Introduction
Large amounts of volatile organic compounds, such as isoprene, limonene, and
α-pinene from biogenic sources and aliphatic and aromatic compounds
from anthropogenic sources, are released into the atmosphere. These compounds
can be oxidized by a complex series of atmospheric reactions to form
lower-volatility products that condense to form secondary organic aerosols
(SOAs) (Hallquist et al., 2009; Kanakidou et al., 2005). SOA makes up
approximately 30 %–70 % of the mass of atmospheric particles (Kanakidou
et al., 2005; Jimenez et al., 2009). Due to the hygroscopic nature of SOA, an
important component of SOA particles is water (Bateman et al.,
2015; Hildebrandt Ruiz et al., 2015; Massoli et al., 2010). The amount of
water in SOA particles is determined by the relative humidity (RH); as the
RH increases, the water activity (aw) (and hence water content) in SOA
particles increases to maintain equilibrium with the gas phase. SOA
particles can influence climate either directly,
by absorbing and scattering
sunlight, or indirectly, by acting as cloud condensation nuclei (CCN) and ice nuclei (IN) (Kanakidou et al., 2005; Murray et al., 2010; Solomon,
2007; Wang et al., 2012). SOA particles can also influence air quality and
public health (Baltensperger et al., 2008; Jang et al., 2006; Pöschl and
Shiraiwa, 2015; Shiraiwa et al., 2017b).
Despite the importance of SOA particles in climate and air quality, their
physicochemical properties remain poorly understood (Hallquist et al.,
2009). This leads to uncertainties when predicting the role of SOA particles
in atmospheric chemistry, climate, and air quality (Hallquist et al.,
2009; Shiraiwa and Seinfeld, 2012; Shrivastava et al., 2017a; Zaveri et al.,
2014). One physicochemical property that remains poorly known is the rate of
diffusion of organics within SOA particles (Liu et al., 2016; Shiraiwa et
al., 2013; Shrivastava et al., 2017a; Ye et al., 2016). Information on
diffusion rates is needed to predict the reactivity and photochemistry of
SOA particles (Chu and Chan, 2017; Davies and Wilson, 2015; Gržinić
et al., 2015; Houle et al., 2015; Li et al., 2015; Lignell et al.,
2014; Shiraiwa et al., 2011; Wang et al., 2015). Diffusion rates are also
needed to predict the growth rates, size distributions, cloud condensation
ability, and ice nucleating ability of SOA particles (Boyd et al.,
2017; Huff Hartz et al., 2005; Murray et al., 2010; Perraud et al.,
2012; Riipinen et al., 2011; Shiraiwa and Seinfeld, 2012; Solomon et al.,
2007; Taina et al., 2017; Wagner et al., 2017; Wang et al., 2012; Zaveri et al.,
2014, 2018). Slow diffusion of molecules in particles also has
implications for the long-range transport of pollutants (Bastelberger et
al., 2017; Shrivastava et al., 2017b; Zelenyuk et al., 2012; Zhou et al., 2012)
and the optical properties of particles (Adler et al., 2013; Robinson et
al., 2014).
To estimate diffusion rates of organics in SOA particles, it is common to
use viscosity measurements together with the Stokes–Einstein relation (Booth et al., 2014; Hosny et al., 2013; Koop et al., 2000; Power et al.,
2013; Renbaum-Wolff et al., 2013a; Shiraiwa et al., 2011, 2017a; Song et al., 2015, 2016),
D=kT6πηRH,
where D is the diffusion coefficient of the diffusing species, k is the
Boltzmann constant, T is the temperature, η is the dynamic viscosity,
and RH is the hydrodynamic radius of the diffusing species. Until now,
the accuracy of the Stokes–Einstein relation for predicting diffusion rates
of organics in SOA particles has not been quantified, leading to
uncertainties when estimating diffusion rates from viscosity measurements.
Motivated primarily by the food industry, there have been a few tests of the
Stokes–Einstein relation for predicting diffusion rates of organics in
organic–water matrices, such as saccharide–water matrices (Bastelberger
et al., 2017; Champion et al., 1997; Chenyakin et al., 2017; Corti et al.,
2008; Price et al., 2016). In these cases, the matrices contained only two
species (one organic and water), which is very different from SOA matrices
that contain thousands of different species (Nozière et al.,
2015).
In the future, researchers will likely continue to use viscosity data
combined with the Stokes–Einstein relation to estimate diffusion rates of
organics in SOA particles, because several techniques have been developed
recently to measure the viscosities of SOA matrices and proxies of SOA
matrices (Bateman et al., 2015; Grayson et al., 2016; Lee et al., 2017; Marsh
et al., 2017; Price et al., 2015; Reid et al., 2018; Renbaum-Wolff et al.,
2013a; Song et al., 2015; Zhang et al., 2015). As a result, the accuracy of the
Stokes–Einstein relation for predicting diffusion rates of organics in SOA
particles needs to be quantified.
In the following, we measured the viscosities of brown limonene SOA (brown
LSOA) as a function of aw using the bead-mobility technique. The brown
LSOA is a product of exposure of white limonene ozonolysis SOA to ppb levels
of ammonia vapor (Laskin et al., 2010), and it is a model system for the
formation of secondary brown carbon (Laskin et al., 2015). In addition,
we measured diffusion coefficients of intrinsic fluorescent organic
molecules within brown LSOA matrices using a technique called rectangular
area fluorescence recovery after photobleaching. These new data, combined
with viscosity data that already exist in the literature for brown
LSOA–water matrices, were used to test the accuracy of the Stokes–Einstein
relation for predicting diffusion rates of organics within SOA particles. We
also used the measured diffusion coefficients to estimate mixing times of
organics within 200 nm brown LSOA particles at RHs typically found in the
planetary boundary layer (PBL; the region of the atmosphere from the surface to
an altitude of up to 1 km). We focused on brown LSOA for the following
reasons: first, brown LSOA contains light-absorbing molecules that are also
fluorescent (here referred to as intrinsic fluorescent organic molecules)
and capable of rapid photobleaching (Lee et al., 2013). These
intrinsic fluorescent organic molecules offer a key advantage because one
can measure diffusion coefficients within brown LSOA using rectangular area
fluorescence recovery after photobleaching without the need to add a foreign
tracer fluorescent molecule to the SOA matrix. Second, limonene accounts for
roughly 10 % of the global emissions of monoterpenes (and is thus an
important source of SOA in the atmosphere) (Kanakidou et al.,
2005; Sindelarova et al., 2014).
Experimental
Generation of brown LSOA
Brown LSOA was produced at the University of California, Irvine (UCI)
following the procedure outlined in Hinks et al. (2016). First, particles
consisting of limonene secondary organic material (LSOA) were generated in a
20 L flow tube by dark ozonolysis of d-limonene. Mixing ratios of ozone and
d-limonene (97 % Sigma-Aldrich) were both 10 ppm prior to reaction.
Ozone was produced externally to the flow tube by an electric discharge in
pure O2 (ultra-high purity, Airgas). After the ozonolysis reaction,
the mass concentration of LSOA particles within the flow tube was
approximately 1000 µg m-3. At the exit of the flow tube, the
carrier gas and LSOA particles were passed through a charcoal denuder to
eliminate excess ozone and gas-phase organics, followed by collection of the
LSOA particles on hydrophobic slides (Hampton Research; Aliso Viejo, CA, USA)
using a Sioutas impactor with a single stage “D” (0.25 µm cut
point at 9 SLM collection flow rate). After LSOA production, the hydrophobic
slides containing the LSOA were placed within a small glass petri dish, which
was left floating on the surface of a solution of 0.1 M ammonium sulfate
(>99 %, EMD) in a larger, covered petri dish. Over a period
of 3 to 5 days, the ammonia vapor in equilibrium with the ammonium sulfate
solution (concentration estimated to be 300 ppb NH3 using the
Extended AIM Aerosol Thermodynamics Model II) (Clegg et al., 1998) reacted
with the fresh LSOA forming a visible brown color. After production of the
brown LSOA, the samples were shipped to the University of British Columbia
for viscosity and diffusion coefficient measurements.
Viscosity measurements
The viscosities of brown LSOA particles were determined at aw of
approximately 0.7, 0.8, and 0.9, using the bead-mobility technique (Renbaum-Wolff et al., 2013b). At lower aw, the
viscosities were too high for measurements with this technique. In short,
small particles (5–50 µm in diameter) of brown LSOA were deposited on
fluorinated glass slides (Knopf, 2003) from the samples received from
UCI using the tip of a needle (BD PrecisionGlide™ Needle, 0.9 mm × 40 mm).
A dilute solution containing hydrophilic melamine beads (actual diameter:
(0.87±0.04) µm, Sigma Aldrich, no. 86296) was then nebulized
over the fluorinated glass slides containing the brown LSOA particles. This
resulted in melamine beads being incorporated into the brown LSOA particles.
The fluorinated glass slides containing the brown LSOA particles were then
placed in a flow cell (Renbaum-Wolff et al., 2013b).
The RH within the flow cell was controlled by passing a nitrogen carrier gas
through a water bubbler, which was located in a temperature-controlled bath.
The dew point of the nitrogen gas flow was measured with a hygrometer
(General Eastern; Model 1311DR), and the temperature of the flow cell was
measured with a thermocouple. From the dew point and the temperature of the
flow cell, the RH was determined. The RH was calibrated at the beginning of
each set of measurements using the deliquescence point of ammonium sulfate.
Once the fluorinated glass slides containing the brown LSOA particles were
placed in the flow cell, a constant flow (1100 to 1200 sccm) of humidified
nitrogen gas (Praxair, ultrapure) was passed over the brown LSOA particles,
which caused a shear stress on the surface of the particles and circulation
of the beads within the particles. The velocity of the beads was determined
using an optical microscope (Zeiss Axio Observer). For each aw studied,
the speed of 7 to 16 beads in 2 to 5 brown LSOA droplets was measured and
the bead speed was averaged. Once determined, the velocity of the beads was
converted to viscosity using a calibration curve based on sucrose–water
particles and glycerol–water particles from Grayson et al. (2017). Prior to
measuring the velocity of the beads in an experiment, the brown LSOA
particles were equilibrated with the RH within the flow cell for
approximately 20 min, which should be long enough to ensure equilibration (Sect. S1 in the Supplement).
Viscosities for the same brown LSOA at aw of 0.05 and 0.3 are available
from previous poke–flow measurements by Hinks et al. (2016). Briefly, in
these studies brown LSOA was collected on hydrophobic glass surfaces using a
procedure similar to the procedure described above. This resulted in
supermicron particles with a spherical cap geometry. The particles were then
poked with a sharp needle, generating a half-torus geometry. After poking,
the material flowed and returned to its spherical cap geometry due to
surface tension forces. From simulations of fluid flow, the viscosities of
the material were determined. This technique is limited to viscosities ≥103 Pa s (Grayson et al., 2015). In addition,
the upper and lower limits of viscosity from this technique differ by
roughly a factor of 15 to 150. This uncertainty stems mainly from
uncertainties in the parameters used when simulating the fluid flow.
Diffusion coefficient measurements
Generation of thin films of brown LSOA with a known aw for the diffusion coefficient measurements
Brown LSOA contains light-absorbing molecules that are also fluorescent and
easily photobleachable (Lee et al., 2013). Diffusion coefficients
of these intrinsic fluorescent organic molecules were determined using
rectangle area fluorescent recovery after photobleaching (discussed below).
For this technique, thin films (20–90 µm thick) containing brown LSOA
with a known aw were needed. To produce thin films of brown LSOA with a
known aw, particles of brown LSOA with diameters of 50–200 µm
were deposited on hydrophobic slides from the samples received from the UCI
using the tip of a needle (BD PrecisionGlide™ Needle, 0.9 mm × 40 mm). The
super-micrometer brown LSOA particles were then located within a flow cell
or sealed glass jar with controlled RH to set the aw within the brown
LSOA (at equilibration, aw within the brown LSOA equals RH/100). The
times used to condition the brown LSOA particles to the controlled RH are
given in Table S1 and discussed in
Sect. S1. After equilibration, the brown LSOA particles were sandwiched
between two hydrophobic glass slides to generate a thin film of brown LSOA
with a thickness of 20–90 µm. Assembly of the films occurred within a
glove bag that had a RH set to match the RH used for conditioning the brown
LSOA particles in order to ensure the aw within the LSOA did not change
during assembly of the films. The thickness of the films was controlled by
aluminium spacers inserted between the two hydrophobic glass slides prior to
assembly. After assembly, the brown LSOA within the thin films was isolated
from the surrounding atmosphere using a layer of vacuum grease around the
perimeter of the films. For further details, see Chenyakin et al. (2017) and
Fig. S1.
Measurements of diffusion coefficients
Fluorescence recovery after photobleaching (FRAP) has often been used to
determine diffusion rates of fluorescent molecules in biological samples
such as in the cytoplasm and nuclei of cells (Axelrod et al.,
1976; Deschout et al., 2010; Jacobson et al., 1976; Meyvis et al., 1999; Seksek
et al., 1997). To determine diffusion coefficients of the intrinsic
fluorophores in the brown LSOA, we used a version of FRAP, referred to as
rectangular area fluorescence recovery after photobleaching (rFRAP) (Deschout et al., 2010). rFRAP was chosen over circular FRAP,
since rFRAP has a closed-form expression for the recovery process. In rFRAP,
a rectangular region of a thin film containing fluorescent molecules is
photobleached with a high-intensity laser beam of a confocal laser scanning
microscope (Fig. S2). After photobleaching, the fluorescence signal within
the photobleached region recovers due to diffusion of fluorescent molecules
from outside the photobleached region into the photobleached region. The
recovery of the fluorescence signal over time is monitored and used to
determine the diffusion coefficient of the fluorescent molecules.
Images of brown limonene SOA films at three different aw
(0.33, 0.6, and 0.9) recorded during a rectangular fluorescence recovery
after photobleaching (rFRAP) experiment. Times shown in each panel
correspond to times after photobleaching. The orange rectangles depict the
area to be photobleached.
The rFRAP measurements were conducted with a laser scanning confocal
microscope (Zeiss Axio Observer LSM 5 10 MP) with a low numerical aperture
objective (Zeiss EC-Plan Neofluar 10×, 0.3 numerical aperture) to ensure
near-uniform photobleaching in the z direction. One-dimensional scanning
with a pixel dwell of 2.56 µs and an image scan time of 1.57 s were
used. The images were acquired with 512×512 pixels with a pinhole set to
80 µm. The scanning laser power was varied between 17.0 and
42.6 µW depending on the fluorescence of the sample. In order to
achieve a bleach depth (decrease in fluorescence intensity) of 30 %–50 %, as suggested by Deschout et al. (2010) for rFRAP experiments, the
laser power for photobleaching was varied between 93 and 297 µW,
depending on the sample (Deschout et al., 2010).
A rectangular area was used for photobleaching with length (x) and width
(y). The recovery time in the rFRAP experiments were related to both the
photobleaching area and diffusion rate. When the diffusion rate was fast
(e.g., high water activities), we used a larger photobleaching area, and when
the diffusion rate was slow (e.g., low water activities), we used a smaller
photobleaching area to give experimentally accessible recovery times. The
image sizes used in the rFRAP experiments were chosen in relation to the
bleach size with larger image sizes used for larger bleach sizes. For
example, at aw≥0.8, photobleached areas of 20 µm by
20 µm and image sizes of 199.6 µm by 199.6 µm were
used, while at aw=0.33, photobleached areas of 5 µm by
5 µm and 3 µm by 3 µm and image sizes of 30 µm by
30 µm were used. All rFRAP experiments were carried out at a
temperature of 294.5±1.0 K. Shown in Fig. 1 are examples of images of brown LSOA films with aw of 0.33, 0.6, and
0.9 recorded during rFRAP experiments.
Extraction of diffusion coefficients
Based on Fick's second law of diffusion, Deschout et al. (2010) developed
the following equation to describe the fluorescence intensities in thin
films after photobleaching a rectangular area with a confocal microscope (Deschout et al., 2010):
F(x,y,t)F0(x,y)=1-K04erfx+lx2w(D,t,r)-erfx-lx2w(D,t,r)×erfy+ly2w(D,t,r)-erfy-ly2w(D,t,r),
where F(x,y,t) is the fluorescence intensity at coordinate (x,y)
and time t after photobleaching;
F0(x,y) is the fluorescence intensity at
coordinate (x,y) prior to photobleaching; K0 is the effective bleach depth, which describes the
decrease in the fluorescence intensity within the photobleached area;
lx and ly are the lengths of
the photobleached area; r is the lateral resolution of the microscope; and D
is the diffusion coefficient of the fluorescent molecules. The parameter
wD,t,r is given by the following
equation:
wD,t,r=r2+4Dt.
In a first step of the analysis for the extraction of diffusion
coefficients, the images recorded after photobleaching were normalized to an
image recorded prior to photobleaching using the open-source program ImageJ (Schneider et al., 2012).
The resolution of the images was changed from
512×512 pixels to 128×128 pixels by averaging to reduce the noise. Then, Eq. (2) was used to extract wD,t,r from each image. In the
fitting procedure used to extract wD,t,r, K0 and a normalization factor were left as free parameters. Next, wD,t,r was plotted as a function of t and a straight line was fit to the
data. The diffusion coefficient, D, was calculated from the slope of the
straight line using a linear fit to Eq. (3). Examples of plots of wD,t,r vs. t are shown in Fig. 2.
Plot of w(D,t,r) as a function of time at aw of 0.9, 0.6, and
0.33. The red line is a linear fit to the data. The blue circles represent
the data points that were included in the linear fit, and the red circles
represent data that were not included because of possible reversible
photobleaching. The diffusion coefficients were obtained from the slopes.
Equation (2) assumes that the only mechanism for recovery in the photobleached
region is diffusion of unbleached molecules. The spontaneous recovery of the
fluorescence signal without diffusion, referred to as reversible
photobleaching, has been observed in previous studies at
short timescales (Sinnecker et al., 2005; Stout and Axelrod, 1995; Verkman, 2003). To
determine if this process
occurred during our diffusion measurements with
brown LSOA, a separate set of experiments was carried out. Particles of
brown LSOA (40 to 90 µm in diameter) were conditioned to an aw
of 0.6 and the entire particle was photobleached until the fluorescence
intensity decreased by between 17 % and 47 %. The photobleaching was
performed across the entire particle in order to rule out fluorescence
intensity recovery due to diffusion of fluorescent molecules. Within the
first 5 s after photobleaching a small amount of the fluorescent
signal recovered (1 %–3 % of the photobleached signal), which we attribute
to reversible photobleaching. To ensure this process did not impact our
diffusion measurements, the data recorded during the first 5 s
after photobleaching in the rFRAP experiments were not included when
determining diffusion coefficients.
Possible heating of the sample during photobleaching by the laser was not
expected to impact the diffusion measurements since local heating during
photobleaching should be dissipated to the surroundings much faster than the
time of the diffusion measurements. Nevertheless, to support this
expectation, two experiments were carried out with different laser
intensities but on the same sample conditioned to an aw of 0.9. A laser
intensity of 139.9 µW was used for a bleach depth of 20 % and a
laser intensity of 330 µW was used for a bleach depth of 50 %.
Within uncertainty, the diffusion coefficients determined with both bleach
depths were in agreement: (2.5±0.5)×10-9 cm2 s-1 was obtained for a laser intensity of 139.9 µW and
(2.8±0.1)×10-9 cm2 s-1 was obtained for a laser intensity of 330 µW
(uncertainties correspond to 95 % confidence intervals).
Equation (2) assumes that the fluorescence intensity is proportional to the
concentration of the intrinsic fluorescent molecules, which is a valid
assumption when the transmittance of light through the samples is ≥95 % (Fonin et al., 2014). In our experiments the
transmittance of light through the samples was ≤93 %. To take into
account the nonlinearity between the fluorescence signal and concentration,
the measured fluorescence signal was first converted to concentration using
the following equation:
C(x,y,t)C0(x,y)=log1-(1-T0)⋅Fx,y,tF0(x,y)log(T0),
where C(x,y,t)C0(x,y) is the normalized concentration
of the intrinsic fluorescent dye, F(x,y,t)F0(x,y) is the
normalized fluorescence signal, and T0 is the transmittance prior to the
photobleaching process. Equation (4) is derived in Sect. S2. After the
normalized concentrations were calculated, they were used in Eq. (2) in place
of the normalized fluorescence signal. Note that the application of Eq. (4) to
account for nonlinearity between the fluorescence signal and concentration
changed the diffusion coefficients by less than the uncertainties in the
measurements.
Results and discussion
Viscosity of brown limonene SOA
Figure 3 shows the viscosity of brown LSOA as a
function of aw measured with the bead-mobility technique. For
comparison, the known viscosity of pure water and the viscosity of brown
LSOA measured previously using the poke-and-flow technique are also included (Hinks et al., 2016). Overall, Fig. 3 shows that the viscosity
increases by 3–5 orders of magnitude as the aw decreases from 0.9 to
approximately 0.05. An increase in viscosity with a decrease in aw is
expected due to the plasticizing effect of water (Koop et al., 2011; Power
et al., 2013; Zobrist et al., 2011). A liquid has a viscosity of <102 Pa s, a semisolid has a viscosity between 102 and
1012 Pa s, and an amorphous solid has a viscosity of
>1012 Pa s (Koop et al., 2011; Mikhailov et
al., 2009; Shiraiwa et al., 2011). Based on Fig. 3, the brown LSOA studied
here can be considered as a liquid above an aw of 0.7 and as a
semisolid at aw below roughly 0.5.
Diffusion coefficients and mixing times of intrinsic fluorophores in
brown limonene SOA
Figure 4a shows the measured diffusion
coefficients of the intrinsic fluorophores in brown LSOA as a function of
aw. The average diffusion coefficient decreases from 5.5×10-9 to 7.1×10-13 cm2 s-1 as the aw
decreases from 0.9 to 0.33. The strong dependence on aw is due to the
plasticizing effect of water as mentioned above (Koop et al., 2011; Power
et al., 2013; Zobrist et al., 2011). Also included in Fig. 4 (secondary
y axis) is the mixing time of the intrinsic fluorophores by molecular
diffusion within a 200 nm brown SOA particle based on the measured diffusion
coefficients. Mixing times were calculated with the following equation (Seinfeld and Pandis, 2016; Shiraiwa et al., 2011):
τmixing=Dp24π2Dorg,
where Dp is the diameter of the particle and Dorg the measured
diffusion coefficient of the intrinsic fluorophore. The mixing time is the
time after which the concentration of the diffusing molecules at the center
of the particle deviates by less than 1/e from the equilibrium concentration (Shiraiwa et al., 2011). Based on the measured diffusion
coefficients, for the brown LSOA studied here mixing times of the organics
within 200 nm particles range from 0.002 to 14 s for aw from 0.9 to
0.33.
Viscosity of brown LSOA as a function of aw (primary x axis)
and RH (secondary x axis). The green bars show the viscosities that were
measured by Hinks et al. (2016) and the blue triangles show the viscosities
that were measured in this study using the bead-mobility technique. The
black circle is the viscosity of water measured by Crittenden et al. (2012).
(a) Measured diffusion coefficients of the intrinsic
fluorophore in brown LSOA as a function of aw (primary x axis) and RH
(secondary x axis). The secondary y axis shows the mixing time, which is the
time that would be needed for intrinsic fluorophores to mix within a 200 nm
brown limonene particle. The y error bars correspond to the highest and
lowest diffusion coefficient measured. The x error bars correspond to
uncertainty of the RH measurements (±2.5 %). (b) The
aw distribution in January (blue line) and July (green line) in the
planetary boundary layer (PBL) when monthly averaged concentrations of
organic aerosol (OA) are >0.5 µg m-3 at the surface
based on GEOS-Chem. (c) The temperature distribution in January and
July in the PBL when monthly averaged concentrations of OA are >0.5 µg m-3 at the surface based on GEOS-Chem.
Also shown in Fig. 4 is the frequency distributions of aw (panel b)
and temperatures (panel c) found in the planetary boundary layer for
the months of January and July. We calculated these frequency distributions
using GEOS-Chem version v10-01 (Pye et al.,
2010), which was driven by 6 h average GEOS-5 meteorology fields. Following Maclean et al. (2017), when determining the
frequency distributions of aw and temperatures within the PBL, we only
included grid cells in a column up to the top of the PBL if the monthly
averaged concentrations of organic aerosol (OA) were >0.5 µg m-3 at the surface, based on GEOS-Chem
version v10-01 (Pye et al., 2010). Based on this model, OA
concentrations were almost always <0.5 µg m-3 above the
surface of the oceans. Hence, Fig. 4b, c do not include most conditions over
the oceans. We excluded cases when OA concentrations were <0.5 µg m-3
at the surface since these concentrations are not expected to
be important for climate or health. OA concentrations were >0.5 µg m-3 in all
but one of the previous surface measurements of OA
at remote locations (Spracklen et al.,
2011).
Figure 4b shows that aw in the PBL is most often ≥0.33 when the
organic mass concentrations are higher than 0.5 µg m-3 at the
surface. Figure 4c shows that the temperature in
the PBL is often within 5 K of the temperature used in our experiments
(294.5 K). Based on Fig. 4, mixing times of
intrinsic fluorophore in the brown LSOA studied here are often short
(<1 h) for aw values and temperatures most often found in the
PBL when the organic mass concentrations are higher than 0.5 µg m-3.
The diffusion coefficients and mixing times reported here correspond to brown
LSOA generated using mass concentrations of 1000 µg m-3 in a
flow reactor. For some types of SOA (SOA from ozonolysis of α-pinene,
limonene, 3-hexenyl acetate and 3-hexen-1-ol) the viscosity of the SOA
increases as the mass concentration used to generate the SOA decreases (Grayson et al., 2016; Jain et al., 2018). Since mass concentrations of
biogenic SOA particles found in the atmosphere are most often ≤10 µg m-3 (Spracklen et
al., 2011) the values reported here likely represent the lower limit for the
viscosities and upper limit for the diffusion coefficients. Additional
studies are needed to determine diffusion coefficients and mixing times for
more atmospherically relevant mass concentrations. In addition, the brown
LSOA was generated using a ratio of limonene to ozone ∼1,
which suggests that not all double bonds in limonene were oxidized.
Additional studies are also needed to determine if diffusion coefficients in
brown LSOA are sensitive to the extent of oxidation of LSOA molecules.
Ye et al. (2018) studied the timescale for mixing of organics from toluene
oxidation within limonene SOA particles using mass spectrometry (Ye et al., 2018). In these studies, the limonene SOA
particles were generated with mass concentration of 16–22 µg m-3. Based on the studies by Ye et al. (2018) the mixing times of
organics within limonene SOA particles are on the order of 3–4 h for RH
values ranging from 10 % to 30 %, with little evidence for an RH dependence.
At 33 % RH, we calculate a mixing time of approximately 14 s. This
corresponds to a difference in diffusion coefficients of a factor of roughly
1000. A possible explanation for the apparent difference between the current
results and the results reported by Ye et al. (2018) is the difference in
the mass concentrations used to generate the SOA, and the low extent of
oxidation of LSOA compounds, as discussed above.
Comparison between measured diffusion coefficients and Stokes–Einstein
predictions
Shown in Fig. 5 are the measured diffusion
coefficients and predicted diffusion coefficients based on viscosity
measurements and the Stokes–Einstein relation. The viscosity measurements
include our new bead-mobility viscosity results
(Fig. 3) and previous poke–flow viscosity
measurements by Hinks et al. (2016), as well as viscosity measurements of
pure water for comparison (Crittenden et al., 2012; Hinks et al., 2016).
To predict diffusion coefficients from the viscosity measurements and the
Stokes–Einstein equation, the average dimension of the intrinsic
fluorophores is needed. The exact molecular identities of the chromophores
and fluorophores in brown LSOA is not known. Previous studies suggest that
there is a distribution of chromophores with a broad range of molecular
weights on the order of 500 g mol-1 (Nguyen et al., 2013).
Therefore, we tested a range of molecular weights from 300 to 800 g mol-1,
corresponding to hydrodynamic radii from 4.5 to 6.2 Å with an assumed
density of 1.3 g cm-3 (Saathoff et al.,
2009) and an assumed spherical geometry of the intrinsic fluorophores.
Measured and calculated diffusion coefficients in brown LSOA as a
function of aw (primary x axis) and RH (secondary x axis). The red
squares show the measured diffusion coefficients of intrinsic fluorophores
in brown LSOA. The blue triangles show the calculated diffusion coefficients
of the intrinsic fluorophore in brown LSOA based on viscosities measured in
this study using the bead-mobility technique and the Stokes–Einstein
equation. The y error bars for the diffusion coefficients measured in this
study (red squares) and the diffusion coefficients calculated from
bead-mobility viscosity measurements (blue triangles) show the highest and lowest
values measured. The green vertical bars depict the highest and the lowest
limit of calculated diffusion coefficients of brown LSOA based on viscosity
measurements from Hinks et al. (2016) and the Stokes–Einstein equation. The
black circle depicts the calculated diffusion coefficient of the intrinsic
fluorophore in pure water based on viscosity measurements of Crittenden et
al. (2012) and the Stokes–Einstein equation. The uncertainties for the
calculated diffusion coefficients take into account the uncertainty of the
hydrodynamic radii of the diffusing molecules (4.5 to 6.2 Å).
Figure 5 shows that the difference between the
measured and predicted diffusion coefficients is less than the uncertainty
of the measurements for diffusion coefficients as small as roughly
10-12 cm2 s-1, which corresponds to a viscosity of between
4×102 and 1.2×104 Pa s, based on
Fig. 4. This conclusion is consistent with most
previous studies that have investigated the accuracy of the Stokes–Einstein
relation for predicting diffusion coefficients of large organic molecules in
organic–water mixtures. For example, Chenyakin et al. (2017), Champion et
al. (1997), and Price et al. (2016) showed that the Stokes–Einstein relation
predicts diffusion coefficients of large organics in sucrose–water solution
consistent with measurements (i.e., within the uncertainty of the
measurements) when the viscosity is 1×104 Pa s (Champion et al., 1997; Chenyakin et al., 2017; Price et al., 2016). In
contrast, Longinotti and Corti (2007) and Corti et al. (2008) found
disagreement between measured and predicted diffusion coefficients of large
organics in organic–water solutions at slightly lower viscosities (Corti
et al., 2008; Longinotti and Corti, 2007).