Introduction
Black carbon (BC) is a subset of the aerosol population that is emitted as a
result of incomplete combustion. Since BC particles strongly absorb solar
radiation, they can modify the climate directly. Based on the current
best-estimates the BC direct radiative forcing from all present-day sources
is +0.88 W m-2; however, the uncertainty associated with this number
is approximately 90 %. The uncertainty in the BC direct radiative forcing
estimates stems from several factors which include the removal rates of BC
from the atmosphere through wet or dry deposition (Bond et al., 2013).
BC particles can also potentially act as cloud condensation nuclei (CCN) and
contribute to the indirect effects of aerosols on climate (Bond et al., 2013).
The current best estimates of the indirect radiative forcing of BC is +0.23 W m-2
(Bond et al., 2013).
However, similar to the direct radiative forcing estimate, this indirect
radiative forcing estimate is also highly uncertain, with an uncertainty of
approximately 90 % (Bond et al., 2013).
The uncertainty in the indirect effect radiative forcing estimate is
partially due to an uncertainty in BC–cloud interactions (Bond et al., 2013).
To better understand the direct and indirect effects of BC on climate, a
better understanding of the activation of BC into cloud droplets is needed.
Despite the importance of activation of BC particles into cloud droplets,
there have only been a small number of studies that have investigated the
activation of BC particles into cloud droplets under real atmospheric
conditions (see Table 1 in Cozic et al., 2007, as well as Pratt et al., 2010, and Granat et al.,
2010). Of these studies, most have been carried out at mid- to high-altitude
mountain sites (Cozic et al., 2007; Hitzenberger et al., 2000, 2001; Kasper-Giebl et al., 2000; Sellegri et al.,
2003). Only a few studies have investigated the activation of BC particles
at marine or coastal sites (Gieray et al., 1997; Granat et al., 2010). In addition, almost all of the previous studies
have focused on the fraction of total BC mass activated into cloud droplets.
For example, Hallberg et al. (1992) measured the
mass scavenging of BC into fog droplets at a polluted site in the Po Valley
(Italy). They found that the mass fraction of scavenged BC (0.06) was
statistically smaller than the scavenged fraction of sulfate (0.18).
Similar results were obtained when sampling stratocumulus clouds at a
mountaintop site at Kleiner Feldberg, Germany. There, a statistically
significant difference in scavenging was also observed; the scavenged
fraction of sulfate at this site was 0.52 while the scavenged fraction of
BC was 0.15 (Hallberg et al., 1994). In this latter case,
observations showed that BC particles found as cloud droplet residuals were
of mixed composition, often having a water-soluble component that varied as
a function of size. These studies reporting mass scavenging of BC can be
useful for validating models. However, since the CCN properties of refractory black carbon (rBC)-containing particles are more closely linked to number and particle size,
the studies that focus on BC mass scavenging are unable to determine the
relative contribution of particle size and composition to the activation of
BC into clouds.
Recent studies have compared concentrations of BC particles measured over
the central Pacific from 85∘ N to 67∘ S during the HIAPER
(High-Performance Instrumented Airborne Platform for Environmental Research)
Pole-to-Pole Observations (HIPPO) campaign, with predictions using a global
chemical transport model (Wang et al., 2014). The authors
concluded that most models may not be accurately simulating the scavenging
of BC particles into cloud droplets (Wang et al., 2014). To
help better constrain these models, additional studies on the activation of
BC into cloud droplets under real atmospheric conditions and at different
locations and times would be helpful.
The single particle soot photometer (SP2) is an instrument recently
developed to determine the refractory black carbon (rBC) mass of individual
particles (Moteki and Kondo, 2007; Schwarz et al., 2006; Stephens et al., 2003). With this
instrument, size distributions of rBC can be obtained in real time. In
addition, this instrument provides information on coating thicknesses of the
rBC-containing particles. The SP2 has now been used extensively to determine
the size distribution and coating thicknesses of rBC particles in the
atmosphere. Here, we apply this technique to investigate the activation of
rBC particles in stratocumulus clouds at a marine boundary layer site.
Specific questions to be addressed include the following: (1) what is the
activated fraction of rBC as a function of particle size in the marine
stratocumulus clouds studied? (2) Do small (sub-100 nm) rBC cores get
incorporated into the cloud droplets? (3) What is the thickness of the
coating on the rBC cores that are incorporated into the cloud droplets? (4)
Is the rBC coating volume fraction and the total diameter (rBC core and
coating thickness) important for activation of rBC into cloud droplets? (5)
Are the results consistent with κ-Köhler theory, which is used in
advanced modeling studies to describe the activation of rBC particles into
cloud droplets (e.g., Fierce et al., 2013; Riemer et al., 2010)?
Site, sampling and analysis
Site description
The sampling site was located below the peak of Mt. Soledad (251 m a.m.s.l.)
which is ∼ 2 km from the coast of the Pacific Ocean in La
Jolla, CA (32.8400∘ N, 117.2769∘ W) and has mostly light
commercial and residential activities in the area. The cloud periods
occurred primarily at night when these activities are at a minimum. The city
of La Jolla is predominately residential with a population of approximately
43 000 people and is situated 24 km north of San Diego (population 1.3 million), the closest urban center
(Zhao et al., 2014).
Data was collected from 27 May to 18 June 2012 using instruments housed in a
modified shipping container. A total of three stratocumulus cloud events
were sampled during this time frame. The first cloud event was excluded from
this analysis due to an instrumental error. The second cloud event occurred
from 12 June 2012, 20:43 to 13 June 2012, 11:35 PDT, and is hereinafter called
Cloud 2. The third cloud event took place from 17 June 2012, 20:36 to 18 June
2012, 07:52 PDT, and is called Cloud 3 for the remainder of the document.
Inlets
Two inlets, referred to as the total inlet and residual inlet, were used
during this study (Fig. 1). The total inlet measured both interstitial and
cloud residual particles during cloud events. This heated inlet was designed
and built following the specifications reported by Bates et al. (2002) and
therefore assumed to have the same transmission efficiency, namely
> 95 % for particles less than 6.5 µm, using a
∼ 900 Lpm bypass flow. The instruments sampling from the plenum of the
total inlet (Fig. 1) were connected sequentially to a common sampling line
(0.25 in. stainless steel tubing). A pump was placed at the end of this
sampling line creating a bypass flow of ∼ 2 Lpm.
Schematic showing the configuration of the inlets and
instrumentation housed in the shipping container.
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The intake of the residual inlet was a counterflow virtual impactor (CVI, see
Sect. 2.3 and Sect. S1 in the Supplement) that enabled the sampling of cloud
droplets without contamination from interstitial particles, or ambient gases,
thus only the residual particles of the cloud droplets were sampled. This
inlet was used only during cloudy periods and was connected to a branch of
the total inlet by a three-way valve (Fig. 1). During a cloud event, the valve
was manually switched so that cloud droplets were sampled through the CVI and
cloud residuals were measured by instrumentation connected downstream of the
valve. At times when no clouds were present the valve was switched such that
all instruments were sampling ambient particles. All instruments downstream
of the three-way valve were sequentially connected to a common sampling line
(0.25 in. stainless steel tubing). A pump was also placed at the end of the
sampling line creating a bypass flow of ∼ 2 Lpm.
Since much of the analysis used in this paper is based on a measured ratio
of particle number concentrations it was necessary to ensure that there were
no significant losses of particles due to the inlet configurations.
Therefore, particle losses from diffusion, sedimentation, turbulent inertial
deposition and inertial deposition from both bends and contractions for the
total and residual inlets (assuming cloud-free sampling) were calculated
using the Particle Loss Calculator (Von der Weiden et al., 2009)
and found to be < 2 % for particles with diameters between 0.07
and 1 µm, covering the size range used for this analysis.
Counterflow virtual impactor sampling
The CVI was based on the design of Noone et al. (1988), where droplet-laden
air was drawn into the CVI using a high velocity air intake vacuum (≈ 92 m s-1). Only those droplets with enough inertia to overcome a
counterflow of zero air with an average flow rate of ≈ 5 Lpm made
it past the region known as the stagnation plane and were entrained into the
sample flow and transported to the instruments downstream. Water from these
droplets began evaporating upon impact with the warm dry counterflow air,
held at a constant temperature of 40 ∘C, and particles were further
dried by a heated section of the sampling tube, also at 40 ∘C,
leaving only the droplet residuals to be sampled downstream. If the droplets
were completely evaporated, any volatile gases in the cloud droplets, such as
nitric acid, likely evaporated and were not part of the residual particles
(Zhao et al., 2014). If some water was retained by the residual particles at
this temperature, a fraction of highly soluble volatile components may have
also remained.
The smallest droplet diameter for which 50 % of the droplets are sampled
is considered to be the CVI cut-size (CVI-D50) and is the diameter for
which a droplet's stopping distance is greater than the CVI inlet diameter
and the length to the end of the stagnation plane (Anderson et al., 1993; Noone et al., 1988). For the clouds sampled in this study, a
CVI-D50 of 11.5 ± 0.7 µm and 11.6 ± 0.7 µm
for Cloud 2 and Cloud 3, respectively, were calculated (Sect. S1).
Due to the properties of a CVI, particle concentrations are enhanced at the
exit of the CVI compared to ambient conditions. Enhancement factors (EF) of
7.1 and 7.4 for Cloud 2 and Cloud 3, respectively, were calculated based on
the flow rates used during sampling (Sect. S1).
Black carbon measurements
Refractory black carbon (rBC) was measured from the total inlet and the
residual inlet using two separate single particle soot photometers (SP2, DMT,
Boulder, CO). These instruments are referred to as the total SP2
(SP2Tot) and the residual SP2 (SP2Res). The location
of these instruments is shown in Fig. 1. The SP2 has been described in detail
elsewhere (Moteki and Kondo, 2007; Schwarz et al., 2006; Stephens et al.,
2003). Briefly, particles are sampled at ≈ 0.12 Lpm and carried
directly into a chamber housing a high intensity (≈ 1 MW cm-2) intra-cavity Nd : YAG laser operating at λ=1064 nm. BC particles are rapidly heated, through absorption, to
incandescence, where the emitted visible light is detected by two
photomultipliers. The mass of individual rBC particles can be determined
using a calibration plot, where the amplitude of the detector response is
proportional to the mass of a reference material. The two SP2s used in this
study were calibrated pre and post-campaign with
Aquadag® (Moteki et al., 2009), using
effective densities reported by Gysel et al. (2011). Based on the
recommendations by Baumgardner et al. (2012), the average peak heights
determined for each of the Aquadag® sizes
were scaled downward by 0.75 since Aquadag®
has been shown to cause a higher SP2 signal response per unit mass than
ambient BC.
The calibration parameters used to determine mass were taken from a linear
fit of the combined pre and post-campaign data. The uncertainty in the rBC
mass (at the 95 % confidence limit) stemming from uncertainty in the fit
of the calibration was 1–16 % for SP2Res (depending on particle mass)
and 3–25 % for SP2Tot (depending on particle mass). A volume
equivalent diameter was also determined from the measured mass assuming a
black carbon density of 1.8 g cm-3 (Bond and Bergstrom, 2006).
The SP2Res was a four-channel instrument with a detection range of
approximately 70 to 220 nm, whereas the SP2Tot was an eight-channel
instrument with a detection range of 70 to 558 nm.
It is well known that the detection efficiency of an SP2 decreases when the
diameter of rBC cores becomes small (i.e., < ∼ 70–90 nm; Laborde et al., 2012; Schwarz
et al., 2010). Since the main conclusions about black carbon in this
manuscript are based on relative measurements taken with two SP2s (i.e., the
residual SP2 and the total SP2) the detection sensitivities of the two
instruments as a function of size need to be similar. To ensure that this
was the case, we carried out the following test: we measured the rBC size
distributions with both SP2s from side-by-side ambient sampling of room air
during the post-campaign calibration. Since the two instruments gave
slightly different results, we applied a size-dependent correction factor to
the SP2 connected to the total inlet to bring the two results in agreement.
Shown in Fig. S1 are rBC size distributions measured during cloud-free
sampling conditions before the corrections were applied, the size-dependent
correction factor applied to the total SP2, and the rBC size distributions
measured during cloud-free sampling after the correction factors were
applied. After applying the correction factors to the total SP2, the two
SP2s agreed to within 6 % for the total number concentration of rBC
particles having diameters between 70 and 220 nm.
Refractory black carbon coating thickness measurements
In addition to measuring the incandescence signal, the SP2 measures the
elastically scattered light from rBC and non-rBC-containing particles with
two avalanche photodiodes (APDs). Both APDs were set to the high gain
setting for collection, and one of the APDs was a split detector. The APDs
generate a time dependent signal as particles pass through the Gaussian
laser beam. The split detector APD can be used to obtain position
information, whereas the APD without the split detector is used to obtain
information on the elastic scattering intensity from particles (Gao et al., 2007). The information from
the two APDs combined can be used to determine the coating thickness on rBC
cores as described by Gao et al. (2007).
However, in the study presented here, a large fraction of rBC particles
evaporated before the notch position in the split detector, due to poor
alignment of the split detector. As a result, position information could not
be obtained reliably for a large fraction of the rBC particles. A similar
observation has previously been reported (Taylor et al., 2014). Since position information could not be determined reliably for
a large fraction of rBC particles, coating thicknesses were not determined
using the approach described by Gao et al. (2007). Instead, we used the maximum intensity in the elastic scattering
signal from the non-split APD detector to determine lower limits to the
coating thickness on the rBC particles. A similar approach has been
previously used (Subramanian et al., 2010). This
coating analysis was only performed on the data from the residual SP2. In
other words, we only extracted coating information for rBC-containing
particles sampled from the residual inlet. When rBC-containing particles
intersect with the laser beam the particles are heated, and any coating
material will evaporate. As a result, the maximum elastic scattering signal
measured with the non-split APD detector may not represent the original size
of the coated rBC particle. Because of the evaporation process, the maximum
intensity from the non-split APD detector only provides a lower limit to the
coating thicknesses of rBC-containing particles (Gao et al., 2007;
Subramanian et al., 2010).
The signal from the non-split detector was calibrated using polystyrene
latex (PSL) beads (200 and 300 nm in diameter). This gives a calibration
curve that relates the amplitude of the measured scattering signal to the
scattering intensity determined from Mie calculations. These Mie
calculations involved calculating the scattering intensity for each PSL size
over the solid angle of the SP2 detector (a full-angle cone of 65∘ at
45∘ and 135∘ from the laser axis (Gao et al.,
2007; Schwarz et al., 2008b) using a Mie code (Leinonen) based on that of Mätzler (2002a, b). The refractive index used for the PSL
Mie calculations was 1.59–0.0i.
Since the mass of the rBC core is known from the incandescence signal and
the scattering amplitude is known from the non-split APD detector, a
core–shell Mie model can be employed to determine what coating thickness
would give the measured scattering signal for that particular particle (Gao et al.,
2007; Schwarz et al., 2008b). In this work a core–shell Mie model was used to
construct a lookup table for core diameters of 60 to 220 nm (in 1 nm
increments) and shell thicknesses from 0 to 360 nm (in 1 nm increments). The
complex index of refraction used for the core was 2.26–1.26i (Moteki et al., 2010; Taylor et al., 2014) and
for the shell, 1.5–0.0i, which is consistent with that of dry sulfate or
sodium chloride (Metcalf et al., 2012; Schwarz et al., 2008a, b). The PSL calibration was used to
scale all calculated values to measured values. The elastic scattering
amplitudes and the rBC core diameters were then used with this lookup table
to determine the lower limits to the coating thicknesses for each rBC-containing
particle. It should be noted that the coating thicknesses have not been
validated experimentally, but merely provide consistency between the
observed optical scattering and Mie theory.
For small particles, although the incandescence measurements can size rBC
cores down to ∼ 70 nm, the SP2 elastic scattering optical
detection limit means that scattering from bare rBC cores below
∼ 110 nm cannot be measured. As particle size decreases below
110 nm, thicker and thicker coatings are required to produce a measurable
scattering signal. In this analysis any particle with no measurable
scattering signal was assumed to have a coating thickness of 0 (i.e., they
were assumed to be bare rBC cores), even though they may actually have had a
thin coating. This also leads to a lower limit for coating thicknesses for
particle sizes below ∼ 110 nm. The fraction of particles with no
detectable scattering was 33 % for Cloud 2 and 17 % for Cloud 3.
For large rBC cores, the optical detector became saturated when even
relatively modest coatings were present. For example, the scattering from a
220 nm rBC core with a coating thickness of 40 nm would saturate the SP2
optical detector. In this analysis, the coatings for particles with
saturated scattering signals were calculated using the saturation limit of
the detector, again resulting in a lower limit for coating thickness. The
fraction of particles with saturated scattering signals was 6 % for Cloud 2 and 4 % for Cloud 3.
In summary, due to the optical detection limits of the non-split detector
and due to evaporation of the coatings in the laser beam, the coating
thicknesses determined in this work, are lower limits to the true coating
thicknesses.
Size distribution measurements of the bulk aerosol
Two instruments were used to measure size distributions of the bulk aerosol
(see Fig. 1). Size distributions of the bulk aerosol sampled from the total
inlet were determined with a scanning electrical mobility spectrometer
(SEMS, model 2002, BMI, Hayward, CA) coupled to a condensation particle
counter (CPC, model 3781, TSI, St. Paul, MN), which counted particles into
61 discrete size bins from 0.01 to 1 µm with a 5 min scan time interval.
Size distributions of bulk aerosol, sampled from the residual inlet, were
determined with a scanning mobility particle sizer (SMPS, model 3034, TSI,
St. Paul, MN), which recorded particle counts into 55 size bins from 10 to 487 nm with a 3 min scan time interval. Both the SEMS and SMPS operate based on
the coupling of a size-selecting differential mobility analyzer and a
condensational growth particle counter. During cloud-free sampling periods,
the total number concentration of particles between 70 and 400 nm measured
with the SMPS and SEMS agreed to within 4 %.
Aerosol mass spectrometry
To characterize the chemical composition of the cloud droplet residuals an
online aerosol mass spectrometer (HR-ToF-AMS, Aerodyne Research Inc.,
Billerica, MA) was operated downstream of the CVI on the residual inlet. The
HR-ToF-AMS measures non-refractory, sub-micrometer aerosol chemical
composition at high time resolution (DeCarlo et al., 2006). Here we only consider data measured by the HR-ToF-AMS in its
mass-spectrum and V modes of operation. These data were recorded as 2 min
averages every 4–6 min, depending on how many other modes of
operation (W-mode, light scattering) the instrument was alternating between.
Size-resolved composition data for the residual particles measured by the
HR-ToF-AMS in time-of-flight mode are not considered here since the signal
was generally at or below the detection limit. Standard quantification
procedures (Allan et al., 2004) were applied to the mass
spectra measured by the HR-ToF-AMS to determine the relative concentrations
of the non-refractory species (organic, nitrate, sulfate, ammonium and
chloride) typically reported by aerosol mass spectrometry.
Back trajectories
Air mass back trajectories were calculated using the NOAA Hybrid Single
Particle Lagrangian Integrated Trajectory Model (HYSPLIT; Draxler and Rolph, 2013;
Rolph, 2013). All trajectory calculations used the National Centers for
Environmental Predictions EDAS meteorological data set. Trajectories were
calculated starting at 10 m a.g.l., 96 h backwards in time, and at hourly
intervals throughout the entire period of cloud sampling.
Cloud properties
A fog monitor (FM-100, model 100, DMT, Boulder, CO), which is a forward
scattering optical spectrometer, was located approximately 50 cm above the
top of the container, 1 m from the residual inlet, and 1.5 m from the total
inlet. The instrument was mounted on a freely rotating board allowing it to
be turned into the wind when the wind direction was obvious. Details of the
operational theory of the FM-100 can be found in Eugster et al. (2006) and
Spiegel et al. (2012). Briefly, ambient droplet-laden air is pumped through a
wind tunnel and carried to a sizing region where droplets pass through a laser beam
(wavelength = 658 nm). Light that is scattered in the forward direction
from a droplet crossing the laser beam is collected by photodetectors and the
signals measured are used to assign the droplet to a size bin.
From the measured cloud droplet size distribution both the total cloud
droplet number concentration (CDNC) and the amount of liquid water content
(LWC) present can be determined (Spiegel et al., 2012). The FM-100 used in
this study collected droplet counts from droplets with diameters from
2 to 50 µm using the manufacture's predefined 20 size bins. The size
bin widths using this configuration were 2 µm for droplets
< 20 µm and 3 µm for droplets
> 20 µm. Calibrations of the FM-100 were performed by
Droplet Measurement Technologies prior to installation.
In-cloud HYSPLIT 96 h back trajectories ending at hourly intervals
for Cloud 2 (12 June 21:00 to 13 June 12:00 PDT) in (a) and
(c), and Cloud 3 (17 June 21:00 to 18 June 08:00 PDT) in
(b) and (d). All back trajectories started at 10 m a.g.l.
Darker yellow regions on land in panels (a) and (b)
indicate densely developed urban areas containing 50 000 or more people
(United States Census Bureau). Panels (c) and (d) show the
vertical profiles over the same hourly intervals shown in (a) and
(b).
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Results and discussion
Back trajectories
The back trajectories for Cloud 2 (Fig. 2a, c) show that the air mass spent
most of the previous 96 h over the Pacific Ocean and arrived at the sampling
site from a northwesterly direction. During the first part of Cloud 2 (from
12 June 21:00 to 13 June 08:00 PDT), the back trajectories became
progressively more northerly and the air mass began traveling towards large
populated urban regions. Towards the end of the cloud event (at ≈ 09:00 PDT on 13 June) the winds shifted to southwesterly. Based on the
back trajectories, the air mass for Cloud 2 traveled ≈ 40–50 km
over land before reaching the sampling site. In addition, the air mass spent
a significant amount of time close to the ocean surface prior to being lifted
up to the sampling site (Fig. 2c).
Time series data for both Cloud 2 (left side) and Cloud 3
(right side) showing liquid water content (LWC, blue trace) and ambient
temperature (red trace) in (a); wind speed and direction in (b);
cloud droplet number size distributions with the CVI-D50 (black trace)
overlaid in (c); the number size distribution for the total aerosol in
(d), and the residual aerosol in (e). All data shown are 5 min
averages and meet the criteria discussed in the text.
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The back trajectories for Cloud 3 (Fig. 2b, d) also show that the
air mass spent the majority of the previous 96 h over the Pacific Ocean
before arriving at the site. At the start of Cloud 3 (17 June, 21:00 to 22:00 PDT) the air mass arrived from the northwest. Throughout the remainder of
the cloud event (17 June 23:00 to 18 June 08:00 PDT) the air mass continued
to shift farther north, and by the end of the cloud event (18 June 08:00 PDT)
the air mass was traveling south along the coastline before arriving at the
sampling site. The back trajectories indicate that the air mass traveled
≈ 10–20 km over land prior to arriving at the sampling site.
Similar to Cloud 2, the air spent a significant amount of time close to the
ocean surface prior to being lifted up to the sampling location (Fig. 2d). Since the trajectories during both cloud events are close to the coastline
for a period of time, it is likely these air masses contained both marine
particles and anthropogenic emissions.
Meteorological conditions and cloud properties
For the purposes of this study, the data were classified as in-cloud and
included for analysis if they met the following criteria: (1) the 5 min averaged CVI counterflow was within ± 6 % of the mean
counterflow (i.e., ± 5σ, where σ is standard deviation)
to ensure only periods of stable CVI flows were included; and (2) the 5 min averaged LWC was greater than 0.05 g m-3 to remove periods of
entrainment, or “patchy” regions of the cloud as much as possible (Cozic et al., 2007).
Average cloud droplet number size distributions for Cloud 2
(a) and Cloud 3 (b) measured by the FM-100 (black circles) and
fit with a lognormal distribution function (black dashed lines). The average
cloud droplet volume distributions (blue squares) and lognormal fits (blue
dashed lines) are also shown for each cloud event. The CVI-D50 is
indicated on each panel by a red dashed line.
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The measured cloud properties as a function of time are shown in Fig. 3a–c, where Cloud 2 is shown on the left side and Cloud 3 is shown on the
right side of the plot. Cloud 2 was characterized by a median temperature of
13.4 ∘C, a median wind velocity of 0.5 m s-1 (10th and 90th percentiles of 0.3 and 0.8 m s-1) a median wind direction of
126∘ (10th and 90th percentiles of 60 and 297∘), and a median LWC of 0.10 g m-3. During the middle portion of Cloud 2
(13 June, 01:00 to 02:00 PDT), the droplet distributions clearly show an
interval where the number of droplets above the CVI-D50 (black trace
overlaid on panel c) increases significantly, which coincides, in time, with
a sharp increase in LWC. Cloud 3 was characterized by a median temperature
of 15.2 ∘C, a median wind velocity of 1.4 m s-1 (10th and 90th percentiles of 1.1 and 2.0 m s-1), a median wind
direction of 328 ∘ (10th and 90th percentiles of 322 and 341 ∘), and a median LWC of 0.09 g m-3.
The cloud droplet number and volume size distributions, averaged over the
entire event, are shown in Fig. 4, and further summarized in Table 1. Cloud 3 had a CDNC of 146 cm-3, a factor of 2 higher than during
Cloud 2 (68 cm-3).
From the calculated CVI-D50 and the fits to the droplet size
distribution (Fig. 4), the number and volume fraction of droplets
sampled by the CVI were determined. The results are summarized in Table 1. During Cloud 2, the number
fraction of droplets larger than the CVI-D50 was about 38 % and for Cloud 3 the fraction
sampled was about 24 %. Since only the larger droplets were sampled by the CVI during these
two cloud events, the results presented herein are only representative of
the larger droplet population.
Summary of cloud microphysical properties showing the average CVI
cut-size (CVI-D50) where the uncertainty stems from the calculated
cut-size (see text for details); average liquid water content (LWC) and 1
standard deviation; and the cloud droplet number
(CDNCTot) and volume (VolTot)
concentration for droplets with diameters between 2 and 50 µm. Also
shown are the number CDNCSampCDNCTot
and volume VolSampVolTot fractions of
droplets sampled, where CDNCSamp and
VolSamp are the number and volume concentrations,
respectively, for the fraction of droplets sampled.
Cloud no.
Date Sampled
CVI-D50 (µm)
LWC (g m-3)
CDNCTot (cm-3)
CDNCSampCDNCTot
VolTot
VolSampVolTot
(µm3 m-3)
2
12–13 June 2012
11.5 ± 0.72
0.13 ± 0.07
67.67
0.38 ± 0.03
1.24 ×105
0.91 ± 0.02
20:43–11:35 PDT
3
17–18 June 2012
11.6 ± 0.72
0.09 ± 0.02
145.8
0.24 ± 0.1
8.88 ×104
0.68 ± 0.10
20:36–07:52 PDT
Size distributions
Average size distributions of the bulk aerosol particles and rBC particles
measured from the total and residual inlets for both Cloud 2 and Cloud 3 are
shown in Fig. 5. Data are plotted in two ways: on a log scale, in panels a
and b and normalized to the respective maximum, in panels c and d. Table 2
summarizes the results obtained from the size distribution analysis. All
size distributions shown in Fig. 5 have been corrected for differences in
instrument sensitivity, and all residual distributions have been corrected
for the CVI enhancement factor (Sect. S1) and droplet transmission through the CVI (Sect. S4).
Summary of the averaged number size distributions for Cloud 2
(a, c) and Cloud 3 (b, d) for the total aerosol (red solid
lines); residual aerosol (red dashed lines); total rBC as a function of core
diameter (black solid lines); residual rBC as a function of core diameter
(black dashed lines). Both the aerosol and rBC for each cloud event are shown
in two ways: a log scale (a, b) to highlight the relative
differences between the aerosol and rBC as well as normalized to the
respective maximum value (c, d) to highlight the shift in size
distributions. All residual distributions have been corrected for instrument
sensitivity (Fig. S1), CVI enhancement (Sect. S1), and droplet losses
(Sect. S4).
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Averaged number (N) and mass (M) concentrations and modal
parameters Dg and σg for aerosol and rBC particles during
the two cloud events measured at Mt. Soledad. The subscripts Tot and Res
represent measurements made from the total and residual inlets, respectively.
Cloud 2
Cloud 3
Aerosol
rBC
Aerosol
rBC
NTot (cm-3)
980.8
75.24
994.0
62.13
MTot (ng m-3)
–
73.41
–
61.83
Dg,Tot (nm)
107.7
< 0.07
80.54
< 0.07
σg,Tot
1.577
–
1.703
–
NRes (cm-3)
43.46
2.000
83.15
3.86
MRes (ng m-3)
–
2.741
–
4.735
Dg,Res (nm)
331.9
87.30
269.2
80.72
σg,Res
1.187
1.259
1.281
1.268
Size distributions measured from the total inlet (BulkAero<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Tot</mml:mi></mml:msub></mml:math></inline-formula> and rBC<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Tot</mml:mi></mml:msub></mml:math></inline-formula>)
The average size distributions of the bulk aerosol measured with the total
inlet (referred to as BulkAeroTot for the remainder of the document)
and the average size distributions of the refractory black carbon measured
with the total inlet (referred to as rBCTot for the remainder of the
document) are shown in Fig. 5. A single mode lognormal distribution function
was fit to the BulkAeroTot data, yielding mean geometric diameters
(Dg) of 108 and 81 nm with geometric standard deviations (σg) of 1.58 and 1.70 for Clouds 2 and 3, respectively. Integration of the
number distribution during Cloud 2 results in a total number concentration
(NTot) for the bulk aerosol of 981 cm-3. Likewise,
NTot during Cloud 3 was measured to be 994 cm-3. Previous measurements in
the marine boundary layer have classified the environment as “clean” marine
if the number of particles is ≤ 300–500 cm-3 and “polluted” marine
if the number concentrations are ≥ 400–1500 cm-3 (Andreae, 2009;
Bates et al., 2000; Glantz and Noone, 2000; Hawkins et al., 2010; O'Dowd et
al., 2001; Pirjola and O'Dowd, 2000; Twohy et al., 2005). Thus, the particle
concentrations measured at Mt. Soledad, in addition to the back
trajectories, suggest that for both clouds the air masses can be classified
as polluted marine aerosols. The size distributions of BulkAeroTot as a
function of time are also included in Fig. 3d for comparison.
The rBCTot size distributions for each cloud are shown in Fig. 5. The
Dg for rBCTot (assuming the number distributions are lognormal)
during both events lies somewhere in the nucleation mode at < 70 nm,
which is outside the detection range for the SP2. Integration of the
rBCTot distributions, from 70 to 220 nm, yields an NTot of 75 cm-3 during Cloud 2 and 62 cm-3 in Cloud 3. Assuming a black
carbon density of 1.8 cm-3 the total mass concentrations of rBC
(MTot) are 73 and 62 ng m-3 for Clouds 2 and 3, respectively
(Table 2). The rBCTot mass concentrations observed at Mt. Soledad
were higher than concentrations measured in clean marine air (Cooke et al., 1997; Shank et al., 2012), but
considerably lower than concentrations measured in most urban environments
(see Table 1 in Metcalf et al., 2012).
Size distributions measured from the residual inlet (BulkAero<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Res</mml:mi></mml:msub></mml:math></inline-formula> and rBC<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Res</mml:mi></mml:msub></mml:math></inline-formula>)
Average size distributions of the bulk aerosol measured from the residual
inlet (referred to as BulkAeroRes for the remainder of the document)
are also shown in Fig. 5. The size distributions of the
BulkAeroRes indicate that it was mostly the larger particles of the
BulkAeroTot distributions that were incorporated into the sampled cloud
droplets. The size distributions of BulkAeroRes as a function of time
for both cloud events are included in Fig. 3e for comparison.
The size distributions for BulkAeroRes shown in Fig. 5 have a local
minimum at 110 nm for Cloud 2 and 90 nm for Cloud 3. The particles observed
at sizes less than the local minima may be due to droplet shattering, a leak in the CVI (Pekour and Cziczo, 2011; Schwarzenboeck, 2000; Vidaurre et al., 2011), or possibly entrainment
or precipitation processes in the clouds (Targino et al., 2007).
Figure 5 also shows the size distributions of the rBC residuals
measured with the CVI. Figure 5 shows that rBC cores smaller than 100 nm are
incorporated into cloud droplets. In addition, they are overall larger than
the rBCTot. Fitting the rBCRes size distributions (assuming these
distributions are lognormal) results in mean geometric diameters of 87 and
81 nm for Clouds 2 and 3, respectively.
Size-resolved activated fraction
The size-resolved activated fraction [AF(Dp)] for rBC and the bulk aerosol
were calculated by taking the ratio of the number distributions measured
with the residual inlet to the number distributions measured with the total
inlet. Prior to calculating AF(Dp), a spline interpolation algorithm was
applied to the rBC and bulk aerosol size distributions. After a spline
interpolation was applied to the data, the following equation was used to
calculate the size-resolved activated fraction:
AFDp=NResDp×CF(Dp)NTot(Dp)×EF×DT,
where NRes(Dp) is the number of residual particles as a function of
size, CF(Dp) is the size-resolved instrument sensitivity correction
factor, NTot(Dp) is the number of particles measured with the total
inlet as a function of size, EF is the CVI enhancement factor (Sect. S1), and DT is the droplet transmission factor through the
CVI. Calculations of the droplet transmission factor are discussed in the
Supplement Sect. S4 and plotted in Fig. S3. CF(Dp), which
correct for variances in instrument detection efficiencies, were determined
from a 12 h period of cloud-free air on 5 June 2012 for the bulk aerosol and
from side-by-side ambient sampling of room air during the post-campaign for
rBC. Additional information on the measurement of CF(Dp) for rBC is
given in the Supplement (Sect. S2).
Shown in (a) and (f) are the median size-dependent
activated fraction (AF) for the aerosol (red circles), and rBC (black
triangles) for Clouds 2 and 3, respectively, where the error bars represent
the 10th and 90th percentiles. The bottom axes represent particle diameter
for the aerosol and core diameter for rBC. Panels (b) and
(g) show a 2-D histogram of coating thickness with the median values
(white circles) overlaid on top, where the error bars show the 10th and 90th
percentiles. Panels (c) and (h) show rBC total diameter
(i.e., the core and the coating), (d) and (i) the coating
volume, and (e) and (j) the coating volume fraction, all as
a function of rBC core diameter.
![]()
The median AF(Dp) for the bulk aerosol and rBC are presented in Fig. 6, where
the error bars represent the 10th and 90th percentiles for each 10 nm bin. Un-coated rBC particles with sizes < 100 nm are not expected
to be incorporated into cloud droplets by nucleation for typical
supersaturations reached in stratocumulus clouds. Figure 6a and b show that
the AF of rBC cores is significant, even for core diameters ≤ 100 nm.
These results can be explained by the presence of large coatings surrounding
the core (see Sect. 3.6 below). Since the rBC size distributions were
normalized to differences in instrument sensitivity, the decreased rBC AF at
smaller diameters is not a result of the different detection efficiencies of
the SP2 instruments. Figure 6a and b also show that during both clouds the
AF for rBC cores is larger than the AF for the bulk aerosol at diameters
< ≈ 150 nm. Again, this can be explained by the presence of
thick coatings on the rBC cores. Since the fraction of cloud droplets
sampled by the CVI was < 100 %, the calculated AF should be
considered as lower limits to the total fraction activated during the two
cloud events.
Mechanism of incorporating rBC into cloud droplets
Two possible mechanisms exist for incorporating rBC-containing particles
into cloud droplets: nucleation scavenging and coagulation between the rBC-containing particles and cloud droplets. Based on calculations (Sect. S3), the fraction of rBC-containing particles
expected to be incorporated into the cloud droplets by coagulation was on
the order of < 1 %. This suggests that the dominant mechanism for
incorporating rBC particles into the cloud droplets studied was nucleation
scavenging. First, the fraction of rBC-containing particles activated into
cloud droplets increases as the size of the rBC cores increases (Fig. 6a, b). If coagulation dominated, we would expect to see an opposite trend.
Second, calculated coagulation rates together with estimated lifetimes of
the cloud droplets cannot explain the fraction of rBC-containing particles
activated into the cloud droplets – the calculated coagulation rates are too
small (Sect. S3).
Lower limits to coating thickness of rBC residuals
Lower limits to the coating thicknesses on the rBC cores were determined
using a core and shell Mie model. The median values from this analysis are
shown in Fig. 6b and g, where the error bars represent the 10th and
90th percentiles and the symbols represent the medians for each size
bin. When calculating lower limits to the coating thicknesses, the particles
were idealized as a pure BC core uniformly coated with a non-absorbing
material, although the actual particle morphology may be more complicated (Sedlacek et al., 2012). The results shown in Fig. 6b and g give
a qualitative explanation for why we see activation of rBC cores with sizes
< 100 nm: these rBC cores have relatively thick coatings, which can
lower the critical supersaturation required for activation. For example, 95 nm rBC cores incorporated into the cloud droplets had a median coating
thickness of 65 nm.
Figure 6b and g show that as the rBC core diameter increased from 75 to
approximately 100 nm the lower limit to the coating thickness also
increased. This is likely because as the rBC core diameter increased from 75
to 100 nm, the fraction of particles above the optical detection limit
increased. Recall that for rBC-containing particles with diameters
< ≈ 100 nm, a relatively large fraction of the coated
particles are below the optical detection limits and hence are assigned a
coating thickness of zero (Sect. 2.5). After the median coating
thickness reached a maximum at an rBC core diameter of approximately 100 nm,
the lower limit to the coating thickness decreased with an increase in rBC
core diameter. This may suggest that the larger rBC cores had thinner
coatings than the smaller rBC cores that were incorporated into the cloud
droplets. Part of the decrease in the lower limit to the coating thickness
with an increase in rBC core diameter could be due to saturation of the
optical detector. As mentioned in Sect. 2.5, the optical detector became
saturated when the rBC cores were relatively large and contain a modest
coating. In Fig. 6c and h, we plotted the overall diameter of the rBC-containing particles. In other words, we plotted the sum of the rBC core
diameter plus 2 times the coating thickness. If we disregard the point at 75 nm
(which is likely strongly influenced by the fact that a large fraction of
the rBC-containing particles with this core size are below the optical
detection limit), we conclude that in order for the rBC-containing particles
to be incorporated into the cloud droplets, the overall median diameter of
rBC-containing particles must be at least 165 nm in diameter. Figure 6c and
h suggest that the overall diameter of the rBC-containing particles is
important for activation. This finding is consistent with previous work that
has shown that particle diameter is important for activation of non-rBC-containing particles (e.g., Wang et al., 2008).
To further investigate the factors that control activation of the rBC-containing particles, we plotted the coating volume (Fig. 6d, i) and
coating volume fraction (Fig. 6e, j) as a function of rBC core diameter.
For discussion purposes we focus on the coating volume fraction as a
function of size and rBC core diameters ≥ 85 nm. As discussed above,
coating volume fraction at 75 nm rBC core diameter, is likely strongly
influenced by the fact that a large fraction of rBC-containing particles,
with this core size, are below the optical detection limit. Figure 6e and j
show that for rBC core diameters from 85 to 95 nm, the median coating volume
fraction is at least 0.9. This finding also gives a qualitative explanation
for why we see relatively large activated fractions of small rBC cores in
the cloud residuals.
As the rBC core diameter increased above approximately 100 nm, the lower
limit to the coating volume fraction decreased. This could be because larger
rBC cores need less coating material in order to be incorporated into cloud
droplets. Part of the decrease in coating volume fraction at rBC core
diameters above 100 nm could also be due to the saturation limit of the
optical scattering detectors, as discussed above.
In-cloud aqueous-phase chemistry
In the discussion above, we assumed the coatings on the rBC cores were
present before incorporation into the cloud droplets. However, some of the
coating material may have formed after the rBC cores were incorporated into
the cloud by aqueous-phase chemistry. As mentioned in the Supplementary
Material (Sect. S3), the upper limits to residence times of air parcels
in the clouds sampled at Soledad were likely ∼ 1 h. Whether significant
aqueous-phase chemistry can occur on this timescale depends on the level of
SO2 and oxidants. When SO2 is absorbed by a cloud droplet, it
partitions in different forms as a function of pH: at lower pH values, the
primary aqueous-phase oxidant of dissolved SO2, or S(IV) is
H2O2; for higher pH values, ozone and catalyzed aerobic oxidation
are important oxidation pathways. Depending on the pH and available
oxidants, conversion of the dissolved S(IV) to S(VI) can be fast or slow.
The absorption of large amounts of HNO3 or N2O5 can reduce
the pH significantly, which will require the presence of H2O2 in
order to significantly convert S(IV) to S(VI). Since the clouds at Soledad
occurred mostly overnight, the primary oxidant (H2O2) was likely lower
(and probably near zero). Also, analysis of the cloud water indicated that
nitrate was high, and thus the pH was probably low. Based on these factors,
we suspect that aqueous-phase production of sulfate was not large. However,
a quantitative estimate of the sulfate produced is not possible since the
measurements of SO2 and H2O2 were not performed at this site.
Based on the discussion above, we assumed that a large fraction of the
coatings were present before rBC particles were incorporated into the cloud
droplets. However, the production of coating material from in-cloud aqueous-phase chemistry cannot be ruled out.
Comparison of rBC<inline-formula><mml:math display="inline"><mml:msub><mml:mi/><mml:mi mathvariant="normal">Res</mml:mi></mml:msub></mml:math></inline-formula> as a function of size with predictions based on <inline-formula><mml:math display="inline"><mml:mi mathvariant="italic">κ</mml:mi></mml:math></inline-formula>-Köhler theory
Sections 3.4 and 3.6 provide a qualitative explanation for how small rBC
cores are incorporated into cloud droplets – the rBC cores have thick
coatings leading to overall particle diameters greater than
approximately 165 nm. In the following we expand on this qualitative
explanation by carrying out a quantitative analysis that shows that the
presence of small rBC cores in the cloud residuals is consistent with
κ-Köhler theory. This quantitative analysis consists of the
following steps: (1) an estimation of the bulk aerosol composition; (2) an
estimation of the critical diameter for activation of the cloud droplets
sampled; (3) an estimation of the critical supersaturation required to form
the droplets sampled; and (4) a prediction of the critical diameter for
activation of rBC cores. Steps 1–3 are required to carry out the predictions
in step 4.
Bulk aerosol composition
A HR-ToF-AMS was used to measure the bulk aerosol composition in residual
particles downstream of the CVI. Five species (organic, nitrate, sulfate,
ammonium, and chloride) were quantitatively differentiated. Then, based on a
simplified ion-pairing scheme similar to Gysel et al. (2007; Sect. S5), the mass fractions of ammonium
nitrate, ammonium sulfate, ammonium bisulfate, sulfuric acid, and ammonium
chloride were calculated. The results of these calculations are shown in
Fig. 7. In order to determine the bulk aerosol hygroscopicity (Eq. 3), the mass
fractions of these individual components were first converted to volume
fractions using an organic density of 1.4 g cm-3 (Moore et al., 2012)
and densities reported in Lide (2001) for the inorganic salts.
The critical diameter for activation of the bulk aerosol in the cloud droplets sampled
The critical diameter for activation (Dcrit) of the bulk aerosol is
often calculated by integrating the droplet number distribution from the
largest to smallest diameters until the number concentration equals the CDNC
sampled (see for example Hersey et al., 2013). Using
this method, Dcrit was found to be 241 and 239 nm for Cloud 2 and
Cloud 3, respectively. Note these Dcrit values apply only to the cloud
droplets sampled (i.e., cloud droplets greater than ≈ 11 µm).
Different Dcrit values would be expected if the entire cloud droplet
population were sampled.
Critical supersaturation for the cloud droplets sampled during the two cloud events
To estimate the critical supersaturation (SC) for the formation of the
cloud droplets sampled during the two cloud events (i.e., cloud droplets
greater than ≈ 11 µm), the single parameter κ-Köhler
model (Petters and Kreidenweis, 2007) was used. This model
describes the relationship between the water vapor saturation ratio (S) over
an aqueous solution droplet, which can be calculated using the following
equation:
Sub-micrometer non-refractory average aerosol mass fractions
for Clouds 2 and 3 based on an ion-pairing scheme (see text and Sect. S5) and measured from a high resolution
time-of-flight aerosol mass spectrometer.
![]()
S=D3-Dp3D3-Dp3(1-κBulk)exp4σMwρwRTD
where D is the droplet diameter; Dp is the dry particle diameter;
σ is the droplet surface tension and is assumed to be that of
water, 0.072 J m-2; Mw is the molecular mass of water; ρw is the density of water; R is the universal gas constant; T is the
temperature; and κBulk is a compositionally specific parameter
that describes the bulk aerosol's hygroscopicity. Equation (2) was used to
find the SC needed for a particle of dry diameter Dp to activate (Petters and Kreidenweis, 2007).
Panel (a) shows the critical supersaturation (SC, black
lines) as a function of particle dry diameter based on measured AMS bulk
compositions and an ion-pairing scheme. Panel (b) shows SC as a function
of rBC core diameters with coatings ranging from 0 to 200 nm. In (b), the
coatings are assumed to have the same composition as the bulk residual
aerosol (Fig. 7). The solid lines are for Cloud 2 and the dashed lines are
for Cloud 3. Panel (c) shows SC as a function of rBC coating volume
fraction at three different rBC core diameters (75, 100, and 200 nm), where
each data point is colored by its corresponding κ. Also shown in panel
(c) is the estimated SC (pink line) determined for both clouds in this
study.
![]()
The overall hygroscopicity of a particular aerosol follows a simple mixing
rule and can be calculated from
κBulk=∑iεiκi,
where εi is the volume fraction and κi is the
hygroscopicity parameter for each component i discussed in Sect. 3.8.1.
The individual component κ values used in Eq. (2) were 0.1 for
organic (Lance et al., 2013; Moore et al., 2012; Rose et al., 2010); 0.67 for ammonium nitrate
(Petters and Kreidenweis, 2007); 0.61 for ammonium sulfate and
ammonium bisulfate (Petters and Kreidenweis, 2007; Wu et al., 2013); and 0.71 for sulfuric acid, which is the average of
the range reported in Shantz et al. (2008). The value for
ammonium chloride κ (1.02) was calculated according to Eq. (A28) in Rose et al. (2008) using a Van 't Hoff factor of 2.
Using the above κi values and the εi
values discussed in Sect. 3.8.1 in Eq. (3), κBulk values of
0.50 and 0.41 were calculated for Cloud 2 and Cloud 3, respectively. The
κ values determined during this study are consistent with the κ
values suggested by Andreae and Rosenfeld (2008) for marine
aerosols during Cloud 2 and lower than the κ values suggested during
Cloud 3.
Shown in Fig. 8a are plots of SC as a function of dry diameter for Cloud 2 (solid line) and Cloud 3 (dashed line) calculated using Eqs. (2) and (3).
Combining Dcrit (Sect. 3.8.2) with the results plotted in Fig. 8,
SC for the cloud droplets sampled can be determined. The points at
which Dcrit intersect with the calculated SC traces shown in
Fig. 8 result in estimations of SC values of 0.05 % for both clouds. Note
these critical supersaturations apply only to the cloud droplets sampled by
the CVI. Different SC values would be expected if the entire droplet
population had been sampled. Theory predicts that the largest droplets in
the distribution should have been the first to form, thus formed on
particles activated at the lowest supersaturations. During this study, a CCN
instrument was also connected to the residual inlet and sampled residual
particles during the cloud events. Data from this instrument were used to
derive an upper limit to the cloud supersaturation applicable to the cloud
droplets sampled by the CVI (Modini et al., 2015), and was found to be
approximately 0.1 %. This upper limit to the cloud supersaturation is
approximately consistent with the SC values reported here using the
estimation technique discussed above.
In this determination of SC, several assumptions were made which are
addressed separately below: (1) the predominant mechanism for incorporation
of particles into droplets was nucleation scavenging, and influences by
impaction were negligible (Sect. 3.5); (2) the contribution from sea
salt aerosols could be neglected. Based on sea salt mass concentrations
measured by the HR-ToF-AMS behind the CVI and calibrated against collocated
ion chromatography measurements following a procedure similar to that
introduced by Ovadnevaite et al. (2012), we estimated an upper
limit of approximately 15 % for the sea salt mass fraction of the cloud
residuals (these results will be discussed in detail in a future
publication). A sensitivity study (not shown here) indicated a < 8 % decrease in the estimated SC when a sea salt fraction of 15 %
was included; (3) we assumed that the particles were internally mixed and
the composition did not depend on size. Since, during this study, the size-dependent AMS data were at or below the detection limit we could not
determine if the composition was size dependent. Additionally, no
measurements of bulk aerosol mixing state were carried out; and (4) we
assumed that the entire fraction of organics was water soluble and
represented by a κ of 0.1. To determine if SC was sensitive to
this value, κ for organics was varied from 0 to 0.2, which is roughly
consistent with the range of κ values reported in the literature for
organics (Chang et al., 2010; Lathem et al., 2013; Mei et al., 2013). Over this range of
κ values, SC varied by < 4 %.
Predictions of the critical diameter for activation of rBC cores
In Fig. 8b the critical diameter for activation of rBC cores for the cloud
droplets sampled is calculated using κ-Köhler theory and assuming
coating thicknesses ranging from 0 to 200 nm, which covers the range of coating
thicknesses measured. In these calculations the composition of the coating
was assumed to be the same as determined by the AMS (Sect. 3.8.1), and
the rBC cores were assumed to be insoluble with a κ=0 (Rose et al., 2010). As expected, in Fig. 8b, SC
decreases as the coating thickness increases at a constant rBC core
diameter. Figure 8b also suggests that if the SC is ≈ 0.05 % and the diameter of the rBC core is 95 nm, the coating thickness
must be between 50 and 75 nm. Our lower limits to the coating thicknesses
for an rBC core diameter of 95 nm shown in Fig. 6b and g are consistent with
these predictions.
In Fig. 8c we plotted SC as a function of the rBC coating volume
fraction assuming rBC core diameters of 75, 100, and 200 nm. This
figure illustrates that in order to activate 75 and 100 nm rBC cores at a
SC of 0.05 % the rBC coating volume fraction must be greater than
0.9. Figure 8c also shows that for an rBC core diameter of 200 nm, the
coating volume fraction needs to be approximately 0.6. For 100 nm rBC cores
the measurements are in good agreement with the predictions (compare Fig. 8c
with Fig. 6e, j). For 75 and 200 nm cores the measurements are
lower than the predictions. However, the measurements are not inconsistent
with the calculations since the measurements represent lower limits.