Particles consisting of SOM were produced by the photo-oxidation of isoprene compounds in an OFR (Kang et al., 2007). The procedures were described in detail in Liu et al. (2013, 2015). Table 1 lists the experimental conditions used in this study. The volume of the OFR was 13.3 L and the OFR was operated at a flow of 7.0 and 9.5 L min-1, resulting in residence times of 114 and 84 s, respectively. The temperature used in the OFR experiments was 293 ± 2 K. RH in the reactor was maintained at 13 ± 3 % during particle generation. For injection of isoprene vapor into the OFR, 2 mL of liquid isoprene (Sigma-Aldrich, 99 %) was placed in an upright Teflon tube with the lower end sealed and the upper end connected to a T-fitting. The fitting was flushed by purified air, thereby producing a gas flow containing isoprene vapor. The injected isoprene concentration was 4–7 ppm. Ozone was produced external to the flow reactor by irradiating pure air with the ultraviolet emission from a mercury-vapor lamp (λ= 185 nm). The injected ozone concentration was 10–13 ppm. Hydroxyl radicals were produced inside the OFR by the following photochemical reactions: O3+hν→O2+O(1D), O(1D)+H2O→2OH.

Although the OH concentration was not measured in the OFR in this study, an OH concentration in the OFR in the range of 2 × 108 to 2 × 1010 molec cm-3 was expected based on previous experiments under similar conditions (Lambe et al., 2011a). This OH concentration corresponds to a lifetime of isoprene between 0.5 and 50 s. For comparison, the O3 concentrations used in these experiments correspond to a lifetime of isoprene of approximately 3.6 min. The OH concentration in the OFR was adjusted by changing the power of the UV lamps as described in Lambe et al. (2011a). For the experiments in this study, the lamp power was always full; therefore, the OH concentration in this study should have been close to 2 × 1010 molec cm-3, and the OH pathway should have dominated the oxidation of isoprene.

Based on the flow tube residence times and the expected OH concentrations, OH exposures were expected to be in the range of 2.0 × 1010 to 1.8 × 1012 molec cm-3. When one assumes an average atmospheric OH concentration of 1.5 × 106 molec cm-3, this range of exposures is equivalent to ∼ 0.15 to ∼ 15 days of atmospheric oxidation by OH (Lambe et al., 2011a).

The concentration of the major oxidants (O3, OH, and HO2) in the OFR is higher than in environmental chambers or the atmosphere, but the ratios of O3 to OH and OH to HO2 are similar to those encountered in the atmosphere and in environmental chambers. As a result, the OFR is used to simulate oxidation processes in the atmosphere and environmental chambers. Recent measurements with an aerosol mass spectrometer have shown that the composition of isoprene-derived SOM produced with an OFR is the same, within the uncertainty of the measurements, as isoprene-derived SOM produced with an environmental chamber (Lambe et al., 2015).

In the current study, the O : C ratio of the isoprene-derived SOM was not measured. However, in previous studies using the Harvard OFR, an O : C value of 0.82 for isoprene-derived SOM was measured using lower concentrations of isoprene (700 ppb). In these previous studies the O : C was calculated using the explicit approach described by Chen et al. (2011). In addition, the average O : C values of isoprene-derived SOM was found to be 0.64 to 0.79 by Chhabra et al. (2010) and 0.75 to 0.88 by Chen et al. (2011) in environmental chamber studies and 0.64 to 1.1 by Lambe et al. (2011b, 2015) in explicit studies using a similar OFR. The O : C values reported here for Chhabra et al. (2010) and Lambe et al. (2011b) have been scaled up by a factor of 1.27 as suggested by Canagaratna et al. (2015). Based on this information, we estimate that the O : C of isoprene-derived SOM in the current experiments was in the range of 0.64 to 1.1.

Particles consisting of SOM produced from the photo-oxidation of isoprene were collected onto hydrophobic substrates using an electrostatic precipitator (TSI 3089, USA) connected to the outflow of the OFR. Shown in Fig. 1a is an example of an image of particles collected on a hydrophobic substrate using this process. Teflon substrates were used as the hydrophobic substrates for the bead-mobility experiments (see Sect. 2.3). Glass slides coated with trichloro(1H,1H,2H,2H-perfluorooctyl)silane (Sigma-Aldrich) were used as hydrophobic substrates for the poke-flow experiments (see Sect. 2.4). The method of coating glass slides with a silane is described in Knopf (2003).

Particles of 20–60 µm were required to perform bead-mobility and poke-flow experiments (see Sect. 2.3 and 2.4). To make the appropriate particle sizes for these experiments, the hydrophobic substrates containing particles collected from the OFR were placed in a RH-controlled flow cell coupled to a reflectance microscope (Zeiss Axiotech, magnification of 50 times) (Pant et al., 2006; Bertram et al., 2011). The RH in this flow cell was then increased to over 100 %, which resulted in growth of the SOM particles by water uptake. The RH was then maintained over 100 % for 30–60 min to grow and coagulate the SOM particles. After the growth and coagulation process, the RH was decreased to 80–90 % to evaporate the water. The activation, growth, and coagulation processes resulted in particles having diameters of 20–60 µm (see Fig. 1b). This method of producing 20–60 µm particles was introduced by Renbaum-Wolff et al. (2015).

The bead-mobility technique has been described in detail by Renbaum-Wolff et al. (2013b). Insoluble melamine beads (∼ 1 µm in diameter, Sigma-Aldrich, 86296) were incorporated into the supermicron SOM particles deposited on a hydrophobic substrate by nebulizing a suspension of the melamine beads in water over the supermicron SOM particles. The hydrophobic substrate with the SOM particles was then placed in a flow cell coupled to a light-transmitting microscope (Zeiss Axio Observer, magnification 40 ×). Once the supermicron particles were located in the flow cell, a continuous flow of N2/H2O gas (∼ 1200 sccm) was passed over the supermicron particles. By adjusting the ratio of N2 and H2O in the flow, the RH in the cell was controlled. The RH in the flow cell was measured using a hygrometer with a chilled mirror sensor (General Eastern, Canada), which was calibrated by observing the deliquescence RH for pure ammonium sulfate particles (80.0 % RH at 293 K; Martin, 2000). The uncertainty of the RH was ±0.5 %.

The continuous flow of N2 / H2O gas caused a shear stress on the surfaces of the SOM particles and resulted in internal circulations within the SOM particles. These internal circulations were quantified by monitoring the movement of the beads within the SOM particles with the optical microscope. Images of the beads within the SOM particles were recorded with a CCD camera every 0.2 s–10 min depending on the velocity of the beads. Typically one to seven beads within a particle were observed over 50–100 frames. Within the same particle, bead speeds varied by a factor of 2–3 depending on the location within the particle. Shown in Fig. 2 are examples of optical images of an isoprene-derived SOM particle at 80 % RH recorded during a typical bead-mobility experiment. Three beads that were monitored during this experiment are marked with arrows. Also included are the x and y coordinates of the beads recorded at the three different times. From these coordinates the average speed of individual beads in a single particle was determined.

Once the average bead speeds were determined, the bead speeds were converted to viscosity using a calibration line, which was generated from measurements of bead speed as a function of viscosity in sucrose particles (see Fig. 3). Renbaum-Wolff et al. (2013b) showed that the calibration line for converting bead speed into viscosity is independent of the type of organic materials used to generate the line for a wide range of oxygen-to-carbon ratios, surface tensions, and molecular weights of the organic materials.

The method of applying physical force to estimate the phase of a particle was introduced by Murray et al. (2012). The poke-flow method in conjunction with fluid simulations to determine viscosities of particles was introduced by Renbaum-Wolff et al. (2013a) and further extended and validated by Grayson et al. (2015). Supermicron SOM particles (20–60 µm in diameter) suspended on a hydrophobic substrate were located inside a flow cell with RH control. The flow cell was similar to the one used for the bead-mobility technique except it contained a small hole on the top through which a sterilized sharp needle (0.9 mm × 40 mm) (Becton-Dickson, USA) could be inserted. The needle was mounted to a micromanipulator (Narishige, model MO-202U, Japan) to allow precise control of the movement of the needle. The needle was first positioned over the top of a SOM particle and then moved down to pass through the center of the particle (i.e., the particle was poked). The geometrical changes during and after poking a particle were recorded using a reflectance optical microscope (Zeiss Axio Observer, 40 × objective) equipped with a CCD camera.

Figure 4 shows typical geometrical changes of the SOM particles that were observed optically. Prior to poking, the particles had a spherical cap (Fig. 4a1 and b1). Just after poking, the particle had a half-torus geometry consisting of a ring of material with a hole at its center, which is energetically unfavorable (time t=0, Fig. 4a2 and b2). To minimize the surface energy, the material flowed to fill the central hole (Fig. 4a3 and b3). The area of the inner hole of the half-torus geometry was measured using Zen software (Zeiss, Canada). The diameter of the equivalent hole area was calculated based on the relationship d=(4Aπ)12, where d is the equivalent area diameter of a hole of area, A (Reist, 1992). The experimental flow time, τ(exp⁡,flow), was determined as the time taken for the equivalent area diameter to reach 50 % of the initial value. For a3 and b3 in Fig. 4, the τ(exp⁡,flow) was determined to be 1.3 s at 26.5 % RH and 273.9 s at 0 % RH. The τ(exp⁡,flow) values were converted to viscosity using simulations of fluid flow.

Fluid flow simulations were performed to obtain the relationship between viscosity and modeled flow time, τ(mod,flow), which is the time when the inner hole of a poked particle reaches half of its initial diameter. Using the relationship between modeled flow time, τ(mod,flow), and viscosity, we converted experimental flow time, τ(exp⁡,flow), to viscosity. Simulations of material flow were carried out using COMSOL Multiphysics (version 4.3a), which describes transport of mass and momentum, including the effects of surface tension. The arbitrary Lagrangian–Eulerian method was used to track the time evolution of the fluid as it flowed to minimize the surface energy of the system. In the simulation, a half-torus geometry consisting of an air–fluid interface and fluid-substrate interface was used, which is similar to the geometry observed in the poke-flow experiments. The mesh size used in the model was 4.04–90.9 nm. Details of the simulation were described by Grayson et al. (2015).

For the simulations, the following physical parameters were needed: slip length, surface tension, contact angle, and material density for isoprene-derived SOM. Table 2 shows the values used for these physical parameters in the simulations. The lower and upper limits of the slip length used in the simulations were 5 nm and 10 µm based on literature data of the interactions between fluids and solid surfaces (Schnell, 1956; Churaev et al., 1984; Watanabe et al., 1999; Baudry et al., 2001; Craig et al., 2001; Cheng and Giordano, 2002; Tretheway and Meinhart, 2002; Jin et al., 2004; Joseph and Tabeling, 2005; Neto et al., 2005; Choi and Kim et al., 2006; Joly et al., 2006; Zhu et al., 2012; Li et al., 2014). The upper limit for surface tension of SOM was 72 mN m-1, corresponding to the surface tension of pure water at 293 K (Engelhart et al., 2008), and the lower limit was 17 mN m-1, corresponding to the surface tension of liquid isoprene at 293 K (http://cameochemicals.noaa.gov). The density of isoprene-derived SOM used was based on the observed density of isoprene-derived SOM (Kuwata et al., 2011; Nakao et al., 2013). Contact angles were determined using 3-D fluorescence confocal images of the SOM particles on the substrates, which range from 60 to 90∘ (Fig. 5). In the simulation, the relationship between viscosity and contact angle was dependent on the ratio of tube radius to the inner hole radius (see Table 2). Other input to the simulations included the inner and outer diameters of the torus geometry, which were based on the optical images of the material after poking the particles.

Shown in Fig. 6a are the mean bead speeds as a function of RH at 295 ± 1 K determined in the bead-mobility experiments. The different colors represent different samples (Table 1). Each symbol corresponds to the mean bead speed determined for one sample at one RH. The speeds of at least three beads were used to determine a mean bead speed. Figure 6b shows viscosities calculated from the mean bead speeds shown in Fig. 6a and the calibration line shown in Fig. 3. The y error bars in Fig. 6b represent the 95 % prediction intervals from the calibration line. Figure 6b illustrates that the change in viscosities with a change in concentration of the SOM in the OFR (when going from 300–400 to 500–1000 µg m-3) is less than the uncertainties in the measurements. Since the viscosities do not appear to vary with concentrations of the SOM in the OFR over the range studied, we group the data in Fig. 6b by RH to provide an overall summary from the bead-mobility technique (see Fig. 6c). Three data points were included in each group. Figure 6c also illustrates that the viscosity for isoprene-derived SOM increased from ∼ 2 × 10-1 to ∼ 3 × 101 Pa s as the RH decreased from 84.5 to 63.7 %. Viscosities were not determined for RH < 60 % using the bead-mobility technique because the circulation rate of beads in a particle became too slow to readily observe.

RH-dependent τ(exp⁡,flow) values of three different isoprene-derived SOM samples measured at 295 ± 1 K by the poke-flow technique are shown in Fig. 7a. Each symbol in Fig. 7a represents the measured τ(exp⁡,flow) from one particle poked at one RH. Figure 7a illustrates that the variation from sample to sample is less than the variation within individual samples. Figure 7b presents the lower and upper limits of viscosities calculated from the individual τ(exp⁡,flow) values shown in Fig. 7a. For each data point in Fig. 7b, the uncertainty in the viscosity is approximately 2 orders of magnitude. This uncertainty is due to the uncertainties in the physical parameters used in the simulations (see Table 2). In Fig. 7c, the viscosities of the particles were grouped by RH with at least four data points in each group. The x error bars in Fig. 7b represent the range of RH values in the group as well as uncertainty of the RH measurements. The y error bars represent the lower and upper limits of viscosity within the group. Figure 7c illustrates that the viscosity ranges from approximately 2 × 103 to 3 × 105 Pa s as the RH changes from 25.1 to 0 % RH. Viscosities were not determined for RH > 30 % using the poke-flow technique because the material flows too fast to observe.

Figure 8a displays together the viscosities of isoprene-derived SOM (marked by purple) measured by the bead-mobility technique (Fig. 6c) and the viscosities of isoprene-derived SOM measured by the poke-flow technique (Fig. 7c). Based on our data, for RH > 60 % the isoprene-derived SOM falls into the range for a liquid phase (viscosity < 102 Pa s) while for RH < 30 % the isoprene-derived SOM falls into the range for a semisolid phase (102 Pa s < viscosity < 1012 Pa s). At no RH is the studied SOM a solid. Based on the rebound behavior of submicron isoprene-derived SOM particles, Bateman et al. (2014) show that the semisolid-to-liquid phase transition of these particles is in the range of 40–60 % RH for a viscosity transition in the range of 102 to 100 Pa s (light blue in Fig. 8a). Saukko et al. (2012) measured the bounce fraction of SOM submicron particles derived from isoprene photo-oxidation and inferred from their results that the particles were semisolid or solid for < 55 % RH. Our results are consistent with these previous bounce and rebound experiments.

Viscosities of SOM generated from the ozonolysis of α-pinene are shown in Fig. 8b based on values reported in the literature (Perraud et al., 2012; Abramson et al., 2013; Robinson et al., 2013; Bateman et al., 2014; Kidd et al., 2014; Pajunoja et al., 2014; Wang et al., 2014). The RH-dependent viscosities of the water-soluble component of SOM generated from the ozonolysis of α-pinene are also included in Fig. 8b (Renbaum-Wolff et al., 2013a). The values plotted at RH values ≥ 70 % and RH values ≤ 30 % were taken directly from Renbaum-Wolff et al. (2013a). Between 40 and 70 % we determined viscosities by converting τ(exp⁡,flow) values reported in Renbaum-Wolff et al. (2013a) to viscosities using the simulation discussed above (Sect. 2.4) and presented in Grayson et al. (2015). For RH values between 40 and 70 %, we did not take the viscosities directly from Renbaum-Wolff et al. (2013a) since they only used simulations to estimate upper limits to viscosities in this RH range.

Based on a comparison of Fig. 8a and b, the viscosity of isoprene-derived SOM (Fig. 8a) is on average lower than the viscosity of α-pinene-derived SOM (Fig. 8b). This conclusion is consistent with work by O'Brien et al. (2014) who also concluded that the viscosity of isoprene-derived particles is lower than the viscosity of α-pinene-derived particles based on the how much the particles flattened after impaction on a substrate. The differences may be due to a difference in the molecular weights of the two SOMs since viscosity can increase as the molecular weight of an organic compound increases (Zobrist et al., 2008; Koop et al., 2011). Although we do not have information on the characteristic range of molecular weights of the SOM, it is reasonable to expect that the median molecular weight of α-pinene-derived SOM will be larger than that of isoprene-derived SOM since the molecular weight of the precursors differ roughly by a factor of 2. The O : C ratio is also expected to affect the viscosity of the SOM, with higher O : C values leading to higher viscosities and glass transition temperatures (Koop et al., 2011; Berkemeier et al., 2014). However, O : C alone is unlikely to explain the difference in viscosity between isoprene-derived SOM and α-pinene-derived SOM since the O : C of isoprene-derived SOM in our experiments is expected to be between 0.64 and 1.1 (see Sect. 2.1) while the O : C of SOM from the ozonolysis of α-pinene is typically in the range of 0.3 to 0.5 (Chen et al., 2011).

Using the viscosities determined in this study, we calculated diffusion coefficients of large organic molecules (Dorg) within isoprene-derived SOM using the Stokes–Einstein relationship: Dorg=kT6πηr, where k is the Boltzmann constant, T is the temperature (K), r is the hydrodynamic radius of a representative molecule of SOM within the SOM bulk matrix, and η is the viscosity (Pa s). The Stokes–Einstein relation is not expected to predict with high accuracy the diffusion rates of small gas molecules (e.g., O3, OH, NOx, H2O) close to the glass transition RH (Champion et al., 2000; Shiraiwa et al., 2011; Power et al., 2013). However, the Stokes–Einstein relation should give a reasonable estimate of diffusion rates when the viscosity is lower than that of a glass and when the molecules undergoing diffusion are roughly the same size or larger than the molecules in the SOM matrix. When we assume the SOM matrix is dominated by molecules similar to 2-methyltetrol and 2-methylerythritol (C5H12O4), which have been identified as key oxidation productions of isoprene and have an isoprene skeleton (Cleaeys et al., 2004; Carlton et al., 2009; Kleindienst et al., 2009), then the Stokes–Einstein equation should be applicable when the viscosity is lower than that of a glass (1012 Pa s) and for organic molecules with a molecular weight approximately ≥ 136 g mol-1, although additional work is required to confirm these assumptions.

Shown in Fig. 8a on a secondary y axis are the diffusion coefficients calculated using this equation and assuming 0.4 nm for the hydrodynamic radius (Renbaum-Wolff et al., 2013a). Figure 8a suggests that the diffusion coefficients of organic molecules within the isoprene-derived SOM vary from ∼ 2 × 10-8 to ∼ 2 × 10-10 cm2 s-1 between 84.5 and 63.7 % RH and from ∼ 2 × 10-12 to ∼ 2 × 10-14 cm2 s-1 between 25.1 and 0 % RH.

From the diffusion coefficients, we calculated the mixing times by diffusion, τmixing, of large organic molecules within an SOM particle using the following equation (Shiraiwa et al., 2011; Bones et al., 2012; Renbaum-Wolff et al., 2013a): τmixing=d24π2Dorg, where d is the particle diameter (taken as 200 nm, which is typical for the accumulation mode of atmospheric particles; Shiraiwa et al., 2011). After the mixing time, the concentration of the representative molecules anywhere in the particles deviates by less than e-1 from the equilibrium value. The mixing times calculated with Eq. (2) are plotted in Fig. 8a on a secondary y axis. Between 84.5 and 0 % RH, the mixing times within the isoprene-derived SOM particles range from less than ∼ 3.6 × 10-4 s (∼ 1 × 10-7 h) to ∼ 0.1 h. Compared to the total isoprene-derived SOM, water-soluble α-pinene-derived SOM shows longer mixing times ranging from ∼ 1.1  × 10-2 s (∼ 3 × 10-6 h) to as high as ∼ 5 × 105 h over the RH range of 90 to 25 %. Both isoprene-derived and α-pinene-derived SOM can be classified as biogenic SOM, yet they clearly have different viscosities and mixing times at a given RH.