The production of SOM particles in the flow tube reactor largely followed the procedures described in Shrestha et al. (2013). Additional information on materials and methods is presented in Sect. S2 of the Supplement. Briefly, because particles were produced from the homogeneous nucleation of supersaturated organic vapors, a temperature control of 293.0±0.1 K across 12 to 24 h for individual experiments was necessary for reproducible particle number–diameter distributions. The flow tube and the associated gas-flow systems were therefore housed in a temperature-controlled, double-walled, water-jacketed stainless steel box (Fig. S2 in the Supplement). Ozone and α-pinene concentrations of the different experiments are listed in Table 1. The relative humidity was < 5 %. The aerosol flowing out of the reactor was passed through an ozone diffusion scrubber, which reduced ozone concentrations sufficiently to curtail further SOM production and thus to provide a well-defined reaction time. The aerosol subsequently flowed into either a 0.9 or 6.6 L flask for an average residence time of 45 or 310 s, respectively, during which additional particle coagulation took place at various RH. The aerosol flow continued into a region of RH control. The apparatus for adjusting RH, including exposure time, consisted of a Nafion RH conditioner (Perma Pure, Model PD-200T-12) to set the RH of the aerosol flow, followed by a 0.9 or 6.6 L flask to serve as a plenum for RH exposure (i.e., 45 or 310 s, respectively), followed by two diffusion dryers and a second Nafion RH conditioner to reset RH to < 5 %.

Exiting the RH control system, the aerosol flow was divided into two streams (Fig. S2 in the Supplement). The first stream was sampled by a Differential Mobility Analyzer (DMA) (TSI model 3081) (Knutson and Whitby, 1975). The DMA outflow consisted of a subpopulation of particles with a central electric mobility diameter. The central diameters of the different experiments are listed in Table 1. The DMA outflow was sampled by an Aerosol Particle Mass Analyzer (APM) (APM-3600, KANOMAX Inc.) (Ehara et al., 1996), and the particle number concentration in the APM outflow was measured by a Condensation Particle Counter (CPC; TSI model 3022a) (Agarwal and Sem, 1980). The APM voltage was scanned at fixed rotation speed to measure the number–mass distribution of the particle population (Kuwata and Kondo, 2009). The second flow stream from the reactor outflow was sampled by a Scanning Mobility Particle Sizer (SMPS; TSI, model 3071A; CPC; TSI, model 3772) to characterize the number–diameter distribution of the produced particle population (Hoppel, 1978). The DMA, APM, and SMPS were regularly calibrated using aerosol particles of polystyrene latex (PSL) or ammonium sulfate, both of which were produced by nebulization (Model 3076, TSI Corporation) (Biskos et al., 2008).

An aerosol population of SOM particles was produced in a flow tube using 500, 700, and 1000 ppb of (+)-α-pinene and 12 to 30 ppm of ozone for < 5 % RH at 1 atm. The number concentrations and mode diameters are listed in Table 1 for < 5 % RH. Because the concentrations were high in the flow tube, coagulation occurred. Depending on the number–diameter distribution and the reactor residence time, this resulted in several types of coagulated particles being formed. Scanning electron micrographs are shown in Fig. 1 (cf. column 1). The smallest features apparent in the images of column 1 are on order of 5 to 10 nm and represent the primary nucleated particles in the flow tube. These nanoparticles coagulated in the flow tube to larger particles on order of 20 to 40 nm that then exit the flow tube. Each of these particles is referred to as a monomer and is represented by a red circle in the images in Fig. 1. After the flow tube, there was a retention volume in which additional coagulation of the monomers occurred. Dimers, trimers, and high-order agglomerates formed from monomer coagulation (images A1, B1, and C1, respectively). The dimers and trimers, having aspherical shapes at < 5 % RH and making up < 0.25 % of the total particle population (cf. Fig. S1), constituted the core of the experimental strategy.

The instrumental approach for characterizing the shapes of the suspended particles consisted of a DMA (Knutson and Whitby, 1975) coupled to an APM (Ehara et al., 1996) (Fig. S2). The DMA was used to select a subpopulation of controlled mobility diameters from the overall particle population. The number–mass distribution of this subpopulation was then measured using the APM. The dimensionless dynamic shape factor χ was then calculated as follows (Sect. S1) (Kuwata and Kondo, 2009): χ=dm(6mp/πρ)1/3CC((6mp/πρ)1/3)CC(dm) for particle mass mp, mobility diameter dm, and material density ρ. A material density of 1.2×103 kgm-3 was used. The Cunningham slip correction factor is given by CC. The values dm and mp were taken as the central values of the DMA setting and the APM measurement, respectively. Instrument calibration and employed material densities are discussed in Sects. S2 and S3. The χ value of spheres is unity whereas that of submicron dimer and trimer particles ranges from 1.03 to 1.16 and 1.12 to 1.28, respectively, in the transition regime (i.e., Knudsen number from 0.1 to 10) (Hochrainer and Hanel, 1975; Hansson and Ahlberg, 1985; Kousaka et al., 1996; Zelenyuk et al., 2006).

Examples of the number–mass distributions recorded in three replicate experiments are shown in Fig. 2. The DMA was set to select only the large-diameter particles in the tail of number–diameter distribution of the particle population (cf. Fig. S1). The selected particle subpopulation had a central mobility diameter of 126.0 nm compared to a mode diameter of 52.0 nm in the original population, which had 0.1 and 99.9 % diameter intervals of 20.2 and 151.2 nm, respectively (cf. Fig. S1). Contributions from monomers, as well as from dimers of disparate monomer sizes (e.g., one large + one small) and other higher-order agglomerates, were therefore absent in the analyzed data sets. Although doubly charged particles were present in the outflow of the DMA, the mass range covered in Fig. 2 corresponds only to singly charged particles.

As a result of these filtering strategies, the subpopulation represented in Fig. 2 consisted of singly charged dimer, trimer, and higher-order agglomerates. By use of Eq. (), the dynamic shape factor of particles at the central value of the number–mass distribution was 1.18. Examples of the intrinsic width of the DMA-APM instrument train are denoted by the three dashed curves. The data are seen to be wider than the instrumental width. The subpopulation, therefore, consisted of particles having a quasi-monodisperse mobility diameter yet a range of dynamic shape factors, corresponding to a variety of different types of coagulated aspherical particles. Vertical lines are shown for χ values at 1.10 and 1.29, in addition to the central value of 1.18 as well as a reference value of 1.0. Diagram representations of some examples of the types of particles that may be associated with the shape factors are represented as insets in the figure. Section S4 presents additional data concerning the dependence of χ on the variability of synthesis conditions of the agglomerate particles as well as on the DMA-selected mobility diameter.

The particle populations of dimer, trimer, and higher-order agglomerates produced at low RH were subsequently exposed to elevated RH for a controlled residence time. At sufficiently high RH, the particle material flowed. The micrographs of column 2 in Fig. 1 show that nearly spherical particles resulted from exposure to sufficiently high RH. Correspondingly, this resulted in spherical particles of unity shape factor. The complete processing of the particle population was thus primary production, secondary coagulation for < 5 % RH, exposure of agglomerates to an elevated variable RH for a controlled time period, and instrumental characterization of shape factors for < 5 % RH. The final RH adjustment to < 5 % RH removed water from the particles, both serving to simplify interpretation of the sizing data of the DMA-APM and to freeze the particle shape after a controlled time period of possible material flow at elevated RH. This approach assumed that the particle shape did not change with rapid removal of water, as was reasonable considering the overall scenario of quick drying times relative to the slow material flow rates and the absolute water content of < 1 % by volume.

Figure 3 represents the experimental strategy and expected results of the RH-dependent experiments in a diagram. For specific conditions (Fig. 3a), the production of dimer and trimer agglomerates of large shape factors was favored (leftmost to middle column). For non-optimized conditions, Fig. 3b shows that coagulation events became sufficiently numerous that higher-order agglomerates were produced, resulting in particles of polyhedral shape and of correspondingly smaller shape factors. The middle-to-rightmost columns show the transition from aspherical to spherical particles after exposure to elevated RH for a sufficiently long time period.

In a series of RH-dependent experiments, aerosol particles produced from 700 pbb of α-pinene at ozone concentrations ranging from 14 to 30 ppm were exposed stepwise to up to 80 % RH in a retention volume having an average residence time of 310 s. The aerosol then flowed into a region of reduced RH (< 5 %), and χ values of selected diameter fractions were determined. Figure 4a shows the dependence of χ on RH for particle subpopulations having central mobility diameters of 126.0, 175.0, and 195.0 nm. The respective χ values for < 5 % RH were 1.21±0.02, 1.09±0.02, and 1.08±0.02 (one-sigma uncertainty), suggesting that the particle populations were composed largely of dimers and trimers in the first case and of higher-order agglomerates for the latter two cases. The uncertainty estimate is based on repeated measurements. As the RH was increased, χ decreased for all three populations, reaching a final value of 1.02±0.01 at 35 % RH and corresponding within uncertainty to spherical particles. The monotonic decrease in χ for increasing relative humidity implied a likewise monotonic decrease in viscosity. An alternative hypothesis of reactive chemistry with H2O for changing RH was not supported because the organic portion of the particle mass spectrum did not change upon exposure to elevated RH (Sect. S4).

Given that the extent of flow and hence the extent of shape change are expected to be tightly coupled to exposure time at elevated RH, experiments were conducted to investigate the effect of exposure time on the observations. Figure 4b shows results for a humidification time of 45 s compared to that of 310 s. For an exposure time of 310 s, the χ value of the selected 126-nm particles, which were identified by SEM as dimers (cf. Supplement, Sect. S4), decreased to unity by 35 % RH. By comparison, for an exposure time of 45 s, the χ value of the selected 165-nm particles, which were identified by SEM as trimers, remained unchanged for < 5 to 20 % RH, decreasing to nearly unity only at 50 % RH. The two curves were offset by approximately 20 % RH. This result is consistent with the explanation that the shape change arose from material flow and that the flow required a finite amount of time to complete the full transformation to nearly spherical particles. A corollary is that the same extent of shape change at a shorter exposure time implies a decreased viscosity, all other factors being equal.

The experimental results show a conversion from an aspherical to a nearly spherical shape within a specific time period, implying a rate of material flow and hence viscosity. The viscosity can therefore be estimated from the experimental results. To do so, a model was constructed using a commercial software package for numerical solutions to fluid flows (cf. Sect. S5). An example of the model simulation is shown in Fig. 5. A dimer consisting of two 90-nm diameter spheres having an overlap of 5 nm between the spheres was modeled for an exposure of 310 s to elevated RH (cf. Fig. S3). The two panels of Fig. 5 show the initial and final particle shapes (cf. film clip S1 in the Supplement). In 310 s, the dimer transformed to a sphere for a viscosity of (1.0±0.2)×108 Pa s, as obtained by numerical optimization. Please note that even though the RH was measured up to 100 % in the experiment (cf. Fig. 4), the highest RH that could be studied (58 %) was limited by the full transformation to a spherical particle within the fastest experimental residence time (45 s). An analytical result described in Frenkel (1945) for the full transformation of a dimer into a sphere leads to an estimated viscosity of 9.8×107 Pa s, which is in good agreement with the numerical result. The numerical approach has the advantage that it can also be applied to partial transformations. The uncertainty estimate on the optimized value was based on a sensitivity analysis of the modeling results. A range of surface tensions, particle shapes (including extent of monomer overlap), and other factors was investigated (Sect. S6).

The example of Fig. 5 corresponds to the experimental results of Fig. 4b showing the full transformation from χ of 1.21 for < 5 % RH to χ of 1.02 for 35 % RH in 310 s. Viscosities for other RH values were obtained by using the other data points of Fig. 4b, which corresponded to partial transformations. The results plotted in Fig. 6 show that the viscosity of α-pinene SOM corresponded to a semisolid rather than a liquid to at least 58 % RH. Part I represents data for changes in the shape factor data for a residence time of 310 s. Part II represents data for 45 s, for which a linear trimer consisting of 90-nm spheres was modeled, again with an overlap of 5 nm between spheres.

For comparison, results from other experimental studies are also plotted in Fig. 6. The estimated viscosity for < 20 % RH agrees well with that of Abramson et al. (2013) and lies within the uncertainty of that of Pajunoja et al. (2013). Abramson et al. (2013) estimated the viscosity of α-pinene SOM based on the evaporation rate of co-incorporated pyrene from the particles at < 5 % RH. Pajunoja et al. (2013) observed the shape of substrate-supported, submicron particles in vacuum by scanning electron microscopy and used the relaxation time of particle coalescence for < 30 % RH to estimate viscosity. Kidd et al. (2014) estimated the viscosity of α-pinene SOM by examining the deposition patterns of impacted particles at 87 % RH. Bateman et al. (2015) observed a transition at 70 % RH from rebounding to non-rebounding particles of α-pinene SOM and calibrated this response as a transition in viscosity from 100 to 1 Pas (i.e., semisolid to liquid) based on the rebound behavior of sucrose particles of known viscosity. For comparison to the latter two studies of Kidd et al. and Bateman et al., the RH range of the present study was < 5 to 58 % RH. Renbaum-Wolff et al. (2013) measured the RH dependence of the viscosity of the water-soluble component of α-pinene SOM by using optical microscopy to track the movement of small beads. The central values of the estimated viscosities of the present study are lower for < 30 % RH and higher for >40 % RH, implying a reduced sensitivity of viscosity to RH for the present study compared to that reported for Renbaum-Wolff. These differences could relate to differences in sample preparation. Renbaum-Wolff et al. (2013) studied supermicron particles reconstituted from the water-soluble portion of SOM, which can be compared to the present experiments that studied whole SOM in aerosol form without post-processing. Given the differences in hygroscopicity and hence the volume fraction of water that can act as a plasticizer, the viscosity of the water-soluble portion of SOM can be expected to have greater sensitivity to RH than that of whole SOM.

The model used in the present study to estimate viscosity has several embedded assumptions. A surface tension of 5.5×10-2 Nm-1 was used to obtain local stress from local shape (Wex et al., 2009). This value is the average of 83 organic compounds (Korosi and Kovats, 1981). Diameter changes because of hygroscopic growth were taken as negligible for the studied RH range of < 5 to 58 % RH. A uniform value of viscosity throughout the particle was assumed, requiring that the uptake and diffusion of water throughout the particle was fast (< 1 s) compared to the exposure times of 45 and 310 s. This assumption is justified by observations of water uptake showing that submicron particles of α-pinene SOM equilibrate with surrounding gas-phase water in less than 1 sec (Smith et al., 2011). The diffusion coefficient of water in α-pinene SOM for low to middle RH is above 10-13 m2s-1 (Price et al., 2015), hence leading to a characteristic diffusion time τ throughout a 100-nm particle of ≪1 s (Shiraiwa et al., 2011). The model also assumed a specific exposure time (i.e., 45 or 310 s) to elevated RH, whereas it was expected that the actual residence times of individual particles in the exposure flask had a distribution which approaches that of Poisson statistics at the limit of a continuously mixed flow reactor (Kuwata and Martin, 2012b).

Under the assumption that the concentration of a species in the gas phase maintains rapid equilibrium with its concentration in surface layer of a particle and in the absence of chemical reaction, the characteristic time τ to obtain a well-mixed particle by molecular diffusion is as follows (Seinfeld and Pandis, 2006): τ=d24π2D for particle diameter d and molecular diffusion coefficient D. Use of Eq. () assumes that D is uniform throughout the particle. With some limits to applicability (Price et al., 2014), the Stokes–Einstein equation relates the diffusion coefficient of a molecule within a host matrix of viscosity η, as follows (Lindsay, 2009): D=kT6πreffη for Boltzmann constant k, temperature T, and effective radius reff of the diffusing species. Combining Eqs. () and () leads to the following expression for the characteristic mixing time: τ=3reffηd22πkT

For a case study, Table 2 lists mixing times obtained for a typical atmospheric particle diameter of 100 nm and for the viscosities of the present study for < 5 and 58 % RH at 293 K. Molecules such as C19-20H28-32O10-18, which correspond to a family of low-volatility molecules produced during α-pinene ozonolysis, are considered for the case study (Ehn et al., 2014). The effective radius of this family is on order 1.5 nm. The mixing times listed in Table 2 and Fig. 6 range from 5.0 h to 11.5 days for < 5 to 58 % RH, respectively. The SOM particles considered in the case study are, therefore, expected to reach equilibrium with the chemical composition of the gas phase rather slowly in some cases, especially in light of typical atmospheric residence times of 7 to 10 days. For < 5 % RH, the characteristic mixing time can be more than a week, supporting the suggestion that chemical transport models significantly overestimate SOM particle mass concentration and underestimate gas-phase concentrations by assuming instantaneous chemical equilibrium between the two phases (Riipinen et al., 2011; Perraud et al., 2012). At 58 % RH, the characteristic mixing time can approach several hours. The implication is that smaller molecules like ozone or water that diffuse faster in an SOM matrix than predicted by the Stokes–Einstein relationship might penetrate deeply into the particles, whereas organic molecules exchanged with the gas phase might be confined to the outer layer of the particle, thereby setting up a gradient in chemical composition and hence reactivity within the particle. The molecules at the surface in many cases might be kinetically determined rather than thermodynamically controlled, implying many non-surfactants at the surface.

The results of the present study can improve model estimates of gas uptake into particles and thereby improve model accuracy of particle growth rates and reactive processes. For low and intermediate RH and in the absence of a fast reaction, small molecules like O3 or NOx are expected to diffuse rapidly to the center of atmospheric SOM particles, at least those in the Aiken and accumulation diameter modes and those represented well by α-pinene SOM. Larger organic molecules, however, are expected to remain in the surface region of the particles for one or more days. Even so, the range of experimental conditions of a single study is necessarily limited, and future additional studies to track the variability of viscosity at higher RH and both warmer and cooler temperatures are well motivated. The viscosity of SOM generated from volatile organic compounds other than α-pinene, as well as mixed chemical systems, also merits further investigation.

The scope of applicability of the approach introduced herein to determine viscosity of submicron particles in aerosol form can be considered. The lower limit for the RH that can be probed is related to the first discernible detection of shape change within the exposure time to elevated RH. In the present study, for 45 s of exposure, the lower limit of RH was 20 %. For 300 s, the lower limit was < 5 %. The upper limit is related to the full transformation to a spherical particle within the exposure time to elevated RH. In the present study, for 45 s of exposure, the upper limit of RH was 58 %. For 300 s, the upper limit was 25 %. The lower and upper limits for the viscosities that can be probed are related both to the particle diameter and the time for material flow (i.e., corresponding to the exposure time to elevated RH). For 100-nm particles, viscosities as low as 104 Pa s and as high as 1012 Pa s for exposure times on order of 10 s and 10 min, respectively, can be inferred by flow modeling to match shape changes. This viscosity range corresponds to varying degrees of semi-solidity. A future apparatus design for shorter residence times and larger particle diameters is an ongoing effort so that viscosity values can be probed at the transition point from semi-solidity to liquid. There might also be a limit on how small the non-liquid monomers can be, which were 20 to 40 nm in the present study and were coagulated to make the larger non-spherical particles; Cheng et al. (2015) have suggested that monomers on order 20 nm and smaller might be liquid.

In summary, the changing shapes of suspended submicron organic particles were monitored for RH exposures ranging from < 5 to 58 % RH at 293 K, and the characteristic times of the shape changes were used to estimate the RH-dependent viscosities of the constituent organic material. The viscosities decrease from 10(8.7±2.0) to 10(7.0±2.0) Pa s (two-sigma) as RH increases from < 5 to 58 % at 293 K. The methodology developed in the present study of using the DMA-APM system to estimate viscosity for particles in situ as an aerosol, rather than being collected on a substrate for subsequent analysis, can avoid several potential artifacts specific to the semivolatile nature of SOM. If deployed for field measurements, the approach also has the promise of providing sufficient time resolution to track atmospheric variability.