Corresponding author: A. L. Robinson, Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA. (firstname.lastname@example.org)
 Atmospheric organic aerosol concentrations depend in part on the gas-particle partitioning of primary organic aerosol (POA) emissions. Consequently, heating and dilution were used to investigate the volatility of biomass-burning smoke particles from combustion of common North American trees/shrubs/grasses during the third Fire Lab at Missoula Experiment. Fifty to eighty percent of the mass of biomass-burning POA evaporated when isothermally diluted from plume- (~1000 µg m−3) to ambient-like concentrations (~10 µg m−3), while roughly 80% of the POA evaporated upon heating to 100°C in a thermodenuder with a residence time of ~14 sec. Therefore, the majority of the POA emissions were semivolatile. Thermodenuder measurements performed at three different residence times indicated that there were not substantial mass transfer limitations to evaporation (i.e., the mass accommodation coefficient appears to be between 0.1 and 1). An evaporation kinetics model was used to derive volatility distributions and enthalpies of vaporization from the thermodenuder data. A single volatility distribution can be used to represent the measured gas-particle partitioning from the entire set of experiments, including different fuels, organic aerosol concentrations, and thermodenuder residence times. This distribution, derived from the thermodenuder measurements, also predicts the dilution-driven changes in gas-particle partitioning. This volatility distribution and associated emission factors for each fuel studied can be used to update emission inventories and to simulate the gas-particle partitioning of biomass-burning POA emissions in chemical transport models.
 Biomass-burning emissions contribute ~75% of global combustion primary organic aerosol (POA) [Bond et al., 2004]. Until recently, POA has been assumed to be nonvolatile in emissions inventories and chemical transport models, but studies during the last decade have demonstrated that a large fraction of biomass-burning POA emissions is semivolatile [Lipsky and Robinson, 2006; Grieshop et al., 2009; Huffman et al., 2009; Cappa and Jimenez, 2010]. The contribution of these semivolatile emissions to ambient particulate matter concentrations will vary with changing atmospheric conditions due to perturbations to thermodynamic equilibrium. However, few studies have quantitatively constrained the gas-particle partitioning of biomass-burning POA, which is essential for updating emissions inventories and chemical transport models to account for its semivolatile nature.
 Gas-particle partitioning of atmospheric organics is a sorptive process; vapors can absorb into organic solution or adsorb onto the surface of soot, mineral dust, and other solid substrates, while dissolution of organics into aqueous particles can also affect gas-particle partitioning. The relative contributions of these mechanisms depend on the amount of sorptive material present. In the atmosphere, absorption into an organic solution is generally thought to be the primary partitioning mechanism [Liang et al., 1997; Roth et al., 2005; Arp et al., 2008]. Therefore, at phase equilibrium, the POA emission factor (EFOA) and the mass fraction of total lower-volatility organic emissions residing in the particulate phase (Xp) can be expressed as
where Ci*(T) is the effective saturation concentration of species i at temperature T (related to liquid saturation vapor pressure), COA is the OA concentration, EFOA is the emission factor for OA (e.g., g OA kg-dry-fuel-consumed−1), fi is the mass fraction of species i, and EFtot is the emission factor of all lower-volatility organics (OA and organic vapors).
 Traditional source tests often estimate EFOA by collecting samples on quartz filters and then relating the measured OA mass to the mass of fuel consumed (e.g., g OA kg-fuel−1) [Andreae and Merlet, 2001; Hays et al., 2002; McMeeking et al., 2009]. Quartz filters capture particle-phase organics as well as a fraction of the organic vapors that adsorb to the filter (positive sampling artifact) [Turpin et al., 2000]. Lipsky and Robinson  determined that as much as 70% of the total organic carbon (OC) collected on a bare quartz filter can be a sampling artifact (i.e., adsorbed vapors), depending on dilution conditions. Furthermore, there may be a partitioning bias in source test data because COA during source tests is often much greater than ambient conditions, which shifts gas-particle partitioning toward the particle phase following equation ((1)) [Robinson et al., 2010]. Robinson et al.  estimate that as much as 80% of the OC collected on a quartz filter during traditional source testing may exist as vapors at ambient conditions due to a combination of positive sampling artifacts and partitioning biases associated with high COA. In other words, existing emissions inventories may overestimate the contribution of biomass-burning POA emissions to ambient particulate matter concentrations, as a substantial fraction of the semivolatile organic material will likely evaporate with dilution during transport away from the source. To account for the variability in the gas-particle partitioning of the POA emissions, the volatility distribution (set of fi) of the organics collected on the quartz filter (which are typically used to define POA emission factors) must be known. Equation ((1)) can then be used to calculate the POA emission factor or POA concentration at any atmospheric condition (accounting for differences in COA and/or T).
 In theory, volatility distributions can be derived from composition measurements. However, the majority of the lower-volatility organics that contribute to POA are not resolvable on a molecular level with traditional analytical instrumentation [Rogge et al., 1998; Schauer et al., 2001]. Furthermore, the saturation concentration (i.e., saturation vapor pressure) of identified compounds may not be known. Therefore, equation ((1)) is typically applied semiempirically using a surrogate set of compounds that reproduce the gas-particle partitioning of the bulk POA [Donahue et al., 2006; Robinson et al., 2010]. These surrogate compounds are often represented using a one-dimensional volatility basis set (VBS) [Donahue et al., 2006], which distributes lower-volatility organics (here defined as all organics having Ci* ≤ 3 × 106 µg m−3) over a logarithmically spaced set of bins of Ci*. The volatility basis set enables the simulation of gas-particle partitioning of all organic emissions without complete molecular identification.
 Few studies have quantified volatility distributions for biomass-burning POA emissions. Grieshop et al.  report a volatility distribution for wood smoke emitted from a small stove, while Cappa and Jimenez  derive volatility distributions for open biomass-burning OA inferred from factor analysis of ambient and thermally denuded OA from Mexico City. However, it is unclear whether these parameterizations are applicable to fresh open biomass burning or whether they capture the variability associated with different fuels and burning conditions.
 The objectives of the laboratory study described here and in E. J. T. Levin et al. (manuscript in preparation, 2013) are as follows: (1) to systematically investigate the gas-particle partitioning of biomass-burning POA emissions from a variety of fuels using thermodenuder and dilution measurements and (2) to derive volatility distributions and EFtot to predict this partitioning across the entire range of atmospheric conditions. This work focuses on thermal perturbations of gas-particle partitioning, while E. J. T. Levin et al. (manuscript in preparation, 2013) focus on dilution-based perturbations. The derived parameterizations are designed to update existing biomass-burning PM emissions inventories and chemical transport models to account for semivolatile POA.
2 Experimental Methods
 Experiments were conducted to investigate the gas-particle partitioning of POA emissions from laboratory fires during the third Fire Lab at Missoula Experiment (FLAME-III) at the U.S. Forest Service Fire Science Laboratory (FSL) in Missoula, MT during September–October 2009. FLAME-III investigated an array of fuels associated with prescribed burning and wildfires in North America (Table S1). Additional description of the experimental setup is presented by Hennigan et al. . This paper focuses on gas-particle partitioning measurements made using the sampling configuration and instruments shown schematically in Figure 1.
 Briefly, during each experiment, a small mass of fuel (0.3–1.0 kg) was ignited electrically inside the FSL combustion chamber (3014 m3) and allowed to burn to completion, filling the room with smoke. After allowing roughly 30 min for mixing, samples were then drawn from the FSL combustion chamber to characterize the emissions. Gas-particle partitioning was investigated by heating the sample in a thermodenuder and by dilution. Volatility distributions were derived by fitting the thermodenuder data; predictions based on these fits were then evaluated by comparing the predictions to the dilution data.
2.2 Emission Factors
 Emission factors were calculated using a carbon mass balance approach [Andreae and Merlet, 2001]:
where ΔCi is the background-corrected pollutant concentration (e.g., organic aerosol and total organics) and Xc is the mass fraction of carbon in the fuel (assumed to be ~0.5 based on McMeeking et al. ). The terms in the denominator are the background-corrected CO2 (LiCor Biosciences Model 820), CO (Teledyne-API Model 400A), carbonaceous PM (OC + elemental carbon, EC; Sunset Laboratories Lab OC-EC Aerosol Analyzer) and total hydrocarbons (THC; from Thermo Environmental Model 51 analyzer using flame ionization detection) concentrations expressed on a carbon mass basis (kg-C m−3 for all terms).
2.3 Dilution Measurements
 Two different types of dilution data are considered here. First, smoke concentrations inside FSL combustion chamber were slowly diluted over a period of several hours by infiltration of outside air, as the combustion chamber is a large room that is not air tight. The OA concentrations in the outside air were very low (< 2 µg m−3); therefore, this infiltration reduced the concentrations of the POA in burn chamber by a factor of 5 to 10 over the course of the experiment (~3 h). The median temperature within the laboratory was 21.4°C with a range of 11.1–29.1°C.
 Second, the smoke was also diluted by transferring it from the FSL combustion chamber into the Carnegie Mellon University (CMU) portable Teflon® environmental chamber (~7 m3) using injector diluters (Dekati DI-1000). This was done after the smoke had become well mixed in the FSL chamber (roughly 30 min after completion of the fire) [Hennigan et al., 2011]. After filling, the smoke inside the CMU chamber was a factor of ~25 to 35 more dilute than smoke inside the FSL combustion chamber, inducing evaporation of semivolatile organic material. This dilution into the sealed CMU chamber was performed using dried, HEPA- and activated-carbon-filtered air to minimize the introduction of any background organic material.
 OA concentrations in the FSL chamber were measured using a high-resolution time-of-flight aerosol mass spectrometer (HR-ToF-AMS; Aerodyne Research, Inc.) [DeCarlo et al., 2006]. Changes in partitioning due to dilution via infiltration of outside air were characterized using the measured OA-to-sulfate ratio:
where EFOA,t = 0 is the initial OA emission factor, EFOA,t is the OA emission factor at time t, and the Org:SO42− terms are the OA-to-sulfate ratio at the initial time (t = 0) and time t. Equation ((3)) corrects for both dilution and particle wall loss to the chamber walls, assuming sulfate and organic aerosol mass are lost at the same rate. Dilution via infiltration is described in detail in E. J. T. Levin et al. (manuscript in preparation, 2013).
 Nonrefractory, submicron aerosol mass inside the CMU chamber was characterized using both an HR-ToF-AMS and an Aerodyne quadrupole aerosol mass spectrometer (Q-AMS) [Canagaratna et al., 2007]; collection efficiency in the AMS was assumed to be in unity [Hennigan et al., 2011; Heringa et al., 2011]. Particle size distributions were measured using a scanning mobility particle sizer (SMPS; TSI 3081/3722; TSI, Inc.). The evolution of EFOA with dilution from the FSL chamber to the CMU chamber was also tracked using the change in the OA-to-sulfate ratio measured by the HR-ToF-AMS (equation ((3))). The CMU chamber was located outdoors and not temperature controlled. Its median temperature was 9°C with a range of ~1–20°C.
2.4 Thermodenuder Measurements
 Two thermodenuders (TD) were used to investigate the effects of heating on gas-particle partitioning; one TD-perturbed OA sampled from the FSL chamber and the other perturbed OA sampled from the CMU chamber. Briefly, a TD is a heated tube followed by a room temperature activated carbon denuder to strip the evaporated organic vapors to minimize recondensation [Huffman et al., 2008]. Both TDs were based on the design of Huffman et al. . Additional information on the TD sampling from the CMU chamber can be found in the supporting information.
 To characterize the extent of evaporation in the TD, the aerosol was alternately sampled through the TD and a bypass line maintained at ambient temperature. TD data are presented as the mass fraction remaining (MFR) in the particle phase:
where CTD and Cbypass are the OA concentrations measured downstream of the thermodenuder and bypass line, respectively. The HR-ToF-AMS was used to measure the OA downstream of the FSL combustion chamber TD; the Q-AMS was used to measure the OA downstream of the CMU chamber TD. The TD sampling directly from the FSL chamber scanned from 30 to 120°C with a centerline residence time (tres) of 13.9 sec at 25°C; the TD sampling from the CMU chamber was operated at fixed temperatures of 40, 80, and 120°C at two tres (18.6 and 6.2 sec). TD data were corrected for particle number losses (mainly due to thermophoresis) using a laboratory calibration performed with ammonium sulfate particles; losses ranged from ~5 to 15% as a function of temperature (for additional details, see the supporting information). No systematic comparison between the two AMS was performed during this study as much of the time when the HR-ToF-AMS was sampling from the CMU chamber coincided with the Q-AMS sampling through the CMU TD, complicating a direct comparison.
3 Interpreting Gas-Particle Partitioning Data
 A major goal of this work was to derive a volatility distribution to describe the gas-particle partitioning data. If the aerosol is in phase equilibrium, a volatility distribution can be derived by fitting equation ((1)) to the gas-particle partitioning data; if the aerosol is not in equilibrium, then a kinetic model must be used to interpret the data. The equilibration time scale τ for an aerosol can be approximated as the inverse of the condensation sink (CS) [Seinfeld and Pandis, 2006]:
where dp is the mass-median particle size, Nt is the total aerosol number concentration, D is the diffusion coefficient for the organic vapors in air (assumed to be 5 × 10−6 m2 s−1) [Riipinen et al., 2010], and F is the Fuchs-Sutugin correction factor, which accounts for non-continuum effects. Kn is the Knudsen number (= 2λ/dp, where λ is the mean free path of organic molecules in air at 1 atm and 25°C and taken to be 65.2 nm), and α is the mass accommodation coefficient.
Saleh et al.  recommended that a system should be considered to be in equilibrium only if the ratio of tres/τ > 5. If α is greater than or equal to 0.1, this criterion was met for all of the FSL combustion chamber data and most CMU environmental chamber data. The FSL chamber was slowly diluted over a period aerosol several hours versus τ values of ~0.5–25 sec if α = 1 and ~3–170 sec if α = 0.1. The smoke was allowed to equilibrate in the CMU chamber for 30 min before sampling versus τ values of ~0.5–5 min for α = 1 and ~4–26 min for α = 0.1. If the aerosol had not equilibrated in the CMU chamber prior to characterization, then our analysis will underestimate the volatility of the biomass-burning POA.
 The relatively short residence times within the TD suggest that the aerosol likely did not achieve gas-particle equilibrium (tres/τ < 5). Consequently, the TD data were analyzed using the evaporation kinetics model developed by Riipinen et al. , rather than the equilibrium model presented in equation ((1)). This model tracks both particle- and gas-phase concentrations in each one-dimensional volatility basis set (VBS) [Donahue et al., 2006], bin i:
where Cp,i is the particle-phase concentration of i, Cg,i is the gas-phase concentration of i, Xm,i is the mass fraction of i in the particle phase, and Kei accounts for the changes in saturation concentration (vapor pressure) due to the surface curvature of the particle. Expressions defining Xm,i and Kei are provided in the supporting information. These equations were used to model only the heated section of the TD, and the aerosol entering the TD was assumed to be in phase equilibrium.
 Recondensation [e.g., Cappa, 2010; Fuentes and McFiggans, 2012] or evaporation in the denuder [Cappa and Wilson, 2011] can complicate the analysis of TD data. We did not consider either of these phenomena in the analysis. Saleh et al.  argue that there is little perturbation to the aerosol in the denuding section. Although no measurements were made through the TD at room temperature, only 10% of the OA has evaporated at T = 30–40°C, suggesting that evaporation in the denuding section was not very significant (see Figure 3a below). If recondensation occurred in the TD, then our derived volatility distributions will be less volatile than the true distribution. In other words, we would be underestimating evaporated OA mass.
 The TD data were collected at three different residence times to investigate the mass accommodation coefficient (α). Recent work has suggested that α may be less than unity for oxidized organic aerosol. Saleh et al.  estimated α of ambient OA ranging from 0.28 to 0.46, while Cappa and colleagues have determined that α > 0.01 using laboratory-generated and ambient OA [Cappa and Jimenez, 2010; Cappa and Wilson, 2011].
4 Experimental Results
 Partitioning theory (equation ((1))) indicates that gas-particle partitioning of semivolatile organics depends on COA. To investigate the variation of EFOA with COA, measurements were performed at different levels of dilution using both the FSL and CMU chambers. Emissions data from both chambers are presented in Figure 2 as partitioning plots (EFOA versus COA). Figure 2a highlights data from two experiments (Burns 38 and 57); Figure 2b compiles data from all of the different burns. Closed markers represent single scans from the HR-ToF-AMS sampling from the FSL chamber, while open markers represent data averaged over 1 h from the Q-AMS sampling from the CMU chamber. The initial EFOA was calculated immediately after the emissions became well mixed inside the entire FSL combustion chamber using equation ((2)). This corresponds to the highest EFOA (i.e., t = 0) for each experiment. The changes in partitioning with dilution were then tracked using the organic-to-sulfate ratio (equation ((3))) for both the FSL and CMU chamber. The organic-to-sulfate ratio isolates the changes in gas-particle partitioning by correcting the data for both dilution and particle losses to the chamber walls.
 Figure 2 indicates that the combination of the two chambers enabled EFOA measurements for the same burn to be made over a very wide range of COA. The median initial COA inside the FSL combustion chamber was ~500 µg m−3 with a range from ~100 to 5000 µg m−3. This is much higher than typical ambient concentrations but comparable to those in fire plumes. Infiltration of outside air then reduced the COA inside the FSL chamber by a factor of 5 to 10 over the course of the experiment (roughly 3 h). COA inside the CMU chamber ranged from 5 to 50 µg m−3 (25 to 35 times lower than the initial, well-mixed conditions inside the FSL combustion chamber). Therefore, the CMU chamber data are representative of ambient conditions.
 Two conclusions can be drawn from Figure 2. First, as expected, a very wide range of EFOA values were measured across the set of experiments with values ranging from ~0.5 to ~300 g OA kg-dry-fuel−1 based on the AMS measurements. This variability is consistent with the large body of biomass-burning emissions data [Andreae and Merlet, 2001; Hays et al., 2002; McMeeking et al., 2009]. It reflects the fact that biomass-burning emissions depend on fuel composition and combustion conditions. These experiments did not control for combustion phase or intensity, and a wide range of combustion conditions occurred including primarily flaming fires versus primarily smoldering fires, driven by fuel type and fuel moisture content. The highest-emitting fuels (~100–300 g OA kg-dry-fuel−1) had high water contents leading to less efficient combustion [Watson et al., 2011]. The fire-integrated modified combustion efficiency and emission factors are listed in the supporting information.
 The second important conclusion shown in Figure 2 is that, for a given burn, the measured EFOA decreased with decreasing COA. For example, Figure 2a shows that dilution from the FSL combustion chamber into the CMU environmental chamber reduced EFOA by roughly a factor of 2 (the CMU data roughly correspond to the t = 0 FSL data point). Figure 2b shows that this trend was observed across the entire set of experiments. However, in two burns, similar EFOA was measured in both the CMU and the FSL chamber (e.g., burns 42 and 53). This may be observed because the CMU chamber was roughly 10°C colder than the FSL chamber, which promotes recondensation of organic vapors that evaporated during dilution.
 The TD data provide additional evidence that a significant fraction of the POA emissions are semivolatile. Both the FSL and CMU chamber TD data are presented in Figure 3a. In every experiment, the POA evaporated (i.e., MFR decreased) with heating; for example, roughly 20% of the POA evaporated with heating to 40°C. Significant evaporation was observed with heating at both ambient- (COA ~5 µg m−3) and plume-like concentrations (COA ~500 µg m−3). This demonstrates that POA is semivolatile over a wide range of conditions. There was some scatter in the TD data which was largely due to differences in COA and particle size (see equations (5)–(6)). Some MFR values were slightly greater than unity (the theoretical maximum) due to low Q-AMS signal-to-noise at low COA.
 The extent of evaporation (MFR) did not vary strongly with residence time. For example, in the CMU TD, the median value of MFR at 80°C was 0.53 for the long tres (18.6 sec) versus 0.61 for the short tres (6.2 sec), thus having a relative percent difference of ~14%. If α = 1 or 0.1, then equation (6) predicts a relative percent difference of ~17% and ~12% between the two residence times for values of α = 1 and 0.1, respectively. As α become smaller, the difference in MFR between the two residence times decreases since the evaporation rate is slower (e.g., for α = 0.01, the relative percent difference between the two tres is ~5%). This suggests that there was little mass transfer resistance to evaporation inside the TD, provided that ΔHvap was similar to that recently inferred for aerosol mixtures [e.g., Grieshop et al., 2009; Ranjan et al., 2012] rather than pure components [e.g., Epstein et al., 2010]. A similar conclusion is implied by the lack of a plateau in the thermograms in Figure 3a [e.g., Cappa and Jimenez, 2010].
 Figures 2 and 3 clearly demonstrate that a large fraction of the POA is semivolatile. The large, systematic changes in gas-particle partitioning over a wide range of measured COA and temperature implies a broad distribution of organic compound volatilities. Finally, the similarity in the partitioning behavior (i.e., similar ΔEFOA/ΔCOA or ΔMFR/ΔT) across the set of experiments using different fuels suggests that a single volatility distribution may be adequate to predict the gas-particle partitioning of the entire data set.
5 Inferring Volatility Distributions From the Thermodenuder Data
 In this section, a single set of partitioning parameters (fi, ΔHvap,i and α) is presented to represent all of the TD data. These parameters were derived by fitting equation (6) to all of the TD data presented in Figure 3a. These data span a broad range of conditions—COA (~1–5000 µg m−3) and T (~30–120°C)—enabling the fits to constrain the volatility distribution over a wide range of Ci* values (10−2 to 104 µg m−3). Therefore, the derived parameterizations are constrained by data across both plume- and ambient-like conditions. All of the TD data were fit simultaneously since there appears to be only modest experiment-to-experiment differences in gas-particle partitioning behavior.
 Since ΔHvap,i and α are generally unknown a priori, uniqueness is a major problem when fitting TD data [Cappa and Jimenez, 2010]; that is, the TD data can be equivalently described using multiple combinations of partitioning parameters (fi, ΔHvap,i and α). To investigate this issue, solutions for a set of volatility distributions were derived by fitting the entire TD data set using different combinations of ΔHvap,i and α. The fitting was performed using a brute-force algorithm that systematically considered a large number (9900) of combinations of fi, ΔHvap,i, and α. The evaporation kinetics model of Riipinen et al.  was then used to calculate the extent of evaporation (MFR) for each combination of inputs (ΔHvap,i, α, and fi). The model performance for each combination of inputs was assessed by computing the sum of the square of the residuals (SSR) between measured and predicted MFR.
 The 9900 different combinations of input parameters for the brute-force fitting are summarized in Table 1. The goal was to consider a wide, but physically realistic range, in each parameter. First, a log-linear relationship was assumed between ΔHvap,i and Ci* [Epstein et al., 2010]. The range of slope and intercept values for this relationship is listed in Table 1; they were defined based on results from Grieshop et al.  and Epstein et al. . There is similar uncertainty in the value of α [Kolb et al., 2010]. In the literature, α is generally assumed to be in unity; however, recent studies have suggested that α may have values between 0.01 and 1 [Saleh et al., 2009; Cappa and Jimenez, 2010; Lee et al., 2010; Riipinen et al., 2010; Saleh et al., 2012]. Therefore, the calculations were performed with α values of 1, 0.1, and 0.01. While the actual value of α may fall in between these logarithmically spaced values, the different partitioning parameters are correlated. In other words, the effects of changing α can be compensated for, to some extent, by adjusting ΔHvap,i and fi. Therefore, without additional constraints, the fitting procedure cannot provide a highly refined value of α. The range of α considered here does provide some insight into the importance of mass transfer resistance.
Table 1. Parameter Ranges Used for Brute-Force Fitting
ΔHvap intercept (kJ mol−1)
ΔHvap slope (kJ mol−1)
70, 85, 100, 115, 130
4, 6, 8, 11
0.01, 0.1, 1
log Ci* (µg m−3)
Minimum fi value
Maximum fi value
 For each combination of ΔHvap,i and α, model calculations were performed for 165 different volatility distributions defined between the upper and lower bounds listed in Table 1. These bounds were defined based on a preliminary analysis using a subset of the data from the CMU TD. In this preliminary analysis, it was determined that there must be some mass in the Ci* = 10−2 µg m−3 bin; hence, the minimum value of this bin was constrained to be nonzero. In the atmosphere, material in this Ci* = 10−2 µg m−3 bin will essentially always be in the particle phase, so any less volatile material (Ci* < 10−2 µg m−3) is incorporated into this bin.
 Other inputs for the model were the experimentally measured mass-median dp (using the SMPS) and COA (from the HR-ToF-AMS or Q-AMS). Size distributions were not measured in FSL combustion chamber; therefore, we used the particle size distributions measured in the CMU environmental chamber for all of the analyses. This assumption is not strictly valid because dilution causes the particles to shrink when they are transferred from the FSL combustion chamber to the CMU environmental chamber. However, additional processes such as coagulation complicate extrapolating the CMU chamber size data back to the FSL chamber. Therefore, we assume that growth due to coagulation will roughly offset shrinkage due to evaporation, although in reality, the particle size distributions are likely different. Finally, values of D, σ, ρ, and MWi were taken from the literature (summarized in Table S2); prior work has demonstrated that the model is not overly sensitive to these parameters [Riipinen et al., 2010; Fuentes and McFiggans, 2012].
 SSR values for all 9900 different combinations of input parameters are presented in Figure 4 as contours that are a function of the assumed slope (x axis) and the assumed intercept for the log linear ΔHvap relationship (y axis) as well as α (different panels). An acceptable solution was defined as one that described the experimental data within experimental uncertainty. Using the measurement uncertainties (estimated to be ± 20% (1σ) for the measured mass concentrations in the AMS [Bahreini et al., 2009] and ± 10% for measured diameters in the SMPS based on product literature), a threshold value of 4.18 for the maximum SSR was defined for an acceptable solution (see supporting information for additional information).
 A large number (441 out 9900) of the combinations of fi, ΔHvap,i, and α describe the entire set of TD data within the experimental uncertainty. Therefore, there is no single unique solution. The dashed line in Figure 4 encloses the range of ΔHvap,i and α for which at least one of the input volatility distributions yielded an SSR value less than the experimental uncertainty. For most of these combinations, multiple acceptable distributions have been found, as shown in Figure S2; the symbols indicate the minimum SSR for a given combination of ΔHvap,i and α.
 Figure 4 suggests that ΔHvap,i and α were strongly correlated; for example, low values of ΔHvap,i, were required when α = 1 versus higher values when α < 1. However, the values of ΔHvap,i that yield statistically acceptable fits were lower than those of pure components (based on the semiempirical correlation of Epstein et al. ). This ΔHvap lowering was likely an artifact of the representation of the partitioning behavior of thousands of organic compounds using seven surrogate species [Donahue et al., 2006]. Finally, for the ranges of the parameters considered in this analysis (Table 1), mass transfer limitations do not appear to be significant because only 0.4% of the statistically acceptable solutions from the input parameter space were found for α = 0.01. Obtaining additional solutions for α = 0.01 requires physically unrealistic values of ΔHvap (values greater than that from pure components based on Epstein et al. ).
 The best fit (lowest SSR) volatility distribution and associated ΔHvap,i derived for biomass-burning POA emissions are listed in Table 2. This entire set of parameters (fi, ΔHvap,i and α) must be used together to describe partitioning data (i.e., if ΔHvap,i or α are changed, the data must be refit to find a new set of fi). The best solutions for α = 0.1 and α = 0.01 are provided in Table S3 in the supporting information.
Table 2. Recommended Volatility Distribution for Biomass-Burning POA Emissions (α = 1, ΔHvap = 85 − 4 log Ci*)
log Ci* (@ 298K)
 Figure 3a compares the best fit volatility distribution to the experimental data. The solid line is the prediction using the median observed values of COA and dp, while the gray region shows the range of predictions for all possible combinations of measured COA and dp. Almost all of the data are bounded by the gray region, suggesting that the α = 1 solution captures most of the variability in the observed MFR data by simply accounting for variations in COA and dp.
 Figure 3b provides a more robust assessment of the goodness of fit. It presents a scatterplot of measured versus calculated MFR. The best fit set of parameters listed in Table 2 reproduces more than 95% of the TD data within the experimental uncertainty. This demonstrates that a single set of partitioning parameters can reproduce the entire TD data set that included a wide range of fuels and combustion conditions. Figure 3b also demonstrates that the scatter in the TD data shown in Figure 3a was primarily due to differences in COA and dp that affect the evaporation rate. Since this parameterization is able to reproduce both the FSL chamber and CMU chamber TD data reasonably well, the recommended parameterization appears robust for describing biomass-burning POA gas-particle partitioning for both plume- and ambient-like conditions.
6 Emission Factors for Lower-Volatility Organics (EFtot)
 This section compares predictions based on partitioning parameters derived from the TD data (Table 2) to the dilution data from both chambers presented in Figure 2. This provides an important, independent test of the proposed set of partitioning parameters because the dilution data were not used to derive the parameters listed in Table 2.
 To predict POA emission factors and concentrations, the best fit partitioning parameters listed in Table 2 (fi, ΔHvap,i, and α) must be combined with an emission factor for lower-volatility organics (EFtot in equation ((1))). Although a single set of partitioning parameters (fi, ΔHvap,i, and α) appears to describe all of the data, there were large burn-to-burn variations in EFtot. This is demonstrated by the large range of EFOA shown in Figure 2 (roughly two orders of magnitude separate the lowest-emitting burn and the highest-emitting burn). Therefore, separate values of EFtot were derived for each burn. These were calculated by applying equation ((1)) to the measured EFOA data in Figure 2 using the best fit volatility distribution listed in Table 2.
 The quality of the predictions of EFOA using the parameters in Table 2 is shown in Figure 2. Most of the predictions fall within the uncertainty range of the data (±30%). However, there are some exceptions. Underpredictions of EFOA in the combustion chamber are likely attributed to particle and vapor wall loss (see E. J. T. Levin et al. manuscript in preparation, 2013 for more details), while underpredictions of EFOA in the CMU chamber appear to be large due to differences in temperature between the FSL chamber and the CMU chamber, as the median ΔT between the two chambers was ~10°C. One additional factor that could contribute to the systematic bias between the measurements and the model is if the aerosol had not reached equilibrium in the CMU chamber; this could occur if α was less than 0.1. Finally, we are unable to explain the observed behavior of smoke from Burns 53 and 60, during which EFOA increased with dilution. We attribute this increase to experimental uncertainty. Nevertheless, the model representation of the data is generally robust.
 A final detail is that the volatility distribution (and EFtot) can only be constrained over the range of the experimental data. The maximum concentrations in the FSL combustion chamber were ~5000 µg m−3, which means that experimental data only provide information on the emissions up to a Ci* value of about 104 µg m−3 (the maximum volatility bin in Table 2). Therefore, the derived EFtot values can only account for emissions with a Ci* value less than or equal to ~104 µg m−3. We refer to this value of EFtot as EF10000, which corresponds to the emission factor of all lower-volatility organics that fall in the Ci* = 104 µg m−3 and lower bins. This limitation does not affect the utility of the proposed distribution for predicting gas-particle partitioning of the POA because atmospheric (and even plume) COA are generally orders of magnitude smaller than 104 µg m−3. However, vapors having Ci* > 104 µg m−3 likely contribute to secondary organic aerosol formation [Robinson et al., 2007]; these vapors are not included in the EF10000 values derived here.
 Figure 5 presents the EF10000 values for each burn. As expected, they span a wide range, from ~5 g kg-fuel−1 to ~500 g kg-fuel−1. The error bars in Figure 5 represent the relative standard deviation (~10–20%) in predicted EF10000 for each burn for all 441 statistically acceptable solutions. Direct comparisons of these values to emission factors from literature are complicated because quartz filter measurements are influenced by both partitioning biases and sampling artifacts. Our EF10000 are comparable to quartz-filter-derived emission factor values reported in the literature, but it is not known what subset of organics the literature values represent (e.g., EFOA and EF10000).
 Figure 6 presents emissions data as particle fractions (Xp; equation ((1))) calculated by normalizing EFOA in Figure 2 with the EF10000 values in Figure 5. Xp is simply the ratio of EFOA measured with the AMS to EF10000 for that burn. This causes all of the data to cluster along a single curve, which demonstrates that the volatility distribution listed in Table 2 provides a reasonable (yet imperfect) representation of measured changes in partitioning with dilution.
 The solid line in Figure 6a represents the predicted partitioning using equation ((1)) and the volatility distribution listed in Table 2 at 25°C. The gray area in Figure 6a indicates the range of predictions based on all 441 statistically acceptable fits. Equilibrium calculations (equation ((1))) were performed for comparisons with the chamber data because the best fit solution has an α value of 1, so the OA should be in phase equilibrium (see section 3).
 Figure 6b indicates that the model/measurement agreement for most points was within ±30% (the experimental uncertainty). The model predictions shown in Figure 6a were not derived by fitting the dilution data. Therefore, this figure provides an independent evaluation of the parameterization. However, the model based on the parameters in Table 2 does not perfectly reproduce the data. The most notable model/measurement discrepancy is the CMU chamber data, most of which falls well outside the error bounds. The CMU chamber data suggest that the aerosol was less volatile than the predictions based on our recommended parameters. However, the CMU chamber was, on average, 10°C colder than the FSL chamber. The base comparison shown in Figure 6 does not account for this temperature difference. Figure 6 also provides a model prediction at the median CMU chamber temperature (9°C; dashed line). Accounting for this temperature difference greatly improves the model performance, shifting the model predictions to within the experimental uncertainty. Another factor that could potentially contribute to the discrepancy is if the CMU chamber has not reached phase equilibrium (i.e., if α ≤ 0.1).
 These deviations between the model predictions and dilution data must be kept in perspective. First, the proposed volatility distribution provides a much more accurate representation of the data than the assumption of nonvolatile POA (i.e., no change in Xp with COA). Second, using a single distribution to represent all of the data (albeit imperfectly) has significant advantages over using multiple distributions specific to individual fuels or combustion conditions, even if those other distributions provide slightly improved model performance.
7 Discussion and Atmospheric Implications
 Both the thermodenuder and dilution data clearly demonstrated that the majority of the POA emissions from laboratory fires investigated here were semivolatile across a very wide range of atmospheric conditions. The FSL chamber dilution and TD data indicated that both heating and dilution of biomass-burning POA under plume-like conditions cause substantial evaporation. Substantial evaporation was also observed when the biomass-burning POA was under ambient-like conditions inside the CMU chamber. As expected, the total emissions of lower-volatility organics (i.e., EFtot representing organic material spanning Ci* 10−2 to 104 µg m−3) varied widely with fuel composition and burning conditions. However, essentially all of the partitioning data can be represented (within experimental uncertainty) using a single-partitioning parameterization (fi, ΔHvap,i and α).
 Given the variability in the composition of biomass smoke [Fine et al., 2001; Schauer et al., 2001; Fine et al., 2002; McMeeking et al., 2009], one might consider the similarity in the measured partitioning behavior across the set of experiments surprising. However, the behavior of the bulk POA is determined by a complex mixture of hundreds of lower-volatility organic compounds. When taken together, the overall partitioning behavior of all these mixtures (i.e., the emissions from all biomass fuels considered in this study) was similar enough to be represented reasonably well using a single parameterization. Parameterizations of somewhat higher statistical quality can be achieved if one considers the data from each burn individually. However, in our opinion, the very modest improvements in model performance are not worth the added complexity of having to treat the partitioning behavior of each type of smoke differently. Having one set of parameters simplifies accounting for gas-particle partitioning of biomass-burning POA in emissions inventories and chemical transport models. Although we investigated emissions from 15 fuels over a variety of combustion conditions, additional laboratory or field data are needed to further test the proposed partitioning parameterization across an even broader range of emissions. Furthermore, emissions experiments and inventories must report an emission factor as well as the OA concentration and temperature at which that emission factor was measured in order to account for gas-particle partitioning with atmospheric transport.
 Uniqueness complicates the derivation of gas-particle partitioning parameterizations from thermodenuder data. Of the 9900 different combinations of properties considered in this analysis, 441 provided statistically acceptable fits that agreed within experimental uncertainty. Although all of these fits provide a reasonable representation of the experimental data, an important question is how well constrained the solutions are as one extrapolates away from measurement conditions.
 Figure 7a presents Xp calculated using the parameters in Table 2 over a wide range of atmospheric conditions. These calculations were performed using equation ((1)) by varying COA and T. Figure 7b provides the percent relative standard deviation (% RSD) of all the different values of Xp across the set of 441 statistically acceptable solutions. From Figure 7, we can draw several conclusions. Gas-particle partitioning (i.e., Xp) varies by more than an order of magnitude across the atmospheric range of COA and T (Figure 7a). This implies that material present in the particle phase in one part of the atmosphere will likely exist in the gas phase elsewhere (e.g., from the immediate proximity of a fire to an area with lower biomass-burning emissions) and vice versa (e.g., with undiluted lifting of a biomass-burning plume to the colder free troposphere by dry convection). Therefore, inventories and models need to explicitly account for gas-particle partitioning of biomass-burning POA.
 As expected, the partitioning predictions from the set of statistically acceptable solutions diverge (i.e., % RSD increases in Figure 7b) as we extrapolate away from the experimental conditions (COA ≈ 5–50 µg m−3) toward more dilute conditions (COA ≈ 0.1–1 µg m−3). Fortunately, the differences among the set of 441 solutions was relatively small across a wide range of atmospheric conditions (% RSD ≈ 10–30%). Therefore, all of the acceptable solutions predict similar atmospheric behavior. Furthermore, the variability across the set of solutions (%RSD < 30%) was much less than the changes in gas-particle partitioning across the range of atmospheric conditions (more than a factor of 10), suggesting that all solutions could be used interchangeably with similar results.
 Figure 7a also demonstrates the predicted sensitivity of gas-particle partitioning of biomass-burning POA to changes in temperature and concentration over a wide range of atmospheric conditions. Within the range of COA = 0.5–30 µg m−3 (OA levels in the Northern Hemisphere) [Zhang et al., 2007], isothermal dilution causes Xp to change by ~2.5% (µg m−3)−1. Xp is most sensitive to changes in COA at clean conditions (i.e., at low concentrations). The sensitivity of Xp to changes in temperature is ~0.7% °C−1, between T = −50 to 50°C. Consequently, changes in both COA and T can strongly influence gas-particle partitioning of biomass-burning POA.
 The lowest volatility bin considered in our analysis was 10−2 µg m−3. In reality, organic material having Ci* < 10−2 µg m−3 is likely present in the emissions. In the supporting information, we provide an alternate solution extending Ci* to 10−6 µg m−3, which may prove useful for modeling thermal desorption techniques (e.g., from the impactor in the micro-orifice volatilization impactor chemical ionization mass spectrometer) [Yatavelli et al., 2012] or in advanced chemical modeling (new particle formation [Pierce et al., 2011] or atmospheric lifetime using the 2D-VBS [Donahue et al., 2013]). Both the recommended (Table 2) and alternate (Table S4) solutions are derived following the same approach and yield nearly identical results for atmospheric gas-particle partitioning.
 We thank the staff at FSL and especially Cyle Wold, Emily Lincoln, and Wei Min Hao for supporting this project. We also thank Mike Cubison, Amber Ortega, and Sanna Saarikoski for their assistance in collecting data. Funding was provided by the National Park Service, Joint Fire Science Program and the EPA STAR program through the National Center for Environmental Research (NCER) under grants R833747 and R834554, and DOE (BER, ASR program) DE-SC0006035. The views, opinions, and/or findings contained in this paper are those of the authors and should not be construed as an official position of the funding agencies. Although the research described in this article has been funded in part by the United States Environmental Protection Agency, it has not been subjected to the Agency's required peer and policy review and therefore does not necessarily reflect the views of the Agency and no official endorsement should be inferred.