The experimental data we use are the same as reported in Buchholz et al. (2019, 2020). We briefly summarize the measurement setup below. We generated the particles with a potential aerosol mass (PAM) reactor (Kang et al., 2007; Lambe et al., 2011) from the reaction of α-pinene with O3 and OH at three different oxidation levels (average oxygen-to-carbon (O:C) ratios of 0.53, 0.69 and 0.96). We focus on the lowest O:C (0.53) and medium-O:C (0.69) experiments in this work. The closer analysis of the high-O:C experiments suggests particle-phase reactions during the evaporation (Buchholz et al., 2019, 2020). To avoid the uncertainty that would arise from unknown particle-phase reactions, we chose not to include the high-O:C data in our analysis.

We selected a monodisperse particle population (mobility diameter dp = 80 nm) with two nano-tandem-type differential mobility analyzers (nano-DMA; TSI Incorporated, model 3085) from the initial polydisperse particle population. The size selection diluted the gas phase, initiating particle evaporation. The monodisperse aerosol was left to evaporate in a 100 L stainless-steel residence time chamber (RTC). We measured the particle size distribution during the evaporation with a scanning mobility particle sizer (SMPS; TSI Incorporated, models 3082 and 3775). The RTC filling took approximately 20 min, and we performed the first size-distribution measurement in the middle of the filling interval. To obtain short residence time data (data before 10 min of evaporation) we added a bypass to the RTC, which led the sample directly to the SMPS. By changing the length of the bypass tubing, we were able to measure the particle size distribution between 2 and 160 s of evaporation. We measured the isothermal evaporation up to 4–10 h, depending on the measurement. We performed the measurements for each oxidation level both at high relative humidity (RH = 80 %) and at dry conditions (RH < 2 %). The change in particle size with respect to time is called an evapogram. In an evapogram, the horizontal axis presents evaporation time, and the vertical axis shows the evaporation factor (EF), i.e., the measured particle diameter divided by the initially selected particle diameter.

To classify the oxidation level of the particles, we derived the average O:C ratio from composition measurements with a high-resolution time-of-flight aerosol mass spectrometer (AMS; Aerodyne Research, Inc.). Furthermore, we conducted detailed particle composition measurements with an Aerodyne Research, Inc. FIGAERO (Lopez-Hilfiker et al., 2014) coupled with a chemical ionization mass spectrometer (CIMS), with iodide as the reagent ion (Aerodyne Research Inc.; Lee et al., 2014). Previous studies using FIGAERO–CIMS with iodide as the reagent ion found 50 % or better mass closure compared to more established methods of quantifying organic aerosol (OA) mass (albeit with high uncertainties; Isaacman-VanWertz et al., 2017; Lopez-Hilfiker et al., 2016). Therefore, it appears that the bulk of reaction products expected from α-pinene oxidation contains the functional groups required for detection by our FIGAERO–CIMS.

In the FIGAERO inlet, particles are first collected on a polytetrafluoroethylene (PTFE) filter. Then the collected particulate mass desorbs slowly due to a gradually heated nitrogen flow. The desorbed gaseous compounds are then transported into the CIMS for detection. We derived the average chemical composition of the particles by integrating the detected signal of each ion over the whole desorption interval. For each ion, the change in detected signal with desorption temperature is called a thermogram, and generally, the temperature at the maximum of the thermogram (Tmax) is correlated to the volatility of the detected ion. Similar to Bannan et al. (2019) and Stark et al. (2017), we calibrated the Tmax–volatility relationship using compounds with known vapor pressure. The calibration procedure is described in the Supplement.

We collected particles for FIGAERO–CIMS analysis at two different stages of the evaporation. We refer to these samples as either “fresh” or “RTC” samples. The fresh samples were collected for 30 min directly after the selection of the monodisperse population. The RTC samples of the residual particles were collected for 75 min after 3–4 h of evaporation in the RTC. The collected particulate mass was 140–260 and 20–70 ng for the fresh and the RTC samples, respectively. More details about sample collection, desorption parameters and data analysis can be found in Buchholz et al. (2020).

We represent the myriad of organic compound in the SOA particles with a one-dimensional volatility basis set (1D VBS; below only VBS; Donahue et al., 2006). The VBS groups the organic compounds into “bins” based on their effective (mass) saturation concentration C∗, defined as the product of the compounds' activity coefficient and saturation concentration. Generally, a bin in the VBS represents the amount of organic material in the particle and gas phases. In our study, the walls of the RTC have been shown to work as an efficient sink for gaseous organic compounds (Yli-Juuti et al., 2017). Thus, we can assume that the gas phase in our experimental setup does not contain organic compounds, i.e., the amount of organic matter in a bin is the amount in the particle phase. To distinguish from a traditional VBS that groups the organic compounds to bins such that there is a decadal difference in C∗ between two adjacent bins, we call the VBS in our work a volatility distribution (VD). We present the amount of material in each VD bin as the dry mole fraction, i.e., the mole fraction of the organics, excluding water. In the analysis presented below, we assign properties to each VD bin (e.g., molar mass), treating each bin as if it consisted of only a single organic compound with a single set of properties. The physicochemical properties of each VD bin are assumed to be the same. These properties and the ambient conditions of each evaporation experiment are listed in Table 1.

We followed a similar approach as in Yli-Juuti et al. (2017) and Tikkanen et al. (2019) to derive a VD at the start of the evaporation from an evapogram. To model the evaporation at high RH, we used a process model (liquid-like evaporation model, hereafter LLEVAP) that assumes a liquid-like particle, i.e., a particle in which there are no mass transfer limitations inside the particle and where the mass flux of a VD bin in the particle phase can be calculated directly from the gas-phase concentrations of the VD bin both near the particle surface and far away from the particle (Vesala et al., 1997; Lehtinen and Kulmala, 2003; Yli-Juuti et al., 2017). In this case, the main properties for defining the evaporation rate are the saturation concentrations of each VD bin and their relative amounts in the particle.

We used the LLEVAP model to characterize the volatility range that can be interpreted from the evaporation measurements. We calculated the range by modeling the evaporation of a hypothetical particle that consists of one organic compound evaporating in dry conditions. We calculated the evaporation for the range of log10(C∗) values from -5 to 5. We determined the minimum C∗ value to be the value that still showed “detectable evaporation”, i.e., at least 1 % change in particle diameter during the evaporation time (up to 6 h), and the maximum C∗ value to be the value before “complete evaporation” occurred, i.e., 99 % particle diameter change within the first 10 s. The minimum log10 (C∗) calculated with this method was -3 and the maximum log10 (C∗) was 2. We then modeled the particle composition with six VD bins with C∗ values between these minimum and maximum values. Each VD bin has a decadal difference in C∗ to an adjacent VD bin (like in the traditional VBS). We note that, based on this analysis, all the compounds with log10 (C∗) < -3 will not evaporate during the experimental timescale. This means that any compounds with lower C∗ than this threshold will be assigned to the log10 (C∗) = -3 VD bin. Similarly, any compound with log10 (C∗) > 2 will be classified into the log10 (C∗) = 2 VD bin or not be detected at all due to evaporating almost entirely before the first measurement point.

We calculated the dry particle mole fraction of each VD bin at the start of the evaporation by fitting the evaporation predicted with the process model to the measured evapograms. Our goal was to minimize the mean squared error in a vertical direction between the experimental data and the LLEVAP output. We used the Monte Carlo genetic algorithm (MCGA; Berkemeier et al., 2017; Tikkanen et al., 2019) for the input optimization. In the optimization, we set the population size to be 400 candidates, number of elite members to 20 (5 % of the population), number of generations to 10 and number of candidates drawn in the Monte Carlo (MC) part to 3420, which corresponds to half of the total process model evaluations done during the optimization. We performed the optimization 50 times for each evapogram and selected the best-fit VD estimate for further analysis.

The VD derived from the evapogram is hereafter referred to as the VDevap. The initial composition of the SOA particles in the dry and wet experiments was the same and can be described by the same fitted VDevap as the particles were generated at the same conditions in the PAM and only the evaporation conditions changed.

As shown by Bannan et al. (2019) and Stark et al. (2017), the peak desorption temperature, Tmax, can be used together with a careful calibration to link desorption temperatures from the FIGAERO filter to C∗ values for the detected ions. In principle, this would allow us to assign one C∗ value to each ion thermogram. But this assumes that one detected ion characterized by its exact mass is indeed just one compound. In practice, this is not always the case, and for some ion thermograms, a bimodal structure or distinct shoulders and/or broadening is visible. This can be caused by isomers of different volatility which cannot be separated even by high-resolution mass spectra.

Another complication arises due to the thermal-desorption process delivering the collected aerosol mass into the CIMS. Especially multifunctional and, hence, low-volatility compounds may thermally decompose before they desorb from the filter and, thus, are detected as smaller ions. The apparent desorption temperature is then determined by the thermal stability of the compound and not its volatility. Typically, this decomposition process starts at a minimum temperature and will not create a well-defined peak shape (Buchholz et al., 2020, Schobesberger et al., 2018), presumably because an observed decomposition product may have multiple sources, especially when including all isomers, and the ion signal for the respective composition may overlap with the signal of isomers derived from true desorption. For example, a true constituent of the SOA particle may give rise to an observed main thermogram peak, but it may be broadening and/or tailing if a decomposition product has the same composition. By ignoring this and simply using the Tmax values, the true volatility of the SOA particle constituents will be overestimated, i.e., the derived VD will be biased towards higher C∗ bins.

One more potential source of bias is our implicit assumption of a constant sensitivity of the CIMS towards all compounds, which follows from the lack of calibration measurements for our data sets (which indeed is a challenging endeavor; e.g., Isaacman-VanWertz et al., 2018). It is plausible that less volatile compounds tend to be detected at higher sensitivity (Iyer et al., 2016; Lee et al., 2014), up to a kinetic limit sensitivity. Consequently, a volatility distribution derived from FIGAERO–CIMS thermograms may be biased towards lower volatility (C∗ bins), at least for compositions not associated with thermal decomposition.

To separate the multiple sources possibly contributing to each ion thermogram (isomers and thermal decomposition products), we applied the positive matrix factorization (PMF; Paatero and Tapper, 1994) to the FIGAERO–CIMS data set. PMF is a well-established mathematical technique in atmospheric science mostly used to identify the contribution of different sources of aerosol particle constituents or trace gases in the atmosphere. PMF represents the measured matrix of the time series of mass spectra, X, as a linear combination of a known (or unknown) number of constant source profiles, F, with varying contributions over time, G, as follows: 1X=G⋅F+E. E is a matrix containing the residuals between the measured (X) and the fitted data (G⋅F). Values for G and F are found by minimizing this residual, Eij, scaled by the corresponding measurement error, Sij, for each ion i at each time j as follows: 2Q=∑i=1m∑j=1nEi,jSi,j. Each row in F contains a factor mass spectrum and each column in G holds the corresponding time series of contribution by each factor. In the case of FIGAERO–CIMS data, the time series is equivalent to the desorption temperature ramp during the thermogram and will be called the “mass loading profile” below. The absolute values (temperature or time) are irrelevant for the performance of PMF as the “x values” are only used to determine the order of the data points but have no influence on the model output (Paatero and Tapper, 1994). This allowed us to combine multiple separate thermogram measurements into one data set and conduct a PMF analysis. This simplified the comparison of factors between measurements. More details about the PMF method in the specific case of FIGAERO–CIMS data can be found in Buchholz et al. (2020).

Once the PMF algorithm was applied to the FIGAERO–CIMS data, we calculated the VD from the mass loading matrix G. Due to the very low signal strength of many ions, the CIMS data had been averaged over 20 s, leading to an enhanced reliability of the high-resolution analysis. This leads to an average desorption temperature difference ΔTdesorp≈4∘C between two adjacent data points. To overcome this coarse Tdesorp grid, we interpolated each factor's mass loading profile with a resolution of 100 sample points between two temperature steps to gain sufficient statistics for further analysis. Tmax was determined as the temperature at the maximum signal in the factor mass loading profile. We integrated the factor mass loading profile and defined the temperatures where the value of the integral reached 25 % and 75 % of its maximum value. This temperature interval formed the factor's desorption temperature range, and the corresponding C∗ values will be used in Sect. 3.3. We converted the Tmax values into C∗ values and the desorption temperature range into a C∗ range with a parametrization derived from calibration measurements (see the Supplement for details) with organic compounds with known C∗ values. 3C∗=expα+βTfactorMorgRTambient109, where C∗ is the effective saturation concentration in units  µgm-3, Morg is the molar mass of the organic compound assumed to be Morg = 0.2 kgmol-1, R is the universal gas constant, Tfactor (in ∘C in Eq. 3) is the temperature of the mass loading profile and Tambient (in Kelvin in Eq. 3) is the ambient temperature at which the evaporation happens (see Table 1). α and β are the fitted coefficients from the calibration data, where α = (-1.431 ± 0.31) and β = (-0.207 ± 0.006) ∘C-1. We applied the lower and higher bounds of the fitting coefficients' uncertainty when we calculated the C∗ range in Sect. 3.3. Finally, the signal fraction of each factor was calculated by dividing the integral of a factor's signal over the whole temperature range with the sum of integrals of all factors. We compare this signal fraction to the dry mole fraction in the VDevap. We refrained from converting the counts per second signal into moles as no adequate transmission and sensitivity measurements were available for the FIGAERO–CIMS setup used. We refer to the volatility distribution, calculated from the PMF data using the Tmax values of each factor as VDPMF, later in this work.

With Eq. () we can calculate the minimum and maximum C∗ values that can be resolved from a FIGAERO thermogram. The desorption temperature was ramped between 27 and 200 ∘C, but defined peaks (and thus Tmax values) can be detected only between 30 and 180 ∘C. Thus, the resolvable log10 (C∗) values range from 1.6 to -11.9. It has to be kept in mind that, strictly speaking, this calibration only applies to the Tmax values of a single ion thermogram.

To model the mass transfer limitations observed in the evaporation measurements at dry conditions (Buchholz et al., 2019), we used the kinetic multilayer model for gas particle interactions (KM-GAP; Shiraiwa et al., 2012), with modifications described in Yli-Juuti et al. (2017) and Tikkanen et al. (2019). The main modification to the original model was that, during evaporation, the topmost layer (the quasi-static surface layer) merged with the first bulk layer if the thickness of the layer was smaller than 0.3 nm. We calculated the viscosity at each layer of the particle as follows: 4log10ηj=∑i=1NXmole,i,jlog10bi, where Xmole,i,j is the mole fraction of the VD bin i in layer j, and bi is a coefficient that describes the contribution of each VD bin to the overall viscosity.

Since we generated the particles in the same environment (PAM chamber) and only the evaporation happened at different conditions, the VD at the start of the evaporation derived from high-RH data also represents the composition at the start of the evaporation in dry conditions. Then we can use the best fit VDevap from the high-RH data as input for KM-GAP and fit the bi values in Eq. () to the dry data set. We set the minimum and maximum allowed values for bi to 10-15 and 1020, respectively. To estimate the bi values when modeling the evaporation with VDPMF in dry conditions, we calculated these bi terms using the mass spectra of each factor (F in Eq. 1) and the Vogel–Tammann–Fulcher (VTF) equation (DeRieux et al., 2018; Angell, 2002, 1995) as follows: 5ηi=η∞expT0,iDT-T0,i, where ηi is the viscosity of the ith VD bin and/or PMF factor. ηi can be seen as a proxy for bi in an ideal solution. η∞ is the viscosity at infinite temperature, T0,i is the Vogel temperature of the ith VD bin and D is a fragility parameter. Setting η∞ = 10-5 and η (Tg) = 1012 Pas-1 (e.g., DeRieux et al., 2018; Gedeon, 2018), where Tg is the glass transition temperature of a compound, yields the following: 6T0,i≈39.14Tg,i39.14+D. We calculated Tg for every compound in the PMF mass spectra with a parametrization for SOA matter developed by DeRieux et al. (2018). This parametrization requires the number of carbon, oxygen and hydrogen atoms to calculate the Tg. We then computed Tg for each PMF factor as a mass fraction weighted sum of the glass transition temperatures of individual compounds (DeRieux et al., 2018; Dette et al., 2014). Based on the Tg,i of each PMF factor, we calculated the viscosity of each PMF factor with Eqs. () and () and used them as an approximation for bi. We used fragility parameter value D=10 in the calculations, according to DeRieux et al. (2018).

Figure S2 in the Supplement shows the mass loading profiles derived from the FIGAERO–CIMS measurements of medium- and low-O:C particles at high RH. The corresponding factor mass spectra can be found in Figs. S3 and S4 in the Supplement. A key step in any PMF analysis is determining the “right” number of factors as this can affect the interpretation of the results. We carefully investigated the Q/Qexp, the time series of scaled and unscaled residuals, and the ability of a PMF solution to capture the characteristic behavior of as many single ion thermograms as possible (see Buchholz, 2020, for details). Based on this analysis, a seven-factor solution was chosen for the medium-O:C cases and a nine-factor solution for the low-O:C ones. The two additional factors in the low-O:C case were needed to capture a contamination on the FIGAERO filter during the dry, fresh sample (factors LC1 and LC2 in Figs. S2 and S4). As these two factors were clearly an artifact introduced by the FIGAERO filter sampling, we omitted their contribution for the following analysis. From careful comparison of the factor profiles and mass spectra with filter blank measurements, we determined that factor MB1 in the medium-O:C case and factor LB1 in the low-O:C case describe the filter and/or instrument background and are thus also excluded from the VD comparison presented below.

Factors 1–5 in both O:C cases exhibit a monomodal peak shape and can thus be characterized by their Tmax values. Factor MD1 in the medium-O:C case and factor LD1 in the low-O:C case need to be investigated more closely, as their factor mass spectrum and the sometimes bimodal mass loading profile suggest that these factors contain compounds stemming from both direct desorption (desorption T < 100 ∘C) and thermal decomposition (desorption T > 100 ∘C; see Buchholz et al., 2020, for details). To account for this, the factor is split into two, with the first half containing the signal from desorption temperatures below 100 ∘C (factor M/LD1a) and the second half containing temperatures above 100 ∘C (factor M/LD1b). We treat these factors separately. We note that now the latter half of the split factor is dominated by thermal decomposition products, so the apparent desorption temperature is actually the temperature at which thermal decomposition leads to products which desorb at this temperature. This apparent desorption temperature is thus a lower limit for the decomposing parent compound, i.e., the true volatility of these parent compounds is even lower. However, the desorption temperatures are so high that they lead to log10 (C∗) < -3 and are thus below the comparable range for VDevap. Figure 1 (high-RH data) and Fig. S10 in the Supplement (dry-condition data) show the mass loading profiles derived from FIGAERO–CIMS measurements of medium- and low-O:C particles after we excluded the contamination and background factors and split the decomposition factors.

To compare VDevap and VDPMF, we need to determine the time interval in the evapogram that the VDPMF represents. We collected the fresh samples directly after the size selection. As the particles were collected for 30 min, the collected sample represents particles that have evaporated from 0 up to 30 min in the organic vapor-free air. We note that this is different from the standard FIGAERO–CIMS sample collection in which the particles are collected in a quasi-equilibrium with the surrounding gas phase, and no significant evaporation occurs (Lopez-Hilfiker et al., 2014). For RTC samples, we also need to consider that not all particles have evaporated for the same time due to the filling of the RTC for ca. 20 min. We determined the minimum time the particles have evaporated in the RTC as the time when we started the sample collection minus the RTC filling time. We determined the maximum evaporation time in the RTC to be the time when we stopped the sample collection plus the filling time. These minimum and maximum comparison times are shown in Table S1 in the Supplement, and they are referred to as minimum and maximum (sample) evaporation time. The mean (sample) evaporation time is defined as being at the middle of the sample collection interval. For simplicity, we will show, in the main text, the results from the analysis in which the FIGAERO–CIMS samples were assumed to represents the particles at the mean sample evaporation time. We show the analysis in which the samples were assumed to represent the particles at minimum and maximum evaporation time in the Supplement. The choice of sample evaporation time does not affect the conclusions we draw about the analysis presented in this section.

Figure 2 shows VDevap and VDPMF for medium- (Fig. 2a–b) and low-O:C (Fig. 2c–d) particles in high-RH experiments. In the VDPMF calculated from the Tmax value of each factor (black crosses), the factors fall into three different volatility classes within our chosen particle size and experimental timescale, namely practically nonvolatile (log10 (C∗) ≤ -2), slightly volatile (-2 < log10 (C∗) ≤ 0) and volatile (log10 (C∗) > 0). We use these three volatility classes to compare the volatility distributions in Fig. 3 where each VD bin is grouped to these three volatility classes. Figure 3 compares VDPMF to what VDevap is at the mean time that the FIGAERO samples had evaporated prior to collection. We show the same comparison for the minimum and maximum evaporation time in Fig. S6 in the Supplement.

After the volatility class grouping is applied, we see that there are differences between VDevap and VDPMF. With VDPMF of the fresh samples, there are excess amounts of matter in the lowest volatility class (volatility class 1) and less material in volatility class 2 compared to VDevap for both oxidation conditions. In addition, the VDPMF of the low-O:C fresh sample shows more material in the highest volatility class (volatility class 3) compared to VDevap.

To investigate the observed discrepancies further, we used the VDPMF shown in Fig. 2 as an input to the LLEVAP model and calculated the corresponding isothermal evaporation behavior (i.e., the evapogram). We show these simulated evapograms in Fig. 4a for the medium-O:C case and in Fig. 4b for the low-O:C condition together with the simulated evapogram calculated using VDevap as an input for the LLEVAP model. The simulated evapograms calculated with the VDPMF of the fresh samples do not match the measured evapograms, while the evapogram calculated with VDevap agrees well with the experimental evapogram (black lines in Fig. 4), as expected, since this is the goal of the VDevap determination. The simulation calculated with the VDPMF of the fresh sample (light blue lines in Fig. 4 for the mean evaporation time; Fig. S7 in the Supplement for other evaporation times) shows slower evaporation than the observations or the simulation calculated with VDevap. This is consistent with the results show in Fig. 3, where the VDPMF contained more low-volatility material than the VDevap.

Figure 4 also shows the simulated evapograms calculated with VDPMF of the RTC samples (light brown lines in Figs. 4 and S7). In these cases, the particles size decreases little within the simulation timescale. With medium-O:C particles, the simulated evaporation matches the measured evaporation well. With low-O:C particles, the evaporation calculated with VDPMF is too fast. The shape of the evapogram does not match the measured one.

The Tmax value is a practical choice for the characteristic temperature of the desorption process. However, as we saw in Sect. 3.2, the VDPMF calculated from the peak desorption temperatures did not produce the measured evapogram when used as an input for the LLEVAP model. Working under the assumption that all material collected on the FIGAERO filter, including the higher volatility material, is detected in the CIMS and then captured in the PMF analysis, we will relax the assumption that the volatility of the factor is characterized strictly by the Tmax value of the factor and investigate the VDPMF further. We will explore how the VDPMF changes when the desorption temperature and the resulting C∗ are interpreted to contain uncertainty and if the VDPMF, considering these uncertainty ranges, is consistent with the observed isothermal evaporation. The uncertainty in the desorption temperature raises from the fact that compounds volatilize from the FIGAERO filter throughout the heating, and therefore, one value might not be adequate to characterize the C∗ of a factor and each PMF factor contains multiple compounds with distinct C∗.

We calculated the 25th and 75th percentiles of the desorption temperatures of each factor and converted them to effective saturation concentrations, as described in Sect. 2.4 (see diamond markers in Fig. 1). We show the resulting C∗ ranges in Fig. 2 as solid horizontal lines, where the line color matches the color of the factors in Fig. 1. We then ran the MCGA optimization by setting the number of compounds equal to the number of PMF factors, the molar fraction for each compound at the FIGAERO–CIMS sampling time fixed to the molar fraction of the corresponding factor and the C∗ as the optimized variables restricted to the range corresponding to the 25th and 75th percentile desorption temperature. In the optimization, the goodness-of-fit statistic was calculated as a mean squared error, similar to the determination of VDevap.

As the fresh samples were collected between 0 and 30 min from the start of the evaporation, we sought a fitting set of C∗ values for evaporation starting at 0, 15 and 30 min. Again, we show the results for the mean sample evaporation time (15 min) in the main text and the results for the other evaporation times in the Supplement. Due to scarcity of particle size measurements at the collection time of the RTC sample, we will apply this analysis only to the VDPMF of the RTC sample at its minimum evaporation time. In each optimization, we set the initial particle diameter to be the same as what is simulated with VDevap. We derived 50 C∗ estimates for both samples. From these 50 estimates, we chose the best-fit evapogram. We refer to these optimized volatility distributions as VDPMF,opt to separate them from the VDPMF where we used Tmax to characterize C∗ of a PMF factor.

We show the optimized C∗ values forming VDPMF,opt in Table 2 (see Table S2 in the Supplement for results with minimum and maximum sample evaporation times). Figure 5 shows the best-fit evaporation simulations calculated with VDPMF,opt. The other sample evaporation times are displayed in the Supplement (Fig. S8). For both oxidation conditions, the simulations resemble the experimental evapogram and the evapogram calculated with VDevap, although the simulation of the medium-O:C condition shows a 5 times larger goodness-of-fit value compared to the simulation calculated with VDevap. The evapograms determined with the VDPMF,opt of the RTC samples agree with the measured evaporation as well.

Overall, the results demonstrate that the information derived from the fresh and RTC FIGAERO–CIMS samples can describe the volatility of the evaporating particles when uncertainties in the desorption temperature are considered.

In this section, we compare VDPMF,opt of the fresh samples to VDPMF of the RTC sample to study if the two VD are similar. We compare the two VD at the mean evaporation time of the RTC sample. We calculated the evapograms with the VDPMF,opt of the fresh sample as the initial particle composition and recorded the mole fraction of each factor at the mean evaporation time of the RTC sample (216 min for medium-O:C particles and 211 min for low-O:C particles). Figure 6a and c show this comparison for both medium- and low-O:C particles. The factors are grouped into the three volatility classes described in Sect. 3.2. In Fig. 6, we show the results from the analysis where VDPMF,opt was optimized by assigning the fresh sample composition at the mean sample evaporation time. Similar comparisons using the minimum and maximum evaporation time of the fresh sample are shown in Fig. S9 in the Supplement. To ensure that the factors are grouped to the same volatility classes for each studied VD, we used the C∗ values of the VDPMF,opt at the mean sample evaporation time as a basis for the grouping.

The compositions simulated, based on the VDPMF,opt of the fresh samples, are comparable to the corresponding VDPMF of the RTC sample in both oxidation conditions (Fig. 6). The agreement is good, especially for the low-O:C case for which the VDPMF,opt showed a slightly smaller contribution in volatility class 1 and a corresponding higher contribution in volatility class 2 compared to the VDPMF of the RTC sample (Fig. 6c). For the medium-O:C case, the VDPMF,opt predicted a higher contribution of volatility class 1 and a lower contribution of volatility class 2 compared to VDPMF (Fig. 6a).

These results show that the particle composition measured after a few hours of evaporation is consistent with the composition predicted, based on the composition observed at the start of evaporation, while considering the uncertainties of the interpreted C∗ values.

Next, we analyzed the evaporation experiments in dry conditions where the evaporation rate was reduced compared to the high-RH conditions. We interpreted this difference as an indication of particle-phase diffusion limitations in dry conditions (Yli-Juuti et al., 2017). Using the initial particle composition information obtained from the high-RH experiments and the FIGAERO–CIMS data, we explored the effect of particle viscosity on the evaporation process. Our aim is to test if the slower evaporation, presumably due to higher viscosity of the SOAs, can be captured with a recently developed viscosity parametrization based on glass transition temperatures of various organic compounds (DeRieux et al., 2018). We also compare the results, using the viscosity parametrization, to an approach where we fit both the viscosity and VD to the evapogram.

First, we investigated the range of particle viscosities that are required to explain the observed slower evaporation in dry conditions. For this, we simulated the particle evaporation in dry conditions based only on the evapogram data. We used the VDevap (i.e., the initial particle composition obtained by optimizing mole fractions of VD bins with respect to the observed evapogram in high-RH conditions) as the initial particle composition estimate for the simulations and optimized the bi values (Eq. 3) for each VD bin. The best-fit simulation from this optimization agrees well with the observed size decrease in the dry experiments for both low- and medium-O:C particles (Fig. 8; black line). Based on these simulations, the viscosity of the particles needs to increase from below 105 Pas to approximately 108 Pas during the evaporation in order to explain the evaporation rate observed for the dry particles.

Second, we tested the performance of the composition-dependent viscosity parameterization by DeRiuex et al. (2018) together with the PMF results. For this, we calculated the volatility distribution, VDPMF,dry, based on the Tmax values of the factors from the fresh sample of the evaporation experiment at dry conditions (in the same way as for VDPMF for the high-RH case). The mole fraction of each factor was calculated from the mass loading profile to give the initial mole fraction of each VD bin for the simulations. We assigned this VDPMF,dry as the particle composition at the mean evaporation time of the fresh sample, i.e., 15 min, and simulated the particle evaporation from there onwards. The particle size at the beginning of the simulation (i.e., at 15 min of evaporation) was taken from the above simulations and optimized based only on the evapogram data, which fitted well to the measurements. We calculated the viscosity parameter bi value for each VD bin, as described in Sect. 2.5, based on the mass spectra of the factor and the parameterization by DeRieux et al. (2018). In practice, this resulted in too high a viscosity for the particles to evaporate at all during the length of the experiment for both low- and medium-O:C particles (dashed gray line in Fig. 8). Therefore, we also conducted a simulation where the viscosity parameter bi value for each factor was calculated based on the viscosity parameterization by setting the Tg values of all compounds 30 K lower than the parametrization predicted, which is in line with the uncertainties reported by DeRiuex et al. (2018). In this case, the simulated evaporation was faster than observed for the medium-O:C conditions (solid gray line in Fig. 8a) and similar to the evapogram calculated with the VDevap for low-O:C conditions (solid gray line in Fig. 8b). This suggests that the observed evaporation rate at dry conditions and the viscosity parametrization by DeRieux et al. (2018) may be consistent with each other within the uncertainty range of the viscosity parametrization and the uncertainty range of the C∗ of PMF factors.

Similar to Fig. 3, we show in Fig. 7 the comparison of VDPMF,dry (C∗ from Tmax) to the VDevap in dry conditions and at the mean sample evaporation time, with the VD bins grouped into the three volatility classes. We show the mass loading profiles and the volatility distributions of the experiments in dry conditions in Figs. S10 and S11 in the Supplement. Figure S12 in the Supplement shows the same comparison as Fig. 7 for other sample evaporation times. For medium-O:C particles, VDPMF,dry calculated from the fresh sample has more contributions from volatility classes 1 and 3 and less from volatility class 2, compared to the corresponding VDevap. For the low-O:C particles, the VDPMF,dry of the fresh sample has more contribution from volatility class 3 and less from volatility classes 1 and 2, compared to the VDevap. For medium-O:C particles, the differences between the VDPMF,dry and VDevap leave open the possibility that the underestimated evaporation rate calculated using VDPMF,dry is partly a result of inaccuracy in the volatility description and not solely due to the high estimated viscosity. For the low-O:C particles, the underestimated evaporation most likely stems from the high estimated viscosity since VDPMF,dry is shifted towards higher volatility compounds than VDevap.

As a third investigation of the viscosity, we again used the PMF results of the fresh sample in dry conditions to initialize the particle composition in the model at the mean fresh sample evaporation time. The mole fraction of each factor was calculated from the mass loading profile, giving the initial mole fraction of each VD bin for the simulations a similar one to the high-RH analysis. Then, using the MCGA algorithm together with the KM-GAP model, we estimated the bi coefficient and C∗ of each VD bin by optimizing the KM-GAP-simulated evapogram to the measured evapogram in dry conditions. This way, we obtained both the initial volatility distribution (VDPMF,dry,opt) and viscosity parameters bi simultaneously. For this optimization, we restricted the C∗ values of the factors based on the 25th and 75th percentile of the desorption temperature of the factors (similar to what was done above for VDPMF,opt) and the viscosity parameter bi values, based on the DeRieux et al. (2018) parameterization. The bi values calculated with the original parametrization by DeRieux et al. (2018) were set as the upper limit for the bi values. The lower limit for the bi values was calculated by setting the glass transition temperature of each compound 30 K lower than the parametrization predicted. As above, in these simulations the initial particle size was also taken from the simulations where the optimization was based only on the evapogram data. For both medium- and low-O:C particles, it was possible to find a set of C∗ and bi values that produced an equally good match to the experimental data as the VDevap (purple and yellow lines in Fig. 8).

Figure 6b and d show the comparison of the measured and simulated particle composition, grouped into the three volatility classes, at the RTC sample collection time for the dry experiments for low- and medium-O:C particles. The measured composition is the VD calculated from the PMF results of the RTC samples in dry conditions. The optimized C∗ values of the factors from the corresponding dry experiment were used for these VD. The simulated particle composition is taken from the optimized model run (optimized VDPMF,opt,dry and bi) at the mean RTC sample collection time, similar to the high-RH cases presented in Fig. 6a and c. For low-O:C particles, there is a clear discrepancy as the VDPMF,dry,opt implies a much larger relative contribution from volatility classes 2 and 3 and a smaller contribution from volatility class 1 when compared to the measurements. This inconsistency may be related to the rather high viscosities in the simulations. The viscosity of the low-O:C particles in this optimized simulation was rather high, at η > 108 Pas throughout the evaporation, slowing the evaporation of the higher volatility compounds. A similar evaporation curve could be obtained with lower viscosity and lower volatilities of the VD bins.