Introduction
The formation of new particles from the gas phase is a frequent and
important process in the atmosphere. Substantial progress has been made in
recent years in describing the chemical systems and the mechanisms that could
potentially be relevant to atmospheric new particle formation (NPF).
Observed atmospheric boundary-layer nucleation rates typically correlate
with the concentration of gaseous sulfuric acid (Kulmala et al., 2004; Kuang
et al., 2008). Moreover, it is generally accepted that the presence of water
vapor enhances nucleation in the binary (H2SO4–H2O) system.
However, nucleation under typical ground-level conditions cannot be
explained by the binary nucleation of sulfuric acid and water vapor (Kulmala
et al., 2004; Kerminen et al., 2010), even if the enhancing effect due to
ions is taken into account (Kirkby et al., 2011). Therefore, assuming that
sulfuric acid is required for nucleation, at least one additional compound
is necessary to stabilize the nucleating clusters (Zhang et al., 2012).
Ammonia, amines and highly oxidized organic compounds have been identified
in ambient samples or tested in laboratory experiments (Ball et al., 1999;
Hanson and Eisele, 2002; Chen et al., 2012; Kulmala et al., 2013). Recent
chamber experiments showed that the observed atmospheric boundary-layer
nucleation rates can, in principle, be explained by sulfuric acid acting in
combination with either amines or the oxidation products from α-pinene (Almeida et al., 2013; Schobesberger et al., 2013; Riccobono et
al., 2014).
Nucleation has also frequently been observed in the free troposphere, where
the temperature and gas mixture differ from those at the surface (Brock et
al., 1995; Weber et al., 1995; Clarke et al., 1999; Lee et al., 2003). An
important source for stratospheric particles is the tropical tropopause
region, where nucleation-mode particles have been observed. Additionally, new
particle formation has also been observed in the free troposphere (Brock et
al., 1995; Clarke et al., 1999; Borrmann et al., 2010; Weigel et al., 2011).
Due to the volatility and the identification of sulfur in collected
particles, it was concluded that binary nucleation contributes to (or
dominates) the formation of these particles (Brock et al., 1995). Binary
homogenous nucleation also seems to play an important role in forming the
mid-stratospheric condensation nuclei layer, although ion-induced binary
nucleation cannot be ruled out (Campbell and Deshler, 2014). Several studies
provide evidence that ion-induced nucleation may be an important process in
the free troposphere (Lee et al., 2003; Lovejoy et al., 2004; Kanawade and
Tripathi, 2006; Weigel et al., 2011). These studies suggest that binary
nucleation is important on a global scale – especially in regions where
very low temperatures prevail, and where the concentrations of stabilizing
substances involved in ternary nucleation are low.
Nucleation in the binary system starts with the collision of two hydrated
sulfuric acid monomers, which form a dimer (Petäjä et al., 2011). In
this study, the notation “dimer” refers to a cluster that contains two
sulfuric acid molecules plus an unknown amount of water and, in the ternary
system, ammonia. The term monomer refers to clusters with one sulfuric acid,
irrespective of whether the cluster also contains ammonia and/or water
molecules or not. Unless stated otherwise the terms “monomer” and
“dimer” describe the neutral, i.e., uncharged, molecules and clusters. The
probability that a dimer will or will not grow larger depends on its
evaporation rate as well as its collision rate with monomers and larger
clusters. Therefore, it is crucial to know the evaporation rate (or the
equilibrium constant) of the sulfuric acid dimer in order to understand and
model binary nucleation. Hanson and Lovejoy (2006) measured the dimer
equilibrium constant over a temperature range of 232 to 255 K. However, no
direct measurements have been performed for lower temperatures. Moreover,
evidence exists that ammonia is an important trace gas influencing new
particle formation in some regions of the atmosphere (Weber et al., 1998;
Chen et al., 2012). Numerous studies using quantum chemical calculations
have been conducted to study the cluster thermodynamics for the sulfuric
acid–ammonia system (Kurtén et al., 2007; Nadykto and Yu, 2007; Torpo et
al., 2007; Ortega et al., 2012; Chon et al., 2014). To our knowledge,
however, only very few studies have yet reported experimentally determined
dimer concentrations for this system (Hanson and Eisele, 2002; Jen et al.,
2014). In order to model NPF for the ternary system involving ammonia, it is
essential to better understand the thermodynamics of the clusters involved
in the nucleation process. Cluster properties derived from measurements can
be used for a comparison with the theoretical studies. Such a comparison
provides a consistency check for both the models and the measurements.
Here we present experimentally derived dimer evaporation rates for the
binary system (H2SO4–H2O) at temperatures of 208 and 223 K.
The measurements of the sulfuric acid monomer and dimer were made with a
chemical ionization mass spectrometer (CIMS) at the Cosmics Leaving OUtdoor
Droplets (CLOUD) chamber. The data are discussed and compared to previously
published dimer evaporation rates for the binary system (Hanson and Lovejoy,
2006). Dimer measurements are also available for the ternary system
(H2SO4–H2O–NH3) at 210, 223, and 248 K and some ammonia
mixing ratios (< ∼ 10 pptv). The thermodynamics (dH and
dS) of the H2SO4⚫NH3 cluster were retrieved from
comparison of the measured monomer and dimer concentrations with those
predicted using a simple model. Furthermore, neutral cluster measurements
using chemical ionization–atmospheric pressure interface time-of-flight
(CI-APi-TOF) mass spectrometry are presented for the binary system at 206 K
for clusters containing up to 10 sulfuric acid molecules.
Methods
CLOUD chamber
CIMS monomer and dimer measurements were conducted primarily during the
CLOUD5 campaign in October and November 2011. Additional CI-APi-TOF
measurements were made during one experiment in November 2012 (CLOUD7). The
CLOUD chamber has been described in previous publications (Kirkby et al.,
2011; Duplissy et al., 2015). The 26.1 m3 electropolished
stainless-steel chamber provides an ultra-clean environment for studying new
particle formation and growth. A well-insulated thermal housing and
temperature control allow measurements down to 193 K with a stability of a
few hundredths of a degree. For cleaning purposes the chamber can be heated
up to 373 K and flushed with ultra-clean air at a high ozone concentration.
Pure neutral nucleation was studied by applying a high voltage (±30 kV) to upper and lower transparent field cage electrodes (termed clearing
field high voltage, or CFHV, in the following). Sampling ports are located
around the mid-plane of the cylindrical chamber, where the clearing field is
at 0 V. Grounding the electrodes allows measurements of ion-induced
nucleation. In the absence of a clearing field, galactic cosmic rays produce
ion pairs at a rate of ∼ 2 cm-3 s-1. Much higher
ion pair production rates can be achieved by illuminating a section of the
chamber (approximately 1.5 m × 1.5 m) using a defocused pion beam from
CERN's Proton Synchrotron (Duplissy et al., 2010). Ultra-clean gas is
provided to the chamber by mixing nitrogen and oxygen from cryogenic liquids
at a ratio of 79:21. Different relative humidities (RH) can be achieved by
passing a portion of the dry air through a Nafion humidification system. The
temperature and the dew/frost point inside the chamber are monitored
continuously; the RH is calculated using the equations given by Murphy and
Koop (2005). A fiber optic system (Kupc et al., 2011) feeds UV light into
the chamber, which initiates the photolytic production of sulfuric acid when
H2O, O2, O3, and SO2 are present. Two mixing fans
continuously stir the air inside the chamber, assuring its homogeneity
(Voigtländer et al., 2012).
The CLOUD5 campaign was dedicated to experiments investigating new particle
formation at low temperatures (down to ∼ 208 K) for the binary
(H2SO4–H2O) and the ternary
(H2SO4–H2O–NH3) systems. The particle formation rates at
low temperature will be reported in forthcoming papers; this publication
focuses on measurements of the sulfuric acid monomer and the sulfuric acid
dimer. One future paper will also focus on the determination of the ammonia
mixing ratios at the low temperatures. These were evaluated from a careful
characterization of the CLOUD gas system, which delivers ammonia diluted in
ultra-clean nitrogen and air to the CLOUD chamber. The gas system was
characterized by measurements with a long-path absorption photometer (LOPAP;
Bianchi et al., 2012), an ion chromatograph (IC; Praplan et al., 2012) and a
proton transfer reaction mass spectrometer (PTR-MS; Norman et al., 2007).
Table 1 gives an overview over the main findings relevant to this study
obtained from the two different campaigns.
CIMS and CI-APi-TOF mass
spectrometer
During CLOUD5 a CIMS was used for the measurement of sulfuric acid monomers
and dimers (Kürten et al., 2011). Using nitrate ions
NO3-(HNO3)x=0-2, sulfuric acid can be selectively
ionized; detection limits below 105 cm-3 (referring to the monomer
of sulfuric acid) can be reached for short integration times, thereby
enabling high time resolution (Eisele and Tanner, 1993; Mauldin et al.,
1999; Berresheim et al., 2000). The instrument was calibrated before and
after the campaign using a system that produces a known concentration of
sulfuric acid (Kürten et al., 2012). In this way, the recorded ion
signals – for the primary ions and the reactant ions – can be converted
into a concentration of sulfuric acid.
Overview over the different conditions, instruments, and main
findings relevant to this study from the CLOUD5 and CLOUD7 campaigns.
Campaign
Instruments
Binary system
Ternary system
Main findings
CLOUD5
CIMS, APi-TOF
investigated at 208 and 223 K, RH ∼ 10 to 60 %
investigated at 210, 223, and 248 K, ammonia between ∼ 0.5 and 8 pptv
(a) binary system: ion effect on apparent CIMS dimer measurements (Sect. 3.1) (b) binary system: thermodynamics of sulfuric acid dimers (Sect. 3.3) (c) ternary system: thermodynamics of H2SO4⚫NH3 cluster (Sects. 3.5 and 3.7)
CLOUD7
CIMS, CI-APi-TOF
investigated at 206 K
not investigated at low temperatures
observation of neutral clusters containing up to 10 sulfuric acid molecules (Sect. 3.4)
HSO4- (the product ion from the sulfuric acid monomer) and
HSO4-(H2SO4) (the product ion from the sulfuric acid
dimer) are formed by reactions such as
NO3-(HNO3)x+(H2SO4)1-2⚫X→HSO4-(H2SO4)0-1(HNO3)y+(x-y+1)⚫(HNO3)+X.
The compound X is, in most cases, water, but in the case of the ternary
system, both experiments and quantum chemical calculations suggest that
dimers could also be bound to ammonia (Hanson and Eisele, 2002; Kurtén
et al., 2007). Ammonia (or X) is expected to evaporate rapidly after the
ionization (Ortega et al., 2014). It should be noted here that even if X did
not evaporate after the ionization it would probably be removed in the CIMS
collision dissociation chamber (CDC). In the CDC any remaining water
molecules are stripped off from the core ions and the
NO3-(HNO3)0-2 ions yield mostly NO3- due to
the declustering. Therefore, the monomer and dimer sulfuric acid
concentrations are estimated to be
H2SO4=CLmonomer⋅ln1+CR97CR62,
H2SO42=CLdimer⋅ln1+CR195CR62.
Here, CR denotes the count rate for the primary ions (CR62 at m/z 62 for
NO3-), the HSO4- ions (CR97 at m/z 97), and the
HSO4-(H2SO4) ions (CR195 at m/z 195).
The constant C is derived from a calibration and has been evaluated as
1.1×1010 cm-3 with a typical uncertainty of ∼ 30 %
(Kürten et al., 2012). The same calibration constant is used for the
monomer and the dimer because it is not possible to calibrate the dimer
signal. Since both H2SO4 and (H2SO4)2 are thought
to react with the nitrate ions at the collision limit, this assumption is
well justified. The factors Lmonomer and Ldimer take into account
the penetration through the sampling line from the CLOUD chamber to the CIMS
ion source. A sample flow rate of 7.6 standard liters per minute (L min-1) and a
sampling line length of 100 cm were used to calculate the transmission. The
diffusion coefficient has been calculated for the respective temperature and
RH for the monomer from the data given by Hanson and Eisele (2000). It was
assumed that the diffusivity of the hydrated dimer (see Henschel et al.,
2012) equals 0.06 ± 0.01 cm2 s-1 at 298 K and varies with
temperature as (298 K/T)1.75.
Some dimer dissociation in the CIMS CDC section cannot be ruled out,
although the HSO4-(H2SO4) ion has a very high bond
energy (Curtius et al., 2001). However, as described in the next section,
this effect is very likely minor, and, to the extent that it occurs, it is
taken into account in the characterization of the dimer detection
efficiency.
During the CLOUD7 campaign, sulfuric acid and its clusters were measured with
two CI-APi-TOF mass spectrometers (Jokinen et al., 2012; Kürten et al.,
2014); the H2SO4 monomer was also measured by the CIMS. However,
during CLOUD7 it was not possible to measure the dimers with the CIMS due to
instrumental problems. The CI-APi-TOF has a chemical
ionization source almost identical to the CIMS but which uses a time-of-flight mass spectrometer
with high mass resolution (around 4500 Th/Th) and mass accuracy (better than
10 ppm). These features as well as the wide mass range (up to around 2000 Th) enable detection and unambiguous identification of the elemental
composition of clusters. As will be shown in Sect. 3.4, neutral clusters
containing as many as 10 sulfuric acid molecules were detected during a
binary experiment at 206 K.
Quantification of sulfuric acid dimer concentration
As it is not possible to calibrate the CIMS or the CI-APi-TOF with a known
concentration of sulfuric acid dimers, a different method was chosen to
allow the quantification of the dimer concentration. To estimate the
relative sensitivity towards the dimers (m/z 195) in comparison to the monomer
(m/z 97), ion-induced clustering (IIC) during calibration can be evaluated. If
the sulfuric acid monomer concentration is large enough, efficient formation
of HSO4-(H2SO4) can occur due to clustering of
HSO4- and H2SO4 within the CIMS ion drift tube (Hanson
and Eisele, 2002). The estimated dimer count rate through this process is
(Zhao et al., 2010; Chen et al., 2012)
CR195,IIC=12⋅k21⋅treact⋅CR97⋅C⋅ln1+CR97CR62.
The reaction time treact is approximately 50 ms in our case (Kürten
et al., 2012). A value of 8×10-10 cm3 s-1 was used for
k21, the rate constant for reaction between HSO4- and
H2SO4 (Zhao et al., 2010). The measured count rate CR195 was
compared to the expected count rate during a calibration in which a high
concentration of sulfuric acid monomers was presented to the CIMS. From this
comparison, we concluded that the dimer signal is suppressed by a factor of
1.2 relative to the monomer signal. The discrepancy can be due to either
mass discrimination or to some fragmentation in the CIMS CDC. In any
case, it means that the measured dimer signal needs to be multiplied by a
factor of 1.2 (with an estimated statistical uncertainty of less than
10 %) when its concentration is evaluated.
The background signal, e.g., from electronic noise, is always subtracted
before the dimer concentration is evaluated according to Eq. (1b). The
background was obtained by averaging over a certain period just before the
experiment started, i.e., before the UV lights were turned on and the
H2SO4 was produced. In addition to the background, the
contribution from IIC is subtracted from the dimer signal (Chen et al.,
2012). This effect becomes relevant at about 1×107 cm-3 for the
sulfuric acid monomer under the conditions of this study.
Sulfuric acid dimer evaporation rate
The goal of this study is to determine sulfuric acid dimer evaporation rates
from data obtained by monomer and dimer measurements. In order to derive a
formula for the evaporation rate it is useful to start with the basic
equations governing the loss and the production of the clusters. Since low-temperature conditions (208 and 223 K for the binary system) are considered
in this study, the assumption is made that only the smallest clusters (dimer
and trimer) have appreciable evaporation rates (Hanson and Eisele, 2006).
The balance equation for the dimer concentration in this case is
dN2dt=0.5⋅G1,1⋅K1,1⋅N12+k3,e⋅N3-k2,w+kdil+∑i=1nG2,i⋅K2,i⋅Ni+k2,e⋅N2,
where Ni is the concentration of the cluster containing i sulfuric acid
molecules. The evaporation rate ki,e refers to the evaporation of one
sulfuric acid molecule from a cluster containing i sulfuric acid molecules.
In a chamber experiment such as CLOUD, three loss processes are relevant for
neutral particles; these include the wall loss rate ki,w, the dilution
rate kdil through the replenishment of the chamber air (independent of
particle size), and coagulation with the coefficient Ki,j describing
collisions between the clusters i and j. The factor Gi,j represents an
enhancement in the collision rates due to dipole–dipole interactions
(McMurry, 1980; Chan and Mozurkevich, 2001). In order to derive an
expression for the dimer evaporation rate, we assume steady state
(dN2 / dt=0). Equation (3) can then be written as
k2,e=0.5⋅G1,1⋅K1,1⋅N12N2+k3,e⋅N3N2-k2,w+kdil+∑i=1nG2,i⋅K2,i⋅Ni.
It is useful to estimate the relative importance of the three terms on the
right-hand side of Eq. (4). The numerator in the first term describes
the production rate of dimers from monomers. The collision constant for two
monomers is approximately 2.8×10-10 cm3 s-1 at 208 K. If the
enhancement factor G due to dipole–dipole interactions is included, this
value is ∼ 6.9×10-10 cm3 s-1 (McMurry, 1980;
Chan and Mozurkevich, 2001). As an example, at 208 K under binary
conditions, the smallest monomer concentration evaluated is
2×106 cm-3, at which point the dimer was evaluated as 1×104 cm-3
(Sect. 3.3). These values yield 0.2 s-1 for the first term. The
second term is significantly smaller than the first term, so it can be
neglected due to the reasons listed in the following. The trimer
concentration (although it was not measured) should be smaller than the
dimer concentration because the trimer is produced from the dimer. Moreover,
the trimer evaporation rate is expected to be lower than the dimer
evaporation rate (e.g., 1.6×10-3 s-1 for the trimer, and
0.3 s-1 for the dimer at 208 K and 20 % RH; see Hanson and Lovejoy,
2006). The third term includes losses due to walls, dilution, and
coagulation. The wall loss rate for a dimer is approximately 1.5×10-3 s-1, while loss due to dilution is ∼ 1×10-4 s-1
(Kürten et al., 2014). The loss due to coagulation depends on the
particle size distribution, and can be important when the dimer evaporation
rate is small. Loss of dimers due to collisions with monomers (i.e., growth
to form trimers) then dominates the coagulation term, which is usually on
the order of 10-2 s-1 (e.g., N1=1×107 cm-3 and
G1,1⋅K1,1=6.9×10-10 cm3 s-1). All
elements of the third term are, thus, small compared with the first term,
and so these can also be neglected. For the conditions of this study,
consistent with the extrapolated data by Hanson and Lovejoy (2006), the
evaporation rates are, however, larger than 10-2 s-1. This means
that evaporation dominates over the other losses; therefore, k2,e can be
approximated by
k2,e=0.5⋅G1,1⋅K1,1⋅N12N2.
The concentrations used in Eq. (5) are averages over periods when
conditions are close to steady state. These periods are defined by
conditions where the production and loss rates for the dimer and the monomer
are almost identical and the concentrations are not subject to significant
changes anymore. If losses by processes other than evaporation were not
negligible, retrieval of evaporation rates would require use of a numeric
model that also includes larger clusters since coagulation loss depends on
concentrations of all other clusters. Nevertheless, model calculations
simulating cluster and particle concentrations are needed to evaluate other
effects relevant to this study, as will be discussed in the next sections.
Comparison of the rate constants used for the reactions between
HSO4- and H2SO4 (Sect. 2.3) and between
H2SO4 and H2SO4 yields that the neutral–neutral
collision rate is about the same as the charged–neutral collision rate. This
is due to the relatively large enhancement factor from dipole–dipole
interactions for the neutral–neutral rates (McMurry, 1980; Chan and
Mozurkevich, 2001) and the observation that the reaction between the
bisulfate ion and sulfuric acid seems not to proceed at the collisional rate
(Zhao et al., 2010). We have no mechanistic explanation as to why the formation of
HSO4-(H2SO4) should proceed at a rate slower than the
collision rate. Comparison with similar ion–molecule reactions shows, for example,
that the formation of NO3-(H2SO4) proceeds at the
collision rate (Viggiano et al., 1997), whereas this does not seem to be the
case for the formation of NO3-(HNO3) (Viggiano et al., 1985).
Uncertainties regarding the rate of formation for the
HSO4-(H2SO4) cluster remain, and these need to be
addressed in future studies. Further discussion about the consequences this
uncertainty has on the present study is provided in Sect. 3.8.
SAWNUC model
The Sulfuric Acid Water NUCleation (SAWNUC) model of Lovejoy et al. (2004)
simulates ion-induced nucleation in the binary system. Cluster growth is
treated explicitly by a step-by-step addition of sulfuric acid molecules,
while equilibrium with water molecules is assumed due to the relatively high
concentration and evaporation rate of H2O compared to H2SO4.
SAWNUC takes into account sulfuric acid condensation and evaporation,
coagulation, and losses due to walls and dilution (Ehrhart and Curtius,
2013). In SAWNUC, evaporation rates of small, negatively charged clusters
are based on measured thermodynamics and partly on quantum chemical
calculations (Lovejoy and Curtius, 2001; Froyd and Lovejoy, 2003). More
detailed information on SAWNUC can be found in Lovejoy et al. (2004), Kazil
and Lovejoy (2007), and Ehrhart and Curtius (2013).
As this study focuses on neutral binary nucleation, we neglect the
charged-cluster channel and only simulate the neutral channel. Coagulation
coefficients have been calculated according to Chan and Mozurkewich (2001).
They quantified London–van der Waals forces (dipole–dipole interactions) for
particles in the binary system based on the theory by Sceats (1989). Within
this study of nucleation at low temperatures, only dimer (and sometimes
trimer) evaporation has been taken into account. The exact input parameters
are specified in the following sections.
Dimer transmission through the sampling line
Previous dimer evaporation rates were evaluated with the CIMS ionization
source integrated within a temperature-controlled flow tube (Hanson and
Lovejoy, 2006). This setup ensured that the temperature did not change
between the times when the dimers were formed and when they were ionized.
In the present study, the dimers formed inside the CLOUD chamber, which is
very precisely temperature-controlled. However, the monomers and dimers had
to be transported from the chamber to the CIMS through a 100 cm long
sampling line. The first ∼ 80 cm of this line was held at the
same temperature as the chamber because it protruded through the thermal
housing and into the chamber. Moreover, the sampling line was enclosed by an
insulated copper tube. Since a large part of the copper volume was placed
inside the thermal housing, the cold temperature was maintained over the
full length of the copper tube due to efficient heat conduction even for a
short section of the tube that was located outside the chamber, while the
insulation minimized heat transfer to the surrounding air. The CIMS ion
drift tube was connected to the tip of the copper-jacketed sampling line by
means of a short tube that was not temperature-controlled, exposing the last
15 to 20 cm (the measured length is closer to 15 cm, but to be conservative
we took into account a somewhat longer distance) of the sampling line to
warmer temperatures. In this region the dimers could in principle have
suffered from evaporation.
To estimate the evaporation effect, a finite-difference method was used to
calculate the temperature profile, as well as the dimer concentration across
the sampling line over its full length. The differential equations for the
monomer (i=0) and dimer (i=1) concentrations ci were solved as a
function of the radial and axial coordinates r and z (Kürten et al.,
2012):
∂ci∂t=Di⋅1r⋅∂ci∂t+∂2ci∂r2+∂2ci∂z2-2QπR2⋅1-r2R2⋅∂ci∂z+si,
where Di is the diffusivity, Q is the flow rate, and R is the radius of the
tube. A parabolic flow profile was assumed and the geometry was divided into
small areas in order to solve the differential equations by a finite-difference method. The source terms si include evaporation and
production of dimers and loss and production of monomers due to
self-coagulation and evaporation of dimers. Further reactions (coagulation
with larger clusters/particles) were not taken into account since the time
is rather short (< 1 s for Q=7.5 L min-1, R=0.005 m, and L=1 m)
and the other loss terms are dominant. A similar differential equation is
used to determine the temperature inside the tube before the concentrations
are calculated. This temperature is used to calculate the evaporation of
dimers in each of the small areas. The time-dependent equations (time t) are
repeatedly solved until a reasonable degree of convergence is reached.
Figure 1 shows the results for a chamber temperature of 223 K. The walls of
the first 80 cm of the sampling line were held at 223 K, while those of the last
20 cm were held at 293 K (which was a typical maximum daytime temperature in
the experimental hall during the CLOUD5 campaign). It should be noted that
this is an extreme case because, in reality, the temperature would slowly
approach 293 K over the last 20 cm due to heat conduction along the walls of
the sampling line. However, the calculations performed here are used to
obtain an upper-bound estimate of the error due to evaporation. The
temperature of the walls is indicated in black (223 K) and grey (293 K). Figure 1 shows the normalized concentration of dimers
after initializing the monomer concentration to 1×107 cm-3; the
dimer was assumed to be at equilibrium initially. It was further assumed
that both monomers and dimers are lost to the walls due to diffusion, and
that at the same time dimers are formed due to collisions of monomers but
can also evaporate. Larger clusters or particles were not taken into
account. The dimer evaporation rate as a function of temperature was taken
from the literature at this stage (Hanson and Lovejoy, 2006).
Simulated transmission of dimers through the CIMS sampling line at a
temperature of 223 K for the incoming air. The temperature of the sampling
line is fixed to 223 K for the first 80 cm (black line along top axis) and to
293 K for the last 20 cm (grey line along top axis). Wall loss is the dominant
loss process over the first 80 cm, whereas evaporation is an additional loss
process for the last 20 cm. The overall transmission (diffusion loss and
evaporation) is 22.8 % at a flow rate of 7.6 L min-1, while it is
47.5 % when evaporation is neglected (diffusion loss only). See text for
details.
The profile shown in Fig. 1 indicates that, during the first 80 cm, dimers
are lost primarily via diffusion because, in this section, they are
essentially in equilibrium regarding formation and evaporation; only over
the last 20 cm does evaporation have an appreciable effect on the dimer
concentration. However, only the region close to the walls of the sampling
line shows a rise in the gas temperature; the center of the sample flow is
essentially unaffected. The estimated overall transmission efficiency for
dimers is 0.228 at a flow rate of 7.6 L min-1 in the half-inch tube (inner
diameter ∼ 10 mm). If the temperature were held constant at
223 K over the entire tube length, the transmission would increase to 0.475
because only wall losses would take place. Since the dimer concentration is
corrected for the effect of diffusion loss (see Eq. 1b), the
additional loss factor due to evaporation would be (1/0.228)/(1/0.475)=2.08. However, this is an upper-bound estimate of the error introduced
through evaporation since the temperature is, in reality, gradually changing
over the last 20 cm instead of increasing as a step function as simulated.
For the lower temperature of 208 K, the effect is even smaller. From the
estimations presented in this section it can, therefore, be concluded that,
while the sampling conditions are not ideal, the maximum error introduced is
very likely smaller than a factor of 2 (see also error discussion in Sect. 3.8).
Results and discussion
Neutral vs. ion-induced experiments
Figure 2 (upper panel) shows the measured monomer and dimer concentrations
from a binary experiment at 208 K. The experiment is started when the UV
lights are turned on (at 14:16 UTC). The first stage is conducted in a
neutral environment with the CFHV enabled. At 16:00 UTC (marked by the
dashed vertical line) the electrodes are grounded and galactic cosmic rays
(GCRs) lead to a buildup of ions in the chamber. While the monomer
concentration is not affected significantly by the GCRs because the small
ion concentration is generally only on the order of a couple of thousand
(Franchin et al., 2015) and the HSO4- ions are not efficiently
being detected by the CIMS (Rondo et al., 2014), the dimer concentration is.
For the neutral conditions the dimer signal above background is due to
neutral (H2SO4)2. During the GCR stage of the experiment, the
dimer signal gradually increases. This could be due to either neutral dimers
being charged in the CIMS or charged dimer ions forming within the CLOUD
chamber.
Unfortunately, there was no ion filter installed in the CIMS sampling line
during CLOUD5 to eliminate the ion contribution to the CIMS signal. However,
evidence exists that the additional signal during GCR conditions is caused
by a buildup of chamber ions rather than formation of additional neutral
dimers during the ion-induced experiments. Recently, it was reported that
HSO4- ions clustered to large oxidized organic molecules (OxOrg)
can be efficiently detected by the CIMS (Rondo et al., 2014).
When both ions and sufficient H2SO4 are present in the chamber,
HSO4-(H2SO4)n with n≥1 will be formed (Eisele
et al., 2006); these ions are apparently being detected by the CIMS as
dimers to some extent. The light HSO4- ions will be rapidly lost
to the walls of the CIMS sampling line, whereas the larger
HSO4-(H2SO4)n≥1 ions will have a lower loss
rate. Therefore, the larger ions tend to have a higher chance to survive the
transport to the CIMS, where they can be eventually detected as artifact
dimers. If this were the case, some of the observed dimer signal from the
GCR stage in Fig. 2 might not be related to the neutral dimers, and should
be discarded.
The atmospheric pressure interface time-of-flight (APi-TOF; Junninen et al.,
2010) mass spectrometer measured the ion composition during the first part
of the CLOUD5 campaign. Figure 2 (lower panel) shows the
HSO4-(H2SO4)n (n=0 to 8) cluster ion signals
during a binary beam experiment at 223 K. In addition, the apparent CIMS
dimer concentration is displayed. The dimer signal is well correlated with
the HSO4-(H2SO4)n signal for n≥5 (e.g.,
Pearson's correlation coefficient between the dimer and the
HSO4-(H2SO4)5 signal is 0.93), indicating that the
dimer signal due to ions arises mostly from larger cluster ions (hexamer and
larger) which, at least partly, fragment to HSO4-(H2SO4)
before they reach the mass spectrometer. It is, however, not clear whether
only the relatively large charged clusters fragment, or if only these large
clusters reach the mass spectrometer due to an enhanced transmission. The
study by Rondo et al. (2014) indicates that ions need to be relatively heavy
(or have a low enough electrical mobility) in order to reach the CIMS ion
drift region. It is, therefore, also possible that ions that are smaller
than the hexamer could, in principle, contribute to the CIMS dimer channel,
but since they are not efficiently reaching the CIMS, their contribution is
negligible. Either possibility would lead to the large charged clusters
contributing to the dimer signal (Fig. 2).
Upper panel: observed ion effect on CIMS sulfuric acid dimer
(m/z 195) measurements at 223 K. The first part of the experiment is under
neutral conditions, whereas the second part is a GCR run with ions present in the
chamber. The increase in the dimer signal during the GCR stage is due to
ions detected by the CIMS and not due to neutral dimers. Lower panel:
comparison between the APi-TOF signals and the CIMS dimer measurements for a
different ion-induced experiment at 223 K. The ion clusters (S6, i.e.,
HSO4-(H2SO4)5 and larger) show a clear correlation
with the apparent dimer signal, which indicates that fragmented cluster ions
contribute to the CIMS dimer measurement (Pearson's correlation coefficient
between dimer and S6 is 0.93).
Another interesting observation is that the dimer signal comes mainly from
the neutral clusters when ammonia is present in the chamber. Recent
publications on the ternary ammonia system investigated at CLOUD have shown that
the APi-TOF detects HSO4-(H2SO4)n(NH3)m
with m≥1 when n≥3 (Kirkby et al., 2011; Schobesberger et al.,
2015). Our findings support the observation that the mixed sulfuric acid
ammonia ion clusters are more stable than pure sulfuric acid clusters
because they do not seem to fragment to the same extent. As a consequence of
the observations discussed in this section, only neutral experiments were
considered for the evaluation of the dimer evaporation rates in the binary
system.
Effect of fragmentation during neutral experiments
In the binary system, large cluster ions can fragment and contribute to the
measured dimer signal. In this section the maximum error due to the observed
fragmentation described in Sect. 3.1 is estimated. For neutral cluster
measurements, this process is, however, different from that described in the
previous section. Under ion-induced conditions the ions are directly sampled
from the CLOUD chamber. Therefore, a relatively low concentration of cluster
ions can contribute significantly to the dimer signal because the ionization
process in the CIMS drift tube is not needed for their detection.
In a worst-case scenario all cluster ions larger than the dimer (originating
from neutral clusters after ionization) would fragment and yield one
HSO4-(H2SO4), thereby increasing the apparent dimer
concentration. It is important to note that even a very large charged
cluster could only yield one HSO4-(H2SO4) because the
clusters carry only one negative charge. The cluster concentrations (dimer
and larger) can be calculated using the SAWNUC model. In any case, the
cluster concentrations decrease with increasing size, so the potential
contribution decreases with increasing cluster size. Figure 3 provides an
upper-bound estimate of the magnitude of this effect. In an example
calculation for a temperature of 223 K, a sulfuric acid monomer
concentration of 2×107 cm-3 and dimer and trimer evaporation
rates from the literature (Hanson and Lovejoy, 2006) are used, while all
other evaporation rates are set to zero. The model yields concentrations for
the neutral dimer and all larger clusters. Summing the concentrations from
the dimer up to a certain cluster size, and normalizing the sum with the
dimer concentration, yields the results shown in Fig. 3, which indicate that
the contribution of the larger clusters to the dimer is, at most, a factor
of 3 larger than that of the dimers, even as one considers the contributions
from very large clusters. Again, in this estimation it is considered that
even a large fragmented cluster can contribute only one
HSO4-(H2SO4) because all clusters are singly charged.
For this reason the cluster number concentrations are summed and not the
number of neutral dimers in a cluster.
Simulated summed cluster concentrations at 223 K and 20 % RH
(k2,e=5.8 s-1 and k3,e=0.056 s-1; all larger
evaporation rates are zero). The cluster concentrations are summed up to a
certain number of sulfuric acid molecules in a cluster starting with the
dimer concentration. The values on the x axis indicate the number of sulfuric
acid molecules in the largest cluster considered in the summation. All
concentrations are normalized by the dimer concentration (at 2×107 cm-3 monomer concentration).
The estimated factor in this section is an upper limit. It is unlikely that
all clusters will fragment, or that they always yield
HSO4-(H2SO4) as the product. Instead, HSO4-
might result from the fragmentation, because, not being an equilibrium
process, fragmentation would not always yield the most stable cluster
configuration. Moreover, since evaporation cools the cluster, evaporation of
neutral sulfuric acid molecules from the largest clusters may be incomplete.
Another argument why the data from Fig. 3 provide an upper estimate is due
to the reduction in transmission efficiency for the components of the mass
spectrometer that is generally observed with increasing mass. In summary,
the maximum effect of fragmentation is very likely on the order of a factor
of 2, or lower (see also error discussion in Sect. 3.8).
Binary
(H2SO4–H2O)
dimer concentrations and evaporation rates
Figure 4 shows the steady-state dimer concentrations as a function of the
monomer concentrations at a temperature of 208 K. The data are segregated
into binary neutral (solid circles) and ion-induced (open triangles). The
color code indicates the relative humidity (RH) over supercooled water. The
black lines show the results from the SAWNUC model assuming four different
dimer evaporation rates between 0 and 1 s-1 (indicated in the legend of
the figure). Comparison between the modeled curves and the experimental data
gives an indication of the magnitude of the dimer evaporation rates, but the
actual values are calculated with Eq. (5) and will be discussed in the
context of Fig. 7. While the model curves for 0.1 and 1 s-1 are
straight lines with a slope of 2 on a log–log plot, the lines for 0 and
0.01 s-1 show a pronounced curvature with a slope that approaches a
value of one for the high monomer and dimer concentrations. This curvature
indicates that a full model calculation would be required in order to derive
even smaller evaporation rates than those observed in this study. If the
evaporation rate is comparable to the other loss rates, these mechanisms
need to be taken into account when estimating k2,e. Only when the
evaporation rate dominates dimer loss over the full range of
[H2SO4] can other mechanisms be neglected. The neutral binary data
in Fig. 4 indicate that the dimer evaporation rate varies between 0.2 s-1 for ∼ 12 % RH and 0.04 s-1 for 58 % RH at
208 K. Therefore, relative humidity has a relatively strong effect, one that
is more strongly pronounced than the higher-temperature (232 to 255 K) data
of Hanson and Lovejoy (2006) suggest (see discussion below). Our
signal-to-noise ratio was, however, not high enough to quantify the dimer at
temperatures above 223 K for direct comparison. Figure 4 also gives an idea
of the magnitude of the ion effect on the CIMS dimer measurements (open
triangles). As discussed in Sect. 3.1, the ion-induced binary experiments
show systematically higher apparent dimer concentrations than do the neutral
experiments. For this reason they are discarded when deriving dimer
evaporation rates.
Sulfuric acid dimer concentration as a function of the monomer
concentration at 208 K for binary conditions. The full circles are from
neutral experiments obtained at steady state and the open triangles from
ion-induced experiments. The black lines indicate the modeled dimer
concentration for a given dimer evaporation rate with all other cluster
evaporation rates set to zero. The color code indicates the relative
humidity over supercooled water.
Figure 5 shows the monomer and dimer data for a temperature of 223 K. Again,
the data show a pronounced influence of relative humidity. The dimer
evaporation rate is approximately 8 s-1 at 12 % RH and 0.6 s-1
at 50 % RH. The ion enhancement effect can be divided into two regimes:
one in which it seems to be limited by the availability of sulfuric acid,
and a second one in which it is limited by the availability of ions and
reaches a plateau where the dimer signal ceases to increase with the
sulfuric acid monomer concentration (open triangles).
Same as Fig. 4 but for a temperature of 223 K.
The evaporation rates derived herein can be compared with the rates reported
by Hanson and Lovejoy (2006) after some unit conversions. The equilibrium
constant Keq for sulfuric acid dimer formation from monomers in the
presence of water has been reported as (Hanson and Lovejoy, 2006)
Keq=p2p12=1Pa⋅expAT-B,
with A= (9210 ± 930) K and B=31.4 ± 3.9 for the temperature,
232≤T≤255 K, and a relative humidity of 20 % over supercooled
water. Given the reported values for A and B, the thermodynamic properties are
estimated to be dH=-18.3 ± 1.8 kcal mol-1 and dS=-39.5 ± 7.8 cal mol-1 K-1 (Hanson and Lovejoy, 2006).
Equation (7) provides the equilibrium constant in units of Pa-1 since
the partial pressures p of the monomers and dimers are used. In order to
calculate evaporation rates it is necessary to convert the equilibrium
constant to units of cm3 and to further apply the relationship between
equilibrium constant, evaporation rate, and collision constant for the
dimers (Ortega et al., 2012), leading to
ke=0.5⋅G1,1⋅K1,1kB⋅T⋅106⋅Keq,
where kB is the Boltzmann constant. We converted equilibrium constants
reported by Hanson and Lovejoy (2006) to evaporation rates using Eq. (8). Hanson and Lovejoy (2006) determined evaporation rates at 20 %
RH, while our measurements were made at different RHs. Because RH has a
significant influence on the dimer evaporation, further analysis is necessary
to make the two data sets comparable.
Dimer evaporation rate as a function of the RH for two different
temperatures (208 and 223 K). Power law fit curves are shown and the slopes
p are indicated in the figure legend.
Figure 6 shows the evaluated dimer evaporation rates as a function of the
relative humidity (with respect to supercooled water) for two different
temperatures (208 and 223 K). The rates from this study are based on the
data shown in Figs. 4 and 5 and Eq. (5). The data were fitted by
simple power law fits, and the slopes of p=-1 (at 208 K) and p=-1.6 (at
223 K) indicate that the evaporation rates decrease significantly with
increasing RH. Qualitatively this is in agreement with a previous experiment
(Hanson and Lovejoy, 2006) and quantum chemical calculations (Ding et al.,
2003). However, Hanson and Lovejoy (2006) reported p=-0.5, where the
exponent p has an uncertainty of ±100 %. Our data indicate a
somewhat stronger influence of RH on the evaporation rates, which also seems
to be dependent on temperature.
The evaporation rates from Fig. 6 with RH between 10 and 30 % were
interpolated to 20 % RH using the reported slopes. Figure 7 shows the data
from this study and from Hanson and Lovejoy (2006). Fitting the combined
data set for 20 % RH gives the following formulation for the equilibrium
constant
Keq=1Pa⋅exp10 109±609KT-35.03±2.61.
Comparison of the sulfuric acid dimer evaporation rates from this
study (circles) and from the literature (triangles; see Hanson and Lovejoy,
2006) as a function of temperature. The color code indicates the relative
humidity during the experiments. Diamond symbols represent the data from
this study scaled to 20 % RH. The solid line shows a best fit through the
data with the thermodynamic properties dH=-20.1 ± 1.2 kcal
mol-1 and dS=-46.7 ± 5.2 cal mol-1 K-1 at 20 % RH.
The black line in Fig. 7 shows the dimer evaporation rates derived from
Eq. (9). The uncertainties in Eq. (9) are based on 95 %
confidence intervals. Overall, the two data sets are, within errors,
consistent with one another, and yield dH=-20.1 ± 1.2 kcal mol-1 and dS=-46.7 ± 5.2 cal mol-1 K-1. We caution
that in this study the assumption is made that dH does not vary with
temperature; generally this variation should, however, be small. These data
are slightly different than what has been reported by Hanson and Lovejoy
(2006). However, our data agree within errors with results from quantum
chemical calculations, taking into account the effect of water vapor (Ding
et al., 2003). According to measurements by Hanson and Eisele (2000) and
quantum chemical calculations (Temelso et al., 2012; Henschel et al., 2014),
the sulfuric acid monomer and dimer can contain water molecules. Therefore,
the data from Ding et al. (2003) taking into account the effect of water
vapor are relevant for this study. Table 2 shows a comparison between
different studies dealing with the sulfuric acid dimer formation. Regarding
the effect of water vapor, it should be noted that our experimentally
determined evaporation rates represent an average for dimers containing
different numbers of water molecules. The exact distribution of water
associated with the dimers will be a function of relative humidity and
temperature, which cannot be taken into account explicitly in this study.
The data by Ding et al. (2003) suggest that almost all sulfuric acid dimers
contain four water molecules under the conditions of this study. Therefore,
there exist three possibilities for a sulfuric acid monomer
(H2SO4(H2O)0-2) to dissociate from the dimer with four
water molecules. These reactions are listed in the last three rows of Table 2, where the evaporation rates for the monomer of sulfuric acid without
water have the highest values. These are about two orders of magnitude
faster than the experimentally determined values. One should note, however,
that the data by Temelso et al. (2012) indicate a different hydrate
distribution and this will have a significant influence on the resulting
effective dimer evaporation rate.
Thermodynamic properties (dH and dS) and evaporation rates of the
sulfuric acid dimer from this study and from the literature.
Study
dH(kcal mol-1)
dS(cal mol-1 K-1)
k2,e at 208 K (s-1)
k2,e at 223 K (s-1)
This study (20 % RH)
-20.1 ± 1.2
-46.7 ± 5.2
0.15
3.9
Hanson and Lovejoy (20 % RH)
-18.3 ± 1.8
-39.5 ± 7.8
0.32
6.0
(H2SO4)(H2O) + (H2SO4)(H2O)*
-17.8
-48.3
89.3
1550
(H2SO4)(H2O)2+ (H2SO4)(H2O)*
-21.1
-51.7
0.17
5.0
(H2SO4)+ (H2SO4)(H2O)4*
-22.1
-47.3
1.6 × 10-3
5.7 × 10-2
(H2SO4)(H2O) + (H2SO4)(H2O)3*
-22.8
-45.6
1.3 × 10-4
5.0 × 10-3
(H2SO4)(H2O)2+ (H2SO4)(H2O)2*
-25.6
-55.7
2.4 × 10-5
1.5 × 10-3
* Literature data from Ding et al. (2003).
Neutral cluster measurement with CI-APi-TOF in the binary
system
During the CLOUD7 campaign, experiments were conducted at ∼ 206 K under binary conditions. In addition to the CIMS, two CI-APi-TOFs were
deployed (Jokinen et al., 2012; Kürten et al., 2014). The two
instruments are labeled CI-APi-TOF-UFRA (instrument from the University of
Frankfurt) and CI-APi-TOF-UHEL (instrument from the University of Helsinki).
In contrast to the CIMS used during CLOUD5, the sampling lines of the
CI-APi-TOFs were not temperature-controlled. Therefore, dimer evaporation
was likely more pronounced. For this reason, we did not attempt to quantify
the dimer evaporation rate, although the dimer signals are quantitatively
consistent with the data shown in Fig. 3. However, the CI-APi-TOFs have a
much wider mass range than the CIMS, i.e., a maximum of approximately 2000 Th. This increased mass range allowed larger clusters to be measured;
indeed, neutral sulfuric acid clusters containing up to 10 sulfuric acid
molecules, i.e., HSO4-(H2SO4)n (n from 0 to 9), were
detected (Fig. 8). Eisele and Hanson (2000) previously reported detection of
neutral clusters containing up to eight sulfuric acid molecules in a
flow-tube experiment using a quadrupole mass spectrometer. However, their
measurements were conducted at much higher sulfuric acid concentrations
(∼ 109 cm-3), whereas in this study the conditions
were atmospherically more relevant (sulfuric acid monomer concentration
∼ 1.7×107 cm-3). Therefore, the data presented in
the following indicate that atmospheric binary nucleation should be
directly observable at low temperature, e.g., during aircraft measurements.
Water molecules associated with the clusters were not detected with the
CI-APi-TOFs; these were most likely evaporated during ion transfer into the
high-vacuum section of the instruments. No ammonia was detected in any of
the clusters either, even though ammonia can, in principle, be observed with
a similar instrument that measures charged clusters (Kirkby et al., 2011),
so it can be concluded that the experiment was, indeed, under pure binary
conditions.
Cluster measurements for the binary system at 206 K and an RH close
to 100 % over ice measured with two CI-APi-TOFs (UFRA and UHEL
instruments). The upper panel shows the monomer (S1) and the cluster signals
(Si, i≥2) normalized by the nitrate ion signals as a function of time
(1 min time resolution) for the CI-APi-TOF-UFRA. The lower panel shows
the measured steady-state signals as well as expected signals using
different assumptions as function of the cluster size. See text for details.
The upper panel of Fig. 8 shows the time-resolved signals from one of the
CI-APi-TOFs ranging from the monomer (HSO4-, i.e., S1) up to the
decamer (HSO4-(H2SO4)9, i.e., S10); all of these
signals clearly increase following the start of the experiment at 10:02 UTC.
From the time-resolved data, the steady-state signals for the different
clusters were obtained for both instruments (red and blue symbols in Fig. 8,
lower panel). No attempt was made to derive concentrations from the
count-rate signals due to the unknown influence of cluster evaporation
within the sampling line and transmission within the mass spectrometers.
However, the CIMS, which was operated in parallel to the CI-APi-TOFs with
its own dedicated sampling line, yielded a monomer concentration of
1.7×107 cm-3.
Sulfuric acid dimer concentrations as a function of the sulfuric
acid monomer concentration at three different temperatures for the ternary
system involving ammonia (ammonia mixing ratio indicated by the color code).
The colored circles are the measured concentrations. Lines are from model
calculations indicating the expected concentrations for the binary system
(dashed line) and the kinetic limit (solid line). The numbers indicate the
RH (in %) during an experiment. Open colored triangles are the simulated
dimer concentrations using the reaction scheme from Fig. 10. These are
slightly offset to the right in order to improve readability.
For this experiment we calculated the extent to which ion-induced clustering
(IIC) could contribute to the signals. The equations provided by Chen et al. (2012) were used to estimate the maximum contribution from IIC (Fig. 8,
lower panel). The dashed red line indicates what cluster signals would be
expected if all neutral cluster concentrations (dimer and larger) were zero,
and the only cluster ions were formed by addition of H2SO4
monomers to the HSO4- ions within the CIMS drift tube. The large
discrepancy between the observations (red diamonds) and the dashed red line
(it falls off very steeply with increasing cluster size) shows that the
contribution from IIC is negligible. Using SAWNUC together with the dimer
and trimer evaporation rates (from this study and from Hanson and Lovejoy, 2006, respectively) allows us to predict all cluster concentrations and
then calculate the expected signals (black curve). While the expected
signals from the model calculation are substantially higher than the
measured ones from the CI-APi-TOF-UFRA, the shape of the black (modeled) and
the red (measured) curve is very similar. This suggests that cluster
evaporation rates of the trimer and all larger clusters are not high enough
to significantly affect their concentrations at this low temperature. The
slightly steeper slope of the measurements could be due to a decrease in the
detection efficiency as a function of mass of the CI-APi-TOF-UFRA. In this
context it is also important to note that the CI-APi-TOF-UFRA was tuned
differently than in a previous study (Kürten et al., 2014) in which a
relatively steep drop in the sensitivity as a function of mass was observed.
The tuning in this study might have led to a more constant detection
efficiency as a function of mass. The fact that the measured trimer signal
is lower than the tetramer signal is thought to result from fragmentation of
the trimers. Similarly, the hexamer appears to suffer some fragmentation.
The CI-APi-TOF-UHEL was tuned to maximize the signals in the mass range up
to the pentamer. Consequently, in comparison to the other CI-APi-TOF, this
led to substantially higher signals in the mass region up to the pentamer,
with a pronounced local maximum around the tetramer (blue curve in Fig. 8).
However, for the larger masses the signal drops, reaching levels that are
comparable to those from the CI-APi-TOF-UFRA.
Reaction scheme for the sulfuric acid dimer formation in the
ternary system at a low temperature. “A” denotes a sulfuric acid molecule,
and “B” an ammonia molecule. “Monomer” is the sum of the concentration of
the pure sulfuric acid (A) and the sulfuric acid bound to an ammonia (AB).
“Dimer” is the sum of all clusters containing two sulfuric acid molecules
(A2+ A2B + A2B2) and the same applies for the
“trimer” with three sulfuric acid molecules. The arrows indicate the
relevant reactions and whether only collisional growth (single-ended arrow)
or growth as well as evaporation (double-ended arrow) is important. Losses
due to walls, dilution, and coagulation are included in the model but not
indicated. Small numbers represent concentrations for an example calculation
at a temperature of 248 K, a [monomer] of 1×107 cm-3, and a
[NH3] of 2×108 cm-3. See text for details.
Because so many questions remain regarding fragmentation, cluster
quantification, and the effect of evaporation in the sampling line, the
CI-APi-TOF signals are only discussed qualitatively in the present study.
Sulfuric acid dimer concentrations in the ternary
(H2SO4–H2O–NH3)
system
During CLOUD5, ternary nucleation experiments were conducted at temperatures
of 210, 223, and 248 K. The addition of relatively small amounts of ammonia
(mixing ratios below ∼ 10 pptv) led to a significant increase
in the sulfuric acid dimer concentrations compared to the binary system,
confirming the enhancing effect of ammonia on new particle formation (Ball
et al., 1999; Kirkby et al., 2011; Zollner et al., 2012; Jen et al., 2014).
In the presence of NH3, a fraction of the sulfuric acid will be bound
to ammonia. However, we assume that the sulfuric acid monomers and dimers
will still be ionized by the nitrate primary ions at the same rate as the
pure compounds. The ammonia will, however, evaporate very rapidly after the
ionization (Hanson and Eisele, 2002). For this reason it is not possible to
determine directly the fractions of either the sulfuric acid monomer or the
dimer that contains ammonia. Therefore, in the following we assume that the
measured monomer is the sum of the pure sulfuric acid monomer and the
sulfuric acid monomer bound to ammonia; the same assumption is made for the
dimer. It has been suggested that the sensitivity of a nitrate CIMS
regarding the sulfuric acid measurements could be affected by the presence
of ammonia (or other bases like dimethylamine), which cluster with sulfuric
acid (Kurtén et al., 2011; Kupiainen-Määttä et al., 2013).
However, recent measurements at the CLOUD chamber indicate that this is very
likely a minor affect (Rondo et al., 2015).
Figure 9 shows the measured sulfuric acid dimer concentration as a function
of the sulfuric acid monomer concentration for three different temperatures
(210, 223, and 248 K), as well as several ammonia mixing ratios (< ∼ 10 pptv) under ternary conditions. Two limiting cases that
bracket the possible dimer concentrations and the influence of ammonia are
indicated by the solid black line and the dashed black line. The solid black
line shows the case in which all evaporation rates are set to zero in the
SAWNUC model (the kinetic limit); the dashed black line indicates the case
for binary conditions at 40 % RH. It can be seen that, at the lowest
temperature (210 K), the dimer concentrations are close to the expected
concentrations for kinetically limited cluster formation, as has been
previously reported for the ternary sulfuric acid, water, and dimethylamine
system at 278 K (Kürten et al., 2014). The ammonia mixing ratio is
∼ 6 pptv in this case (Fig. 9, upper panel). At 223 K two
different ammonia mixing ratios were investigated. It can clearly be seen
that the dimer concentrations increase with increasing ammonia mixing ratio.
Different ammonia mixing ratios (∼ 2.5 to 8 pptv) were also
studied at 248 K, but in this case the variation in the ammonia
concentration was smaller than for 223 K; therefore, the dimer concentration
variation is also less pronounced. In addition, the relative humidity
changed from experiment to experiment (RH is indicated by the small numbers
written next to the data points); it apparently influenced the dimer
concentration, which is not surprising given the results described in
Sect. 3.3 and those of Hanson and Lovejoy (2006). Our data show that very
small ammonia mixing ratios (pptv range) can strongly enhance dimer
formation under atmospherically relevant sulfuric acid concentrations and
low temperatures.
Acid–base model
In order to better understand what influences the dimer concentration in the
ternary system, we have developed a simple model (Fig. 10). This heuristic
model is motivated by recent studies which have simulated acid–base
nucleation of sulfuric acid, ammonia, and amines with similar methods, i.e.,
without simulating every possible cluster configuration explicitly (Chen et
al., 2012; Paasonen et al., 2012; Jen et al., 2014). Following the notation
of Chen et al. (2012), a sulfuric acid molecule is termed A, while the base
ammonia is termed B. Dimers (A2 or A2B) may form via two different
routes: (a) two sulfuric acid molecules A can collide and form a pure
sulfuric acid dimer (A2), which can further collide with B and form
A2B, or (b) a sulfuric acid molecule can collide with an ammonia
molecule and form an AB cluster, which can further collide with A (or
another AB cluster) to form A2B (or A2B2). The model further
assumes that trimers either can contain solely sulfuric acid (A3) or
are associated with ammonia (A3Bx).
For all larger clusters we make no distinction between pure sulfuric acid
clusters and ammonia-containing clusters. We further assume that the
clusters cannot contain more bases than acids, so reactions like AB + B
are not considered, as the extra base is expected to evaporate much more
rapidly than it can be gained through collisions at the relatively low base
concentrations (Schobesberger et al., 2015).
The model differs somewhat from that used by Chen et al. (2012) and Jen et al. (2014). They considered two separate schemes; in their first scheme,
they assumed that two different dimer versions exist – a volatile dimer
and a less volatile dimer that is formed through collision between the
volatile dimer and a base molecule. The less volatile dimer can form a
trimer or a tetramer (through self-coagulation), both of which are assumed to be
stable. This scheme is similar to pathway (a) described above. Their second
scheme assumes that the sulfuric acid monomer can form a cluster AB, which
can be turned into a stable dimer. This dimer can then form a trimer that is
allowed to evaporate at a rather slow rate (0.4 s-1 at 300 K). Once the
size of the tetramer is reached the cluster is assumed to be stable. Except
for the evaporation rate of the base-containing trimer, this scheme is
identical to route (b) described above. Our approach combines the two
channels because it seems likely that dimers can be formed through the two
different pathways at the same time (Fig. 10), especially when the
temperature is low and the evaporation of A2 is relatively slow. In
addition, we assume that the only base-containing cluster that can still
evaporate at these low temperatures (248 K and colder) is AB. Quantum
chemical calculations (Ortega et al., 2012) and the measurements of Hanson
and Eisele (2002) support the assumption that the cluster containing two
sulfuric acid molecules and one ammonia molecule is stable even at
relatively high temperature (275 K in the Hanson and Eisele, 2002, study).
Furthermore, since the evaporation rate of the base-containing trimer
reported by Chen et al. (2012) is quite small at 300 K (0.4 s-1), we
assume that, at the very low temperatures of this study, this evaporation
rate becomes negligible.
The quantum chemistry data from Ortega et al. (2012) support the assumption
that a trimer containing at least two bases is relatively stable
(evaporation rate below 0.1 s-1 at 300 K). However, it predicts that
the trimer containing only one ammonia molecule has a high evaporation rate
regarding an acid molecule (∼ 1000 s-1 at 300 K);
additional ammonia in the trimer will lower the evaporation rates. For this
reason the trimer concentration will strongly depend on the ammonia
concentration, which controls the cluster distribution. Therefore, the Chen
et al. (2012) value can be regarded as a best estimate for the overall
trimer evaporation rate for their experimental conditions. Herb et al. (2011) also simulated the effect that one water molecule has on the acid
evaporation rate from
(H2SO4)3(NH3)1(H2O)0,1 clusters. While
the water molecule lowers the evaporation rate, the absolute evaporation rate
is higher (2.9×104 s-1 at 300 K) than for the Ortega et al. (2012)
data.
Thermodynamics of the H2SO4⚫NH3 cluster
Under these assumptions, the model of Fig. 10 was used to probe the kinetics
using the measured sulfuric acid monomer, and ammonia concentrations, along
with the dimer (A2) and trimer (A3) evaporation rates as a
function of relative humidity and temperature from this study and from
Hanson and Lovejoy (2006). The only free parameter in the model is then the
evaporation rate of AB; we adjusted this until the modeled dimer
concentration matched the measured one under steady-state conditions. From
the evaporation rates at the different temperatures the thermodynamics (dH
and dS) of the cluster AB were retrieved from a least-squares linear fit
(logarithm of the equilibrium constant vs. the inverse temperature), which
yields dH=-16.1±0.6 kcal mol-1 and dS=-26.4 ± 2.6 cal mol-1 K-1 for H2SO4⚫NH3.
Unfortunately, the number of data points used to derive the dH and dS values
is quite small. At 210 K the measured dimer concentrations are very close to
the kinetic limit estimation, so the evaporation rates must be very low.
This indicates that small variations in the monomer and dimer concentration
can lead to a large variation in the evaporation rate of AB. These data
points were, therefore, neglected. On the other hand, the effect of the
relative humidity on the evaporation rates of ammonia-containing clusters is
not known, so only those experiments that were conducted at similar RH,
i.e., ∼ 25 %, were considered.
Comparison between measured cluster concentrations by Hanson and
Eisele (2002) and simulated cluster concentrations using the acid–base model
described in Sect. 3.6.
Cluster
Hanson and Eisele (2002)
Acid–base model, this study
N2 (total dimer)
1.1×107 cm-3
7.0×106 cm-3 (-36 %)
N3 (total trimer)
6.5×106 cm-3
5.6×106 cm-3 (-14 %)
N4 (total tetramer)
6.6×106 cm-3
4.7×106 cm-3 (-29 %)
N5 (total pentamer)
∼ 4×106 cm-3
4.1×106 cm-3
Thermodynamic properties (dH and dS) and evaporation rates of the
H2SO4⚫NH3 cluster from this study and from the
literature.
Study
dH
dS
ke at
ke at
ke at
(kcal mol-1)
(cal mol-1 K-1)
210 K (s-1)
248 K (s-1)
300 K (s-1)
This studya
-16.1 ± 0.6
-26.4 ± 2.6
0.11
36
9.8 × 103
Torpo et al. (2007)b
-15.81
-28.57
0.63
200
4.7 × 104
Nadykto and Yu (2007)b
-16.72
-30.01
0.15
64
2.1 × 104
Nadykto and Yu (2007), H2SO4(H2O) + NH3
-15.91
-30.23
1.1
370
9.2 × 104
Nadykto and Yu (2007), H2SO4(H2O)2+ NH3
-15.27
-30.49
6.0
1.5 × 103
3.1 × 105
Nadykto and Yu (2007), H2SO4(H2O)3+ NH3
-15.44
-32.30
10
2.7 × 103
5.8 × 105
Ortega et al. (2012)b
-16.00
-28.14
0.32
107
2.8 × 104
Chon et al. (2014)b
-15.43
-29.63
2.7
720
1.5 × 105
Jen et al. (2014)c
–
–
–
–
400 to 2500
a Experiments conducted at ∼ 25 % RH (with
respect to supercooled water). b No effect of water vapor considered.
c Experiment conducted at ∼ 30 % RH.
Figure 9 also shows the calculated dimer concentrations using the model with
the evaporation rate of AB inferred using the derived thermodynamics (open
colored triangles). The error bars reflect a variation in the evaporation
rate for H2SO4⚫NH3 according to the uncertainties
of the dH and dS values. The lowest dimer concentrations result if the error
of dH is implemented in the positive direction and the error of dS in the
negative direction. The highest dimer concentrations result by reversing the
signs in the error calculation. The good agreement between measured and
modeled values indicates that the model successfully reproduces the dimer
concentrations over a wide range of conditions. Furthermore, we have also
simulated the experiments of Hanson and Eisele (2002) for the ternary system
involving ammonia, who used a sulfuric acid concentration of
1.9×109 cm-3 and an ammonia concentration of 3.8×109 cm-3 at a
temperature of 265 K and an RH of ∼ 10 %. Our calculated
dimer concentration agrees with their measured concentration within about
40 %. Table 3 shows a comparison with the cluster concentrations (dimer to
pentamer) measured by Hanson and Eisele (2002) and the ones from this study
using the acid–base model described above.
Table 4 compares our dH and dS values as well as the corresponding evaporation
rates for selected temperatures with other data obtained from quantum
chemical calculations (Torpo et al., 2007; Nadykto and Yu, 2007; Ortega et
al., 2012; Chon et al., 2014) and from one flow tube experiment (Jen et al.,
2014). Overall, the agreement is good. However, it is difficult to take into
account the effect the model assumptions have on the outcome of the values
from our study. In addition, only a small number of data points have been
taken into account in this study.
One also needs to keep in mind that the cluster formation was observed at
∼ 25 % RH (with respect to supercooled water) in this study,
while most of the theoretical studies did not take into account the effect
of water except the one by Nadykto and Yu (2007). Their data suggest that
the evaporation rate of H2SO4⚫NH3⚫(H2O)x increases when the number of associated water molecules
increase. The study by Henschel et al. (2014) indicates that about one water
molecule is attached for the RH relevant to this study. However, Henschel et al. (2014) reported their results only for a temperature of 298 K, whereas
the temperature of this study is 248 K and lower. Whether the evaporation
rate is increasing with increasing RH cannot be concluded from our data;
however, one needs to keep in mind that, similar to the dimer in the binary
system, the reported evaporation rates and thermodynamic data for the
H2SO4⚫NH3 represent average values that can
include clusters with attached water molecules.
The comparison in Table 4 also lists the experimental study by Jen et
al. (2014), who determined the evaporation rate of H2SO4⚫NH3 at ∼ 300 K from a transient version of their second
scheme (formation of dimers only via AB; see above). The extrapolated value
from the present study is, however, in relatively good agreement with their
value. The somewhat lower evaporation rate of Jen et al. (2014) could be
explained by the fact that they did not consider the formation of dimers by
self-coagulation of A. Furthermore, they assumed that the trimer has an
evaporation rate of 0.4 s-1. Both these assumptions require a slower
evaporation rate for AB than our study suggests to explain the measured
dimer concentrations at a given monomer and base concentration.
Overall, our measurements in the ternary system yield values of the
thermodynamic properties of the H2SO4⚫NH3 cluster
that are in rather good agreement with the results from quantum chemical
calculations. However, since the number of data points is limited, the
uncertainty is rather high.
Uncertainties
The error bars shown in Figs. 4 and 5 include the standard variation in the
individual data points and a 30 % (50 %) systematic uncertainty in the
monomer (dimer) concentration. The two error components are added together
in quadrature. The systematic errors are estimated based on the
uncertainties in the calibration coefficient C for the monomer. Due to the
higher uncertainty of the sampling losses for the dimer and the uncertainty
of the transmission correction factor (Sect. 2.3), a somewhat higher
uncertainty has been chosen in comparison to the monomer. The error bars in
Fig. 7 are obtained when using Gaussian error propagation on Eq. (5)
for the monomer and the dimer concentration.
In addition to these errors, the effects of evaporation of the dimer in the
sampling line (Sect. 2.6) and fragmentation (Sect. 3.2) have been
discussed above. Each of these effects is very likely on the order of a
factor of 2 or smaller. These processes probably influence all of the
dimer data to some extent. However, these errors work in opposite
directions: evaporation will lead to a reduction of the dimer concentration,
while fragmentation of larger clusters will tend to increase the apparent
concentration. Therefore, the two effects partially compensate for each other,
so they were not taken into account in the calculation of the error bars.
One additional uncertainty is introduced by the assumption that the CIMS
detection efficiency is independent of temperature. The study of Viggiano et al. (1997) indicates that the collision rate between nitrate primary ions
and sulfuric acid is only a weak function of temperature between 200 and
300 K. Therefore, we expect that temperature only has a small effect on the
sulfuric acid concentrations.
The exact values of dimer evaporation rates depend on the choice of
G1,1⋅K1,1, i.e., on the overall collision rate between
two neutral dimers, and is therefore subject to an additional uncertainty
because this value is based on theoretical calculations. However, the
thermodynamic data derived in this study do not depend on the value of
G1,1⋅K1,1 because both the data from this study and the
one from Hanson and Lovejoy (2006) in Fig. 7 were calculated using the same
factors. Therefore, when deriving dH and dS, the collision rate cancels out in
the calculations (see Eqs. 5 and 8).
In contrast to the exact value of G1,1⋅K1,1 the
charged–neutral collision rate k21 between HSO4- and
H2SO4 is important because its value scales the dimer
concentrations and evaporation rates from this study while leaving the data
from Hanson and Lovejoy (2006) unaffected. The reported value of
8×10-10 cm3 s-1 for k21 from Zhao et al. (2010)
suggests that this charged–neutral reaction is not proceeding at the
collision limit (value of ∼ 2×10-9 cm3 s-1).
When using the faster reaction rate for the charged–neutral collision limit,
some of the dimer concentrations would exceed the kinetic limit (see Fig. 9,
upper panel) because all dimer concentrations would need to be scaled up by
a factor of 2.5; therefore the faster rate seems to be implausible. However,
using the upper limit for the collision rate results in dH=-23.0 ± 1.6 kcal mol-1 and dS=-58.5 ± 6.9 cal mol-1 K-1.
The estimates of the thermodynamic properties of the
H2SO4⚫NH3 cluster rely on the assumptions made in
the model (Sect. 3.6). One of the important assumptions made is that the
base-containing trimer and tetramer do not evaporate significantly. The data
of Ortega et al. (2012) suggest that the evaporation rates of the
A3B1 and the A4B1 clusters are not negligible, even at
temperatures at and below 248 K. However, the presence of further ammonia
molecules in the trimer and tetramer can lower the evaporation rates and
water should have a similar effect (Ortega et al., 2012; Herb et al., 2011).
In contrast, the base-containing dimer (A2B) has a very small
evaporation rate. No experimental data have been found that support the
relatively high evaporation rates of the base-containing trimer and
tetramer. Instead, the study by Hanson and Eisele (2002) concluded that the
critical cluster in the H2SO4–H2O–NH3 system very likely
contains two sulfuric acid molecules and one ammonia molecule at
temperatures up to 275 K. In addition, an evaporation rate of 0.4 s-1
for the base-containing trimer could explain observed atmospheric nucleation
rates at relatively warm temperatures of 300 K (Chen et al., 2012). This
evaporation rate should decrease further at lower temperatures. Significant
uncertainties remain regarding the evaporation rates of these clusters;
further experiments will be needed to reduce these in the future.
Summary and conclusions
A chemical ionization mass spectrometer (CIMS) was used to measure the
concentrations of the neutral sulfuric acid monomer and dimer during
nucleation experiments at the CLOUD chamber. These experiments were
conducted at temperatures as low as 208 K, making them relevant to
conditions in the free troposphere. Both the binary
(H2SO4–H2O) system and the ternary system involving ammonia
(H2SO4–H2O–NH3) were investigated.
Comparison of neutral and ion-induced nucleation experiments indicates that
the CIMS detected a significant number of fragmented ion clusters. This
confirms the so called “ion effect” on the CIMS measurements that was
recently described by Rondo et al. (2014). However, while Rondo et al. (2014) observed that fragmented HSO4-⚫OxOrg clusters
contributed to the CIMS sulfuric acid monomer measurement, we observed a
similar effect for the CIMS sulfuric acid dimer measurement (m/z 195).
Interestingly, the ion effect on the CIMS dimers was almost absent as soon
as ammonia was present in the CLOUD chamber. This is consistent with the
observation that ammonia stabilizes sulfuric acid clusters and thereby
enhances nucleation (Kirkby et al., 2011; Schobesberger et al., 2015).
From the measured monomer and dimer signals dimer evaporation rates were
derived and compared to previous flow tube measurements made by Hanson and
Lovejoy (2006) for the binary system. Their measurements were performed over
a temperature range of 232 to 255 K. The data from the present study were
obtained at lower temperatures, 208 and 223 K. Together, the two data sets
yield a revised version of the Hanson and Lovejoy (2006) formulation for the
dimer equilibrium constant at 20 % RH with dH=-20.1 ± 1.2 kcal mol-1 and dS=-46.7 ± 5.2 cal mol-1 K-1. This result
is obtained when assuming that the evaporation of larger sulfuric acid
clusters (trimer and larger) does not contribute significantly to the dimer
concentration, which is the case for the conditions of this study. Due to
the wide temperature range (208 to 255 K) covered by the two data sets, this
new estimate provides a high degree of confidence when being used at the
very low temperatures where binary nucleation can be efficient. Regarding
the formation of dimers in the binary system Hanson and Lovejoy (2006)
stated that an increase in the relative humidity leads to an increase in the
dimer equilibrium constant (Kp ∼ RHp) with a power
dependency of p between 0 and 1. The best estimate for the power dependency
was reported to be 0.5 (Hanson and Lovejoy, 2006). Our data indicate that
the exponent is around 1 at 208 K and around 1.6 at 223 K, i.e., at the
upper end of what has been previously assumed.
The ternary experiments involving ammonia
(H2SO4–H2O–NH3) showed that the addition of very small
amounts of ammonia (in the pptv range) strongly enhances the sulfuric acid
dimer concentration. The dimer concentrations are systematically higher than
those for the binary system at a given temperature and sulfuric acid monomer
concentration. Furthermore, they increase with increasing ammonia mixing
ratio. This confirms previous suggestions that ammonia acts as a stabilizing
agent, even for the very small sulfuric acid clusters. In contrast to the
previous experiments, the present results were obtained at atmospherically
relevant concentrations of sulfuric acid and ammonia, and at low
temperature. For the first time the thermodynamics of the
H2SO4⚫NH3 cluster were experimentally investigated
from measurements of the monomer and the dimer. The measurements were made
at temperatures of 210, 223, and 248 K, with ammonia mixing ratios below
∼ 10 pptv. Using a revised version of a simple conceptual
model first proposed by Chen et al. (2012) we were able to derive the
thermodynamic properties of the H2SO4⚫NH3 cluster.
The obtained values of dH=-16.1 ± 0.6 kcal mol-1 and dS=-26.4 ± 2.6 cal mol-1 K-1 are in good agreement with results
from quantum chemical calculations. Using the proposed model with the
evaporation rate of the H2SO4⚫NH3 cluster as a
fitting parameter, the measured dimer concentrations in the ternary system
can be reproduced with a high accuracy for the conditions of this study. A
previous study suggested that the (H2SO4)2⚫NH3 cluster is thermodynamically stable (Hanson and Eisele, 2002). With
this observation, the model can be used to calculate nucleation rates in the
ternary system, which relies on experimentally determined thermochemical
data and on the assumptions that ammonia-containing trimers and tetramers
have insignificant evaporation rates for the conditions of this study.
Finally, large neutral sulfuric acid clusters containing as many as 10
sulfuric acid molecules were observed for the binary system at 206 K. These
clusters were measured with two chemical ionization–atmospheric pressure
interface time-of-flight (CI-APi-TOF) mass spectrometers. Since these
measurements were not made with a temperature-controlled sampling line, the
absolute determination of the cluster concentrations was not attempted.
However, the signals are consistent with the assumption that cluster growth
is essentially kinetically controlled for all of the observed clusters above
the dimer. The observation of these large clusters at the upper end of
atmospherically relevant sulfuric acid monomer concentration of
∼ 1.7×107 cm-3 shows that observation of nucleating
clusters in the atmosphere should be feasible. In the future, aircraft
operation or measurements at high-altitude stations using CI-APi-TOF could
provide insight into the importance of binary vs. ternary ammonia nucleation
in the free troposphere.