www.pnas.org/cgi/doi/10.1073/pnas.
1807604
115
Supplementary Information for
Rapid growth of organic aerosol nanoparticles over a wide tropospheric temperature range
Dominik Stolzenburg et al.
Paul Winkler
E-mail: paul.winkler@univie.ac.at
This PDF file includes:
Supplementary text
Figs. S1 to S6
Table S1
References for SI reference citations
Dominik Stolzenburg et al.
1 of
14
Supporting Information Text
Measurement of particle growth with the appearance time method
Particle-size-distributions are measured by several sizing instruments optimized for a certain size range. Each instrument
was thereby treated separately but we found comparable results in the overlapping regions for all presented experiments.
Particle growth rate measurements were performed with the appearance time method, which can be used especially in chamber
experiments, where a clear front of a growing particle population can be identified during most nucleation experiments.
Key part of this study is the precision measurement of particle-size-distributions in the size range between 1.8-8 nm by a
newly developed instrument, a DMA-train (
1
). It uses six differential mobility analyzers in parallel with the classified size fixed
for every device. Subsequent detection of the size-selected aerosol is done by the usage of six condensation particle counters.
As no scanning is involved, high counting statistics at a single size is achieved, providing unprecedented high sensitivity to low
number concentrations in the crucial sub 10-nm range. At diameters above 5 nm higher counting statistics allow one DMA to
be set alternating every 10 seconds between 6.2 and 8 nm, hence providing in total seven measured sizes for the DMA-train:
1.8, 2.2, 2.5, 3.2, 4.3, 6.2, 8.0 nm (see Fig. S1 (B)).
The other size-ranges were covered by three additional instruments: Below 2.5 nm, a particle size magnifier in scanning
mode was used (
2
). Above 8 nm a scanning mobility particle sizer system, TSI nano-SMPS model 3982, measured up to 65 nm
(
3
). Additionally, a neutral cluster and air ion spectrometer (NAIS) measured between 3-42 nm (
4
). For the size distribution of
particles >10 nm two additional SMPS systems were attached to the chamber, but were not used for detailed growth rate
analysis.
Considering the evolution of particle size-distribution binned into different size-channels as given by most particle size-
distribution measuring instruments, the signal in each size-channel is fitted individually with a four parameter sigmoid function
using a least-square algorithm:
S
d
p
(
t
) =
a
−
b
1 + (
t/t
app
)
d
+
b,
[1]
where
a
and
b
represent the background and plateau value of the sigmoid function respectively,
d
is a parameter for the
steepness of the rising signal and
t
app
is the time at which the 50 % value between plateau and background is reached.
A representative fit for a 3.2 nm size channel of the DMA-train is shown in Fig. S1 (A). All size-channels are cross-checked
manually after the automated fitting and a statistical error of
t
app
is estimated from the covariance of the fit-result. The values
obtained for
t
app
can be plotted against the corresponding diameter as shown in Fig. S1 (B). A linear fit with an orthogonal
distance regression is used to take into account both the uncertainties of
t
app
and of the diameter of the size-channels. The
resulting value of the slope and its associated error can be interpreted as an apparent particle growth rate and its statistical
uncertainty.
For the DMA-train two size-intervals for the growth rate measurement were defined: One between 1.8-3.2 nm and one
between 3.2-8 nm. The choice of the size-intervals is arbitrary but proofed to be representative to show differences between
early and later growth. In (
5
) it was shown that growth driven by biogenic organics shows only a minor size-dependence above
5 nm, i.e. the upper growth rate size-interval of the DMA-train is representative for growth
>
5 nm.
However, this apparent growth rate of the particle size distribution does not necessarily represent the growth caused by pure
condensation, as it omits coagulation and, in chamber experiments, wall losses, which both alter the particle size-distribution
(
6
). Therefore, a systematic uncertainty of the method is estimated to be 50 % (
7
). On the other hand, methods accounting for
coagulation and loss effects do need reliable absolute number concentration measurements and therefore good knowledge of
overall detection efficiencies of the sizing instruments. In the presented experiments there might be high uncertainties due to
possible evaporation effects of particles produced at e.g. cold temperatures and brought into warmer analyzing instruments. To
ensure precise sizing at different chamber temperatures, the sheath-air of all six DMAs of the DMA-train was passed through
an heat exchanger maintained at chamber temperature. All inlet lines and sheath flow lines as well as the DMAs were insulated
to be maintained as close to chamber temperature as possible. Subsequent evaporation losses inside the detecting CPCs are
unlikely to affect the appearance time method. This method does not depend on absolute particle concentrations as long as
there is enough signal detected in a channel to get reliable results with the fit by Eq. 1. To further investigate possible effects
of particle evaporation on the measured growth rates a custom-build SMPS was operated while being completely contained
inside a refrigerator which was kept at chamber temperature for the experiments at +5
◦
C and -25
◦
C. A comparison of this
cooled SMPS with the nano-SMPS used in this study is presented in Fig. S2. The differences in absolute concentrations are
within a factor of 2 and the growth rate measurements inferred are generally agreeing within the measurement uncertainties.
We therefore conclude that the results of the appearance time method should be generally robust with respect to possible
evaporation of the sampled particles and the major uncertainties are covered within the 50 % systematic error given by (7).
Absolute HOM concentration measurements using nitrate-CI-APi-ToF
The nitrate-CI-APi-ToF (nitrate-CI) uses negative nitrate,
(
HNO
3
)
n
(
NO
−
3
)
, as reagent ion (
8
), which shows high charging
efficiencies towards H
2
SO
4
and HOMs. This rather selective ionization technique is used obtain a very clean spectrum of
HOMs (9). The concentration of a HOM species is estimated via
[HOM
i
] =
C
·
T
i
·
SL
HOM
i
·
ln
(
1 +
[HOM
i
·
NO
−
3
]
∑
2
j
=0
[NO
−
3
·
(HNO
3
)
j
]
)
[2]
2 of 14
Dominik Stolzenburg et al.
Here
[
HOM
i
·
NO
−
3
]
is the background corrected peak area which is normalized to the intensity of the main reagent ions.
To obtain a quantitative concentration, three factors are applied: First, a calibration factor
C
, which is inferred from a
calibration using sulfuric acid (
10
) and assuming that all detected HOMs have the same ionization efficiency (
9
). Second, a
mass dependent transmission efficiency
T
i
of the APi-ToF can be inferred in a seperate experiment by depleting the reagent
ions with several perfluorinated acids (
11
). Third, sampling line losses
SL
HOM
i
are estimated assuming laminar flow diffusional
losses in the sampling lines (
12
) with a diffusion coefficient of HOMs scaling with the molecular mass
M
i
of the compound via
D
[cm
2
s
−
1
]
= 0
.
31
·
M
−
1
/
3
i
at 278 K, determined from wall loss measurements in the CLOUD chamber. As the sampling lines of
the nitrate-CI are thermally insulated, for other experiment temperatures
D
∝
(
T/
278
K
)
1
.
75
is assumed. As the compounds
detected by the nitrate-CI are mostly classified ELVOC or LVOC in the temperature range of this study, we can assume that
they all get lost irreversibly to sampling line walls due to diffusion.
Absolute concentration measurements of oxidized organics using PTR3-ToF
The PTR3-ToF (PTR3) uses (H
3
O
+
)(H
2
O)
n
clusters as reagent ions, ionizing
α
-pinene as well as first and higher order
oxidation products by proton transfer or ligand switch reactions (
13
). A contact minimized laminar flow inlet system with core
sampling is used to transfer the sample air into the tripole reaction chamber operated at 80 mbar and reduces transmission
losses. The (H
3
O
+
)(H
2
O)
n
cluster ion distribution can be regulated by a radio-frequency-amplitude applied to the tripole
rods without influencing the reaction time. Increased pressure in the reaction region and longer reaction times compared to
traditional PTR instruments yield a 500 fold increased sensitivity to a broad range of organics. At the operating conditions
of the PTR3, secondary reactions of ionized species with the most abundant neutral VOCs in the sample gas are limited
to less then one percent at the highest measurable concentrations. The new instrument bridges the gap between precursor
measurements at ppbv level to HOM measurements at sub ppt level, complementing atmospheric pressure CIMS techniques.
A quadrupole interfaced Long-ToF mass spectrometer (TOFWERK AG, Thun, Switzerland) is providing the high mass
resolving power needed to separate isobaric compounds. We obtained more than 1500 individual mass peaks, excluding isotopes,
during
α
-pinene ozonolysis experiments. A multi-peak fitting algorithm is applied to separate the major compounds and
assign chemical sum formulas. Extracting the relevant signals is done omitting all masses rising less than 3
σ
above chemical
background noise during ozonolysis measurements and removing peaks with possible uncertainties caused by interference of
higher neighboring peaks. (H
3
O
+
)(H
2
O)
n
clusters are known to be soft ionization reagent ions. Nevertheless we cannot exclude
completely fragmentation of some ionized HOMs loosing most likely H
2
O especially when containing an (-OOH) group.
The PTR3 was calibrated with a gas standard containing 1 ppm of 3-hexanone, heptanone and
α
-pinene in nitrogen, which
was dynamically diluted by a factor of 1000 in VOC-free air to contain 1 ppbv of each compound. Duty cycle corrected
counts per second
dcps
are used in order to compensate for the mass-dependent transmission of the TOF mass spectrometer
(
dcps
(
i
) =
cps
(
i
)
·
(101
/m
i
)
1
/
2
) (
13
). For 3-hexanone and heptanone we obtained a sensitivity which is in agreement with the
calculated sensitivity taking into account the duty cycle corrected (H
3
O
+
)(H
2
O)
n
regent ion count rates, the pressure and the
reaction time in the reaction chamber (80 mbar; 3 ms) and using
2
−
3
·
10
−
9
cm
3
s
−
1
as a fast reaction rate constant close to
the collisional limit value. Consequently, only lower end product concentrations can be given.
In a previous
α
-pinene ozonolysis study PTR3 results showed quantitative agreement for several HOMs with the nitrate-CI
(
13
). The authors estimated 80 % inlet losses for low volatility molecules with
n
O
≥
5
, bringing the two instruments into
reasonable quantitative agreement for common molecular ion signals. However, the assumption for the nitrate-CI, that all
detected molecules get lost on contact with sampling line walls, does not hold for all substances measured by the PTR3. In
the transition from SVOC to LVOC the partitioning of substances between inlet line walls and sample gas is temperature
dependent. We therefore extended the approach of (
13
) with our knowledge about an approximate volatility of the measured
compounds. Assuming that all molecules in the LVOC and ELVOC range get lost by diffusion (the diffusion coefficient of a
molecule is estimated similar to the nitrate-CI) according to (
12
), we can apply a temperature dependent loss-correction for
the sampling line losses, which is split up into three sections:
η
tot
=
η
line
,
int
(
T
)
·
η
line
,
ext
(298K)
·
η
PTR3
(310K)
[3]
We account for losses at the sampling line within the CLOUD chamber
η
line
,
int
at chamber temperature
T
, as well as losses
occurring at the sampling line outside the chamber at room temperature
η
line
,
ext
(as it was not thermally insulated) and losses
within the PTR3 instrument heated to 37
◦
C
η
PTR3
. Therefore, for each sampling section other molecules might be subject to
losses according to their temperature-dependent volatility classification.
Comparison of the used mass spectrometers
The considerations of the two previous sections result in the comparison for data obtained in three representative experiments
at three different temperatures which is shown in Fig. S3, where
η
line
,
int
and
η
line
,
ext
are calculated assuming diffusional losses
similar to the nitrate-CI and
η
PTR3
is estimated to correct for the 80% discrepancy found in (13).
For higher oxygenated molecules the agreement between both mass spectrometers is in a reasonable range including the
additional loss term
η
PTR3
for losses within the PTR3 ion source and inlet. This indicates that the loss in measured concentration
from +25
◦
C to -25
◦
C for the three experiments at similar initial precursor oxidation rates is caused by the reduced reaction
rates of the auto-oxidation process. For lower temperatures and lower oxidized states (n
O
= 4/5/6) a discrepancy between the
instruments gets significant. However, even at elevated temperatures, the nitrate-CI is only detecting a small fraction of all
Dominik Stolzenburg et al.
3 of 14
oxidation products with n
O
= 5/6 observed by the PTR3. Therefore it is concluded that the increasing discrepancy is likely
due to a lowered sensitivity of the nitrate-CI for such compounds. The ionization efficiency in the nitrate-CI depends on the
relative binding energy of a (HNO
3
)(NO
−
3
) cluster compared to a (Analyte)(NO
−
3
) cluster (
14
). A relative shift in binding
energies at lower temperatures that favors (HNO
3
)(NO
−
3
) clustering instead of (Analyte)(NO
−
3
) clustering, could explain the
observed decrease of signal for the lower oxidation states for the nitrate-CI. The higher oxidation states however are unaffected
because the (HOM)(NO
−
3
) clustering is generally very strong and will always dominate the (HNO
3
)(NO
−
3
) clustering, which
explains the good agreement of the two instruments for higher oxidized states.
When combining the two mass spectrometers, for molecular ion signals observed in both instruments the higher signal is
used. Both spectra are background subtracted and therefore a weaker signal in either of the mass spectrometers could point
towards a lower ionisation efficiency.
Combined gas-phase mass defect plots
Fig. S4 shows mass defect plots from the nitrate-CI and the PTR3 during three representative experiments at three different
temperatures. For all three cases the
α
-pinene ozonolysis rate is comparable.
The mass defect plots for all temperatures show the typical pattern of HOMs (
5
). Two bands can be identified, one
representing monomers (n
C
=6-10, 100-400 Th) and one representing dimers (n
C
=16-20, 400-600 Th); molecules with increasing
oxidation state are found towards the lower right of the panels. The reduction in temperature mainly reduces the signal of the
higher oxygenated compounds towards the lower right of the panels. This is in agreement with (
15
) and the observation of
reduced auto-oxidation rates at lower temperatures leading to less highly oxygenated molecules (
16
). This trend is as well
shown in Fig. 5 for some representative molecules.
The symbol color for peaks with an identified composition in Fig. S4 corresponds to a broad temperature-dependent
classification of their volatility, based on the carbon and oxygen numbers of the individual compounds. We place them in
four general groups, according to their saturation mass concentration
C
∗
: extremely low volatility compounds (ELVOC,
log
10
C
∗
≤
-4.5), low volatility compounds (LVOC,
log
10
C
∗
=(-4.5,-0.5]), semi-volatile compounds (SVOC,
log
10
C
∗
=(-0.5,2.5])
and intermediate volatility compounds (IVOC,
log
10
C
∗
>
2.5) (
17
). Compounds in the ELVOC and LVOC ranges have been
shown to contribute to nanoparticle growth (
5
). Comparing this classification for the three different temperatures clearly
indicates the importance of the compounds observed by the PTR3. At -25
◦
C, large quantities of LVOC compounds can be
observed by the usage of this additional ionization technique.
FIGAERO-CIMS: Measurement procedure, data analysis, normalization on aerosol mass and thermogram fitting
Chemical composition of the bulk particle phase composition was measured by the Filter Inlet for Gases and Aerosols (FIGAERO)
(
18
) coupled to a chemical ionization time-of-flight mass spectrometer (CI-ToF-MS) (Tofwerk, HTOF). Measurement cycles were
set to 30 minutes particle sampling at 8 SLPM sampling flow rate, followed by a thermal desorption ramp (10 minutes, maximal
heating rate). The particle phase sampling line outside of the thermal housing (
∼
0.5 m) of the CLOUD chamber was insulated,
and due to the high sampling flow rates we assume that
T
chamber
≈
T
sampling
. Desorption temperature in the FIGAERO is
measured by a thermocouple installed in front of the particle filter. The particle filter was exchanged approximately every 48
hours between the experiments (Zefluor membrane, 2.0
μ
m pore size, 25 mm diameter, PALL, USA). The thermal desorption
gas flow was 2 SLPM ultrapure synthetic air (from the CLOUD liquid nitrogen and oxygen reservoirs). O
−
2
ions are formed by
passing a 2.2 SLPM flow of synthetic air through a radioactive charger (
210
Po, 370 MBq, Model P-2021, NRD Inc., USA) and
into the ion molecule reaction (IMR) chamber, where the chemical ionization occurs. The body of the IMR was heated to
approximately 50
◦
C to avoid condensation of low volatility compounds and kept at 800 mbar using an active pressure control
device (Aerodyne Inc., USA). The voltages of the transfer optics were tuned for maximum sensitivity and strong declustering in
order to minimize cluster ions and maximize the signal of [M-H]
−
ions. Blank particle phase samples were obtained between the
chamber experiments by continuous sampling or by manually switching a HEPA filter in front of the FIGAERO filter during
the experiments. Gas phase concentrations of the majority of oxidation products were too low throughout all experiments to
be monitored in real-time by the gas-phase sampling position of the FIGAERO.
Data analysis using Tofware (version 2.5.11_FIGAERO) gave 10 seconds average mass spectra. A post-acquisition mass
calibration using the ions O
−
2
, CO
−
3
, NO
−
3
, HCO
−
4
and C
16
H
31
O
−
2
resulted in a mass accuracy <10 ppm. High-resolution
peak identification of the particle phase products was done with the constraints of n
C
: 1-20, n
H
: 2-50, n
O
: 0-20. Shoulder
peaks were fitted also when no ion was identified, in order to resolve background signal from varying analyte signal. The
ion signal [ions/s] was normalized by the reagent ion signal ((O
−
2
+ CO
−
3
)
·
10
−
6
), where
10
6
is the reference value. Selected
high-resolution ion traces (C
10
H
15
O
−
3
−
9
) of the FIGAERO desorption ramps of three experimental runs at T=-25, +5 and
+25
◦
C were further processed: The aerosol mass collected (
M
coll
) per FIGAERO filter cycle was calculated by the product of
FIGAERO sampling flowrate and integrated mass of the combined nanoSMPS and SMPS particle size distribution. Aerosol
density was approximated with 1.5 g cm
−
3
. For sampling cycles during which
M
coll
> 10 ng (Fig. S5), the FIGAERO ion
signal was normalized by the sampled mass, providing the thermograms shown in Fig. 4 and enabling quantitative comparison
between results at different temperatures. The number of thermal desorptions (
n
Des
) are 31, 12 and 15 for the experiments
at -25
◦
C, +5
◦
C and +25
◦
C, respectively. Mean and standard error of the mean are calculated from the results of a cubic
smoothing spline fit (smoothparam=0.01) for each normalized thermogram, resulting in the thick lines and shaded areas in
Fig. 4, respectively. During desorption, we observed a lower effective heating rate for the low temperature experiments, since
4 of 14
Dominik Stolzenburg et al.
the tubing and the FIGAERO filter material cooled down during sampling. This observation explains different
T
max
for the
same molecular formulas in the thermograms. Thermograms of monomeric ion signals often exhibit a mode that originates
from fragment ions of compounds that decompose at high temperatures (
19
). For most monomeric ion signals we observed
bimodal thermograms, indicating that thermal decomposition during the temperature ramping is a significant phenomenon.
Therefore, we fitted the thermograms with three modes (monomer mode, dimer (decomposition) mode and background mode)
at different temperature boundaries using a fitting function used in chromatography (
20
). A non-linear least squares solver
(lsqcurvefit, Matlab) was applied for fitting the thermograms and extracting the peak areas from the monomer mode.
Growth rate parametrization
Growth rates were parametrized in Fig. 2 (A) and (B) by the simple exponential relation GR=
m
(
T,d
p
)
·
[k(
T
)
·
ap
·
O
3
]
q
, to
express the correlation between growth rate and
α
-pinene ozonolysis reaction rate. While the coeffcients
m
(
T,d
p
)
depend on
temperature and size-range of the growth rate measurement,
q
is chosen to be independent of both. A minimum least-square
regression yields the results presented in Table S1.
Volatility of HOMs
Direct measurements of volatilities of individual HOM are extremely challenging as they are difficult to synthesize and the
vapour pressures are too low for current volatility measurement techniques. To overcome this problem, vapour pressures can be
inferred by several model calculations, like so-called group contribution methods (
21
) or parametrizations according to the
oxidation state (17). In this study a combined approach is applied.
We use a volatility parametrization according to the carbon
n
i
C
and oxygen
n
i
O
number of the specific molecule
i
. This is
based on two general observed trends that increasing carbon and increasing oxygen number lower the volatility of oxidized
organic molecules. Thus, these quantities are linked to volatility, expressed as the logarithm of the saturation mass concentration
log
10
C
∗
i
for compound
i
:
log
10
C
∗
i
(300
K
) =
(
n
0
C
−
n
i
C
)
·
b
C
−
n
i
O
·
(
b
O
−
b
add
)
−
2
n
i
C
n
i
O
n
i
C
+
n
i
O
b
CO
[4]
where the parameter
n
0
C
=25 is the baseline carbon backbone for a volatility of 1
μ
g m
−
3
without the addition of any functional
groups.
b
C
=0.475 is the roughly half decade decrease in volatility per carbon atom and
b
O
=2.3 is the more than two decade
decrease in volatility per oxygen atom assuming an average of (=O) and (-OH) groups.
b
CO
is a non-linearity term. More
details can be found in (17).
However, other functionalities e.g. hydroperoxides (-OOH) and covalently bound dimers are not included in
b
O
, but are
both abundant in HOMs from
α
-pinene ozonolysis. To account for these specific attributes, a representative set of proposed
products (
5
,
22
) with known structure is analyzed with the group contribution method SIMPOL (
21
). The results are fitted
with Eq. 4 including a free parameter
b
add
altering the effect of oxygen
b
O
. Monomer and dimer products are fitted separately
allowing this parameter to include the covalent binding.
The resulting parametrisation at 300 K is shown in Fig. S6. The free parameter yields
b
add
= 0
.
90
for monomers and
b
add
= 1
.
13
for dimers. Accordingly, for any
α
-pinene ozonolysis product with unambiguously identified composition, a volatility
can be calculated.
However, computed volatilities from group-contribution methods generally tend to underestimate vapour pressures at low
vapour pressures. A recent study investigating the volatility of
α
-pinene oxidation products with quantum-chemical based
model calculations found large deviations due to intramolecular H-bonds (
22
). These deviations were significant especially for
highly oxygenated monomers and dimers, while the agreement for the higher volatilities was much better.
This study focuses on the temperature dependence of the volatilities which is described by:
log
10
C
∗
(
T
) = log
10
C
∗
(300
K
) +
∆
H
vap
R
ln(10)
(
1
300
−
1
T
)
[5]
The evaporation enthalpy
∆
H
vap
can be linked to the saturation mass concentration at 300 K
log
10
C
∗
(300
K
)
according to
(17) and combined with (23):
∆
H
vap
[
kJ mol
−
1
]
=
−
5
.
7
·
log
10
C
∗
(300
K
) + 129
[6]
The correlation between volatility at 300 K and the evaporation enthalpy
∆
H
vap
is very comparable for approaches like
(
23
), (
17
) and (
22
). Moreover, the shift in volatility due to temperature in this study is most important for oxygenated
compounds with volatilities around
log
10
C
∗
(300
K
)
≈
0
, at the transition between LVOC and SVOC. For those molecules also
the predictions of the volatility between the different methods don’t differ drastically (
22
). Therefore, we assume an overall
uncertainty of the volatility description of
±
1 bin (i.e. 1 decade in
C
∗
(300
K
)
for volatility distributions within a volatility
basis set). This uncertainty is shown Fig. 2 (E) and (F) and gives the method uncertainties in Fig. 3.
Dominik Stolzenburg et al.
5 of 14
Aerosol growth model
The measured VBS-distributions can be used to model aerosol growth. The modeling framework is based on the one used in
(
5
) but simplified for the input of direct VBS-distribution measurements. Starting from a VBS-distribution at
t
= 0
the growth
of a monodisperse population of nucleated particles at an initial size of 1.2 nm mobility diameter is modeled. Every VBS bin is
treated like a single surrogate molecule having the properties of the averaged mass and concentration of the bin. It is assumed
that the measured gas-phase concentrations are in steady-state with losses to particles and chamber walls. The condensation
flux
φ
i,p
of every VBS bin
i
should then follow:
φ
i,p
=
N
p
·
σ
i,p
,
·
k
i,p
·
F
i,p
[7]
N
p
gives the number concentration of particles of a given size.
σ
i,p
=
π/
4(
d
p
+
d
i
)
2
is the particle-vapor collision cross-section
including the diameter of the monodisperse particle population
d
p
and mass-diameter of the VBS bin
d
i
.
k
i,p
=
α
i,p
ν
i,p
β
i,p
is
the deposition rate of vapor molecules at surface, with
α
i,p
the mass accommodation coefficient,
ν
i,p
= (8
RT/
(
πμ
i,p
))
1
/
2
the
center of mass velocity for particle and vapor (with the reduced mass
μ
i,p
= (
M
i
M
p
)
/
(
M
i
+
M
p
)
) and
β
i,p
the correction factor
for non-continuum dynamics (
24
).
F
i,p
is the driving force of condensation, closely related to the saturation ratio
S
i
of the VBS
bin by
F
i,p
=
C
0
i
(
S
i
−
X
i,p
γ
i,p
K
i,p
)
. This driving force of condensation for a VBS bin
i
gives the difference between gas phase
activity
S
i
and particle phase activity
(
X
i,p
γ
i,p
K
i,p
)
, which includes the Raoult term
X
i,p
γ
i,p
to account for the mixture effect
of the particles and the Kelvin-term
K
i,p
=
exp (4
σM/
(
RTρd
p
))
accounting for the curvature effect of the particle surface.
The model assumes an ideal mass based solution, i.e. the condensed phase activity is the mass fraction
X
i,p
and hence
γ
i,p
= 1
.
Therefore we use
C
∗
as saturation mass concentration throughout this study, as
C
∗
=
γ
i,p
C
0
.
Solving the above condensation equations for the measured evolution of the VBS-distribution assuming this distribution always
reflects a steady-state between production from
α
-pinene ozonolysis and wall losses and following the growing monodisperse
aerosol population, yields a diameter versus time evolution which can be connected to a growth rate.
Besides from the different input VBS-distributions at different temperature, only the Kelvin-term and the collision-frequency
include a temperature dependence.
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Dominik Stolzenburg et al.
13:30
14:00
14:30
15:00
Time [UTC]
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
concentration in size-channel [cm
3
]
A
3.2 nm
channel
3.2 nm
channel
13:30
14:00
14:30
15:00
Time [UTC]
0
2
4
6
8
10
Diameter [nm]
GR=(6.6±0.8)nm h
1
GR=(8.2±0.2)nm h
1
B
Growth rate 1.8-3.2 nm
Growth rate 3.2-8 nm
Uncertainty range
Signal Appaerance
Fig. S1.
Example for a representative determination of the particle growth rate with the appearance time method for data obtained by the DMA-train. (A) shows the sigmoid
function fit to the measured concentration within the 3.2 nm channel. (B) shows the orthogonal distance regression for the growth rate determination in two intervals.
Dominik Stolzenburg et al.
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