ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-16-8817-2016Relative humidity-dependent viscosity of secondary organic material from
toluene photo-oxidation and possible implications for organic particulate
matter over megacitiesSongMijungLiuPengfei F.https://orcid.org/0000-0001-7280-9720HannaSarah J.ZaveriRahul A.https://orcid.org/0000-0001-9874-8807PotterKatieYouYuanMartinScot T.BertramAllan K.bertram@chem.ubc.cahttps://orcid.org/0000-0002-5621-2323Department of Chemistry, University of British Columbia,
Vancouver, BC, CanadaDepartment of Earth and Environmental Sciences, Chonbuk
National University, Jeollabuk-do, Republic of KoreaJohn A. Paulson School of Engineering and Applied
Sciences, Harvard University, Cambridge, MA, USAAtmospheric Sciences and Global Change Division, Pacific
Northwest National Laboratory, Richland, WA, USASchool of Chemistry, University of Bristol, Bristol, UKDepartment of Earth and Planetary Sciences, Harvard
University, Cambridge, MA, USAAllan K. Bertram (bertram@chem.ubc.ca)19July20161614881788307January201629January201630May201631May2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/16/8817/2016/acp-16-8817-2016.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/16/8817/2016/acp-16-8817-2016.pdf
To improve predictions of air quality, visibility, and climate change,
knowledge of the viscosities and diffusion rates within organic particulate
matter consisting of secondary organic material (SOM) is required. Most
qualitative and quantitative measurements of viscosity and diffusion rates
within organic particulate matter have focused on SOM particles generated
from biogenic volatile organic compounds (VOCs) such as α-pinene and isoprene. In this study, we
quantify the relative humidity (RH)-dependent viscosities at 295 ± 1 K
of SOM produced by photo-oxidation of toluene, an anthropogenic VOC. The
viscosities of toluene-derived SOM were 2 × 10-1 to ∼ 6 × 106 Pa s from 30 to 90 % RH, and greater than
∼ 2 × 108 Pa s (similar to or greater than the
viscosity of tar pitch) for RH ≤ 17 %. These viscosities
correspond to Stokes–Einstein-equivalent diffusion coefficients for large
organic molecules of ∼ 2 × 10-15 cm2 s-1 for
30 % RH, and lower than
∼ 3 × 10-17 cm2 s-1 for RH ≤ 17 %.
Based on these estimated diffusion coefficients, the mixing time of large
organic molecules within 200 nm toluene-derived SOM particles is 0.1–5 h
for 30 % RH, and higher than ∼ 100 h for RH ≤ 17 %. As
a starting point for understanding the mixing times of large organic
molecules in organic particulate matter over cities, we applied the mixing
times determined for toluene-derived SOM particles to the world's top 15 most
populous megacities. If the organic particulate matter in these megacities is
similar to the toluene-derived SOM in this study, in Istanbul, Tokyo,
Shanghai, and São Paulo, mixing times in organic particulate matter during
certain periods of the year may be very short, and the particles may be
well-mixed. On the other hand, the mixing times of large organic molecules in
organic particulate matter in Beijing, Mexico City, Cairo, and Karachi may be
long and the particles may not be well-mixed in the afternoon
(15:00–17:00 LT) during certain times of the year.
Introduction
Volatile organic compounds (VOCs) are released into the atmosphere from both
biogenic and anthropogenic sources. In the atmosphere, VOCs can form
secondary organic material (SOM) through oxidation reactions with OH
radicals, NO3 radicals, and O3. SOM accounts for 20–80 % of
the mass of organic atmospheric particulate matter at various locations
(Zhang et al., 2007; Jimenez et al., 2009). SOM typically consists of
thousands of different compounds, and only 10–20 % of the individual
molecules that make up SOM particles have been identified (Decesari et al.,
2006; Hallquist et al., 2009). The lack of information on the chemical
composition of SOM has resulted in a poor understanding of their physical
properties, including the viscosity and molecular diffusion rates within SOM
particles.
Knowledge of the viscosity and molecular diffusion rates within SOM particles
is needed to predict the properties of these particles and understand their
role in the atmosphere. For example, the size distribution and mode diameter
depend on the diffusion rates of organic molecules within the particles
(Shiraiwa et al., 2013; Zaveri et al., 2014). Simulations show that total SOM
mass concentrations can be overestimated or underestimated depending on what
diffusion rates are used (Shiraiwa and Seinfeld, 2012). Chemical aging of
atmospheric particles by heterogeneous reactions can depend on diffusion
rates within SOM (Shiraiwa et al., 2011; Kuwata and Martin, 2012; Zhou et
al., 2013; Steimer et al., 2014; Houle et al., 2015) and heterogeneous ice
nucleation may be influenced by the viscosity of SOM particles (Murray et
al., 2010; Wang et al., 2012; Ladino et al., 2014; Schill et al., 2014;
Wilson et al., 2012). Moreover, long-range transport of polycyclic aromatic
hydrocarbons can depend on diffusion rates in a particle (Zelenyuk et al.,
2012; Zhou et al., 2013) and the efflorescence of crystalline salts can be
hindered for highly viscous SOM (Murray, 2008; Murray and Bertram, 2008;
Bodsworth et al., 2010; Song et al., 2013).
Most qualitative and quantitative measurements of viscosity and diffusion
rates within organic particulate matter have focused on SOM generated from
biogenic VOCs such as α-pinene and isoprene (Virtanen et al., 2010;
Cappa and Wilson, 2011; Perraud et al., 2012; Saukko et al., 2012; Abramson et al., 2013;
Robinson et al., 2013; Renbaum-Wolff et al., 2013a; Bateman et al., 2015;
Kidd et al., 2014; Pajunoja et al., 2014; Wang et al., 2015; Grayson et al., 2015; Song et al., 2015).
Recently, the viscosity and diffusion rates within SOM particles generated
from anthropogenic VOCs have also been investigated. Using mass spectrometry,
Loza et al. (2013) and Robinson et al. (2013) investigated mixing of
toluene-derived SOM particles and SOM particles from α-pinene
ozonolysis. Results from both studies were consistent with toluene-derived
SOM being in a highly viscous state. From bounce experiments, Saukko et
al. (2012) reported that SOM particles derived from naphthalene and
n-heptadecane are highly viscous upon increasing oxidation. Also from bounce
experiments, Bateman et al. (2015) showed SOM derived from photo-oxidation of
toluene had a viscosity > 100 Pa s for relative humidity (RH) values
< 80 %. Li et al. (2015) showed through bounce experiments that SOM
derived from m-xylene and 1,3,5-trimethylbenzene had a viscosity of
> 100 Pa s at RH values less than 70 %. Li et al. (2015) also used
results of reactive uptake studies to infer that for RH values of
35–45 % the diffusion coefficient of carboxylic acids within SOM
generated from several anthropogenic VOCs (toluene, m-xylene, and
1,3,5-trimethylbenzene) was ∼ 10-13.5±0.5 cm2 s-1.
Although there has been recent progress in measuring the viscosity and
diffusion rates within SOM generated from anthropogenic VOCs, additional
studies are needed to quantify the viscosities and diffusion rates over the
full range of RH found in the atmosphere.
In the following, we measure the viscosities of toluene-derived SOM over the
range of RH values found in the atmosphere. As in previous studies, SOM from
the photo-oxidation of toluene serves as a proxy for organic particulate
matter from anthropogenic sources in megacities (e.g., Pandis et al., 1992;
Robinson et al., 2013). After determining viscosities as a function of RH,
the Stokes–Einstein equation is used to convert the viscosities into
equivalent diffusion rates of large organic molecules within toluene-derived
SOM. The Stokes–Einstein equation should give reasonable values of diffusion
rates when the viscosity is not near the viscosity of a glass
(∼ 1012 Pa s) and when the molecules are roughly the same size
or larger than the molecules in the SOM matrix (Champion et al., 2000; Koop
et al., 2011; Shiraiwa et al., 2011; Power et al., 2013). Finally, the
results are used to estimate the viscosities and diffusion rates in organic
particulate matter over megacities.
Experimental
The production and collection of SOM particles onto hydrophobic substrates
(which are needed for the bead-mobility and poke-flow experiments) are
discussed in Sect. 2.1. The viscosity of toluene-derived SOM was determined
using the bead-mobility technique and the poke-flow technique together with
simulations of fluid flow. These two techniques are discussed in Sects. 2.2
and 2.3.
Experimental conditions for production and collection of
toluene-derived SOM particles using the oxidation flow reactor. Particles
were collected onto hydrophobic substrates using an electrostatic
precipitator or a single-stage impactor.
SOM aerosol particles having diameters less than 1 µm were
generated by toluene photo-oxidation in an oxidation flow reactor (OFR) (Kang
et al., 2007; Lambe et al., 2011). The procedure for generating SOM from
toluene photo-oxidation in the flow reactor has been given by Liu et
al. (2015). Only the details relevant to the current experiments are given
here.
For this study, the volume of the OFR was 13.3 L and the reactor was
operated at a flow rate of ∼ 7 L min-1 with a residence time in
the range of ∼ 110 s. The temperature used in the OFR experiments was
293 ± 2 K and the concentrations of toluene and ozone used in the flow
reactor are listed in Table 1. Ozone was produced external to the flow
reactor by irradiating pure air with the ultraviolet emission from an Hg lamp
(λ=185 nm). The injected ozone concentration was ∼ 30 ppm.
Hydroxyl radicals were produced inside the OFR by the following photochemical
reactions:
O3+hν(λ=254nm)→O2+O(1D),O(1D)+H2O→2OH.
The RH inside the reactor was held constant at
13 ± 3 %. A recent study has shown that the viscosity of α-pinene-derived SOM is dependent on the RH at which the SOM is generated
(Kidd et al., 2014). Additional studies are needed to explore this potential
RH effect on the viscosity of toluene-derived SOM.
Mass concentrations of SOM particles in the OFR were 60–100 and
600–1000 µg m-3 for the two different experimental
conditions (see Table 1). For the mass concentration of
60–100 µg m-3, the oxygen-to-carbon (O : C) ratio was
1.08, calculated from the AMS mass spectra following the approach of Chen et
al. (2011). This value can be compared with the O : C values ranging from
0.9 to 1.3 that were measured for toluene-derived SOM generated in a similar OFR (Lambe
et al., 2015). At the outlet of the OFR, two different methods were used for
the collection of SOM particles. In the first method, SOM particles were
collected on hydrophobic slides using an electrostatic precipitator (TSI
3089, USA). After collection, the SOM particles on the hydrophobic slides,
formed from coalescence during sampling, were smaller than
∼ 5 µm in diameter. For the bead-mobility and poke-flow
techniques, however, particle sizes 20–60 µm in diameter
are needed. To generate these large sizes, the hydrophobic slides containing
the SOM particles were placed inside an RH- and temperature-controlled flow
cell (Pant et al., 2006; Bertram et al., 2011; Song et al., 2012) and the RH
was increased to > 100 %. This procedure caused particle growth by
water uptake and eventual coagulation among particles. This growth and
coagulation process resulted in larger but fewer SOM particles on the
hydrophobic slides. Details of this procedure are given by Renbaum-Wolff et
al. (2015) and Song et al. (2015). This procedure was used for samples 1, 2,
5, and 6 shown in Table 1.
In the second method, SOM particles were collected on hydrophobic surfaces
using a single-stage impactor (Prenni et al., 2009; Pöschl et al., 2010).
During impaction, the collected submicron SOM particles coagulated, resulting
in particles with sizes between 10 and 100 µm in diameter. These
supermicron particles were used directly in the bead-mobility and poke-flow
experiments. This procedure was used to collect samples 3, 4, 7, and 8 shown
in Table 1.
For all the bead-mobility experiments, a Teflon substrate was used. For all
the poke-and-flow experiments, hydrophobic glass slides coated with
trichloro(1H,1H,2H,2H-perfluorooctyl)silane (Sigma-Aldrich) were
used. The coating procedure is described in Knopf (2003).
Bead-mobility experiments
The bead-mobility technique was previously described in Renbaum-Wolff et
al. (2013a, b). Briefly, a water suspension of ∼ 1 µm
insoluble melamine beads (Sigma Aldrich Cat. no. 86296) was nebulized and
incorporated into supermicron SOM particles deposited on a hydrophobic
substrate (toluene samples 1–4, Table 1). The hydrophobic substrate with the
SOM particles and beads was placed in a flow cell with variable RH and a
temperature of 295 ± 1 K. A continuous flow of N2/H2O gas
(flow rate ≈ 1200 sccm) was passed over the supermicron particles.
The flow above the particles resulted in a shear stress on the particle
surface and internal circulations within the particle, which could be
visualized by observing the beads within the particles with a
light-transmitting microscope coupled to a CCD camera (Zeiss Axio Observer,
magnification 40 ×). Figure 1 shows images from a typical
bead-mobility experiment for a toluene-derived SOM particle at 80 % RH.
Typically, 1–7 beads were monitored within a particle over 50–100 frames.
The time between frames ranged from 0.2 s to 10 min depending on the velocity
of the beads. From the location of the beads as a function of time, the speed
of individual beads was determined. These individual speeds were then used to
determine average bead speeds for a given sample and RH. The measured speeds
of 3–10 beads were used to determine a mean bead speed. Bead speeds were not
reported at RH < 60 % since at these RH values the movements of the
beads were too slow to measure for typical observation times.
Optical images from typical bead-mobility experiments for a
toluene-derived SOM particle (toluene sample 8 in Table 1) at 80 % RH.
Three different beads are labeled using colored arrows. The x and y
coordinates of these beads are also indicated. Scale bar:
20 µm.
The average bead speed for a given sample and RH was converted to viscosity
using a calibration line. The calibration line was developed by Song et
al. (2015) from measurements of bead speeds in sucrose-water particles over a
range of RH values. The RH within the flow cell was measured using a
hygrometer with a chilled mirror sensor (General Eastern, Canada), which was
calibrated by measuring the deliquescence RH for pure ammonium sulfate
particles (80.0 % RH at 293 K, Martin, 2000). The uncertainty of the
hygrometer was ±0.5 % RH after calibration.
Poke-flow technique in conjunction with fluid simulations
The poke-and-flow technique in conjunction with fluid simulations was used to
measure the viscosities of SOM particles at RH values less than 50 %.
This technique was not used at RH values > 50 % since the flow rates
of the SOM after poking were too fast to observe at these RH values. The
qualitative method of poking an inorganic particle to determine its phase
(i.e., solid or liquid) was introduced by Murray et al. (2012). Renbaum-Wolff
et al. (2013a) and Grayson et al. (2015) expanded on this method by measuring
the characteristic flow time of a material after poking and extracting
viscosity information from simulations of fluid flow. Briefly, supermicron
toluene-derived SOM particles deposited on a hydrophobic substrate (toluene 5–8,
Table 1) were placed inside a flow cell with RH control. The particles
were conditioned for 30 min at > 70 % RH, 60 min at
60–70 % RH, 2 h at 30–60 % RH, and 3 h at ≤ 30% RH.
These times should be sufficient for the particles to equilibrate with the
surrounding water vapor based on recent measurements of diffusion
coefficients of water within the water-soluble component of α-pinene-derived SOM (Price et al., 2015). For example, the time to
equilibrate with the surrounding of water vapor was calculated to be
25.3 min at 10 % RH based on diffusion coefficients of water within the
water-soluble component of α-pinene-derived SOM (Price et al., 2015).
These diffusion coefficients should be applicable to SOM derived from toluene
studied here, since both SOMs have similar viscosities as a function of RH
(compare Fig. 2 in Renbaum-Wolff et al., 2013a, with Fig. 5 below).
Physical parameters used to simulate material flow in the poke-flow
experiments. R and r indicate the radius of a tube and the radius of an
inner hole, respectively.
Slip length (nm)Surface tension (mN m-1)Density (g cm-3)Contact anglee (∘)Values used to calculate lower limit5a28b1.4c80 (if r< 2R), 100 (if r> 2R)Values used to calculate upper limit10 000a75d1.4c100 (if r< 2R), 80 (if r> 2R)
a The range of slip length, which
is the interactions between fluids and solid surfaces, is based on literature
data (Schnell, 1956; Churaev et al., 1984; Watanabe et al., 1999; Baudry et
al., 2001; Craig et al., 2001; Tretheway and Meinhart, 2002; Cheng and Giordano, 2002; Jin et al.,
2004; Joseph and Tabeling, 2005; Neto et al., 2005; Choi and Kim, 2006; Joly et al., 2006; Zhu et al., 2012; Li et al., 2014).
b The lower limits of the surface tension of toluene-derived SOM
were determined as 28 mN m-1, the surface tension of liquid toluene at
293 K (Adamson and Gast, 1997). c Ng et al. (2007).
d The upper limits of the surface tension of toluene-derived SOM
were determined as 75 mN m-1, the surface tension of pure water at
293 K (Engelhart et al., 2008). e Contact angle of the
toluene-derived SOM on a substrate measured by 3-D fluorescence confocal
microscope ranged 80–100∘. The relationship of viscosity and
contact angle depends on the ratio of the radius of a tube, R, to the
radius of an inner hole, r (Grayson et al., 2015).
After equilibration, particles were poked using a sharp needle
(0.9 mm × 40 mm) (Becton-Dickson, USA) that was mounted to a
micromanipulator (Narishige, model MO-202U, Japan) and inserted through a
small hole in the top of the flow cell. The geometrical changes before,
during, and after poking a particle were recorded by a reflectance optical
microscope (Zeiss Axio Observer, 40 × objective) equipped with a CCD
camera. At 30–50 % RH the action of poking the particles with the
needle resulted in the material forming a half torus geometry (see Fig. 2a).
From the images recorded after poking the particles, the experimental flow
time, τexp, flow, was determined. The experimental flow time was
defined as the time taken for the equivalent-area diameter of the inside of
the half torus geometry to reduce to 50 % of the initial diameter. Here
the equivalent-area diameter, d, is calculated as d=(4A/π)1/2
where A represents the hole area (Reist, 1992). For RH < 20 % the SOM particles shattered after
poking, and no restorative flow was observed over ∼ 5 h (see Fig. 2b).
In this case τexp, flow was set to > 5 h.
Optical images of pre-poking, poking, and post-poking from typical
poke-flow experiments on toluene-derived SOM particles (toluene sample 6) at
(a) 39.5 % RH and (b) 16.5 % RH.
Panels (a1, b1); pre-poking, panels (a2, b2) post-poking immediately after the needle has been removed (time set = 0 s), panel (a3); the experimental flow time, τexp, flow, where the
diameter of hole has decreased to 50 % of its initial size, and panel
(b3) particles shatter and do not flow over a period of 6.5 h.
Scale bar: 20 µm.
To determine viscosities from τexp, flow, simulations of fluid
flow were carried out with the finite-element analysis software package,
COMSOL Multiphysics (Renbaum-Wolff et al., 2013a; Grayson et al.,
2015). The mesh size used in the simulations was 4.04–90.9 nm. The physical
parameters (i.e., slip length, surface tension, contact angle, and density)
used in the simulation are listed in Table 2.
For each particle for which flow was observed, simulations were run using a
half torus geometry, similar to the geometry observed in the experiments
where flow was observed. The radius of the tube, R, in the half torus
geometry and the radius of the hole, r, in the half torus geometry used in
the simulations were based on the images recorded immediately after poking
the particles with the needle. To determine viscosity for each particle,
viscosity in the simulations was adjusted until τmodel, flow was
within 1 % of τexp, flow.
Measured average bead speeds as a function of RH for different SOM
samples (toluene 1, 2, 3, and 4, see Table 1). The bead speeds of 3–10 beads
were used to determine a mean bead speed. The x error bars represent the
uncertainty in the RH measurements and the range of RH values in a given
experiment. The y error bars represent the standard deviation of the
measured bead speeds.
In cases for which the particles cracked, simulations were run using a
quarter-sphere model with one of the flat faces of the quarter sphere in
contact with the substrate, similar to what was observed in the experiments
(Renbaum-Wolff et al., 2013a). The diameter used for the quarter sphere was
20 µm. In this case we determined a lower limit to the viscosity by
adjusting the viscosity in the simulation until the sharp edge of the
quarter-sphere model moved by 0.5 µm within 5 h. A value of
0.5 µm was used since this amount of movement could be observed in
the optical microscope experiments.
Results
Shown in Fig. 3 are the mean bead speeds of individual SOM samples (toluene
1, 2, 3, and 4) measured at different RH values between 60 and 90 % RH
(see Sect. 2.1). As the RH decreased from 89.9 to 60.7 %, the average
bead speed decreased by a factor of 22 from 9.20 × 10-4 to
4.24 × 10-7µm ms-1. Sample-to-sample variation
was less than the uncertainty in the measurements and, within uncertainty,
the results for 60–100 µg m-3 concentration agreed with the
results for 600–1000 µg m-3 concentration.
Figure 4 shows the result of τexp, flow as a function of RH for
the different samples (toluene 5, 6, 7, and 8). The τexp, flow
increased from ∼ 1 to ∼ 2000 s as RH decreased from 50 to
30 % RH.
Results from poke-flow experiments. τexp, flow, where
the diameter of hole has decreased to 50 % of its initial size, measured
for the different samples (toluene 5, 6, 7, and 8, see Table 1). The arrows
indicate particles shattered at the given RH.
Shown in Fig. 5 are the viscosities as a function of RH for toluene-derived
SOM particles determined from the bead-mobility experiments (Sect. 2.2) and
the poke-flow experiments in conjunction with the fluid simulation
(Sect. 2.3). For the bead-mobility experiments, the viscosities were
determined from the mean of the bead speeds. The
y error bars indicate the 95 % prediction intervals from the
calibration line (Song et al., 2015). The x error bars represent the
uncertainty in the RH measurements. The viscosity of the SOM increases from
∼ 0.2 to ∼ 129 Pa s as RH decreases from 89.9 to 60.7 %. As
shown in Fig. 5, differences between the results for the 600–1000 and
60–100 µg m-3 samples are less than the uncertainties in the
measurements.
Viscosities of toluene-derived SOM particles as a function of RH.
For RH > 60 % the viscosities were determined from the mean bead
speeds (see Fig. 3) and a calibration line (Song et al., 2015). The y error
bars for RH > 60 % represent the 95 % prediction intervals from
the calibration line. For RH < 60 % the viscosities were calculated
from the τexp, flow where y error bars represent the
calculated lower and upper limits of viscosity using the simulations. The
x error bars over the entire range of RH represent the range of RH values
in a given experiments and the uncertainty in the RH measurements. The right
y axes present calculated diffusion coefficients of organic molecules in
SOM using the Stokes–Einstein relation, and calculated mixing times within
200 nm particles due to bulk diffusion using Eq. (2). The black lines
represent linear fits for the RH vs. log(lower viscosities) (R2=0.958)
and log(upper viscosities) (R2=0.984) from the entire data set
excluding the RH where particles cracked. Viscosity of toluene-derived SOM
particles from Bateman et al. (2015) (green box) and Li et al. (2015) (blue
box) is also included. The secondary x axis shows
Vwet/Vdry of the SOM, where Vdry is the volume of
SOM at 0 % RH and Vwet is the volume of the SOM after taking up
water at a given RH.
Also shown in Fig. 5 are the calculated viscosities of the toluene-derived
SOM for RH < 50 % from the poke-flow experiments. The viscosity
increases from approximately 7.8 × 103 to
6.3 × 106 Pa s as RH decreases from 47.3 to 30.5 %. The
uncertainty in the viscosity of approximately 2 orders of magnitude arises
from the uncertainties in the physical parameters used in the simulations
(i.e. slip length, surface tension, density, and contact angle). Of these
parameters, the slip length contributed the most to the uncertainty in the
viscosity (Grayson et al., 2015). For RH < 20 %, restorative flow did
not occur over ∼ 5 h resulting in a lower limit to the viscosity of
∼ 2 × 108 Pa s, similar to or greater than the
viscosity of tar pitch (∼ 10 8 Pa s, Koop et al., 2011).
Discussion
Bateman et al. (2015) previously estimated the viscosity of toluene-derived
SOM from particle rebound experiments. From their measurements, they estimated
a viscosity of 100–1 Pa s for RHs between 60 and 80 % with SOM mass
concentrations of 30–50 µg m-3 (green box in Fig. 5), in good
agreement with our measurements.
Li et al. (2015) previously estimated the diffusion coefficient of carboxylic
acids within toluene-derived SOM from measurements of reactive uptake of
NH3. They estimated a diffusion coefficient for carboxylic acids of
10-13.5±0.5 cm2 s-1 for RHs between 35 and 45 % using
SOM mass concentrations of 44–125 µg m-3. If a
hydrodynamic radius of 0.1–1.5 nm is assumed for the carboxylic acids (Li
et al., 2015), viscosity of
1 × 104–2 × 106 Pa s is calculated using the
Stokes–Einstein equation (blue box in Fig. 5), consistent with our
measurements. The good agreement between the current results and the results
from Bateman et al. (2015) and Li et al. (2015) suggests that the viscosity
of the toluene-derived SOM is relatively insensitive to the particle mass
concentrations at which the SOM is produced over the range of 30–1000 µg m-3.
The strong dependence of viscosity on RH shown in Fig. 5 can be understood by
considering the hygroscopic nature of the SOM. To illustrate this point in
Fig. 5, viscosity is also plotted vs. Vwet/Vdry of the SOM
(secondary x axis), where Vdry is the volume of SOM at
0 % RH and Vwet is the volume of the SOM after taking up water
at a given RH. Vwet/Vdry was calculated with the following
equation (Petters and Kreidenweis, 2008; Pajunoja et al., 2015):
Vwet/Vdry=κ100RH-1+1,
where κ is the hygroscopic parameter. A hygroscopic parameter of 0.15
was assumed, consistent with previous measurements for toluene-derived SOM
(Hildebrandt Ruiz et al., 2015). Equation (1) neglects the Kelvin effect,
which is a reasonable assumption for the large particles used in our studies.
Figure 5 illustrates that the water content (top x axis) of the particles
plays a key role in regulating the viscosity.
A liquid is defined as a material with a viscosity less than 102 Pa s;
a semisolid is defined as a material with a viscosity between 102 and
1012 Pa s; and a solid is defined as a material with a viscosity
greater than 1012 Pa s (Koop et al., 2011; Shiraiwa et al., 2011). As
shown in Fig. 5, the viscosities of the SOM produced from toluene
photo-oxidation correspond to a liquid for RH > 60 %, a semisolid for
60 % < RH < 30 %, and a semisolid or a solid for
RH < 20 %. Our results suggest a semisolid-to-liquid phase transition
at an RH between 60 and 70 %, in good agreement with Bateman et
al. (2015) who suggested a semisolid-to-liquid phase transition of
toluene-derived SOM particles in the range of 60–80 % RH.
From the viscosities determined at 295 ± 1 K and the Stokes–Einstein
relationship (assuming a hydrodynamic radius of 0.4 nm for organic molecules
within the toluene-derived SOM, Renbaum-Wolff et al., 2013a), we calculated
the diffusion coefficients of large organic molecules, Dorg, within
toluene-derived SOM (see secondary y axis in Fig. 5). Dorg ranges
from ∼ 3 × 10-8 to
∼ 2 × 10-15 cm2 s-1 for RH from 90 to
30 %. It is lower than
∼ 3 × 10-17 cm2 s-1 for RH ≤ 17 %.
The Stokes–Einstein relation is not expected to predict with high accuracy
the diffusion rates of small gas molecules such as OH, O3, NOx,
NH3, and H2O and may be inaccurate near the glass transition RH
(Koop et al., 2011; Shiraiwa et al., 2011). However, the Stokes–Einstein
relationship should give reasonable estimations of diffusion rates for large
organic molecules for conditions not close to the glass transition
temperature of the matrix (Champion et al., 2000; Koop et al., 2011; Shiraiwa
et al., 2011; Power et al., 2013; Marshall et al., 2016).
Using the diffusion coefficients (Dorg), the mixing time by
diffusion, τmixing, of large organic molecules within a 200 nm
SOM particle was calculated with the following equation, where d is the
particle diameter (Shiraiwa et al., 2011; Bones et al., 2012; Renbaum-Wolff
et al., 2013a):
τmixing=d24π2Dorg.
Here, we are using 200 nm to represent a typical accumulation mode
atmospheric particle, Shiraiwa et al. (2011). The concentration of the
diffusing molecules anywhere in the particles deviates by less than e-1
from the homogeneously well-mixed case at times longer than τmixing. The τmixing values calculated with this
procedure are indicated in Fig. 5 (secondary y axis). At an RH of 45 %
or higher, the mixing times are short, approaching a value less than or equal to
0.1 h. At 30 % RH, the mixing times are between 0.1 and 5 h. At
RH ≤ 17 %, the mixing time is longer than ∼ 100 h (lower
limit of the arrows in Fig. 5).
Monthly average RH and temperature for the megacities of Tokyo,
Delhi, Shanghai, Mexico City, São Paulo, Mumbai, Osaka, Beijing, New
York, Cairo, Dhaka, Karachi, Buenos Aires, Kolkata, and Istanbul. For the
stations, afternoon averages RH values (15:00–17:00 LT) were retrieved
from NOAA's National Climate Data Center for the years from 2004 to 2014.
Boxes show the median, 25th, and 75th percentiles of 3 h averages and the
whiskers show the 10th and 90th percentiles. Green shading indicates that the
afternoon RH (at the 10th percentile level) does not go below 45 % RH
and the median afternoon temperature is 290–300 K. Red shading indicates
that the afternoon RH (at the 10th percentile level) is 17 % or lower and
the median afternoon temperature is 290–300 K.
Atmospheric implications
In the following, we use the mixing times calculated in the previous section
to estimate the mixing times of large organic molecules in organic
particulate matter over megacities. Several caveats should be kept in mind
when applying the mixing times discussed earlier to particles over
megacities. First, organic particulate matter over megacities is most likely
more complicated than toluene-derived SOM. Toluene and other aromatics can
account for a large fraction of nonmethane hydrocarbon emission in urban
environments (Singh et al., 1985; Na et al., 2005; Suthawaree et al., 2012),
and toluene and aromatics are thought to be one of the main sources of SOM
particles in urban environments (Odum et al., 1997; Schauer et al., 2002a, b;
Vutukuru et al., 2006; Velasco et al., 2007, 2009; de Gouw et al., 2008;
Gentner et al., 2012; Liu et al., 2012; Hayes et al., 2015). Nevertheless,
large alkanes and unspeciated nonmethane organic gases also likely play a
role in SOM formation in urban environments. Second, the toluene-derived SOM
was generated using relatively large mass concentrations of particles
(60–1000 µg m-3). The good agreement between our results and
the results from Bateman et al. (2015) and Li et al. (2015), which were
carried out with a mass concentration of 30–1000 µg m-3,
suggests that for toluene-derived SOM the viscosity is not strongly dependent
on the mass concentration of organics used to generated the SOM, but
additional studies are needed to confirm this. Third, as mentioned above, the
Stokes–Einstein equation was used to estimate diffusion coefficients and
hence mixing times, and this equation can underestimate diffusion
coefficients close to the glass transition temperature. Due to these caveats,
the analysis below should be considered as a starting point for understanding
the mixing times of large organic molecules in organic particulate
matter particles
over megacities. Additional studies are needed to explore the implications of
the caveats discussed above.
For this analysis, we define megacity as a metropolitan area with a total
population in excess of 10 million people. Based on the Population Division
Data Query (2014) of the United Nations (http://esa.un.org/; United Nations, Department of Economic and Social Affairs, Population Division, 2014), we
selected the top 15 most populous cities (Tokyo, Delhi, Shanghai, Mexico
City, São Paulo, Mumbai, Osaka, Beijing, New York, Cairo, Dhaka, Karachi,
Buenos Aires, Kolkata, and Istanbul) which meet this criterion.
In order to determine τmixing for organic particulate matter in
megacities, information on the RH and temperature in the cities is needed.
Figure 6 gives information on RH and temperature in the 15 most populous
megacities obtained from NOAA's National Climatic Data Center (NCDC)
(www.ncdc.noaa.gov). The figure shows
boxplots of average afternoon (15:00–17:00 LT) RH and temperature
from these cities for the years 2004–2014. The afternoon
(15:00–17:00 LT) was chosen for this analysis since this is the time
of day when RH is typically the lowest. In the figure, the boxes represent
the median, 25th, and 75th percentiles and the whiskers show the 10th and 90th
percentiles. In addition to RH, viscosity can depend strongly on temperature
(Champion et al., 1997; Koop et al., 2011). For example, the viscosity of
solutions of sucrose and water may increase by 2–3 orders of
magnitude for a 10 K decrease in temperature close to the glass transition
temperature (Champion et al., 1997). However, the effect of temperature on
the viscosity of toluene-derived SOM has not been quantified. As a result, we
have limited the current analysis to months when the median afternoon
temperature is within 5 K of the temperatures used in the viscosity
measurements (i.e., 290–300 K). The fact that the median afternoon
temperature is often below 290 K, highlights the need for low-temperature
viscosity measurements.
In Fig. 6, we indicate with green shading cases when the afternoon RH (at
the 10th percentile level) does not go below 45 % RH and the median
afternoon temperature is 290–300 K. The cases when the afternoon RH (at the
10th percentile level) does not go below 45 % RH are listed in Table 3
(second column). At 45 % RH the mixing time within toluene-derived SOM is
short (i.e., less than or equal to 0.1 h). Figure 6 (green shading) and
Table 3 suggest that, if the organic particulate matter over megacities is
similar to the toluene-derived SOM in this study, in Tokyo, Shanghai, São
Paulo, and Istanbul mixing times during certain periods of the year will be
very short, and homogeneously well-mixed particles can be assumed.
Months when the afternoon RH in the 15 most populous megacities
either does not go below 45 % (at the 10th percentile level) or is
17 % or lower (at the 10th percentile level) and the median afternoon
temperature is 290–300 K. “None” indicates that these criteria are not
met for any month.
MegacityMonths when the afternoon RH (at the 10th percentile level) does not go below 45 %Months when the afternoon RH (at the 10th percentile level) is 17 % or lowerTokyoJun and SepnoneDelhinonenoneShanghaiJun and SepnoneMexico CitynoneJan–May, DecSão PauloJannoneMumbainonenoneOsakanonenoneBeijingnoneApr and MayNew YorknonenoneCairononeMar–AprDhakanonenoneKarachinoneJan and DecBuenos AiresnonenoneKolkatanonenoneIstanbulOctnone
In Fig. 6, we indicate with red shading cases where the afternoon RH (at
the 10th percentile level) is 17 % or lower and the median afternoon
temperature is 290–300 K. The cases when the afternoon RH (at the 10th
percentile level) is 17 % or lower are listed in Table 3 (third column).
As mentioned above, at this RH, the mixing time within toluene-derived SOM is
long (> 100 h), based on the viscosity measurements and Stokes–Einstein
calculations. Figure 6 (red shading) and Table 3 (third column) suggest that
if the organic particulate matter is similar to the toluene-derived SOM in
this study, in Mexico City, Beijing, Cairo, and Karachi, the particles may
not be well-mixed in the afternoon (15:00–17:00 LT) during certain
times of the year.
Kleinman et al. (2009) studied the time evolution of aerosol size
distributions and number concentrations of ambient particulate matter over
the Mexico City plateau during the MILAGRO (Megacity Initiative: Local And
Global Research Observations) field campaign conducted in March 2006. The
particulate matter over Mexico City was primarily organic and as
photochemical aging occurred, Kleinman and colleagues observed an increase in
accumulation-mode volume due to an increase in the accumulation mode
particles, not because of an increase in the average size of the accumulation
mode. The condensing organic vapors from photo-oxidation of toluene and other
anthropogenic VOCs over Mexico City are expected to be semivolatile
(Shrivastava et al., 2013). However, Kleinman et al. (2009) showed that the
observed evolution of aerosol size distribution was not consistent with a
volume growth mechanism in which the semivolatile organic vapors are expected
to readily diffuse within the accumulation mode substrate. This could
indicate that the accumulation mode particles over Mexico City were highly
viscous and did not reach equilibrium with large gas-phase organic molecules
during the observation period. This observation is consistent with our
experimental results that toluene-derived SOM is highly viscous at RH
< 20 % and Fig. 6, which shows that the median RH in Mexico City often
falls below 20 % in March. However, it should be noted that the
particulate matter over Mexico City is likely more chemically complex than
the SOM used in this study.
Summary of conclusions reached after applying the results of the
viscosities, diffusion coefficients, and mixing time of the toluene-derived
SOM to the top 15 most populous megacities. Green circles indicate
megacities where the afternoon RH at the 10th percentile does not go below
45 % RH and the median afternoon temperature is 290–300 K for certain
times of the year. In these cases, well-mixed particles can be assumed. Red
crosses indicate megacities where the afternoon RH at the 10th percentile is
17 % or lower for certain times of the year and the median afternoon
temperature is 290–300 K. In these cases, the particles may not be
well mixed in the afternoon for certain times of the year.
Conclusions
We investigated the RH-dependent viscosities at room temperature of SOM
particles produced from toluene photo-oxidation with the mass concentration
of 60–1000 µg m-3. A bead-mobility technique showed the
viscosities of the toluene-derived SOM increased from ∼ 0.2 to
∼ 129 Pa s as RH decrease from 89.9 to 60.7 %. This indicates
that the toluene-derived SOM particles are a liquid at RH > 60 %. The
RH range for liquid-to-semisolid is in good agreement with Bateman et
al. (2015) who showed the liquid-to-semisolid phase transition of these
particles in the range of 60–80 % RH. A poke-flow technique combined
with fluid simulations showed the viscosities increased from approximately
7.8 × 103 to 6.3 × 106 Pa s as RH decreased
from 47.3 to 30.5 %. For RH ≤ 17 %, the viscosities of the SOM
were greater than or equal to ∼ 2 × 108 Pa s, similar
to or greater than the viscosity of tar pitch. This suggests that the
toluene-derived SOM particles are a semisolid at 20 < RH ≤ 60 %, and a semisolid or a solid at RH ≤ 17 %. Using the
viscosity data and the Stokes–Einstein equation, the diffusion coefficients
of large gas-phase organic molecules within the toluene-derived SOM particles
were calculated to be ∼ 3 × 10-8 to
∼ 2 × 10-15 cm2 s-1 for RHs from 89.9 to
30.5 %, and is lower than
∼ 3 × 10-17 cm2 s-1 for RH ≤ 17 %.
Mixing times by diffusion of large organic molecules within 200 nm
toluene-derived SOM particles was calculated to be less than 0.1 h at
RH > 47.3 %, 0.5–5 h at 30.5 % RH, and greater than
∼ 100 h at RH ≤ 17 %.
To apply the results of the viscosities, diffusion coefficients, and mixing
time of the toluene-derived SOM, we selected the top 15 most populous
megacities. Based on the RH in the cities, and if the organic particulate
matter in megacities is similar to the toluene-derived SOM in this study, in
cities such as Tokyo, Shanghai, São Paulo, and Istanbul, mixing times during
certain periods of the year will be very short and homogeneously well-mixed
particles can be assumed. On the other hand, for certain times of the year in
Beijing, Mexico City, Cairo, and Karachi, mixing times of large organic
molecules in organic particulate matter may be long (≥ 100 h), and the
particles may not be well mixed in the afternoon (15:00–17:00 LT)
during certain times of the year. These results are summarized in Fig. 7.
Acknowledgements
This work was supported by the Natural Sciences and Engineering Research
Council of Canada. Support from the USA National Science Foundation, the
Atmospheric Science Research (ASR) Program of the USA Department of Energy, the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP) (2016R1C1B1009243), and research funds for newly appointed professors of Chonbuk National
University in 2015 is also acknowledged.
Edited by: B. ErvensReviewed by: two anonymous referees
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