ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus GmbHGöttingen, Germany10.5194/acp-15-6305-2015Connecting the solubility and CCN activation of complex organic
aerosols: a theoretical study using solubility distributionsRiipinenI.ilona.riipinen@aces.su.seRastakN.PandisS. N.Department of Environmental Science and Analytical Chemistry, Stockholm University, Stockholm, SwedenCenter of Atmospheric Particle Studies, Carnegie Mellon University, Pittsburgh, PA, USADepartment of Chemical Engineering, University of Patras, Patras, GreeceI. Riipinen (ilona.riipinen@aces.su.se)10June201515116305632226October201417November201415April201511May2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/15/6305/2015/acp-15-6305-2015.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/15/6305/2015/acp-15-6305-2015.pdf
We present a theoretical study investigating the cloud activation of
multicomponent organic particles. We modeled these complex mixtures using
solubility distributions (analogous to volatility distributions in the VBS,
i.e., volatility basis set, approach), describing the mixture as a set of
surrogate compounds with varying water solubilities in a given range. We
conducted Köhler theory calculations for 144 different mixtures with
varying solubility range, number of components, assumption about the organic
mixture thermodynamics and the shape of the solubility distribution, yielding
approximately 6000 unique cloud condensation nucleus (CCN)-activation points.
The results from these comprehensive calculations were compared to three
simplifying assumptions about organic aerosol solubility: (1) complete
dissolution at the point of activation; (2) combining the aerosol solubility
with the molar mass and density into a single effective hygroscopicity
parameter κ; and (3) assuming a fixed water-soluble fraction
εeff. The complete dissolution was able to reproduce
the activation points with a reasonable accuracy only when the majority
(70–80 %) of the material was dissolved at the point of activation. The
single-parameter representations of complex mixture solubility were confirmed
to be powerful semi-empirical tools for representing the CCN activation of
organic aerosol, predicting the activation diameter within 10 % in most
of the studied supersaturations. Depending mostly on the condensed-phase
interactions between the organic molecules, material with solubilities larger
than about 0.1–100 g L-1 could be treated as soluble in the CCN
activation process over atmospherically relevant particle dry diameters and
supersaturations. Our results indicate that understanding the details of the
solubility distribution in the range of 0.1–100 g L-1 is thus
critical for capturing the CCN activation, while resolution outside this
solubility range will probably not add much information except in some
special cases. The connections of these results to the previous observations
of the CCN activation and the molecular properties of complex organic mixture
aerosols are discussed. The presented results help unravel the mechanistic
reasons behind observations of hygroscopic growth and CCN activation of
atmospheric secondary organic aerosol (SOA) particles. The proposed
solubility distribution framework is a promising tool for modeling the
interlinkages between atmospheric aging, volatility and water uptake of
atmospheric organic aerosol.
Introduction
Interactions of atmospheric aerosol particles with ambient water vapor
determine to a large extent the influence that aerosols have on climate. On
one hand, the water content of aerosol particles at atmospheric relative
humidity (RH) below 100 % contributes significantly to the direct effect
they have on the global radiative balance (Seinfeld and Pandis, 2006; Petters
and Kreidenweis, 2007; Swietlicki et al., 2008; Zieger et al., 2011; Rastak
et al., 2014). On the other hand, the water affinity of aerosol constituents,
together with their dry size, defines the efficiency with which these
particles can activate as cloud condensation nuclei (CCN) under
supersaturated conditions (RH > 100 %), form cloud droplets,
and thus affect the properties of clouds (Twomey 1974; Albrecht, 1989;
McFiggans et al., 2006). To quantify the effects of aerosol particles on
clouds and climate, it is thus necessary to understand the ways that aerosol
constituents interact with water.
Organic compounds contribute a large fraction (20–90 %, depending on the
environment) of atmospheric submicron particulate mass (Jimenez et al., 2009)
– which is the part of the aerosol size distribution that typically
dominates the CCN numbers. A significant fraction of this organic aerosol
(OA) is secondary – i.e., produced in the atmosphere from the condensation
of oxidation products of volatile, intermediate volatility and semi-volatile
organic compounds (VOCs, IVOCs and SVOCs). Emissions of biogenic VOCs such as
monoterpenes, isoprene and sesquiterpenes, followed by their subsequent
oxidation and condensation in the atmosphere, are thought to be the dominant
source of secondary organic aerosol (SOA) on a global scale (Hallquist et
al., 2009, and references therein) – although recent studies also suggest a
notable anthropogenic component to the global SOA (Volkamer et al., 2006;
Hoyle et al., 2011; Spracklen et al., 2011).
The solubility in water is one of the key properties governing the water
absorption (i.e., hygroscopic growth) and CCN activation of aerosol
particles. Together with aqueous-phase activity coefficients, surface
tension, density and dry mass of the particle, water solubility affects the
aerosol particle water content in thermodynamic equilibrium (Pruppacher and
Klett, 1997; Seinfeld and Pandis, 2006; Topping and McFiggans, 2012). Atmospheric
organic compounds have a wide range of solubilities (Raymond and Pandis,
2003; Chan et al., 2008; Psichoudaki and Pandis, 2013). OA is thus a complex
mixture of molecules with different CCN behavior to pure compounds. To accurately predict the water content and CCN
activation of atmospheric OA, information on the dissolution behavior and
aqueous-phase interactions of these complex mixtures is needed.
Representation of the complexity of OA is a major challenge for atmospheric
chemical transport models: OA consists of thousands of different compounds
whose properties are poorly known (Golstein and Galbally, 2007; Hallquist et
al., 2009; Kroll et al., 2011). Approaches that simplify the complex nature
of the OA mixture, yet reproduce its behavior accurately enough, are required
to be able to assess the climate and air quality effects of atmospheric
organics in large-scale modeling
applications. One example of such an approach is the representation of the
condensation and evaporation of SOA using a limited number of surrogate
compounds with a range of saturation concentrations, known as the volatility
basis set (VBS, Donahue et al., 2006, 2011, 2012). Similar simplifying
approaches are needed to represent the hygroscopic growth and CCN activation
of OA as well.
When interpreting laboratory and field studies on hygroscopicity and CCN
activation, a number of simplifying assumptions about the OA properties have
been made, for instance, (1) assuming that organics completely dissolve in
water at the point of activation (Huff-Hartz et al., 2006); (2) assuming a
fraction (εeff) of organics to be completely soluble
and the remaining fraction (1-εeff) completely
insoluble in water (e.g., Pruppacher and Klett, 1997; Engelhart et al.,
2008); and (3) lumping the phase-equilibrium thermodynamics, molar masses and
densities of the OA constituents into a single semi-empirical parameter. One
of the most commonly used formulations is the hygroscopicity parameter
κ, which relates the water activity in the aqueous solution to the
water and dry particle volumes, and can be modified to account for limited
solubility as well if the solubilities of the individual aerosol constituents
are known (Petters and Kreidenweis, 2007, 2008, 2013; Petters et al.,
2009a–c; Farmer et al., 2015; see also Rissler et al., 2004, and Wex et al.,
2007, for alternative single-parameter formulations). These common
simplifications of organic aerosol solubility and hygroscopicity are
summarized in Table 1.
Laboratory studies on different types of organic aerosols have provided
important insights into the relationship between CCN activation, hygroscopic
growth and water solubility of the atmospheric OA constituents. Raymond and
Pandis (2002, 2003) and Chan et al. (2008) investigated the CCN activation of
single-component and multicomponent aerosol particles consisting of organic
compounds with known solubilities in water, and found that the particles
activated at lower supersaturations than would have been expected based on
the bulk solubility of their constituents. As an example, the laboratory
studies by Chan et al. (2008) indicate that the CCN activation of material
with water solubility as low as 1 g L-1 could be predicted assuming
complete dissolution. For some model systems, the surface properties
(wettability) of the aerosol particles, instead of the bulk water solubility,
seemed a more important factor defining their CCN activation (Raymond and
Pandis, 2002). Huff-Hartz et al. (2006) attributed part of this effect to
residual water left in the particles upon their generation, causing the
particles to exist as metastable aqueous solutions and thus activate at lower
supersaturations than the corresponding dry material. The rest of the
apparent increase in solubility was attributed to potential impurities in the
particles. In general, the results reported by Huff-Hartz et al. (2006)
suggested that compounds with water solubilities above 3 g L-1 behaved
as if they were completely soluble in water, in general agreement with the
earlier results of Hori et al. (2003).
Simplified descriptions of organic mixture solubilities.
∗csat the solubility (saturation
concentration) in aqueous solution.
Secondary organic aerosol particles generated in the laboratory through
oxidation chemistry and condensation of the reaction products have also been
found to activate as cloud droplets and thus contribute to the atmospheric
CCN budgets (Cruz and Pandis, 1997, 1998; Huff Hartz et al., 2005; VanReken
et al., 2005; Prenni et al., 2007; King et al., 2007, 2009; Engelhart et al.,
2008, 2011; Asa-Awuku, 2009, 2010). These particles probably resemble the
real atmospheric SOA more closely than individual organic species or their
simple mixtures, but the theoretical interpretation of their CCN behavior is
complicated by the variety of their constituents. Despite the fact that CCN
activity of SOA has been reported to vary with the volatile precursor
identity and loading (Varutbangkul et al., 2006; King et al., 2009; Good et
al., 2010), photochemical aging (Duplissy et al., 2008; Massoli et al.,
2010), and temperature (Asa-Awuku et al., 2009), the reported hygroscopicity
parameter κ values determined for different SOA types are remarkably
similar, being typically around 0.1 for the overall SOA and 0.3 for the
dissolved fraction extracted from the aqueous sample (Asa-Awuku et al., 2010;
King et al., 2010). Similarly, Huff Hartz et al. (2005) reported effective
solubilities of as high as 100 g L-1 for both mono- and sesqui-terpene
SOA – although both are known to consist of a range of compounds with
different solubilities. These results demonstrate the importance of knowing
the water-soluble fraction of SOA under varying conditions but suggest that
its exact speciation is probably not necessary for predictive understanding
of the CCN activity of SOA particles (Asa-Awuku et al., 2010; Engelhart et
al., 2011). The κ values inferred from subsaturated or supersaturated
conditions for the same SOA mixtures, on the other hand, are not always
consistent, the subsaturated κ values being typically lower than the
supersaturated ones (Prenni et al., 2007; Duplissy et al., 2008; Wex et al.,
2009; Topping and McFiggans, 2012). Multiple possible reasons for this have
been presented in the literature, including incomplete dissolution of the
aerosol constituents under subsaturated conditions (Petters et al., 2009a),
surface tension effects (Good et al., 2010), RH-driven effects on the
reaction chemistry and thus the composition (solubility and activity) of the
formed SOA (Poulain et al., 2010), evaporation and condensation of
semi-volatile organic compounds (Topping and McFiggans, 2012), or the
non-ideality of the mixtures being more pronounced under the subsaturated
conditions (Kreidenweis et al., 2006; Petters et al., 2009a; Good et al.,
2010).
While the basic theory of cloud droplet activation for pure water-soluble
compounds is relatively well established (Pruppacher and Klett, 1997;
Asa-Awuku et al., 2007; Topping and McFiggans, 2012; Farmer et al., 2015),
and a number of theoretical and experimental studies on the different aspects
controlling the CCN activation of SOA have been presented (see above,
McFiggans et al., 2006; Dusek et al., 2006, and references therein), only a
few of these studies have investigated the implications of the water
solubilities of complex organic mixtures for CCN activation. Understanding
the relationship between the dissolution behavior and CCN activation of
complex organic mixtures is, however, needed to constrain the water-soluble
fraction of SOA under varying conditions as well as to systematically unravel
the mechanisms causing the apparent simplicity in the CCN behavior of complex
organic mixtures.
In this work, we introduce a framework for representing the mixture
components with a continuous distribution of solubilities, similar to the VBS
(Donahue et al., 2006, 2011, 2012). Using this framework in a theoretical
model, we investigate the dissolution behavior of complex organic mixtures
and their CCN activity, focusing on the impact of mixture solubility on CCN
activation. In particular, we study the response of the CCN activation to
varying solubility ranges, distribution shapes, and numbers of components in
the mixture. Furthermore, we compare the CCN-activation predictions using the
simplified solubility representations outlined above (complete dissolution,
soluble fraction εeff, and hygroscopicity parameter
κ without including knowledge about the component solubilities) with
the more detailed description using the full solubility distributions, and
study the relationship of the simplified solubility parameters
εeff and κ with the true mixture solubility
distribution. Although the solubility ranges and other thermodynamic
properties of the mixture have been chosen to represent SOA, many of the
concepts and approaches introduced here can be applied to any particles
consisting of complex mixtures of organic compounds with varying water
solubilities. Finally, we discuss the applicability of the introduced
framework for describing the water interactions of realistic SOA mixtures and
the relevant future directions.
Schematic of the conceptual model used in the equilibrium
composition calculations. The dry particle is assumed to consist of n
organic compounds, each denoted with a subscript i. The wet particle is
assumed to consist of a dry organic (insoluble) phase and an aqueous phase
with water and dissolved organics. The aqueous phase is assumed to be in
equilibrium with the ambient water vapor. Y refers to mole fractions in the
organic phase, X to mole fractions in the aqueous phase, and m to the
masses of the organic constituents and water. ci,eq refers to
the equilibrium concentration of each organic compound in the aqueous
solution and pw,eq to the equilibrium vapor pressure of water
above the aqueous solution.
MethodsTheoretical predictions of CCN activation of complex organic mixtures
Figure 1 schematically summarizes the model system considered in this study.
We consider a monodisperse population of spherical aerosol particles
consisting of an internal mixture of organic compounds. When exposed to water
vapor, these particles grow, reaching thermodynamic equilibrium between the
water vapor and the particle phase. The wet particle is allowed to consist of
maximum two phases: the insoluble organic phase and the aqueous phase. The
compositions of the organic and aqueous phases are determined on the one hand
by the equilibrium between the aqueous phase and the water vapor, and on the
other hand by the equilibrium of the aqueous phase with the organic insoluble
phase. To isolate the effects of solubility from organic volatility effects,
we do not allow the organics to evaporate from the droplet – i.e., we assume
that the equilibrium vapor pressures of the organics are 0 above the droplet
surface. Similarly, no condensation of organics from the gas phase to the
particles is allowed to take place. The validity of this assumption depends
on the gas-phase concentrations of the organic species as well as the
atmospheric temperature during the cloud formation process. Testing it under
different atmospherically relevant conditions deserves some future attention,
accounting for the dynamics of the atmospheric gas phase as well (see also
Topping and McFiggans, 2012). In this study, however, we focus strictly on
the CCN-activation process. The organic composition and dry particle size
were treated as an input to a model calculating the final equilibrium
composition, wet size, and CCN activation behavior of these particles. Note
that, while the solubility in the equations presented in the next Sects. 2.1
and 2.2 is non-dimensional (g gH2O-1), in the presentation
of the results, it is converted into g L-1, assuming constant unit
density of water.
Equilibrium between water vapor and an aqueous phase containing
dissolved material
The Köhler equation (Pruppacher and Klett, 1997) is used to link the
ambient water vapor saturation ratio S with the size, composition and water
content of the aerosol particles in thermodynamic equilibrium (lower panel of
Fig. 1):
S=pw,eqpw,sat=awexp4σvwRTDp,wet,
where pw,eq (Pa) is the equilibrium vapor pressure of water over
the droplet surface, pw,sat (Pa) the saturation vapor pressure
over a pure flat water surface, σ (N m-1) is the surface
tension of the droplet, vw the molar volume of water in the
aqueous phase, Mw (kg mol-1) the molar mass of water, ρ (kg m-3) the density of the aqueous phase, Dp,wet (m) the
diameter of the droplet, T (K) the temperature and R
(J mol-1 K-1) the universal gas constant. aw is the
water activity, defined as the product of the water mole fraction
Xw and water activity coefficient in the aqueous-phase
Γw:
aw=XwΓw.
The activity coefficient describes the interactions between water molecules
and the dissolved organic molecules in the mixture. The saturation ratio at
which the particles of dry size Dp,dry activate as cloud droplets
(i.e., continue growing in size even if the saturation ratio decreases), is
referred to as the critical saturation ratio Sc. Mathematically,
this corresponds to the highest local maximum in the S(Dp,wet)
curve, usually referred to as the Köhler curve.
Equilibrium between the aqueous and insoluble organic phases
The composition of the droplet and the distribution of material between the
organic insoluble and aqueous phases can be calculated by applying the
principles of mass conservation and the thermodynamic equilibrium of the
organic components in an aqueous mixture with the insoluble organic phase. As
the mass transfer of organics between the particles and the gas phase is
neglected, the total mass of the dry particle mdry, being the sum
over all components i, is equal to the total organic mass in the wet
droplet (see Fig. 1):
mdry=∑inmi,insoluble+∑inmi,aqueous,
where n is the total number of organic compounds, mi,insoluble is the mass
of compound i in the insoluble organic phase and mi,aqueous the mass of
compound i in the aqueous phase. The same holds for each organic compound
individually:
mi,dry=yi,drymdry=mi,insoluble+mi,aqueous,
where yi,dry is the mass fraction of i in the dry organic
particle. On the other hand, the concentration of each organic compound in
the aqueous phase is determined by the thermodynamics of the two-phase system
consisting of the insoluble organic phase and the aqueous solution phase. The
mass of each organic compound i in the aqueous phase can be expressed as
(Prausnitz et al., 1998; Banerjee, 1984)
mi,aqueous=γiYi,wetcsat,pure,imwYi,wet>0,mi,dryYi,wet=0,
where γi is the activity coefficient of i in the insoluble
organic phase (where the reference state is the pure component dissolution to
water), Yi,wet and csat,pure,i (here in
g gH2O-1) are the organic-phase mole fraction and pure
component solubility (saturation concentration) of i, and mw is
the total mass of water in the droplet. The former equation corresponds to
the situation where the particle contains an insoluble organic core in
thermodynamic equilibrium, the latter to the case where only the aqueous
phase exists; i.e., all the organic material has dissolved in the water.
Although the mole fraction and the corresponding molar activity coefficient
have been used in Eq. (5), a similar relationship can be defined using the
mass fraction in the organic phase and a corresponding mass-based activity
coefficient. For a multicomponent system in which the molar mass of the
organic species varies, the mole and mass fractions of a given species are
not necessarily equal. In this study, however, we assume a constant molar
mass throughout the organic mixture for simplicity, leading to the mass and
mole fractions in the organic phase to be the same; i.e., Yi=yi for
all compounds. All the equations presented below can be re-derived in a
relatively straightforward manner taking into account a potential difference
between the mole and the mass fractions in the organic phase.
Finding the organic- and aqueous-phase compositions that satisfy
Eqs. (3)–(5) for given water and dry particle masses (mw and
mdry, respectively) requires solving of n coupled equations.
These equations were expressed using the ratio χi of organic compound
i in the insoluble core of the wet particle to the total mass of the
compound (Raymond and Pandis, 2003; Petters and Kreidenweis, 2008):
χi=mi,insolublemi,insoluble+mi,aqueous=mi,insolublemi,dry=mi,insolubleYi,drymdry.
The mole fraction (equal to the mass fraction for the mixtures considered
here) of i in the insoluble core is defined as
Yi,wet=mi,insoluble∑imi,insoluble=χimi,dry∑iχimi,dry=χiYi,dry∑iχiYi,dry.
Finally, combining Eqs. (3)–(7), we get n equations of the form
χi=1-γiχiYi,dryci,sat,puremwmi,dry∑iχiYi,dry,
which can be solved for χi with the constraint 0 ≤χi≤ 1 for given water and dry particle masses.
Representation of complex organic mixtures: solubility distributions and
thermodynamic properties
A novel aspect of this study as compared with previous theoretical work is
the representation of complex mixtures using their aqueous solubility
distribution of the individual species. In our calculations, we used mixtures
of n compounds, whose water solubilities ranged from csat,min
to csat,max, either on a linear or logarithmic basis. The shape
of the distribution could vary as well. In this work, we studied essentially
three types of mass fraction distributions in the dry particle: a uniform
distribution in which all solubilities are equally abundant, distribution
increasing steadily (linearly or logarithmically), and a distribution
decreasing steadily (linearly or logarithmically). The 72 studied solubility
distributions are specified in Table 2, and the solubility distributions for
n=10, csat,min= 0.1 g L-1 and csat,max= 1000 g L-1 are presented in Fig. 2 as examples.
Solubility distributions of the organic mixtures considered
in this study.
DistributionaShapeNumber of[csat,min, csat,max,]bcomponents(g L-1)1Flat, log c axis3, 5, 10, 100Low: [10-5, 103]2Flat, linear c axis3Log. increasingMid: [0.1, 103]4Linear increasing5Log. decreasingHigh: [10, 103]6Linear decreasing
a For all solubility distributions, two assumptions
about the organic-phase activity coefficients: (1) ideal mixture and (2)
unity activity (see text for details); bcsat the
solubility (pure component saturation concentration) in aqueous solution.
Examples of solubility distributions used in the calculations for
saturation concentrations ranging from 0.1 to 1000 g L-1. (a)
Linear and logarithmic flat distributions; (b) linear and
logarithmic increasing distributions; and (c) linear and logarithmic
decreasing distributions. The numbers of the distributions refer to the
numbering in Table 2 (see Sect. 2.1.4).
For simplicity, we assumed that water forms an ideal solution with the
dissolved organics; i.e., Γw= 1, thus yielding an activity
equal to the mole fraction of water, aw=Xw in
Eq. (1). Since information about the activity coefficients of organic species
in purely organic mixtures is still scarce, we studied two alternative
approaches to representing the dissolution thermodynamics of the SOA mixture
in Eqs. (9)–(12): (1) assuming an ideal organic mixture where γ= 1
for all compounds in the insoluble phase; and (2) assuming a constant organic
phase activity γiYi,wet of unity for all compounds –
in which case the dissolution behavior of each i is similar to their
behavior as pure components. These cases probably represent the limiting
cases for the dissolution of SOA components in CCN activation reasonably
well, the former representing a lower limit and the latter an upper limit for
the overall solubility of the dry particle. Applying the two limiting
assumptions about the interactions of the compounds in the organic phase for
the 72 different solubility distributions (Table 2) thus results in a total
of 144 unique representative model mixtures.
The density, surface tension, and molar masses assumed for water and the
organic compounds are summarized in Table 3. Although the density, surface
tension and molar mass of the organics are likely to vary with the
solubility, we kept them constant throughout the organic mixture to isolate
the solubility effects on the CCN behavior. The values were chosen based on
literature studies of the CCN behavior of SOA (Engelhart et al., 2011;
Asa-Awuku et al., 2010). The surface tension σ was approximated by
the surface tension of water, and the molar volume of water in the aqueous
phase was assumed to be the same as for pure water. Furthermore, we assumed
no dissociation of the organics in the aqueous phase.
Properties of water and organic compounds used in Köhler
curve calculations (see Eq. 1).
∗ These properties were chosen based on literature on the
effective molar masses and densities determined for laboratory SOA (Engelhart
et al., 2011; Asa-Awuku et al., 2010), and assumed to be same for every
organic compound i.
(a) Examples of Köhler curves for the flat
logarithmically spaced solubility distribution (distribution 1 in Table 2)
with n=5 and the high solubility range (Table 2). The dots indicate the
point of activation, black indicating incomplete dissolution (ε < 1) and red complete dissolution (ε=1).
(b) The activation points determined from the model calculations (in
total, 7200 Köhler curves; see Table 2), corresponding to in total 5957
points in the activation dry diameter vs. supersaturation space. Also, the
dependence of the dissolved fraction at the point of activation is
illustrated.
Model calculations
We solved Eq. (8) for organic mixtures with Matlab internal function fsolve, for varying water and dry particle masses mw and
mdry, covering 50 different dry particle diameters between 20 and
500 nm. The calculations yielded the composition of the insoluble organic
and aqueous phases, and thus the mole fraction of water in the aqueous
solution Xw. From these results, the Köhler curves
S(Dp,wet) corresponding to each dry particle mass could be
calculated using Eq. (1) (see Fig. 3a for an example of the Köhler
curves). The critical supersaturations sc (defined as
Sc – 1) corresponding to specific dry particle diameters
Dp,dry (also termed activation diameters Dp,act at a
given saturation ratio S or supersaturation s) were determined from the
maxima of the Köhler curves (see Fig. 3a). The temperature was assumed to
be 298 K in all calculations. These calculations for the 144 unique organic
model mixtures corresponded to 7200 Köhler curves yielding 5957
(Dp,act, sc) pairs (activation points; see Fig. 3b).
For the remaining 1143 curves, no activation points were found with the given
combinations of mixture properties and dry diameters. For comparisons with
the simple solubility representations, the dissolved organic fraction defined
as
ε=∑mi,aqueousmdry
was extracted from the model output.
Comparison of the full model output to simple solubility representations
To investigate the performance of the simple solubility representations given
in Table 1 in reproducing the CCN activation of complex mixtures, we fitted
the (Dp,act, sc) data created by the full model using
these simpler models. No fitting is required for the complete solubility
approach. Using the obtained solubility parameters from the optimal fit and
the corresponding simplified forms of the Köhler equation, we then
recalculated new (Dp,act, sc) pairs and compared them
to the predictions by the full model. Furthermore, we investigated the
relationships between the true mixture solubility distribution and the
simplified solubility parameters. The details of the approach used for each
simple model are outlined below.
Complete dissolution
In the case where all of the organic material is assumed to completely
dissolve at the point of activation, the calculation of the aqueous solution
composition becomes trivial as
mi,dry=mi,aqueous
for all the compounds, and the water mole fraction can simply be calculated
based on the dry particle mass as
Xw=mwMwmwMw+mdryMorg,
where mw is the water mass in the droplet, mdry the
dry particle mass (related to Dp,dry through the organic density
ρorg) and Morg the organic molar mass. The
Xw calculated in this way was inserted into Eq. (1) to yield the
corresponding (Dp,act, sc) predictions and was also
applied to calculate the solution density and surface tension as
mass-weighted averages of the water and pure organic values.
Hygroscopicity parameter κ
In many practical applications, the water activity and the difference in the
densities and molar masses of water and the dry material are expressed with a
single hygroscopicity parameter κ, introduced by Petters and
Kreidenweis (2007), defined as
1aw=1+κVsVw,
where Vs and Vw are the volumes of the dry material and water,
respectively. The following formulation of the relationship between water
saturation ratio, aerosol size and composition is referred to as the
κ-Köhler equation:
S=Dp,wet3-Dp,dry3Dp,wet3-Dp,dry3(1-κ)exp4σMwRTρDp,wet,
yielding an approximate expression for the relationship between sc and
Dp,act defined as
sc=234MwσRTρ323κDp,act3-12.
Equation (14) was fitted to all (Dp,act, sc) data
produced for a given organic mixture composition (see Table 2) by the full
model, thus assuming a constant κ value for a given organic mixture.
To mimic the application of Eq. (14) to experimental data with no knowledge
of the exact solute composition, in this case we assumed the surface tension
and density to be those of water when fitting the κ values to the
full model data. The above formulation of κ, which is often used in
the interpretation of experimental data as well, thus contains information
about solubility, potential aqueous-phase non-ideality, as well as molar mass
and density of the solutes (see Farmer et al., 2015).
Soluble fraction εeff
For an ideal solution of water and an organic solute, the κ is
directly proportional to the dissolved fraction and the ratio of the molar
volumes of water and the solute; i.e., κ=εκmax, where κmax= (Mw/Morg)(ρorg/ρw).
Assuming that a single soluble fraction εeff can
represent a given organic mixture (see Table 2) at all considered
supersaturations, substituting these relationships into Eq. (16) yields
sc=234MwσRTρ323MwMsρsρwεeffDp,act3-12,
the corresponding form of the Köhler equation being (see Huff Hartz et
al., 2005)
S=Morgρw(Dp,wet3-Dp,dry3)Dp,wet3(Morgρw)+Dp,dry3(εeffMwρorg-Morgρw)×exp4σMwRTρDp,wet.
Again, we fitted Eq. (17) to the data produced by the full model and assumed
the aqueous solution density and surface tension to be equal to those of
water. When εeff < 1, the following relationship
has been used to estimate the effective saturation concentration of the
mixture (Raymond and Pandis, 2002; Huff Hartz et al., 2005)
csat,eff=ρw(Dp,wet3-Dp,act3)εeffρorgDp,act3.
Connection between εeff and the solubility
distribution of the mixture
Let us now assume that the dissolved fraction at the point of activation for
each considered mixture can be expressed as a sum of two terms, the
contribution from the compounds below a threshold solubility bin it and
the contribution from the compounds over the threshold:
ε=∑i=1itmi,aqueous+∑j=it+1nmj,aqueousmdry=∑i=1itmi,aqueous+∑j=it+1nmj,dry-∑j=it+1nmj,insolublemdry.
We now hypothesize that assuming a single soluble fraction for a given
aerosol mixture is in fact equivalent to assuming that everything above
it is completely dissolved while all the material below this
threshold remains undissolved, i.e.,
εeff=∑j=it+1nmj,drymdry.
On the other hand, ε=εeff if the
following condition is fulfilled (see Eq. 20):
∑i=1itmi,aqueous=∑j=it+1nmj,insoluble=∑j=it+1nmj,dry-∑j=it+1nmj,aqueous.
Substituting Eq. (5) into Eq. (20), we now have
Fw∑i=1itγiYi,wetcsat,pure,i=∑j=it+1nYdry,j-Fw∑j=it+1nγjYj,wetcsat,pure,j,
where
Fw=mwmdry.
At the limit of large n and in the case of a symmetric distribution of
material between the insoluble organic and aqueous phases, Eq. (21) is
satisfied by setting the threshold solubility it so that
limi→itFwγiYi,wetcsat,pure,i=Ydry,it-FwγiYi,wetcsat,pure,i.
In this case, the threshold solubility ct is found from the bin
for which
csat,pure,it=ct≈Ydry,itYwet,it×1γit×12Fw.
This is also equal to the bin where 50 % of the material is partitioned
in the insoluble phase, i.e.,
χit=mit,insolublemit,insoluble+mit,aqueous=11+mit,aqueousmit,insoluble=12.
Finding the solubility threshold ct requires knowledge of the
ratio Fw (Eq. 22). Fw, on the other hand, depends on
the ambient supersaturation and the total soluble mass – thus introducing a
supersaturation dependence to the ε given by Eq. (18) as well.
The magnitude of Fw as a function of supersaturation can be
estimated by substituting Eqs. (15) and (17) into the definition of
Fw (Eq. 22), which, after some rearranging, yields
Fw=ρwρorg2εsc×ρorgρw×MwMorg-1=ρwρorg2εκmaxsc-1.
Results
Figure 3a displays examples of the Köhler curves obtained from solving
Eqs. (1) and (6) for distribution 1 (the flat logarithmic distribution) with
varying solubilities and n=5, assuming that the organics form an ideal
mixture with each other. Each curve corresponds to a different dry size, and
the dots indicate the activation point (Scrit corresponding to
the activation dry diameter Dp,act). Black dots indicate
incomplete dissolution (ε < 0.99) at the point of
activation, while red dots indicate that in practice all the organics are
dissolved into the aqueous phase at the point of activation (ε > 0.99). Qualitatively similar behavior was observed for all
the considered distributions: as the overall solubility of the mixture
increases, the dissolution of the compounds increases, leading eventually to
complete dissolution at the point of activation. The transition from a regime
with two phases (aqueous + insoluble) to a single aqueous phase is
visible in the two maxima in Fig. 3a, in accordance with Shulman et
al. (1996) and Petters and Kreidenweis (2008).
Figure 3b illustrates the parameter space probed in this study, showing the
5957 (scrit, Dp,act) points corresponding to the
Köhler curve maxima calculated for all the considered organic mixtures.
The relationships between the critical supersaturation, activation diameter,
and dissolved fraction ε at the point of activation are also
schematically shown. The chosen dry diameters and supersaturations represent
a conservative range of typical atmospheric conditions – as the total
aerosol number concentrations are dominated by ultrafine (diameters smaller
than 100 nm) particles at most locations. In most considered cases, the
dissolved fractions fall between 0.1 and 1, but the lowest dissolved
fractions at the point of activation are on the order of only a few percent
– thus mimicking nearly insoluble aerosols. Therefore, the cases considered
here represent a reasonable sample of atmospherically relevant conditions and
SOA mixture compositions. The water-to-organic mass ratios Fw
corresponding to the probed conditions and mixtures (see Sect. 2.2.4) range
from values below 1 up to 1000, with most values around 10–100. In many of
the following plots and considerations, we have chosen four specific
supersaturations, 0.1, 0.3, 0.6 and 1 %, as representative values for
typical laboratory experiments, which are also indicated in Fig. 3b.
The dependence of the activation diameter for four different
supersaturations (s=1, 0.6, 0.3 and 0.1 %; see also Fig. 3b) on the
solubility range for the solubility distributions outlined in Table 2 for n=5, and the two assumptions about the organic-phase activity.
An example of the dependence of the activation diameter Dp,act on
the solubility range for all the studied distributions (see Table 2) and n=5 is presented in Fig. 4. As expected, the activation diameter decreases
with increasing supersaturation and solubility range for a given solubility
distribution. The solubility distribution is reflected in the overall
magnitude of the activation diameters: the distributions that have larger
fractions of material at the higher end of the solubility range
(distributions 2, 3, and 4) have generally lower activation diameters for a
given supersaturation as compared with the other distributions. The case when
unity activity in the organic phase is assumed results in smaller activation
diameters for the same supersaturation as compared with the ideal organic
mixture case (see Sect. 2.1.3 for the definitions of the cases).
The activation diameter calculated using the solubility
distributions (Table 2, referred to as the full model) and the simplified
dissolution descriptions (Table 1): (a) complete dissolution
assumption; (b) the hygroscopicity parameter κ; and
(c) the soluble fraction εeff to describe the
solubility of the organic mixture. The symbols correspond to the best fits to
the full model data. The black line shows the 1 : 1 correspondence between
the two data sets.
Figure 5 presents the activation diameters predicted using the simplified
solubility descriptions (Table 1) based on best fits to all available data as
compared with the full description of the solubility distributions (Table 2).
The results clearly show, not surprisingly, that assuming complete
dissolution for all the mixtures consistently under-predicts the activation
diameters (Fig. 5a). Representing the dissolution behavior with only one
additional parameter, i.e., the hygroscopicity parameter κ (Eqs. 15
and 16) or the effective soluble fraction εeff (Eqs. 17
and 18), improves the agreement between the activation diameters considerably
(Fig. 5b and c). Adding the knowledge about the molar mass and density of the
organic mixture, which is the only difference between using the
εeff instead of the single κ, adds only
marginal improvements in predicting the activation diameters for a given
supersaturation. The disagreements between the simplified models and the full
theoretical treatment are largest for the smallest supersaturations. These
are the cases with the widest range of possible ε values at the
point of activation (see Fig. 3b), and the effect is most obvious for the
complete dissolution model: the larger the deviation from complete
dissolution at the point of activation (i.e., the ε∼ 1
case in Fig. 3b), the more significant error we introduce. The activation
diameters predicted assuming complete dissolution are within 10 % of the
correct values if the real dissolved fraction ε is larger than
about 0.7–0.8 at the point of activation.
The performance of the simple solubility models for all the studied
Köhler curves is summarized in Fig. 6: while the complete dissolution
assumption results in systematic under-prediction (up to 40 %) of the
activation diameter, the κ- and εeff-based models
are generally within 10 % (in most cases within 5 %) of the activation
diameter predicted for the full solubility distribution representation.
Figure 7 compares the fitted parameters representing the mixture dissolution
to the corresponding values inferred from the full mixture data for the 144
different mixtures. In Fig. 7a, the effective soluble fractions
εeff are compared to the actual dissolved fractions
ε at the point of activation for all the studied mixtures. While
in the fits a single constant εeff has been assumed to
represent a given mixture (see Eqs. 15 and 16), in reality, ε
varies with supersaturation (Eq. 9). Thus, while the fitted
εeff for a given mixture correlates very well with the
average ε over all activation points (the markers in Fig. 7a),
the performance of the approach can vary considerably with supersaturation
(the grey lines in Fig. 7a). In practice, this means that describing a given
complex mixture with a fixed soluble fraction yields representative average
dissolution behavior, but does not guarantee correct solubility description
for a specific sc if fitted over a range of supersaturations. The
corresponding comparison for the hygroscopicity parameter κ values
describing the data is shown in Fig. 7b. A clear correlation between the
fitted κ and the average ε is observed as expected (see
Sect. 2.2.3), but the variation of ε with supersaturation again
adds scatter to the data – suggesting a dependence of κ on
sc. The maximum κ, on the other hand, is defined
primarily by the molar masses and densities of the organics. For our mixtures
with constant Morg and ρorg, the value of
κmax is 0.15, which is indicated in Fig. 7b. The points
above this theoretical maximum are a result of using the pure water density
instead of the mixture value in the Kelvin term of the Köhler equation
(Eq. 16). These results thus suggest that the κ values of 0.1–0.2
typically observed for SOA particles (Duplissy et al., 2011) are controlled
by the molar masses and densities of the SOA mixtures to a large extent and
can result from quite different SOA mixtures in terms of their solubilities.
The performance of the simplified solubility representations (see
Table 1) in predicting the activation diameter for a given supersaturation as
compared with the full model. The black bars depict the 25th and 75th
percentiles and the grey bars the 10th and 90th percentiles.
(a) The fitted soluble fraction εeff
as function of the true dissolved fraction ε for each considered
mixture (see Table 2). Symbols: mean ε over all activation
points. Grey lines: the range of ε values at the different
activation points for a given mixture. (b) The fitted κ
values as a function of the true dissolved fraction ε for each
considered mixture. The red dashed line denotes the limit of
κmax=0.15 that applies to all the studied mixtures.
1 : 1 lines are also indicated.
The dissolution behavior of the organic mixture corresponding to
distribution 1 with n=100 and the low solubility range (see Table 2) at
the activation point for sc=0.1 % (see Fig. 4). The figures
depict the distribution of material in each solubility bin between the
aqueous and insoluble organic phases for the two different assumptions about
the organic-phase activity. ct refers to the 50 % point of
the partitioning (Eqs. 24 and 25). (a) The ideal organic mixture.
(b) The unity activity assumption.
To illustrate the relationship of the fitted εeff with
the dissolution of a given mixture, the partitioning between the aqueous and
insoluble organic phases is presented in Fig. 8 for distribution 1 with the
“low” solubility range and n=100 at the point of activation when
sc=0.1 % (see Table 2). Figure 8a shows the partitioning
for the case where ideal organic mixture has been assumed and Fig. 8b shows
the corresponding data for the unity activity case (see Eq. 5). The point of
50 % partitioning (ct, Eqs. 20 and 21) is also shown. As
described in Sect. 2.2.4, we expect ct to be a reasonable
estimate for the limit for complete dissolution, if the complex mixture is
reduced to a two-component mixture of completely soluble and insoluble
components. It should be noted, however, that the water content and
ε of the droplet at the point of activation depend on
supersaturation (see Eq. 25), also causing a dependence between
ct and sc. Furthermore, Fig. 8 illustrates a
difference in the solubility dependence of the partitioning behavior for the
two organic activity assumptions. The ideal mixture displays a symmetrical
sigmoidal dependence around ct. For the unity activity case, on
the other hand, the undissolved fraction is asymmetric around the 50 %
value – dropping rapidly to 0 above ct but approaching 1
asymptotically below ct.
The distributions of the ct values (i.e., the 50 %
partitioning point; see Eqs. 24 and 25) at the point of activation for all
the considered mixtures (Table 2) and activation points, and the two
assumptions about the organic-phase activity. (a) The ideal organic
mixture. (b) The unity activity assumption.
Sensitivity of the ct values to supersaturation, molar
mass and number of components for distribution 1 with the mid solubility
range (see Table 2). Only points with limited solubility
(0 < ε < 1) at the point of activation are
included.
Figure 9 shows the distributions of the solubility bins containing the
50 %-partitioning points (ct, Eqs. 20 and 21) on a decadal
basis for all the activation points studied, illustrating also the
differences between the two assumptions about the organic-phase activity. The
ct values for the ideal organic mixture (Fig. 9a, based on 2465
points) display a symmetrical distribution around the median value of about
10 g L-1. Also, a modest dependence of ct on the number of
components is observed: the cases with three and five components display
slightly higher ct values as compared with the cases with larger
n. This apparent dependence is probably due to the discrete nature of the
solubility distributions in combination with the fact that, for the different
solubility ranges (see Table 2), only the lower end of the distribution is
changed, while the upper end is always at 1000 g L-1. The unity
activity case displays a much stronger n dependence (Fig. 9b, based on 3492
points): if analyzed separately, the median ct shifts from about
0.1 to 10 g L-1 when n changes from 100 to 10 and 5, and up to
100 g L-1 for n=3. Unlike the ideal mixture, this behavior is
explained by the actual dissolution thermodynamics: in a system where the
components do not affect each other's solubility directly (i.e., the
dissolution of a compound i is only limited by its own presence in the
aqueous phase), the amount of dissolved material is only dependent on the
total water content and is larger than the number of dissolvable components.
If all the different mixtures are integrated together, the median
ct for the unity activity assumption lies at about 1 g L-1
– a decade lower than for the ideal mixture case. Figure 10 provides a more
detailed look at the sensitivity of ct to supersaturation, n
and molar mass for one of the distributions (distribution 1, mid solubility
range; see Table 2). As expected, ct depends considerably on
supersaturation. It can also be seen that, while ct shows some
sensitivity to the number of components (in line with Fig. 9) and molar mass,
in our case, by far the most critical assumption is related to the organic
mixture thermodynamics.
The fitted εeff values are compared in Fig. 11 to the
fraction of mass with solubilities above the median ct for the
134 mixtures that activated under the probed conditions, individually for
both organic activity assumptions. The fitted dissolved fraction corresponds
well to the fraction of mass with solubilities above the
50 %-partitioning point, as predicted by the theoretical principles
outlined in Sect. 2.2.4. Also, the solubilities of the different
distributions with varying shapes, numbers of components and solubility
ranges can be represented reasonably well with a single median ct
(equal to 10 g L-1 for the ideal mixture case and 1 g L-1 for
the unity activity case; see Fig. 9), with median deviations between the
fitted εeff and the fraction above ct of 9
and 8 %, respectively. On the other hand, these results indicate that the
soluble fractions determined from experimental data on CCN activation provide
information about the fraction of material with solubility above
ct. There are eight points that do not seem to follow the general
trend, however: a group of points with all the material above the threshold
solubility can display a variety of fitted εeff
values. These are all points that correspond to the “high” solubility
ranges. Distributions 5 and 6 (see Table 2) with n=3 are among these
points for both organic activity assumptions. For the ideal mixture case,
distribution 1 with three components also diverges from the general trend,
and for the unity activity assumption, distribution 5 falls into the category
regardless of the number of components. These points thus contribute to the
high ends of the ct distributions in Fig. 9.
The relationship between the fitted dissolved fraction
εeff at the point of activation and the mass fraction over
the median ct for all the considered mixtures and s=1, 0.6,
0.3 and 0.1 %. Closed symbols: the ideal organic mixture assumption
(median ct=10 g L-1). Open symbols: the unity activity
assumption for the organics (median ct=1 g L-1).
The deviations in the activation diameters as predicted by the three
simplified solubility representations (complete dissolution, ε
and κ) are displayed in Fig. 12 as a function of the mixture
properties for sc=0.1, 0.3, 0.6 and 1 %. Again, the two
different assumptions about the organic-phase activity are treated separately
due to their different limiting solubilities ct (Fig. 9) and
different shapes of the partitioning distributions (Fig. 8). Also, the points
close to complete dissolution at the point of activation (ε≥ 0.8; see Fig. 5 and its explanation in the text) are presented with a
different color (grey symbols) than the points where the activation diameter
differs significantly from the complete dissolution prediction (ε < 0.8, black symbols). As expected, the complete dissolution
assumption performs better for the more water-soluble organic mixtures.
Figure 12a and b illustrates this by showing the relationship between the
norm of the error in the predicted Dp,act and the fraction of
material below the median ct (10 and 1 g L-1) for the two
organic activity assumptions. The larger the amount of material below the
solubility limit, the larger the deviation from the full model predictions.
For the κ and ε models, on the other hand, the variable
best correlating with the error in Dp,act induced by the
simplification is different for the different organic activity assumptions –
although close to complete dissolution, these models also do well, nearly
independent of the solubility of the distribution. For the ideal mixture
case, the fraction of mass between 1 and 100 g L-1 correlates better
with the error (Fig. 12c, e) than the mass fraction below any solubility
limit (not shown), while for the unity activity case, the material at the low
end of the distribution (mass fraction below 1 g L-1) performs better
(see Fig. 12d, f). The reason for this lies in the different shapes of the
partitioning distributions resulting from the two assumptions (Fig. 8). For
the symmetric partitioning curve of the ideal mixture case, the predicted
εand κ are most sensitive to differences in the
partitioning behavior between compounds within the range of ct
corresponding to the supersaturation and particle diameter ranges studied
here, i.e., 1–100 g L-1 (see Fig. 12c, e). Anything outside these
boundaries will behave as completely soluble or insoluble throughout the
studied supersaturation space, thus not introducing a significant error when
constant ε is assumed to describe the mixture. However, the more
material that can behave as either insoluble or soluble, depending on the
conditions, the larger the error we introduce by assuming a constant
ε for a given mixture under any conditions. The story is
different for the unity activity case (Fig. 12d, f): as the shape of the
partitioning distribution (Fig. 8) does not depend on ct, the
compounds with solubilities below ct will contribute relatively
much more to the fitted εff than for the previous case,
and thus the more material there is in the “tail” of the partitioning
distribution, the worse the assumption about a single ε for the
whole distribution.
The solubility distribution properties best explaining the
performance of the three simplified solubility models, illustrated with the
norm of the relative deviation of Dp,act as compared with the
full model predictions for s=1, 0.6, 0.3 and 0.1 %. The performance
of the complete dissolution assumption as a function of the mass fraction
with solubilities below the median ct for (a) the ideal
organic mixture (median ct=10 g L-1) and (b)
the unity organic activity (median ct= 1 g L-1)
assumptions. The performance of the κ model as a function of the mass
fraction with solubilities (c) between 1 and 100 g L-1 for
the ideal organic mixture assumption; and (d) below 1 g L-1
for the unity organic activity assumption. The performance of the
ε model as a function of the mass fraction with solubilities
(e) between 1 and 100 g L-1 for the ideal organic mixture
assumption; and (f) below 1 g L-1 for the unity organic
activity assumption. The points close to complete dissolution (ε≥ 0.8) are shown with lighter grey than the rest of the points. The
error bars represent the variability with supersaturation and particle size.
(a) An example of a solubility distribution for SOA
generated in dark ozonolysis of α-pinene SOA. The expected
composition has been taken from Chen et al. (2011), and the pure-component
solubilities have been calculated with the SPARC prediction system (e.g.,
Wania et al., 2014, and references therein). “Misc.” refers to completely
miscible components. (b) The dependence of the ct value
at the point of activation on supersaturation assuming an ideal organic
mixture, with only points corresponding to limited solubility
(0 < ε < 1) displayed.
To relate the theoretical work conducted here to realistic atmospheric
organic aerosol mixtures, Fig. 13 displays an example of a solubility
distribution representing SOA formed from dark ozonolysis of α-pinene
(Chen et al., 2011). The solubilities have been estimated with SPARC (see
Wania et al., 2014, and references therein). The average molar masses and
O : C ratios in each solubility bin are also displayed, along with the
ct values corresponding to the activation points with limited
solubility – assuming that the organics form an ideal mixture with each
other. Most of the material is predicted to have solubilities between 1 and
100 g L-1, indicating that this fresh α-pinene SOA is at the
critical range of solubilities for limited dissolution at the point of
activation. This in turn suggests that the observed difference between the
κ values inferred from hygrosopicity and CCN activation for this
mixture might largely result simply from the distribution of solubilities
present.
Discussion and conclusions
We have studied the relationship between CCN activation and the solubility of
144 different theoretically constructed complex organic mixtures using
Köhler theory, accounting for the partial solubility of the compounds in
water and assuming ideal interactions between the dissolved molecules and
water. The mixtures encompassed a wide variety of solubilities, and were
represented by solubility distributions with various solubility ranges and
shapes (analogously to the volatility basis set, VBS). Two limiting
assumptions (ideal mixture vs. unity activity) about the interactions between
the organics in the insoluble organic phase were tested. The results using
this comprehensive solubility representation (termed “the full model”) were
compared to commonly used simplified descriptions of solubility: (1) assuming
complete dissolution; (2) representing the mixture with single hygroscopicity
parameter κ; and (3) representing the mixture with a single soluble
fraction εeff. The calculations were carried out for
particle dry sizes ranging from 20 to 500 nm and supersaturations between
0.03 and 5 %, thus probing an atmospherically representative parameter
space and resulting in a total of 5957 unique activation points.
Comparing the full model predictions to the simplified solubility
descriptions, we find that assuming complete dissolution under-predicts the
activation diameter up to a factor of about 2 for the studied mixtures. Our
results indicate that about 70–80 % of the material needs be dissolved
at the point of activation for the complete dissolution assumption to predict
activation diameters that are within 10 % of that produced by the full
solubility treatment. Adding a single parameter to describe the mixture
solubility improved the situation considerably: the predictions of activation
diameters based on a single ε or κ for a given mixture
were within 10 % of the full model predictions, the difference between
these two approaches being only marginal.
The fitted soluble fractions, εeff, describing the
solubility distribution (and thus the fitted κ that is directly
proportional to ε) were found to correspond well to the fraction
of dry particle material with solubilities larger than a given threshold
solubility ct. For the ideal organic mixture assumption, the
median ct was 10 g L-1, most of the values falling between
1 and 100 g L-1, depending somewhat on the supersaturation. Since the
material with solubilities outside this range can generally be treated as
completely soluble or insoluble in CCN-activation calculations, the error
made by using the single soluble fraction increased when a larger fraction of
material was present in this critical range. For the unity activity case, the
median ct was 1 g L-1, but decreased with the number of
components present in the mixture, n. For the range of n= 3–100
studied here, the typical ct values were between 0.1 and
10 g L-1. Due to the asymmetric shape of the aqueous–organic-phase
partitioning of the organics in the unity activity case, the simplified
models performed better the more material with solubilities larger than
ct was present in the particles. In general, the median values
for ct represented the soluble fraction with a reasonable
accuracy in most of the studied mixtures, although the exact composition of
the mixtures varied considerably.
Our values for the limiting solubilities for complete dissolution are in
agreement with the values of 3 and 1 g L-1 previously reported by
Huff-Hartz et al. (2006) and Chan et al. (2008) based on experimental data on
specific mixtures. Our results on the two different assumptions about the
organic-phase activities indicate that the mixtures investigated by these
past studies were probably somewhat non-ideal, where the compounds hindered
each other's dissolution less than would be expected for a fully ideal
mixture. On the other hand, in light of our findings, the observations of the
close-to-complete dissolution of SOA at activation (Huff Hartz et al., 2005;
Engelhart et al., 2008) indicate that the majority of the material in the
studied SOA mixtures had solubilities larger than 10 g L-1. Our
results suggest that even with vastly different solubility distributions one
can yield very similar CCN-activation behavior (and consequently values of
κ or ε), as the parameter that matters is the material
above ct.
The above results suggest that the solubility range corresponding to limited
solubility in CCN activation is between 0.1 and 100 g L-1, and
resolving the solubility distributions of aerosol mixtures outside this range
provides little added value for understanding their CCN activation. In fact,
this is probably a conservative estimate, as in most cases, most material
below 1 g L-1 is practically insoluble and most material above
10 g L-1 completely soluble – even considering the uncertainty in the
organic mixture activity. These results can be used to guide the
representation of the cloud activation properties of complex mixtures, and
provide quantitative support for the previous notion that knowing the
water-soluble fraction of the aerosol mixture in question is the key in most
applications. We provide quantitative estimates on how this soluble fraction
should be defined in the case of complex mixtures, and when such a simplified
model is not expected to perform well.
There are, however, some limitations to our approach to keep in mind when
applying the results to laboratory experiments or atmospheric data. Since the
focus of this work was strictly on the links between solubility and CCN
activation, we did not explore in depth how variation of surface activity,
molecular mass, pure-component density, the gas-droplet partitioning of the
organic compounds or non-ideality of water with respect to the aqueous phase
would affect the results (see also Suda et al., 2012, 2014; Topping et al.,
2013). Furthermore, temperature was assumed to stay constant at 298 K. Since
many of the thermodynamic properties relevant to CCN activation are
temperature dependent (see, e.g., Christensen and Petters, 2012), future work
investigating the impact of temperature on the phenomena studied here is
needed. Furthermore, the solubility and organic-phase activity should
naturally be linked to the aqueous-phase activity coefficients predicted and
used in a number of previous studies (see, e.g., Topping et al., 2013, and
references therein), although a lack of well-defined experimental data on
organic-phase activities and mixture solubilities currently hinders
quantitative evaluation of the current multi-phase mixture thermodynamic
models (see, e.g., Cappa et al., 2008). Evaluation of the concepts and
approaches presented here (e.g., the solubility limits ct) with
laboratory studies on well-defined complex mixtures over a wide range of
solubilities, supersaturations and particle diameters would therefore be
warranted.
Another important future step would be applying the introduced solubility
distribution framework in the atmospheric context. On the one hand, the
framework is likely to be useful in modeling the evolution of the CCN
activity of secondary organics. We expect the solubility distributions (and
thus ct) to depend on the SOA mixture properties such as the
O : C ratio and the molar masses of the mixture constituents, which in turn
evolve due to atmospheric chemistry (Kuwata et al., 2013; Suda et al., 2014),
coupling the solubility distributions to the different dimensions of the VBS
(Donahue et al., 2006, 2011, 2012; Kroll et al., 2011; Shiraiwa et al.,
2014). A systematic study investigating the interlinkages between these
variables in light of the available experimental data from field and
laboratory would thus be a valuable future contribution. Furthermore, as
atmospheric aerosol particles are typically mixtures of organic and inorganic
constituents, the molecular interactions between atmospheric organics and
inorganics as well as their effect on the pure-component solubility should be
expanded. On the other hand, the solubility distribution can be used as a
simplifying concept aiding in large-scale model simulations coupling
atmospheric chemistry to the dynamics of cloud formation. With the
assumptions applied here, the CCN-activation calculation itself is
computationally relatively light, slowing down considerably only if n is on
the order 10 000 or larger with typical present-day computational resources.
Therefore, using the solubility distribution framework within an atmospheric
model is a good option if accuracy beyond the simple one-parameter approaches
is required, or as an intermediate tool linking atmospheric age to the
effective ε or κ describing a given mixture.
Acknowledgements
Financial support from European Research Council project ATMOGAIN (grant
278277), Vetenskapsrådet (grant 2011-5120), and European Commission FP7
integrated project PEGASOS (grant 265148) is gratefully
acknowledged. Edited by: A. Nenes
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