse process, namely evaporation of SOA. For example, quantitative estimates of the volatility of both ambient and laboratory OA after heating induced evaporation indicate that there are often components of OA Introduction   Jimenez, 2010;Stanier et al., 2007). In addition, several experiments have observed slower than expected room-temperature evaporation of both ambient (Vaden et al., 2011) and laboratory generated (Saleh et al., 2013;Grieshop et al., 2007;Wilson et al., 2015) SOA during isothermal dilution. It has also been observed that the mass spectrum of α-pinene + O 3 SOA over the range 40-200 amu exhibited negligi-5 ble changes during the heating induced evaporation (Cappa and Wilson, 2011), even though absorptive gas/particle partitioning suggests an SOA composed of components having volatilities spanning several decades of C * . Some other experiments have observed some changes to the observed particle composition (i.e. mass spectrum) upon heating (Hall and Johnston, 2012b;Kostenidou et al., 2009), but overall the changes 10 tend to be small and inconsistent with the particles being composed of individual compounds with a wide range of volatilities. Altogether these observations illustrate that there is a clear gap between the apparent volatility of SOA as characterized during evaporation experiments and the effective volatility of SOA derived from formation studies. 15 In this study, the volatility of α-pinene + O 3 SOA was characterized by heatinginduced evaporation in a thermodenuder (TD) as a function of C OA over the range 1 to 800 µg m −3 . Based on previous SOA formation experiments, the SOA composition is expected to have changed as C OA was increased from 1 to > 140 µg m −3 (Shilling et al., 2009). It follows that the SOA volatility should vary as a function of C OA as 20 well, with an expectation that SOA at higher C OA should be more volatile than that at low C OA and thus should exhibit different responses to heating. Additionally, mass thermograms of SOA that was initially formed at C OA > 380 µg m −3 and rapidly diluted to C OA < 30 µg m −3 were measured. The experimental results are interpreted using the kinetic model of aerosol evaporation in a TD by Cappa (2010) that has been extended 25 from the original formulation that assumed direct evaporation of semi-or low-volatility monomers to include dimer formation and decomposition. Good agreement between the experimental observations and the model predictions provide support for the large influence of oligomer decomposition on SOA evaporation. Introduction

Secondary organic aerosol production
SOA was formed at various total C OA from the homogeneous nucleation of products produced from the ozonolysis of gas-phase α-pinene, in excess, in the absence of seed particles (Fig. S1). Variable amounts of α-pinene were introduced into a stainless steel 5 flowtube (L = 2 m; ID = 2.3 cm) by constantly injecting liquid α-pinene (0.12-0.7 µL h −1 ) into a stream of purified house air at 0.015 L min −1 . The O 3 was generated by passing air through a cell containing a 22.9 cm long Hg pen-ray lamp (UVP, LLC) and then 0.70-1.0 L min −1 of this flow was sub-sampled into the flowtube. The concentrations of αpinene, O 3 and other experiment-specific conditions are given in Table 1. The residence 10 time in the flow tube was typically about 1 min, although slightly variable depending on the total volumetric flow rate (see Table 1 assumed to have a density of 1.2 µg m −3 . The particle mass concentrations were varied from 1 to 800 µg m −3 although were kept stable for the duration of each experiment. Larger concentrations tended to correspond to particle size distributions that peaked at larger sizes. In addition to SOA that was generated at variable C OA , seven experiments involved 20 the dilution of SOA that was initially formed at high C OA (≥ 380 µg m −3 ) and diluted to low C OA . The dilution occurred downstream of the flowtube, charcoal denuder and ozone denuder. To achieve the desired dilution the aerosol-laden airstream was divided into two fractions; one was directed through a HEPA capsule filter with Versapor ® mem- i.e. the level of dilution, was controlled by a needle valve attached to the outlet of the filter.

Thermodenuder
The TD used here is based on the design of Huffman et al. (2008) with the following key modifications: (1) the heated laminar flow reactor is 0.71 m long (as compared to 5 0.41 m) and has a center line fully-heated residence time (τ res ) of 26 s at a flow rate of 0.40 L min −1 , (2) the distance between the actively heated volume and the charcoal denuder has been shortened and is now 4.8 cm (as compared to ∼ 14 cm), (3) there is only one heating region. The shorter distance between the end of the actively heated volume and the charcoal denuder helps to limit re-condensation as the air cools prior 10 to reaching the denuder section. The bypass (i.e. unheated) line had the same volume as the TD, and thus the same total residence time. Further information on the design and characterization of the TD is provided in the Supplement. The room temperature flowrate through the TD was a constant 0.40 L min −1 independent of the total flowrate in the SOA formation flowtube. Measurements of the particle size distribution were made 15 after the particles passed through either the bypass line (room temperature) or the TD. The TD temperature ranged from room temperature (298 K) to 220 • C (493 K). No differences in the mass thermograms were found between experiments based on the order of temperature changes, e.g. whether temperature was increased or decreased.

20
A scanning mobility particle sizer (SMPS; TSI Inc.), composed of a charge neutralizer, a differential mobility analyzer (DMA; Model 3085) and a condensation particle counter (CPC; Model 3772), was used to measure particle size distributions. The extent of aerosol evaporation was characterized by comparing the particle size distribution for particles that passed through the bypass line to that for the particles after passing Introduction dian diameter, d p,V . The particle volume fraction remaining (VFR) after passing through the TD is then: where d p,V,TD and d p,V,bypass refer to the particles that passed through the TD or the bypass, respectively. Under an assumption of constant particle density, the VFR is 5 equivalent to the particle mass fraction remaining (MFR), and plots of VFR vs. temperature are commonly referred to as mass thermograms. The bypass distribution was measured at least every two temperature changes (∼ every 20 min) to account for any changes in the reference particle distribution; in general, the reference distributions were very stable. 10 To facilitate quantitative comparison between experiments at different C OA , each mass thermogram was fit to the sigmoidal type equation from Emanuelsson et al. (2013): where VFR min is the VFR at the low temperature limit, VFR max is the VFR at the high 15 temperature limit (typically zero), S VFR is the slope factor that characterizes the steepness of the VFR curve and T 50 is the temperature at which VFR = 0.50. If there is no evaporation in the TD at room temperature due to the removal of gas-phase compounds (vapor stripping) in the denuder section then the VFR at room temperature ( The kinetic model of evaporation used here is a modified version of the model developed by Cappa (2010) to simulate evaporation in a thermodenuder. The original model simulated gas/particle mass transfer (evaporation and condensation) for a monomodal multi-component aerosol as particles pass through and are heated and cooled in the TD along with loss of vapors to the charcoal denuder. Absorptive partitioning is im-10 plicitly assumed. Compounds evaporate according to their respective saturation vapor concentrations, and it is assumed that the gas/particle system is at equilibrium before entering the TD. The temperature dependence of C * is accounted for using the Clausius-Clapeyron equation. Here, it is assumed that the enthalpy of vaporization, ∆H vap , is related to C * according to the relationship of Epstein et al. (2010), where 15 ∆H vap (kJ mol −1 ) = 131 − 11 × log C * . The temperature profile through the TD is empirically specified (see Supplement). The key input to the model is the distribution of mass (gas + particle) with respect to C * , referred to as a volatility distribution; different distributions will yield different mass thermograms (Cappa and Jimenez, 2010). It is commonplace to assume a distribution where the C * values differ by an order of magni-20 tude at a specified reference temperature, e.g. log C * (298 K) = (−3, −2, −1, 0, 1, 2, 3), and this approach is adopted here. The calculated mass transfer rates can be adjusted to account for mass transfer limitations, as characterized by the mass accommodation coefficient, γ e , which characterizes deviations from the theoretical maximum evaporation rate; γ e is an adjustable parameter as it is not known a priori. The default value 25 used is γ e = 1. The model output for a given set of ∆H vap and C * is dependent on γ e .
At smaller γ e the slope of the mass thermogram is less steep, the T 50 increases and 10005 Introduction for SOA with semi-volatile components an increasing amount of mass remains after TD-processing at room temperature (Cappa and Wilson, 2011). The model can be run with pre-specified volatility distributions or can be used to determine empirical volatility distributions from fitting to observations (Cappa and Jimenez, 2010). The base TD model has been modified to include the influence of dimers and dimer 5 decomposition on the simulated evaporation, and shares some similarities with Trump and Donahue (2014). The dimer model is implemented as follows. The initial equilibrium gas/particle mass distribution is based on a semi-volatile monomer volatility distribution (i.e. that determined from previous growth experiments). The balance between monomers and dimers at equilibrium is then determined from the monomer/dimer equi-10 librium constant, K eqm (cm 3 molecules −1 ), which is equal to the ratio of the forward (k f , cm 3 molecules −1 s −1 ) and reverse (k r , s −1 ) rate coefficients associated with formation from monomers and dimer decomposition, i.e. K eqm = k f /k r . Note that the volume units on K eqm and k f correspond to condensed-phase volume. If K eqm is large then all condensed-phase species would be in dimer form and, at equilibrium, all gas-phase 15 material would be drawn into the condensed phase. Here, this situation is avoided through the following simplification to determine the initial particle state at the TD inlet. First, the gas/particle (monomer only) equilibrium distribution is calculated given the specified volatility distribution and C OA . Then the monomer/dimer equilibrium in the condensed phase is calculated, and the gas-phase concentrations are set to zero to 20 avoid large amounts of condensing material at the next time step. Since a charcoal denuder is placed immediately after the flowtube, this simplification is physically accurate. The resulting gas-monomer-dimer concentrations are used as the initial state. It is assumed that the dimers are non-volatile over the entire temperature range considered, and thus do not directly evaporate. In addition, only homodimers, that is dimers 25 formed from monomers in the same volatility bin, are assumed to form. This is a simplification compared to allowing for all possible cross-reactions and allows for more straight-forward keeping track of the dimer source monomers. As the temperature increases within the TD the dimers decompose into their semi-volatile parent monomers, Introduction  Hall and Johnston (2012b) have shown that dimers in SOA do decompose upon heating. The rate at which dimers decompose is governed by k r and k f , both of which are likely to be temperature dependent. Assuming they exhibit Arrhenius-type temperature dependence, the temperature sensitivity of K eqm can be 5 characterized by the difference in the activation energies of the reverse and forward reactions, ∆E a = E a,r − E a,f , and where the temperature dependence of k r and k f has the form: where R is the universal gas constant (8.314 J mol −1 K), T is the temperature (K) and 10 where Note that the Arrhenius pre-factor, A r , depends on E a,r . Consequently, and ∆E a is as defined above. It should be noted that this formulation differs somewhat 15 from that of Trump and Donahue (2014) in that they assumed that A and E a were independent parameters and further did not account for the T -dependence of k f , which we account for here in the relationship between k r , k f and ∆E a . The key model inputs are then K eqm (298 K), k r (298 K) and ∆E a . Although K eqm governs the equilibrium distribution, k f and k r will control the timescales associated with dimer formation and ACPD 15,2015 The influences of mass loading and rapid dilution on SOA volatility

Isothermal evaporation model
The kinetic thermodenuder model of evaporation was adapted to allow for simulation of particle evaporation at room temperature following from isothermal dilution for any initial input of particle composition including semi-volatile monomers, very low volatility compounds and a mixture of semi-volatile monomers and non-volatile dimers. The 5 extent of dilution is user-selectable as a dilution factor (DF), which simulates SOA and the associated vapors being passed through a DMA and injected into a chamber. The organic vapors are assumed to be removed from the system (i.e. lost to the chamber walls) with a rate characterized by a user-selectable first order loss rate, k loss (s −1 ).
Vapor loss serves to mimic the conditions in some isothermal evaporation experiments 10 where the diluted SOA particles are held in a chamber containing activated carbon (Vaden et al., 2011). The timescales associated with isothermal evaporation are much longer than for the TD experiments and simulations, and the isothermal evaporation model can be run for many hours of model time. When the monomer/dimer equilibrium is used to establish the initial particle composition, the relationships between K eqm , k r , 15 k f and ∆E a are the same as in the TD evaporation model.

Observations
Evaporation and shrinking of the α-pinene + O 3 SOA particles occurred upon heating in the TD. Example size distributions as a function of temperature for an initial C OA =  15,2015 The influences of mass loading and rapid dilution on SOA volatility composition varied with C OA . Results from experiments where SOA was formed at a high C OA (> 380 µg m −3 ) and then rapidly isothermally diluted to a lower concentration (< 30 µg m −3 ) are also reported in Fig. 2. Each experiment was individually fit according to Eq. (3), and the best-fit parameters are given in Table S1. The average T 50 and S VFR for each C OA grouping are given in Table 2.
Within each grouping the mass thermograms are all very similar, especially for the low and medium cases. No evaporation is observed at room temperature from vapor stripping in the denuder section for any case. The maximum variability is observed within the high C OA grouping, although even here the variability is not particularly large, with the average and sample SD S VFR = 16.4 ± 1.5 and in T 50 = 359 ± 7 K. The S VFR 's 10 for all groupings are statistically indistinguishable, as are the T 50 values for the low and medium groupings. However, the T 50 for the high C OA grouping is significantly larger at the p < 0.05 level (p = 0.006 and p = 0.025 as compared to the low and medium C OA groupings, respectively, for a two-tailed test). Visual inspection of Fig. 2a indicates that one experiment, with C OA = 600 µg m −3 , has a notably larger T 50 . If this experiment 15 is excluded the T 50 = 357 ± 5 K, which is still statistically larger than the low C OA T 50 at the p < 0.05 level (p = 0.008 for the two-tailed test) but is only now statistically larger than the medium C OA T 50 at the p < 0.10 level (p = 0.079 for the two-tailed test). This difference could be due to small amounts of re-condensation or to saturation of the gas-phase, both of which become a greater concern at high C OA (Cappa, 2010;Saleh 20 et al., 2011;Cappa and Jimenez, 2010;Fuentes and McFiggans, 2012;Riipinen et al., 2010), although there is no specific dependence of T 50 on C OA within the high C OA group. Regardless, it is apparent that the effective volatility of the SOA at C OA is not higher than at low C OA and that, despite the slight differences, the response to heating of SOA particles formed from products of the ozonolysis of α-pinene is, to a very large 25 extent, independent of the C OA at the point of formation. This then suggests that, from a volatility perspective, the distribution of compounds in the particle is independent of C OA , which stands in contrast to expectations based on the growth-derived volatility distribution. 15,2015 The influences of mass loading and rapid dilution on SOA volatility The mass thermogram of SOA originally formed at high C OA and isothermally diluted to low C OA was also measured (Fig. 2d). Since the evaporation of SOA induced by isothermal dilution occurs very slowly, on the order of many minutes to hours (Grieshop et al., 2007;Saleh et al., 2013), the composition of the diluted SOA is not expected to change substantially from the initial state of formation at high C OA before the particles 5 enter the TD. The T 50 of the SOA formed at high C OA is larger than for the diluted SOA, and significantly different at the p < 0.05 level (p = 0.003 for a two-tailed test), while the average S VFR of the diluted and the high C OA grouping mass thermograms are statistically indistinguishable at the p < 0.05 level (p = 0.443 for the two-tailed test). This strongly suggests that the difference in T 50 of the high C OA grouping results from re-10 condensation or saturation of the gas-phase, although the possibility that there is some real difference in the effective volatility of particles after rapid isothermal dilution cannot be excluded. The average diluted SOA mass thermogram is also almost identical to the average low C OA mass thermogram indicating that the volatility distributions of the compounds in the diluted and low C OA cases are the same. Overall, it is evident 15 that the rapid dilution of SOA does not induce changes to molecular composition that significantly influence particle volatility.

Semi-volatile SOA model
The observed similarity between the mass thermograms for the SOA formed at orders 20 of magnitude different C OA is surprising given that some observations suggest that particle composition depends on C OA (e.g. Shilling et al., 2009). Since the application of absorptive partitioning theory to the interpretation of SOA growth experiments suggests that the particles are (i) composed of compounds with a large distribution of individual volatilities, typically with C * values > 10 −1 µg m −3 and (ii) that the fraction of higher ACPD 15,2015 The influences of mass loading and rapid dilution on SOA volatility  , simulated mass thermograms have been calculated as a function of C OA (for γ e = 1 or 0.001) using the TD model, first assuming that the particles are composed only of monomers (Fig. 3). Results from this model will be referred to as semi-volatile monomer results. Specifically, we use the 7-bin volatility distribution with log C * = [−2, −1, 0, 1, 2, 3, 4] and mass yields 5 of α = [0.001, 0.012, 0.037, 0.088, 0.099, 0.250, 0.800]. The theoretical mass thermograms, for γ e = 1, indicate that a significant dependence of the mass thermograms on C OA should have been observed (Fig. 3a). Further, they indicate that substantial evaporation of the SOA particles at high C OA should have been observed at room temperature due to vapor stripping in the charcoal denuder section of the TD, which occurs 10 to some extent for any species with C * ≥∼ 1 µg m −3 when γ e = 1. Neither of these phenomena were observed, demonstrating that there is a clear disconnect between typical volatility distributions derived from SOA growth experiments and SOA evaporation experiments, as has previously been noted (e.g. Cappa and Jimenez, 2010). Some measurements of time-dependent evaporation profiles of SOA have been in- 15 terpreted as suggesting that γ e is significantly less than unity for α-pinene + O 3 SOA due to mass transfer limitations in the condensed phase (Grieshop et al., 2007;Saleh et al., 2013;Karnezi et al., 2014). Further, some TD-based SOA studies have used γ e as a tunable parameter in data fitting for individual experiments and suggest that γ e < 1 (Lee et al., 2011(Lee et al., , 2010). Therefore, model predictions for C OA dependent mass ther-20 mograms are also reported for γ e = 0.001 (Fig. 3b). As expected, the apparent volatility (i.e. extent of evaporation at a given temperature) is decreased compared to the γ e = 1 case, and the simulated thermograms exhibit a greater similarity to the observations. Also, the extent of evaporation at room temperature is substantially lowered and more consistent with the observations, as now only species with C * ≥∼ 1000 µg m −3 25 will evaporate to any substantial extent in the TD due to vapor stripping alone. However, the simulations also indicate a very strong C OA dependence -higher volatility with higher C OA -is expected when γ e = 0.001, which is inconsistent with the observations here. This demonstrates that conclusions regarding the magnitude of parameters  10 The above discrepancy strongly suggests that the molecular composition of the condensed phase is only indirectly related to the volatilities of the condensing species as determined from growth experiments. Here, the possibility that this discrepancy can be explained through the formation and subsequent decomposition of dimers (and higherorder oligomers) through condensed phase reactions is examined.  son (2011) demonstrated that, although simple applications of equilibrium absorption partitioning theory can explain SOA growth in laboratory chamber experiments, such models are not unique explanations. In particular, they showed it was possible to reconcile SOA growth experiments with the occurrence of condensed-phase reactionseven to the extent that the entire particle is rapidly converted from monomers (that 20 retain the volatility of the condensing species) to non-volatile species. There is now a variety of experimental evidence that many types of SOA particles are composed of a large fraction of oligomers (Kourtchev et al., 2014;Putman et al., 2012;Kundu et al., 2012;Gao et al., 2004a;Muller et al., 2009;Kalberer et al., 2004), which will generally have volatilities lower than the monomeric precursors. For the system considered in 25 this study, α-pinene + O 3 SOA, the oligomeric content is suggested to be greater than 50 % (Tolocka et al., 2004;Gao et al., 2004a, b;Hall and Johnston, 2012a) (Kristensen et al., 2014) and ambient (Kristensen et al., 2013;Yasmeen et al., 2010) measurements have identified several α-pinene + O 3 SOA dimers. Simulated mass thermograms have been calculated as a function of C OA using the modified TD model, in which some fraction of the condensed-phase material is assumed to exist as dimers. The same 7 volatility bins were used with the same 5 mass yields as the semi-volatile monomer case to calculate the initial concentration of monomers in the particle. As described above, the equilibrium coefficient, K eqm , was used to determine the initial monomer/dimer equilibrium while the decomposition rate coefficient, k r , and activation energy, ∆E a , describe the rate and sensitivity to temperature changes of dimer thermal decomposition. None of the parameters are known 10 a priori. Since there is a relationship between all three parameters (K eqm = k f /k r and k r (T ) are dependent on ∆E a ) we have taken the approach of specifying different values of K eqm and then fitting the model to the observations by adjusting k r and ∆E a . The level of model/measurement agreement for the different K eqm was then assessed.

Dimer-decomposition model
The model aerosol used had d p = 90 nm and C OA = 100 µg m −3 as starting con- 15 ditions, and was fit to the average mass thermogram of the medium/low C OA grouping (Fig. 4a). Generally good fits were obtained for all K eqm over the range 10 −18 to 10 −14 cm 3 molecule −1 , with the overall best agreement obtained for K eqm = 10 −17 cm 3 molecule −1 , although the differences are quite small (see the Supplement for the best-fit model parameters for each K eqm ). At smaller K eqm , extensive room temper-20 ature evaporation occurred as a result of the increasing initial fraction of semi-volatile monomers, a result that is inconsistent with the observations. However, even for the simulations at larger K eqm , some evaporation at room temperature was always predicted. The associated best fit k r (298 K) and ∆E a varied with K eqm , from 1.6 × 10 −3 s The range of best-fit k r indicate a dimer lifetime of only 1-10 min with respect to decomposition at room temperature. The range of k f values associated with the best fit K eqm and k r is 1.6×10 −21 to 2.8×10 −16 cm 3 molecules −1 s −1 . Given a typical molecular density of ∼ 10 21 molecules cm −3 , the approximate dimer formation timescale is only a fraction of a second, consistent with the short reaction time in these experiments.

5
Consequently, the dimer decomposition timescale is not the same as the observable timescale associated with particle mass loss at room temperature upon e.g. isothermal dilution (Grieshop et al., 2007). However, there are several potential factors that slow down evaporation at room temperature despite the short dimer lifetime with respect to decomposition, as discussed below when isothermal dilution and evaporation is consid-10 ered. The K eqm , k r , and ∆E a determined above from fitting the medium/low C OA data (i.e. C OA = 100 µg m −3 ) have been used to predict additional mass thermograms for C OA = 1, 10, 70 and 600 µg m −3 (Fig. 5a). The predicted mass thermograms are mostly independent of C OA , in contrast with the semi-volatile monomer model. Thus, when the particle is nearly entirely initially dimers this "dimer-decomposition" model result 15 is generally consistent with the experimental observations, where limited differences were observed between the mass thermograms measured at different C OA , although it should be noted the slight increase in T 50 observed at the highest mass loadings is not reproduced. Also, only the C OA = 1 µg m −3 simulation predicts negligible evaporation at room temperature, as was observed for all C OA . The dimer-decomposition model also 20 predicts that the observable particle composition should remain relatively constant as evaporation is induced (Fig. 6a), consistent with observations. This prediction is consistent with previous measurements in which it was observed that the particle composition, as measured using a vacuum ultraviolet aerosol mass spectrometer (VUV-AMS) remained quite constant during the heating induced evaporation of α-pinene + O 3 SOA 25 (Cappa and Wilson, 2011). There are several experiments where changes to composition were observed. Hall and Johnston (2012b) used an electrospray ionization Fourrier transform ion cyclotron resonance (ESI-FTICR) mass spectrometer to measure ACPD 15,2015 The influences of mass loading and rapid dilution on SOA volatility the fraction of oligomers in the particle before and after heating (393 K) and found that the fraction of oligomers and the O : C ratio increase after heating. Furthermore, when recondensation does occur, the compounds that recondensed appear to be monomer decomposition products. Kostenidou et al. (2009) used a quadropole AMS to quantify the mass fraction of m/z 44 fragments as a function of MFR and found that the fraction 5 of m/z 44 increased as MFR decreased, indicating more oxygenated particles with heating-induced evaporation. Since the dimer model presented here tracks the relative concentration of dimers and monomers due to decomposition, the most comparable study is Cappa and Wilson (2011) because the measurement technique is one that primarily detects the monomer components due, most likely, to thermal degradation 10 during analysis. Trump and Donahue (2014) and Roldin et al. (2014) have previously suggested that accounting for the behavior of dimers within SOA can help to explain observations of SOA evaporation; our observations and analysis support and expand upon this conclusion. The range of k r independently determined here are somewhat larger than the However, their estimates may not have fully accounted for the dynamic nature of the system, and thus underestimated the actual dimer decomposition rates compared to 20 that obtained here. It should be noted that the ∆E a determined here are substantially smaller than that suggested by Trump and Donahue (2014), who give E a,r ∼ 80 kJ mol −1 (and where, it seems, that their E a, r is essentially equal to the ∆E a here as they assume that k f is T -independent). However, this difference can be understood by recognizing that they assumed a constant value for A (= 3 × 10 10 s −1 ) and k r (300 K) and deter-25 mined E a, r using the relationship k r (T ) = A exp(−E a, r (RT) −1 ). Thus, underestimations of k r may lead them to actually overestimate the true temperature sensitivity of the system. 15,2015 The influences of mass loading and rapid dilution on SOA volatility The best-fit K eqm and k r were determined from fitting to T -dependent evaporation experiments that occur over relatively short timescales (∼ 1 min) in the thermodenuder. To facilitate more direct connections with previous experiments that have investigated room temperature evaporation upon dilution, the best-fit dimer-decomposition model for K eqm = 10 −17 cm 3 molecules −1 has been used to simulate the long-time, isothermal, 5 room-temperature evaporation of SOA for the case where the SOA is initially diluted and the evaporating vapors are constantly being stripped from the gas-phase (Fig. 4b).

ACPD
This corresponds approximately to the conditions in a series of experiments investigating SOA evaporation (Vaden et al., 2011;Wilson et al., 2015). A vapor loss rate constant of k loss = 10 −3 s −1 has been used, which is a reasonable estimate given the size of the chambers used in the previous experiments (Matsunaga and Ziemann, 2010;Zhang et al., 2014). The initial (pre-dilution) C OA = 100 µg m −3 , which was diluted by a factor of DF = 30 to induce evaporation. The literature experiments have generally shown evidence for evaporation of SOA on fast, medium and slower timescales, where "fast" corresponds to timescales of around 15 a minute, "medium" corresponds to timescales of around 1 h and "slow" to timescales of many hours. The dimer model simulations for all the K eqm fits exhibit similar behavior, with "fast," "medium" and "slow" periods of mass loss and timescales similar to previous observations. There is a non-monotonic dependence on K eqm , with the least mass loss predicted for K eqm = 10 −16 cm 3 molecules −1 and greater total mass loss predicted for 20 K eqm both larger and smaller. The behavior results from a balance between the k r , k f and evaporation time scales for each K eqm fit. After 15 h the simulated MFR of SOA is 5-27 % of the initial (post-dilution) C OA . The general model behavior, which indicates that evaporation occurs on multiple timescales, can be understood by recognizing that decomposition of dimers composed of higher C * monomers leads to rapid evapora- 25 tion, such that the observable evaporation rate is controlled by the dimer decomposition. In contrast, decomposition of dimers composed of lower C * monomers results in species that do evaporate, but only slowly at room temperature. Given a distribution of monomers with respect to their C * , the result is a time-dependent evaporation profile Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | multiple apparent timescales for evaporation. Further, as evaporation proceeds, the finite rate of vapor loss means that over time the gas-phase concentration may build up, which will also limit the rate of mass loss. The simulated MFR values at the end of 15 h of SOA evaporation are somewhat lower than was observed in the literature experiments for dry, fresh SOA from α-5 pinene + O 3 , where MFR ∼ 0. 35-0.4 at 15 h (Vaden et al., 2011;Wilson et al., 2015). However, the extent of evaporation is dependent on the model assumptions, specifically the k loss and DF. Smaller k loss or DF leads to larger MFR at a given time due to more extensive inhibition of evaporation resulting from faster saturation of the gasphase (Fig. 7a). Conversely, larger k loss or DF lead to more extensive evaporation.
As neither the k loss nor DF are explicitly known for the literature experiments, a more quantitative comparison is not possible. However, it is nonetheless noteworthy that the model suggests that both k loss and DF can play a controlling role in observations of isothermal evaporation. These previous isothermal evaporation measurements also indicate that SOA evaporation is mostly size independent, in contrast to evaporation of 15 single-component particles (Vaden et al., 2011;Wilson et al., 2015). Simulations using the dimer-decomposition model with different starting particle sizes show some dependence on particle size (d p = 90, 180 and 360 nm), with larger particles having smaller MFRs at a given time (Fig. 7a). However, the overall differences are relatively small and reasonably consistent with the observations given that the observations have typically 20 considered a narrower size range than examined here.

Low-volatility SOA model
One alternative possibility to explain the observations of evaporation of SOA in the TD is that the observed heating-induced evaporation results from direct evaporation of low-volatility species. These low-volatility species could be either highly oxygenated 25 monomers (Ehn et al., 2014) or thermally-stable dimers or higher-order oligomers, although the thermal stability of dimers seems unlikely (Hall and Johnston, 2012a are only composed of semi-and low-volatility species, but where the volatility distribution is skewed to much lower C * than suggested from SOA growth experiments (i.e. from the Pathak et al. (2007) volatility distribution). Given that there is negligible evaporation observed at room temperature in the TD for all C OA , including C OA = 1 µg m −3 , the highest volatility bin was set at C * = 1 µg m −3 . The lowest value was set based 5 on the requirement that there remains some particle mass at ∼ 343 K. If ∆H vap is too large then even very low-volatility compounds will not persist to such high temperatures (Cappa and Jimenez, 2010;Cappa, 2010). As such, an upper-limit ∆H vap constraint of 185 kJ mol −1 was placed on the C * /∆H vap parameterization, and a lower bound C * of 10 −9 µg m −3 was used. Following Cappa and Jimenez (2010), a relationship between 10 the total organic mass and C * was assumed, where C i ,tot = a 1 + a 2 exp[a 3 (log C * ) + a 4 ].
Values of the a x parameters have been determined through data fitting; it is difficult to constrain the absolute C OA while determining the a x parameters through fitting, and thus C OA was allowed to vary. The model was fit to the average thermogram for the medium/low C OA grouping, and a good fit was found when the a x = [1.53, 8.5, 0.3, 0.59], 15 with a corresponding C OA of 71 µg m −3 (Fig. 4a). This demonstrates that an alternative model can potentially be used to explain the TD results, namely one in which the condensed-phase species are very low volatility but evaporate directly in response to heating. If the same a x distribution is used, but with C i ,tot scaled up or down to give a different 20 initial C OA (and slightly different distribution of compounds), the simulated volatility decreases slightly as C OA increases (Fig. 5b). This is mostly due to gas-phase saturation at higher concentrations, and subsequently greater recondensation as the SOA cools in the denuder. Nonetheless, this is opposite the C OA dependence predicted by the semi-volatile monomer model and is in the same direction of the observations, where 25 the high C OA grouping exhibited lower apparent volatility. There is, however, some difference in the simulated mass thermograms for low and medium C OA , which was not observed, although the gap between the low (1-10 µg m −3 ) and medium (100 µg m −3 )

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | C OA simulations is smaller than the gap between the medium and high (600 µg m −3 ) C OA simulations. If recondensation of the evaporated species were, for some reason, not particularly efficient (due perhaps to changes in the molecular composition upon heating) then the differences between the different C OA simulations would be lessened. As with the dimer-decomposition model, simulation of isothermal evaporation by the 5 low-volatility monomer model provides evidence for multiple evaporation timescales, with "fast," "medium" and "slow" components (Fig. 4b). For the same k loss (= 10 −3 s −1 ) and DF (= 30), the extent of evaporation from the low-volatility aerosol simulation at 15 h is less than for the various dimer-decomposition simulations. The low-volatility aerosol model exhibits a similar sensitivity to the assumed k loss and DF, and a slightly 10 smaller sensitivity to changes in particle size (Fig. 7b). It is apparent that the lowvolatility aerosol model is compatible with the observations from both our TD and the literature isothermal evaporation experiments (Vaden et al., 2011;Wilson et al., 2015). Although both the low-volatility aerosol and dimer-decomposition models perform equally well in explaining the observed mass thermograms and literature observations 15 of isothermal evaporation, there is a distinct difference between two model results in terms of how the particle composition is predicted to vary with temperature. Unlike the dimer-decomposition model, the predicted relative particle composition undergoes substantial changes as the particles evaporate upon heating for the low-volatility aerosol model (Fig. 6b). This model result would suggest that potentially large changes 20 in composition should be observed upon heating or, more generically, evaporation. This prediction is inconsistent with the various observations that suggest negligible to very moderate changes in the observed particle composition (Cappa and Wilson, 2011;Kostenidou et al., 2009). 25 Overall, the dimer-decomposition model of evaporation provides the most comprehensive explanation in that it can explain not only the current results where the observed ACPD Introduction

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Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | mass thermograms are nearly independent of C OA , but also the minor changes in composition that occur upon heating-induced evaporation of α-pinene + O 3 SOA observed by some (Cappa and Wilson, 2011), the moderately long timescales required for achieving equilibrium upon isothermal dilution (Grieshop et al., 2007) and the bimodality of SOA evaporation upon rapid dilution and subsequent continuous vapor stripping 5 (Vaden et al., 2011). The low-volatility monomer evaporation model can reproduce many of these observations, but suggests large compositional changes upon heating. The semi-volatile monomer model fails to reproduce nearly all of the observations. Additionally, the dimer-decomposition model is potentially consistent with suggestions that SOA particles formed under dry conditions have very high viscosity (Kannosto 10 et al., 2013;Virtanen et al., 2010;Abramson et al., 2013). The viscosity of SOA should decrease rapidly as temperature increases and, to the extent that SOA might actually be a glass, could go through a glass-liquid transition (Koop et al., 2011). If the particles were primarily semi-volatile monomers for which evaporation were limited by diffusion in the particle phase, then changes in viscosity should lead to substantial increases in 15 the observed evaporation rate (Zaveri et al., 2014). The continuous change in VFR with temperature out to relatively high temperatures suggests that the condensed-phase species must have low-volatility such that as the viscosity decreases there is no substantial impact on the observed particle evaporation. This model/observation comparison suggests that for SOA -at least that produced from the α-pinene + O 3 reaction -20 the mass thermogram does not give direct information on the distribution of volatilities of the original condensing compounds (i.e. the monomers), but on the properties of the oligomers, specifically their thermal stability. One limitation of the current kinetic model is the assumption that k r and ∆E a are the same for all dimers, whereas it is likely that the rate and temperature-sensitivity of oligomer decomposition is compound specific Despite the general success of the dimer-decomposition model in reproducing a variety of observations, it does predict some particle evaporation at room temperature in the TD, which was not observed. Further, it seems unlikely that all particle mass is converted to dimers on such rapid timescales as implied by the dimer-decomposition model; although accurate quantification of the relative fractions of dimers (and larger 5 oligomers) vs. monomers in SOA particles has proven challenging, it seems likely that the oligomer fraction is not 100 % (Hall and Johnston, 2012b;Kalberer et al., 2004;Kristensen et al., 2014), some experiments have observed apparent variations in VFR, determined from either heating or vapor stripping, as the particles are "aged" by sitting in the dark (Abramson et al., 2013) or by exposure to oxidants (Kalberer et al., 2004;10 Salo et al., 2011;Emanuelsson et al., 2013), suggesting that compositional changes (including dimer or oligomer formation) may occur on multiple timescales, ranging from seconds to minutes to hours. It therefore seems likely that a more complete representation of α-pinene + O 3 SOA volatility is some hybrid of the dimer-decomposition and lowvolatility species frameworks, where some substantial fraction of the condensed phase 15 mass exists as very low-volatility, effectively non-volatile, dimers or oligomers -or even thermally-unstable, low-volatility monomers -that decompose to produce species with a distribution of volatilities that subsequently evaporate, while some fraction exists as low-volatility (C * < 1 µg m −3 ) species that can directly evaporate but for which the actual volatilities tend to be lower than those predicted from traditional analyses of growth 20 experiments. Regardless of the details, the effective volatility of α-pinene + O 3 is much less than predicted by growth experiments.

Conclusions
Experimental observations of T -dependent SOA evaporation have been presented that demonstrate that the apparent volatility of α-pinene + O 3 SOA, as characterized by 25 heating in a thermodenuder, is mostly independent of the SOA concentration over many orders of magnitude variation. Comparison of these observations with various kinetic models of evaporation in the TD suggest the observations are most consistent with SOA from the ozonolysis of α-pinene being composed of a large fraction of effectively non-volatile, but thermally-unstable species; these species are likely dimers or higher order oligomers, but could also be exceptionally low-volatility monomers. Any monomers that do exist must be of sufficiently low volatility (< ∼ 1 µg m −3 ) that they 5 do not readily evaporate at room temperature. A dimer-decomposition model provided a good fit to the experimental observations when the monomer/dimer equilibrium constant ranged from K eqm ∼ 10 −18 to 10 −14 cm 3 molecule −1 , with corresponding rate coefficients for the reverse (decomposition) reaction ranging from k r (298 K) = 1.6 × 10 −3 to 2.8 × 10 −2 s −1 , and a difference in activation energies between the forward and reverse rate coefficients ranging from ∆E a = 15 to 42 kJ mol −1 . The best-fit dimerdecomposition model can also explain observations of slow rates of evaporation after isothermal dilution (Vaden et al., 2011;Wilson et al., 2015) and nearly constant composition as a function of rapid heating (Cappa and Wilson, 2011). These parameters would, by themselves, suggest that the SOA particles are nearly entirely composed of 15 dimers, which seems unlikely. A model where the particle was assumed to be composed of low-volatility compounds -either highly oxygenated monomers or oligomers -could explain the bulk evaporation observations nearly as well, although suggested that large changes to particle composition upon heating should be observed. Thus, it seems that a hybrid model where the particles are composed of a substantial fraction 20 of dimers (or oligomers) and some smaller fraction of low-volatility compounds may ultimately provide a more complete description. Many laboratory (Cappa and Wilson, 2011;Emanuelsson et al., 2013;Loza et al., 2013;Grieshop et al., 2007;Saleh et al., 2013) and field studies (Cappa and Jimenez, 2010) have aimed to characterize the volatility of SOA. In general, the observations 25 have concluded that the effective volatility of SOA is much lower than the volatility determined from interpretation of formation studies within a gas/particle partitioning framework. The analysis presented here suggests that this apparent discrepancy can be reconciled to a large extent through a combined framework in which the volatility Introduction  Pathak et al., 2007) provides a reasonable description of the properties of the condensing monomers, but where rapid formation of thermally-unstable dimers (and higher order oligomers) occurs, which consequently suppresses the apparent volatility of the SOA. Since the residence time in our flowtube was ∼ 1 min, these accretion reactions must occur on a similar timescale 5 (or faster). This dimer formation timescale is much faster than what is typically used within air quality models (Carlton et al., 2010), which assume timescales on the order of a day, and suggests that air quality models may therefore have SOA that is too volatile and thus overly sensitive to dilution. However, care must be taken in the implementation of any model that allows for such rapid formation of dimers, as the ultimate 10 consequence would be to transfer all semi-volatile material to the condensed phase.
One possible reconciliation is that SOA particles may actually have a very high viscosity (which is, perhaps, a consequence of oligomer formation), which can limit the transport of gas-phase material into the particle bulk and the timescale and extent of transfer of gas-phase material into the particles (Zaveri et al., 2014). Although the oligomeric con-15 tent of ambient biogenic SOA may be less than in laboratory biogenic SOA (Kourtchev et al., 2014) the presence of oligomers has been observed in both and needs to be accounted for in models of SOA volatility. Introduction

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(2) to each experiment. 15,2015 The influences of mass loading and rapid dilution on SOA volatility    15,2015 The influences of mass loading and rapid dilution on SOA volatility   Figure 5. (a) Calculated mass thermograms for variable C OA based on the best-fit parameters for the K eqm = 10 −16 cm 3 molecules −1 dimer-decomposition model as compared to the observations for the average medium/low and high C OA . (b) Same as (a), but for the best-fit low-volatility model. 15,2015 The influences of mass loading and rapid dilution on SOA volatility   Figure 6. Variation in the relative particle composition with temperature from the (a) dimerdecomposition and (b) low-volatility monomer evaporation TD models. The colors correspond to the various dimer and monomer species, defined by the monomer C * values. For the dimerdecomposition model the monomer fractional contributions are too small to be seen, and the reported C * values in the legend correspond to the parent monomer values associated with each dimer. For the low-volatility monomer case, the C * values correspond to the actual evaporating monomer values. The simulations were run for an initial C OA = 100 µg m −3 . 15,2015 The influences of mass loading and rapid dilution on SOA volatility   Figure 7. Dependence of the isothermal evaporation simulations on the assumed vapor loss rate (k loss ), dilution factor (DF) or particle diameter (d p ) for (a) the dimer-decomposition and (b) the low-volatility models. All simulations were run for an initial C OA = 100 µg m −3 . For the dimer-decomposition model, the K eqm = 10 −16 cm 3 molecules −1 best-fit results were used.