Aerosol chamber study of optical constants and N2O5 uptake on supercooled H2so4/H2O/HNO3 solution droplets at polar stratospheric cloud temperatures

Article abstract of DOI:10.1021/jp0513364

The mechanism of the formation of supercooled ternary H₂SO ₄/H₂O/HNO₃ solution (STS) droplets in the polar winter stratosphere, i.e., the uptake of nitric acid and water onto background sulfate aerosols at T < 195 K, was successfully mimicked during a simulation experiment at the large coolable aerosol chamber AIDA of Forschungszentrum Karlsruhe. Supercooled sulfuric acid droplets, acting as background aerosol, were added to the cooled AIDA vessel at T = 193.6 K, followed by the addition of ozone and nitrogen dioxide. N₂O₅, the product of the gas phase reaction between O₃ and NO₂, was then hydrolyzed in the liquid phase with an uptake coefficient γ(N₂O₅). From this experiment, a series of FTIR extinction spectra of STS droplets was obtained, covering a broad range of different STS compositions. This infrared spectra sequence was used for a quantitative test of the accuracy of published infrared optical constants for STS aerosols, needed, for example, as input in remote sensing applications. The present findings indicate that the implementation of a mixing rule approach, i.e., calculating the refractive indices of ternary H₂SO₄/H₂O/HNO₃ solution droplets based on accurate reference data sets for the two binary H₂SO₄/H₂O and HNO₃/H₂O systems, is justified. Additional model calculations revealed that the uptake coefficient γ(N₂O₅) on STS aerosols strongly decreases with increasing nitrate concentration in the particles, demonstrating that this so-called nitrate effect, already well-established from uptake experiments conducted at room temperature, is also dominant at stratospheric temperatures.

Full text of DOI:10.1021/jp0513364

8140
J. Phys. Chem. A 2005, 109, 8140-8148
Aerosol Chamber Study of Optical Constants and N2O5 Uptake on Supercooled H2SO4/H2O/
HNO3 Solution Droplets at Polar Stratospheric Cloud Temperatures
†
Robert Wagner,* Karl-Heinz Naumann, Alexander Mangold, Ottmar M o1 hler,
Harald Saathoff, and Ulrich Schurath
Forschungszentrum Karlsruhe, Institute of Meteorology and Climate Research (IMK-AAF), Karlsruhe, Germany
ReceiVed: March 15, 2005; In Final Form: July 15, 2005
The mechanism of the formation of supercooled ternary H
polar winter stratosphere, i.e., the uptake of nitric acid and water onto background sulfate aerosols at T <
95 K, was successfully mimicked during a simulation experiment at the large coolable aerosol chamber
2 4 2 3
SO /H O/HNO solution (STS) droplets in the
1
AIDA of Forschungszentrum Karlsruhe. Supercooled sulfuric acid droplets, acting as background aerosol,
were added to the cooled AIDA vessel at T ) 193.6 K, followed by the addition of ozone and nitrogen
dioxide. N
2
O
5
, the product of the gas phase reaction between O
3
2
and NO , was then hydrolyzed in the liquid
phase with an uptake coefficient γ(N
2
O ). From this experiment, a series of FTIR extinction spectra of STS
5
droplets was obtained, covering a broad range of different STS compositions. This infrared spectra sequence
was used for a quantitative test of the accuracy of published infrared optical constants for STS aerosols,
needed, for example, as input in remote sensing applications. The present findings indicate that the
implementation of a mixing rule approach, i.e., calculating the refractive indices of ternary H
HNO solution droplets based on accurate reference data sets for the two binary H SO /H O and HNO
systems, is justified. Additional model calculations revealed that the uptake coefficient γ(N ) on STS aerosols
2
SO
4
/H
2
O/
3
2
4
2
3 2
/H O
2 5
O
strongly decreases with increasing nitrate concentration in the particles, demonstrating that this so-called
nitrate effect, already well-established from uptake experiments conducted at room temperature, is also dominant
at stratospheric temperatures.
Introduction
set for the HNO3/H2O system. On the contrary, presumably due
to procedural errors in extracting the refractive indices from
thin film reference spectra, the Biermann et al. data sets for
the two binary systems failed to accurately reproduce our
measured aerosol extinction spectra.
Supercooled ternary H2SO4/H2O/HNO3 solution (STS) drop-
lets form at temperatures <195 K during the polar night when
nitric acid and water condense onto background sulfate aerosols.
With decreasing temperature, the composition of the STS
droplets may vary from almost pure sulfuric acid to almost pure
nitric acid solution droplets, containing only a minor fraction
of H2SO4 (about 5 wt % at temperatures close to the ice frost
1
1
In the present paper, we will extend our study to the refractive
indices of ternary H2SO4/H2O/HNO3 solution droplets. Biermann
1
1
et al. have proposed a mixing rule to calculate the imaginary
part (k) of the complex refractive index for the ternary solutions
as a linear combination of the k values of the two binary data
sets. This approach has already been implemented in several
1
point). Important experimental techniques to directly measure
or to retrieve the STS composition include in situ aerosol
composition mass spectrometry2,3 as well as analysis of
broadband mid-IR spectra recorded by remote sensing instru-
ments.4 In the latter case, the accuracy of the retrieved aerosol
composition crucially depends on the quality of the employed
low-temperature indices of refraction. As highlighted in a recent
discussion of the complex indices of refraction contained in
HITRAN,6 significant differences still exist between individual
laboratory data sets. In recent experiments, conducted in the
large coolable aerosol chamber AIDA of Forschungszentrum
Karlsruhe, we have quantitatively tested the accuracy of different
laboratory data sets of refractive indices for binary H2SO4/H2O
and HNO3/H2O aerosols by comparing directly measured aerosol
parameters (i.e., composition and mass concentration) with those
12,13
retrieval algorithms in remote sensing applications.
However,
,5
there is still a need for an independent study to assess the
accuracy by which FTIR extinction spectra of STS aerosols can
be analyzed in terms of aerosol composition and mass concen-
tration on the basis of this mixing rule. McPheat et al.14 have
observed large spectral differences between a measured STS
droplet extinction spectrum and a Mie calculation using the
,7
1
1
-1
Biermann et al. mixing rule in the 750-1300 cm spectral
region. However, this must not be a result of a deficiency of
the mixing rule but may be fully explained by the poor quality
11
of the Biermann et al. binary data sets, which were employed
in the mixing rule calculation. Hence, in view of the results of
our previous study, we recommend to use the binary data sets
8
retrieved from the analysis of FTIR extinction spectra. We
found close agreement between retrieved and independently
measured aerosol parameters when using the Niedziela et al.
data set for the H2SO4/H2O system and the Norman et al. data
9
10
of Niedziela et al. and Norman et al. in the mixing rule
9
15
approach. This was already tested by Norman et al. when
1
0
comparing the refractive index values calculated using the
mixing rule with directly measured refractive index data for
six discrete STS compositions (see Figures 14 and 15 in their
publication). In view of the simplicity of the mixing rule, which,
*
Corresponding author. E-mail: Robert.Wagner@imk.fzk.de.
Forschungszentrum J u¨ lich, Institute of Chemistry and Dynamics of
†
the Geosphere I (ICG I): Stratosphere, J u¨ lich, Germany.
1
0.1021/jp0513364 CCC: $30.25 © 2005 American Chemical Society
Published on Web 08/19/2005

Optical Constants and N2O5 Uptake on H2SO4/H2O/HNO3
J. Phys. Chem. A, Vol. 109, No. 36, 2005 8141
e.g., neglects chemical interaction between the nitrate and sulfate
components in the mixture, the agreement between the directly
measured and calculated data sets was quite satisfactory.
In our present study, as a further comprehensive test of the
mixing rule approach, we have measured low-temperature FTIR
spectra of supercooled ternary H2SO4/H2O/HNO3 aerosols for
an extended range of different aerosol compositions. This was
done in one single experiment by injecting supercooled H2SO4/
H2O droplets (acting as background aerosol) into the AIDA
chamber, followed by the addition of ozone and nitrogen
dioxide. Gas phase reaction between O3 and NO2 yielded N2O5,
which then hydrolyzed in the liquid phase, forming ternary
H2SO4/H2O/HNO3 solution droplets with gradually increasing
nitric acid concentration. As in our former study, we applied a
fitting algorithm based on Mie theory to retrieve composition
and mass concentration of the STS droplets. These data were
then compared to those independently measured using comple-
mentary techniques (filter analysis, gas phase and total water
measurements, and application of the thermodynamic equilib-
Figure 1. Schematic cross section of the AIDA facility showing the
scientific instrumentation used in this study. The cylindrical aluminum
3
16
vessel, volume 84 m , is mounted inside a large isolating housing. For
rium model by Carslaw et al. ).
the present experiment, the interior of this cold box, and thus the AIDA
In addition to the quantitative test of optical constants for
ternary H2SO4/H2O/HNO3 solution droplets, the present experi-
ment was used to determine the uptake coefficient γ(N2O5) on
liquid sulfuric acid and STS droplets at stratospheric temper-
atures. The N2O5 hydrolysis on H2SO4/H2O has already been
investigated in a number of laboratory studies, summarized in
the IUPAC Subcommittee on Gas Kinetic Data Evaluation -
Data Sheet R1 (http://www.iupac-kinetic.ch.cam.ac.uk/). Most
measurements indicate that the uptake coefficient is only weakly
dependent on the H2SO4 concentration and quite insensitive to
changes in temperature. It was also concluded in the summary
of the IUPAC data sheet that ternary H2SO4/H2O/HNO3
solutions behave identically to the binary H2SO4/H2O system.
However, the results concerning the effect of increasing nitric
acid content on γ(N2O5) are still contradictory. A so-called
nitrate effect, i.e., a reduction of γ(N2O5) on liquid aerosols
with increasing nitrate concentration, has been clearly identified
in recent measurements conducted at ambient temperatures in
21
vessel, was cooled to a temperature of 193.6 K (see M o¨ hler et al. for
technical details concerning the cooling system). The smaller aerosol
vessel, located next to the main chamber, may be used as additional
2
1
expansion volume in AIDA ice nucleation experiments.
significantly reduced in course of time (i.e., increasing nitrate
concentration) to fit the measured N2O5 uptake.
Methods
AIDA Setup. A detailed technical description of the low-
temperature AIDA aerosol chamber facility of Forschungszen-
trum Karlsruhe can be found in our earlier publications.8
Here, we will briefly review the major scientific instrumentation
used for the experiment discussed in this paper, also shown as
schematic cross section in Figure 1.
,21,22
FTIR Spectroscopy. FTIR extinction spectra of the investi-
gated species (i.e., absorption and scattering of the supercooled
solution droplets plus absorbance of the reactive trace gases)
were measured in situ with a White-type multiple reflection cell,
mounted horizontally at 3.5 m height in the AIDA vessel and
allowing optical path lengths of up to 250 m. Spectra were
recorded with a FTIR spectrometer (Bruker, type IFS 66v) from
17
the aerosol chamber at Forschungszentrum J u¨ lich. As the ionic
+
-
equilibrium N2O5(aq) a NO2 (aq) + NO3 (aq) is supposed
1
8
to be the rate-determining step in the N2O5 hydrolysis, an
increasing nitrate concentration would shift the equilibrium
reaction toward undissociated N2O5, thus suppressing the N2O5
reactivity. However, measurements performed by Hanson at
01-230 K showed no clear evidence of a γ(N2O5) reduction
when going from a binary 60 wt % H2SO4 to a ternary 45 wt
-
1
6
000 to 800 cm at a resolution of 4 wavenumbers. The
quantitative analysis of the FTIR spectra (retrieval of aerosol
parameters and trace gas mixing ratios) will be described in a
separate section below.
1
9
2
Humidity Measurements. As in our previous study, we used
the fast in situ Lyman-R hygrometer FISH of Forschungszen-
%
H2SO4 + 15 wt % HNO3 aqueous solution. The observed
1
5-20% decrease in γ(N2O5) was comparable to the estimated
2
3
trum J u¨ lich for water measurements. Because the instrument
was operated in an ex situ mode by sampling AIDA air through
a heated inlet tube (T > 293 K), the total water mixing ratio
2
0
uncertainty range of the data. On the contrary, Zhang et al.,
who worked at temperatures between 195 and 227 K, already
observed a 60% decrease in γ(N2O5) between solutions contain-
ing 53 wt % H2SO4 and 40 wt % H2SO4 + 10 wt % HNO3. A
reduction of γ(N2O5) by a factor of 5 occurred when further
increasing the nitric acid content to 40 wt %.
(i.e., the sum of interstitial water vapor and evaporated particle
water) was recorded. In addition, the interstitial water vapor
pressure was directly measured in situ by tunable diode laser
(
TDL) absorption spectroscopy. This novel TDL system is based
on a near-infrared tunable diode laser, whose laser light
emission at 1370 ( 2 nm) is directed via an optical fiber into
a second White-type multiple reflection cell, mounted at the
To clarify the magnitude of the nitrate effect in the hetero-
geneous uptake of N2O5 on STS aerosols, the present AIDA
experiment is ideally suited due to the fact that the nitric acid
concentration of the in situ produced STS droplets gradually
increases with time. A model calculation for the determination
of γ(N2O5), which uses the uptake coefficient as adjustable
parameter, will clearly show whether a constant γ(N2O5) value
is appropriate to fit the experimental data (meaning that no
nitrate effect could be detected) or whether γ(N2O5) has to be
(
2
4
inner walls of the AIDA vessel. Data evaluation closely
25
follows the procedure described by Gurlit et al. Both the FISH
and the TDL instruments provide a time resolution of about 1
Hz with an overall accuracy of 5-10% including systematic
errors. The difference between the FISH total water and TDL
interstitial water measurements directly gives the liquid water

8142 J. Phys. Chem. A, Vol. 109, No. 36, 2005
Wagner
mass concentration of the supercooled solution droplets, a
quantity needed to infer the composition of the STS aerosols
generated in our experiment.
Aerosol Measurements. Size distributions of the aerosol
particles were measured with a differential mobility analyzer
(DMA), connected to a condensation particle counter (CNC3010,
TSI). To avoid evaporation of the supercooled solution droplets
during size classification, the DMA was modified for operation
2
6
inside the isolating housing of the AIDA chamber. Total
aerosol sulfate and nitrate mass concentrations of the binary
H2SO4/H2O and ternary H2SO4/H2O/HNO3 solution droplets
were determined by ion chromatographic analysis of nylon filter
samples, type Nylabsorb (Gelman Sciences), which minimize
evaporation losses in particular of nitric acid, as described in
Figure 2. Total water (FISH) and water vapor (TDL) measurements
during the N O uptake experiment. Time periods of the addition of
2 5
the H SO /H O aerosol, O , and NO are indicated by arrows. Time
2
4
2
3
2
8
detail in our recent publication. To minimize adsorptive losses
zero denotes the start of the NO
2
inlet.
of HNO3 in the sampling tube, a heated Teflon tube (T ) 293
K) was used in the sampling line. As the filter holders are
located outside the cold housing of the AIDA chamber, nitric
acid vapor from particles evaporating in the sampling tube as
well as the interstitial HNO3 vapor in equilibrium with the STS
droplets will contribute to the Nylon filter loading. However,
at a temperature of 193.6 K, the latter fraction can be neglected
compared to the predominantly particle-bound HNO3 mass
concentration. Furthermore, back-up filters were used to correct
for breakthrough effects. The relative uncertainty in the sulfuric
and nitric acid mass concentration was estimated to be 10%
the total water mixing ratio by the amount of particle water.
Both signals remain constant during the ozone addition but
immediately react to the start of the injection of NO2. The TDL
measurement detects the varying water vapor pressure in
equilibrium with the particles due to the continuously changing
STS aerosol composition, whereas the increase in the total water
signal indicates that besides N2O5 also H2O is taken up into
the liquid phase. The additional water is transported from the
ice covered chamber walls into the aerosol phase. In the next
section we will show how the two humidity measurements were
used to derive the STS aerosol composition during the uptake
experiment.
8
and better.
Uptake Experiment. For the presented experiment, the AIDA
chamber was cooled to a temperature of 193.6 ( 0.3 K and
filled with particle free synthetic air to a pressure of 180 hPa.
The aluminum walls of the aerosol chamber were precoated
with a thin ice layer, thus acting as water reservoir during the
uptake experiment. A mixing fan was permanently operating
at constant speed. Supercooled sulfuric acid aerosol particles,
generated outside the AIDA chamber as described by M o¨ hler
et al., were then added to the aerosol vessel and characterized
by size distribution measurement, filter analysis, and FTIR
extinction spectroscopy. After the analysis of the background
aerosol, the reactive trace gases ozone and nitrogen dioxide were
successively added to the chamber. Ozone was made in pure
oxygen (99.999%, Messer Griesheim) with a silent discharge
generator; a mixture of 1000 ppm NO2 in synthetic air was used
as received from Messer Griesheim. As will be explained below,
the composition of the H2SO4/H2O background aerosol was
Determination of Aerosol Composition. The basic require-
ment for an accurate determination of the continuously varying
STS aerosol composition during the N2O5 uptake is a precise
characterization of the pre-added background aerosol. Various
complementary methods were used to derive the composition
and mass concentration of the binary H2SO4/H2O solution
8
droplets. First of all, as described in our previous paper, we
employed a Mie fitting algorithm to analyze the measured FTIR
extinction spectrum using the optical constants of Niedziela et
2
2
9
al. as input values. This yields an aerosol composition of 38
wt % H2SO4 and a sulfuric acid mass concentration m(H2SO4)
3
16
of 220 µg/m . Consistent with that, the Carslaw et al. ther-
modynamic model predicts 39 wt % H2SO4 as aerosol composi-
tion, which gives rise to the measured water vapor pressure in
equilibrium with the particles. To further check the retrieved
H2SO4 mass concentration, we can derive the H2O mass
concentration of the droplets from the difference of the FISH
and TDL measurements and calculate the amount of sulfuric
acid based on the deduced aerosol composition. This approach
about 38 wt % H2SO4 with a sulfate mass concentration of about
3
2
00 µg/m . To cover an extended range of STS aerosol
compositions in our uptake experiment, i.e., ending with nearly
pure nitric acid solution droplets containing <5 wt % H2SO4,
the quantity of added NO2 had to be adequately chosen, also
taking into account wall losses of N2O5 and HNO3. Hence, a
total amount of 5.46 mmol NO2 (5.7 ppm) was injected into
the AIDA chamber, corresponding to a nitrate mass concentra-
3
leads to m(H2SO4) ) 185 µg/m . In addition, m(H2SO4) ) 175
3
µg/m is obtained from the ion chromatographic analysis of a
Nylon filter sample. The slight deviation of m(H2SO4) retrieved
from the FTIR spectrum analysis may be due to the fact that
low-temperature optical constants of H2SO4/H2O are only
available down to 210 K, but not for the actual AIDA
3
tion of about 4.1 mg/m if all NO2 molecules were processed
temperature of 193.6 K. Averaging over all results, we adopt
to particle-bound nitric acid in course of the experiment. Ozone
was added in excess by a factor of 40 (0.22 mol, 235 ppm),
thus leading to a rapid depletion of NO2 within a time scale of
about 90 min. The different phases of the uptake experiment
are nicely illustrated by the FISH and TDL humidity measure-
ments (Figure 2).
3
3
8 ( 1 wt % H2SO4 and m(H2SO4) ) 195 ( 20 µg/m to
characterize the background aerosol.
After the addition of ozone and NO2, apart from the
accompanying FTIR spectra recording, only the two humidity
measurements operate at an adequate time resolution to detect
the rapid changes in the STS aerosol composition. The time
interval needed for sampling filter probes with a sufficient mass
loading for the subsequent ion chromatographic analysis,
however, is too long, thus providing only some rough average
values of the nitric and sulfuric acid mass concentrations during
the N2O5 uptake. But the technique can be used to determine
Prior to the injection of the H2SO4/H2O droplets, the total
and gas phase water mixing ratios are identical and indicate
the water vapor pressure over ice at 193.6 K due to the ice-
coated AIDA walls. The addition of the background aerosol
leaves the gas phase water concentration unaffected but increases

Optical Constants and N2O5 Uptake on H2SO4/H2O/HNO3
J. Phys. Chem. A, Vol. 109, No. 36, 2005 8143
Figure 4. FTIR spectra series documenting the N
the supercooled sulfuric acid solution droplets. The bottom spectrum
was recorded before the NO inlet; subsequent spectra (from bottom
to top) were monitored in time steps of 90 s after the NO addition.
2 5
O hydrolysis into
2
2
Figure 3. Time evolution of the mass concentration (a) and composi-
tion (b) of the supercooled H
the AIDA uptake experiment, as derived from filter analyses, humidity
measurements, and the Carslaw et al. thermodynamic model. Note
that the solid lines are only intended as guide to the eye; modeled time
profiles of mass concentrations and STS particle compositions are
shown in Figure 7.
2 4 2 3
SO /H O/HNO solution droplets during
addition to broad-band extinction features of the supercooled
solution droplets, they also reveal narrow absorption bands of
the reactive trace gases O3, NO2, N2O4 (in equilibrium with
NO2), and N2O5. Prior to the analysis of the STS extinction
spectra, these gas absorption features were subtracted using
reference spectra obtained from a separate AIDA experiment
studying the O + NO reaction without pre-added sulfuric acid
1
6
the final amount of H2SO4 and HNO3 at stationary conditions
after the depletion of NO2. Analyses of filter samples taken 52
and 84 min after the NO2 addition indicate that, within the given
uncertainty range of the method, the sulfuric acid mass
concentration remains constant; i.e., no detectable aerosol loss
takes place during the time period of the N2O5 uptake. Thus,
3
2
aerosol particles at 193.6 K. Mixing ratios of O and NO were
3
2
retrieved using the KOPRA algorithm with the HITRAN 20006
13
spectroscopic parameters as input values. The spectral intervals
-
1
-1
2160-2040 cm (O ) and 1680-1540 cm (NO ) were used
3
2
for the fit. The N O concentration was obtained using the
2
4
3
we can employ a constant m(H2SO4) ) 195 ( 20 µg/m as
2 4
temperature-dependent 2NO2 a N O equilibrium constant
sulfuric acid mass concentration throughout the entire uptake
experiment. Additionally, the current particle water amount
m(H2O) is obtained at each second from the difference of the
FISH and TDL measurements with an estimated accuracy of
tabulated in the current JPL report (http://jpldataeval.jpl.
nasa.gov/). As for N O , we used the integrated intensity of the
absorption band near 1250 cm measured by Cantrell et al.
2
5
-
1
27
to deduce the mixing ratio. The time evolution of the trace gas
concentrations will be shown in a later section of this article
(Figure 6) when the measured mixing ratios are compared with
those calculated with the numerical model based on tabulated
kinetic data of the O + NO reaction.
1
0%. The remaining quantity needed to deduce the STS
composition, i.e., the particle-bound nitric acid mass concentra-
tion m(HNO3), can be calculated using the measured water vapor
16
pressure in combination with the Carslaw et al. thermodynamic
model. By feeding the model with the measured sulfuric acid
and total water mass concentration, m(HNO3) was iteratively
adjusted until the measured H2O vapor pressure was predicted.
The uncertainty range of the nitric acid mass concentration was
estimated by taking into account a 10% error in the water vapor
pressure, thus reflecting the uncertainty range of the TDL
measurements and possible inaccuracies in the parametrization
of this quantity in the Carslaw et al.1 model.
3
2
Figure 4 shows the sequence of FTIR extinction spectra
recorded after the addition of O and NO with all trace gas
3
2
absorption features subtracted. The subtraction procedure failed
-
1
in the spectral region between 1080 and 1010 cm due to
saturation effects as a result of the high ozone concentration.
The spectra series clearly demonstrates the successive buildup
of nitric acid in the supercooled solution droplets, as can be
seen by the continuous increase of the intensity of the
6
-1
Figure 3a finally shows the time evolution of m(H2SO4),
m(H2O), and m(HNO3) during the uptake experiment, as derived
from the analysis discussed in this section. The results of the
analyses of the two filter probes which where sampled in the
final phase of the uptake experiment at near constant m(HNO3)
are shown for comparison. These data closely fit in the m(HNO3)
time profile derived using the TDL water vapor data in
combination with the Carslaw et al.16 thermodynamic model,
thus validating our approach to derive the STS aerosol composi-
tion. The actual aerosol composition expressed in terms of wt
characteristic doublet feature at about 1310 and 1450 cm with
contributions from the ν3 mode of the nitrate ion centered at
-
1
1350 cm , appearing as doublet in the spectra, and ν3 and ν4
-
1 28
of nitric acid at 1304 and 1429 cm .
To derive the STS composition and mass concentration,
spectra calculated from Mie theory were fitted to the measured
FTIR extinction spectra, assuming log-normally distributed
particle sizes. The imaginary refractive indices k of the STS
droplets with wts ) wt % H2SO4 and wtn ) wt % HNO3 were
1
1
calculated using the Biermann et al. mixing rule (eq 1) with
9
%
H2SO4, wt % H2O, and wt % HNO3 is shown in Figure 3b,
the Niedziela et al. H2SO4/H2O (ks) as well as the Norman et
1
0
documenting the successive conversion of the binary H2SO4/
H2O background aerosol into nearly pure nitric acid solution
droplets. These directly measured aerosol parameters will then
be compared to the values retrieved from the FTIR spectra
analysis, whose procedural details are described in the next
section.
FTIR Measurements: Trace Gas Mixing Ratios and
Retrieval of Aerosol Parameters. FTIR spectra were recorded
at time intervals of 90 s during the uptake experiment. In
al. HNO3/H2O (kn) binary data sets as input values.
wts
wts + wtn
k(λ,T,wts,wtn) )
ks(λ,T,wts+wtn) +
wtn
kn(λ,T,wts+wtn) (1)
wts + wtn
Note that ks and kn data corresponding to an acid weight
percentage of wts + wtn have to be employed in the mixing

8144 J. Phys. Chem. A, Vol. 109, No. 36, 2005
Wagner
rule approach, i.e., implying similar water activities for ternary
solutions with weight percentages wt(total) ) wts + wtn and
binary solutions with wt(total) ) wts or wt(total) ) wtn. A
subtractive Kramers-Kronig (SKK) expression29 was used to
calculate the corresponding real refractive indices n. Here, we
effective reaction probability and Vg is the average thermal
velocity. Please note that Dahneke’s formalism differs from the
simple resistance approach often employed in the literature. The
partitioning of water and HNO3 formed by the heterogeneous
hydrolysis of N2O5 between gas and particle phase is assumed
to establish instantaneously following the parametrization
developed by Carslaw et al. The losses of gaseous N2O5 and
HNO3 to the chamber walls are treated as irreversible first-order
reactions:
1
5
closely followed the guideline presented by Norman et al. to
correct for truncation errors in the Kramers-Kronig transform.
So the wavenumber range of the k data was extended to 400
3
7
-
1
cm using the room-temperature data sets of Palmer and
3
0
28
Williams for H2SO4/H2O and Querry and Tyler for HNO3/
H2O. The expansion point in the SKK integration was set to
5
N O f products
(R4)
(R5)
2
5
-1
000 cm , the corresponding value for the real refractive index
31
was obtained from the model of Luo et al., using the
FORTRAN routine provided by Krieger et al.32 STS composi-
tion and mass concentration were simultaneously retrieved by
minimizing the summed squared residuals between measured
and calculated extinction spectra, using wts and wtn as well as
the parameters of the aerosol size distribution (i.e., N ) aerosol
number density, σg ) mode width, and CMD ) count median
diameter) as fitting parameters. The downhill simplex method
was used as the optimization technique.33 Total aerosol volume
densities were then calculated from the retrieved size distribution
parameters and converted into STS mass concentrations using
an analytical expression for the densities of the ternary solu-
HNO f products
3
The rate constants for R4 and R5 as well as γ are adjusted
for optimum agreement between experimental and model results.
However, because R4 and R5 are completely controlled by
diffusion their rates are linked via the values of the respective
diffusion coefficients. The wall induced depletion of NO2,
NO3, O3, and particulate matter turned out to be negligible under
the conditions of our experiment. Starting from a log-nor-
mal fit to the measured initial size distribution of the sulfuric
acid aerosol, the FACSIMILE code (Computer software for
modeling processes and chemical reactions, MCPA-Software
Ltd, http://www.mcpa-software.com/facsimileframe.html) is used
to compute the time evolution of the trace gas concentrations
as well as the mass and composition of the particulate phase.
Due to the rapid uptake of water by the aerosol droplets during
the early stages of the experiment the water vapor pressure
dropped well below its saturation value (see Figure 2), because
the transport of water from the ice covered walls is too slow to
maintain equilibrium. Therefore, the time evolution of the water
gas phase concentration measured by TDL spectroscopy is used
directly within the numerical simulation.
3
2
tions.
Modeling the N2O5 Uptake. Regarding the gas phase
chemistry, the oxidation of NO2 by O3 (R1) as well as the
simultaneous dimerization/decomposition reactions (R2, R-2)
and (R3, R-3) have to be considered.
NO + O f NO + O
2
(R1)
(R2, R-2)
(R3, R-3)
2
3
3
2
NO + M a N O + M
2 2 4
NO + NO + M a N O + M
2
3
2
5
Results and Discussion
Additional NO3 reactions as well as the homogeneous
hydrolysis of N2O5 proved to be negligible due to the low
temperature encountered in our experiment. The rate constant
for reaction R1 is calculated following the most recent IUPAC
recommendation (http://www.iupac-kinetic.ch.cam.ac.uk). How-
ever, experimental backup for this parametrization was missing
so far for temperatures below 230 K. The equilibrium constants
for the formation and dissociation of N2O4 and N2O5 are taken
from the current JPL tabulation, where the range of validity is
stated as 200 K < T < 300 K. Our experiment thus provides a
first test whether the tabulated temperature dependencies of the
rate and equilibrium constants under consideration may be
extrapolated to temperatures as low as 193.6 K, an interesting
Quantitative Test of the Mixing Rule Approach. Figure 5
shows a compilation of six selected FTIR extinction spectra of
the ternary H SO /H O/HNO solution droplets recorded during
2
4
2
3
the uptake experiment. Measured STS compositions range from
28 wt % H SO + 14 wt % HNO (panel a) to 6 wt % H SO
2
4
3
2
4
+ 45 wt % HNO (panel f). The measured spectra are compared
3
with the best fit results from the Mie calculations using the
optical constants obtained from the mixing rule approach. STS
compositions and mass concentrations retrieved from the
analysis of the FTIR spectra are summarized in Table 1, the
independently measured aerosol parameters are shown as
comparison.
point regarding the modeling of stratospheric processes.
The first remarkable aspect is the overall nice agreement
between measured and calculated spectra. This clearly justifies
the approach of calculating the ternary H SO /H O/HNO k
Similar to our earlier work,3
4,35
the transport rate of N2O5
molecules to the particle surface is calculated using the transition
2
4
2
3
regime correction proposed by Dahneke,36
spectra as linear superposition of the two binary H SO /H O
2
4
2
and HNO3/H2O k data sets, which relies on the assumption that
no solvent induced band shifts or even additional absorption
features become visible in the ternary mixture, e.g., caused by
strong intermolecular interactions or a chemical reaction between
the individual species. The subtle deviations of the Mie
calculations from the measured FTIR extinction spectra, which
can be made out in the spectra collection shown in Figure 5,
J ) 4πRD â(c - c )
(2)
(3)
g
∞
s
with
Kn + 1
2Dg
VgR
D
â )
Kn )
D
2
Kn (Kn + 1)
D
D
+
1
8
were already observed in our previous study, i.e., may be traced
γ
back to slight inaccuracies of the employed binary data sets of
optical constants. So, the extinction band of undissociated HNO3
where R denotes the radius of the particles, Dg is the N2O5 gas
phase diffusion coefficient, and c∞ and cs are the gas phase bulk
and surface concentrations, respectively. γ represents the
-
1
at 1672 cm is barely visible in the measured spectra but
contrarily overestimated in the Mie calculations of the STS

Optical Constants and N2O5 Uptake on H2SO4/H2O/HNO3
J. Phys. Chem. A, Vol. 109, No. 36, 2005 8145
Figure 5. FTIR extinction spectra of supercooled H
2
SO
4
/H
2
O/HNO
3
droplets obtained in this work (black lines) and best fit results based on Mie
-
1
calculations using the mixing rule approach (gray lines). Mie fits only cover the 4700-800 cm range, the wavenumber regime for which the
SO /H O and HNO /H O data sets of optical constants are tabulated. Measured STS compositions are indicated in each panel, together with
corresponding values of the uptake coefficient γ(N ), as derived from the model calculations whose results will be described in detail in the next
section. Retrieved STS compositions and mass concentrations are summarized in Table 1.
H
2
4
2
3
2
2
O
5
spectra with high wt % HNO3. This could be explained by a
temperature effect because the binary HNO3/H2O optical
constants were only obtained at a temperature of 220 K. Cooling
from 220 K down to the actual AIDA temperature of 193.6 K
may further promote the dissociation of HNO3 into nitrate and
hydronium ions, thus explaining this spectral discrepancy.
Furthermore, especially in case studies a and b, there are spectral
wts + wtn of 42-43 wt %. Thus, the subtle spectral mismatch
already introduced into the binary HNO3/H2O system simply
propagates into the extinction spectra of the ternary solution
droplets.
In addition to the good accordance between measured and
calculated infrared extinction spectra of the STS droplets, also
the measured aerosol parameters (composition and mass con-
centration) are precisely matched by those retrieved from the
analysis of the FTIR spectra (Table 1). In most cases, the
retrieved wt % H2SO4 and wt % HNO3 as well as the total STS
mass concentration are only slightly overestimated. Thus, we
can clearly recommend the implementation of the mixing rule
approach in the retrieval algorithms to quantitatively analyze
the FTIR spectra of STS droplets in terms of aerosol composi-
tion and mass concentration, with a precision as indicated by
the uncertainty ranges quoted in Table 1. The small, apparently
systematic deviations between measured and retrieved aerosol
parameters may be a result of a deficiency of the simple
-
1
differences in the wavenumber range from 3600 to 2500 cm ,
+
covering the extinction features of H2O and H3O , where the
-
1
calculated extinction band centered at about 3300 cm is
somewhat broadened as compared to the measured spectra. We
believe that this may be a result of a slightly poorer performance
of the Norman et al.10 HNO3/H2O refractive index data sets in
this wavenumber regime, as already discussed in our previous
8
work. Particularly, the binary k index data sets for 35 wt %
10
HNO3 and 45 wt % HNO3 of Norman et al. show this
-
1
broadened 3300 cm absorption band in comparison with the
11
corresponding Biermann et al. k data sets (see Figures 1 and
8
11
9
in our preceding paper ), presumably reflecting an improperly
Biermann et al. mixing rule, an argument already brought
1
5
subtracted scattering contribution in the aerosol spectra which
were used to extract the refractive index data sets. Exactly an
interpolation between these discrete measurements for 35 and
forward by Norman et al. to explain the small spectral
differences between their directly derived STS refractive index
data sets and those calculated by means of the mixing rule.
Unfortunately, none of the six discrete refractive index data sets
4
5 wt % HNO3 had to be employed to calculate the nitric acid
1
5
absorption contribution to the ternary H2SO4/H2O/HNO3 system
in our case studies a and b, having a total acid concentration
for STS aerosols derived by Norman et al. exactly matched
the STS aerosol compositions evolving in our uptake experi-

8146 J. Phys. Chem. A, Vol. 109, No. 36, 2005
Wagner
TABLE 1: Comparison of STS Compositions (wt % H
wt % HNO ) and Mass Concentrations (mSTS ) m(H SO
m(HNO ) + m(H O)) Retrieved from the Analysis of the
2
SO
4
4
,
3
2
) +
3
2
FTIR Extinction Spectra with Those Simultaneously Derived
from Filter Sampling, Humidity Measurements, and the
Carslaw Thermodynamic Model16
wt % H
a, γ(N
32 ( 2
28 ( 3
2
SO
4
wt % HNO
3
m
STS (mg/m3)
O
2 5
) ) 0.044:
10 ( 2
fit result
measured
0.73 ( 0.03
0.70 ( 0.05
14 ( 3
b, γ(N O
2 5
28 ( 2
25 ( 2
) ) 0.041:
18 ( 2
fit result
measured
0.87 ( 0.03
0.78 ( 0.05
18 ( 3
c, γ(N
2
O
5
) ) 0.036:
31 ( 2
Figure 6. Time evolution of trace gas mixing ratios: circles, NO
squares, N ; triangles, N . The simulation results are represented
by solid lines.
2
;
fit result
measured
17 ( 2
17 ( 2
1.22 ( 0.04
1.11 ( 0.07
O
2 4
2 5
O
28 ( 3
d, γ(N
17 ( 2
14 ( 2
2
O
5
) ) 0.033:
34 ( 2
fit result
measured
1.5 ( 0.1
1.4 ( 0.1
directly measured STS extinction spectra and those calculated
by superposition of binary sulfuric and nitric acid droplet spectra,
are discussed, the aerosol composition of both the binary and
the ternary systems has to be known with high accuracy. For
33 ( 4
e, γ(N
12 ( 2
11 ( 1
O
2 5
) ) 0.029:
41 ( 2
fit result
measured
2.0 ( 0.1
1.8 ( 0.1
38 ( 4
9
10,15
example, Niedziela et al. and Norman et al.
report an
f, γ(N
2
O
5
) ) 0.016:
48 ( 2
uncertainty in composition of approximately (2 wt % for
H2SO4 and HNO3 in their ternary and binary refractive index
data sets. Thus, the combined uncertainties in the composition
of the binary and ternary aerosol spectra may also contribute to
the spectral differences observed between their directly measured
STS refractive index data sets and those calculated by means
of the mixing rule approach. In this context, new measurements
of STS refractive index data sets by Myhre et al.,39 obtained
from specular reflectance spectra of ternary H2SO4/H2O/HNO3
solutions with precisely known composition, might provide a
fit result
measured
9 ( 2
6 ( 1
3.8 ( 0.1
3.2 ( 0.2
45 ( 4
a
A constant (2 wt % error was assumed for the FTIR retriev,a10l
results due to the uncertainty range of the employed optical constants.9
2 5
Also indicated is the value of the uptake coefficient γ(N O ) for the
different STS compositions, as derived from the model calculations
whose results will be described in detail in the next section.
ment. Hence, we cannot examine whether these directly
measured data sets would further improve the already good
quality of our fit results. Biermann et al.11 proposed their mixing
rule on the assumption that the ionic strength and water activity
are the key parameters influencing the absorption features of
the components in the ternary H2SO4/H2O/HNO3 mixture. As
the water activity is nearly constant for a given wts + wtn,
meaning, e.g., that the water activities for binary 40 wt %
sulfuric or nitric acid solutions as well as ternary 10 wt %
H2SO4 + 30 wt % HNO3 or 30 wt % H2SO4 + 10 wt % HNO3
are almost identical, the mixing rule was formulated as shown
in eq 1. To further improve the accuracy of the mixing rule,
the exact ionic speciation in the ternary STS droplets has to be
known, which primarily determines the spectral shape of the
infrared absorption bands. Thus, to accurately describe the
H2SO4 contribution to the infrared absorption spectrum of a
ternary 10 wt % H2SO4 + 30 wt % HNO3 solution, one should
employ the absorption spectrum of the binary sulfuric acid
solution in the mixing rule calculation, which shows the identical
ionic speciation, i.e., the same relative amount of the sulfate
and bisulfate ions, as in the ternary solution. For the same
reason, the binary HNO3/H2O absorption spectrum employed
in eq 1 should exhibit the same degree of dissociation of
molecular nitric acid into nitrate ions as in the ternary 10 wt %
H2SO4 + 30 wt % HNO3 solution. Unfortunately, experimental
data about the dissociation behavior of sulfuric and nitric acid
in ternary solutions, required to test this modified mixing rule
approach, are scarce. The recent Raman spectroscopic study by
Minogue et al.38 provides first insight into the ionic and
molecular speciation in ternary H2SO4/H2O/HNO3 mixtures. The
quantitative analysis, however, was hindered due to band
overlap, thus revealing only semiquantitative results concerning
the concentration and temperature dependence of the ionic
speciation in the ternary system. Generally, it should be noted
11
more stringent test of the Biermann et al. mixing rule.
Uptake Coefficient γ(N2O5) on Liquid Sulfuric Acid and
STS Droplets. Having convinced ourselves that the composition
of the ternary solution droplets could be accurately retrieved
from their FTIR spectra, we now proceed to analyze the overall
multiple kinetics of the uptake experiment. Starting the model
run with an injection of 5.46 mmol of NO2 results in a slight
underestimation of the initial NO2 and N2O4 concentrations
compared to the FTIR data. Optimum consistency between
experiment and simulation is achieved by increasing the amount
of injected NO2 by 3.8%. The time evolution of the trace gas
concentrations calculated this way is compared to the measured
one in Figure 6. The good agreement observed for both NO2
and N2O4 suggests that the recommended parametrization for
the temperature dependence of the rate constant for reaction
R1 remains reliable down to 193.6 K. The same applies to the
equilibrium constant of reactions R2/R-2, because a significantly
incorrect value would inevitably deteriorate the numerically
predicted NO2 mixing ratio.
As soon as NO3 becomes available, N2O5 is rapidly produced
via reaction R3. On the other hand, the dissociation R-3 proceeds
very slowly at temperatures as low as 193.6 K. The dominant
sinks for N2O5 are the uptake into the particles followed by
hydrolysis to HNO3 and the irreversible loss to the chamber
walls. Due to these efficient depletion processes, the N2O5
mixing ratio never exceeded a value of about 40 ppb. Unfor-
tunately, this low concentration is close to the detection limit
of our FTIR analysis, leading to a large uncertainty of about a
factor of 2. Because of these reasons, our experiment was not
sensitive enough to allow for an unambiguous consistency check
of the JPL equilibrium constant recommendation for the reaction
pair R3/R-3.
1
1
that when subtle modifications of the original Biermann et al.
mixing rule approach, deduced from a comparison between
Figure 7 compares the measured and modeled time profiles
of mass concentrations and STS particle compositions. The

Optical Constants and N2O5 Uptake on H2SO4/H2O/HNO3
J. Phys. Chem. A, Vol. 109, No. 36, 2005 8147
Figure 7. Measured and modeled time evolution of mass concentration of aerosol compounds (a) and particle composition (b). The experimental
data correspond to Figure 3 (squares, H O; triangles, HNO ; circles, H SO ). The simulation results for constant effective reaction probability γ are
represented by broken lines (-‚-, H O; - - -, HNO ; -‚‚-, H SO ). The solid lines are calculated assuming γ to decrease exponentially with time. The
dotted line in panel a shows the maximum HNO mass concentration if all injected NO molecules were processed to particle-bound nitric acid.
2
3
2
4
2
3
2
4
3
2
initial value for the effective N2O5 reaction probability γ on
pure sulfuric acid droplets is determined to be 0.05, consistent
with the results cited in the latest IUPAC compilation. However,
because the uptake rate of N2O5 into the particles is controlled
by γ and the wall loss reaction R4, the uncertainty of the
measured N2O5 gas phase mixing ratio propagates into the values
fitted for γ and for the rate constant of R4. Nevertheless, Figure
chamber facility AIDA, we have tested the performance of a
mixing rule approach for the quantitative analysis of the infrared
spectra in terms of aerosol composition and mass concentration.
As a result of our experimental strategy to generate the ternary
solution droplets, i.e., uptake of N O (from the O + NO
2
5
3
2
reaction) into pre-added sulfuric acid droplets at 193.6 K, the
analysis spanned a broad range of different STS compositions,
starting with binary H SO /H O droplets and ending with nearly
7
a clearly demonstrates that the simulation based on the
2
4
2
supposition of γ remaining constant over all phases of the
experiment (broken lines) badly fails to reproduce the measured
time evolution of the aerosol mass concentrations of HNO3 and
H2O. On the other hand, very good agreement between
experimental and modeling results is achieved assuming γ to
decrease exponentially with time (solid lines), i.e., γ ) 0.05
3 2
pure HNO /H O aerosol particles. The aerosol parameters
retrieved from the FTIR spectra were directly compared to those
simultaneously measured with the comprehensive diagnostic
tools of the AIDA chamber. Keeping in mind the results from
8
a previous study, which demonstrated the good performance
9
of the refractive index data sets from Niedziela et al. and
-
4
-1
10
exp(-7.8 × 10
s
× t). Exemplary values of γ for different
Norman et al. in reproducing infrared extinction spectra of
STS compositions, i.e., corresponding to different times during
the uptake experiment, are given in Table 1. Figure 7b reveals
that the relative aerosol composition is rather insensitive to the
diminishing of γ because an overestimated formation of HNO3
is more or less compensated for by an increased uptake of H2O.
Because the wall loss of N2O5 is diffusion controlled and the
speed of the mixing fan was kept constant, it appears unreason-
able to consider an increasing rate of R4 to explain the
suppression of aerosol nitrate formation. We therefore conclude
that due to the increasing concentration of nitrate in the particles
formed by the hydrolysis of N2O5 the effective reaction
probability γ decays with a lifetime (1/e time) of about 21 min
under the conditions of our experiment, which exactly corre-
sponds to the time when the changes in the STS composition
are leveling off (Figure 7b). This finding is not significantly
affected by the uncertainty of the initial value for γ. Therefore,
our study provides additional strong evidence that the nitrate
effect well documented in room temperature experiments is still
operative down to 193.6 K. Preliminary tests seem to indicate
that the low temperature nitrate effect can be alternatively
modeled in a quantitative manner employing a direct functional
dependence of γ on the concentrations of HNO3 and H2O,
binary H SO /H O and HNO /H O solution droplets, we used
2
4
2
3
2
these data sets to calculate the optical constants of the ternary
solution droplets with the mixing rule proposed by Biermann
et al. We observed good agreement between measured and
11
calculated STS extinction spectra. Minor spectral discrepancies
may be a result of (i) slight inaccuracies of the employed binary
data sets, (ii) a temperature effect, as the binary optical constants
are not available for a temperature as low as 193.6 K, or (iii)
the simplicity of the mixing rule, relying on the additivity of
the two binary k spectra in the ternary mixture. Measured STS
compositions and mass concentrations during the uptake experi-
ment were nicely matched by the FTIR retrieval results. The
percentage error in the retrieved aerosol mass concentration
never exceeded 20%, being in most cases even as low as 10%.
Maximum deviations between measured and retrieved aerosol
compositions (wt % H2SO4 and wt % HNO3) were in the order
of 3-4 wt %.
In addition to the spectroscopic results, the uptake experiment
proved to be suitable to clarify the magnitude of the nitrate effect
in the uptake of N2O5 on STS aerosols. A numerical model,
including all important nitrogen oxide gas phase reactions,
chamber specific wall loss rates of N2O5 and HNO3, as well as
the heterogeneous conversion of N2O5 into particle-bound nitric
acid, was employed to calculate the time profiles of trace gas
mixing ratios as well as STS mass concentration and composi-
tion during the uptake experiment. Here, the uptake coefficient
γ was used as adjustable parameter to best fit the experimental
data. Measured NO2 and N2O4 time profiles were nicely matched
by the model runs, illustrating that the parametrizations em-
ployed for the temperature dependence of the required kinetic
1
7
similar in spirit to the formalism proposed by Mentel et al.
and by Hallquist et al.40 However, additional experiments will
be necessary to support this approach.
Conclusions
On the basis of a series of mid-infrared extinction spectra of
supercooled H2SO4/H2O/HNO3 solution (STS) droplets, obtained
from a simulation experiment at the low-temperature aerosol

8148 J. Phys. Chem. A, Vol. 109, No. 36, 2005
Wagner
data are still precise even when extrapolating to a temperature
as low as 193.6 K. Experimental STS mass concentrations could
only be accurately mimicked in model runs with γ exponentially
decreasing in time, i.e., with increasing nitrate concentration
in the particles. From an initial value of γ ) 0.05 for pure
H2SO4/H2O solution droplets, γ dropped well below 0.02 when
exceeding a nitrate mass fraction of about 40 wt % in course of
the uptake experiment, being in good agreement with earlier
results from Zhang et al.20 This shows that the nitrate effect
already observed at room temperature is also important under
stratospheric conditions and should be accounted for in strato-
spheric chemistry models.
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Acknowledgment. We are grateful for the continuous
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and C. E. L. Myhre for helpful discussions about the refractive
indices of STS aerosols. We acknowledge the skillful assistance
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