Recent work has demonstrated that organic and mixed organic–inorganic particles can exhibit multiple phase states depending on their chemical composition and on ambient conditions such as relative humidity (RH). To explore the extent to which water uptake varies with particle-phase behavior, hygroscopic growth factors (HGFs) of nine laboratory-generated, organic and organic–inorganic aerosol systems with physical states ranging from well-mixed liquids to phase-separated particles to viscous liquids or semi-solids were measured with the Differential Aerosol Sizing and Hygroscopicity Spectrometer Probe at RH values ranging from 40 to 90 %. Water-uptake measurements were accompanied by HGF and RH-dependent thermodynamic equilibrium calculations using the Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) model. In addition, AIOMFAC-predicted growth curves are compared to several simplified HGF modeling approaches: (1) representing particles as ideal, well-mixed liquids; (2) forcing a single phase but accounting for non-ideal interactions through activity coefficient calculations; and (3) a Zdanovskii–Stokes–Robinson-like calculation in which complete separation of the inorganic and organic components is assumed at all RH values, with water uptake treated separately in each of the individual phases. We observed variability in the characteristics of measured hygroscopic growth curves across aerosol systems with differing phase behaviors, with growth curves approaching smoother, more continuous water uptake with decreasing prevalence of liquid–liquid phase separation and increasing oxygen : carbon ratios of the organic aerosol components. We also observed indirect evidence for the dehydration-induced formation of highly viscous semi-solid phases and for kinetic limitations to the crystallization of ammonium sulfate at low RH for sucrose-containing particles. AIOMFAC-predicted growth curves are generally in good agreement with the HGF measurements. The performances of the simplified modeling approaches, however, differ for particles with differing phase states. This suggests that no single simplified modeling approach can be used to capture the water-uptake behavior for the diversity of particle-phase behavior expected in the atmosphere. Errors in HGFs calculated with the simplified models are of sufficient magnitude to produce substantial errors in estimates of particle optical and radiative properties, particularly for the assumption that water uptake is driven by absorptive equilibrium partitioning with ideal particle-phase mixing.
Atmospheric aerosols alter the Earth's radiation budget, reduce visibility, and are associated with adverse health effects (Finlayson-Pitts and Pitts, 2000; Pöschl, 2005; Seinfeld and Pandis, 2006). The magnitude of these impacts is influenced by aerosol water content, as this is a major determinant of aerosol particle size. Furthermore, aerosol water can impact gas-phase photochemistry and secondary organic aerosol (SOA) concentrations by serving as a sink for reactive gases and as a medium for aqueous-phase and heterogeneous reactions (Ervens et al., 2011, 2013). As a result, clear understanding of the hygroscopicity of atmospheric aerosols is key to representing aerosol properties and behavior in atmospheric models and to improving our understanding of their impacts on climate and air quality.
Organic aerosol (OA) comprises a substantial fraction of total aerosol mass (20–90 %; Seinfeld and Pandis, 2006). Moreover, particle formation and transformation processes commonly lead to the formation of internally mixed organic–inorganic particles (Seinfeld and Pankow, 2003; Marcolli et al., 2004; Zhang et al., 2005; Murphy et al., 2006; Goldstein and Galbally, 2007; Hallquist et al., 2009). Multiple studies have sought to elucidate the hygroscopic properties of OA, as well as the influence of organic aerosol components on the hygroscopic behavior and phase transitions of inorganic salts. Much of this work has focused on single- and multi-component aerosols comprised of carboxylic, dicarboxylic, and humic acids (e.g., Prenni et al., 2001; Choi and Chan, 2002a; Brooks et al., 2004; Chan et al., 2006; Moore and Raymond, 2008; Hatch et al., 2009; Pope et al., 2010; Lei et al., 2014), as well as mixtures of organic acids with inorganic salts (e.g., Cruz and Pandis, 2000; Choi and Chan, 2002b; Prenni et al., 2003; Wise et al., 2003; Brooks et al., 2004; Svenningsson et al., 2006; Sjogren et al., 2007; Gao et al., 2008). Recent studies have explored water uptake by sugars, higher molecular weight organics, and polymers (Gysel et al., 2004; Mochida and Kawamura, 2004; Tong et al., 2011; Zobrist et al., 2011; Lei et al., 2014; Xu et al., 2014). Such studies have aimed to characterize the hygroscopicity of biomass burning aerosols, highly oxygenated aged SOA, and oligomers. This body of research has demonstrated that the water-uptake behavior of OA components and their influence on the phase transitions of inorganics depend on multiple factors, including the composition and relative amounts of the organic and inorganic aerosol fractions, the physiochemical properties of the organic components, and ambient conditions. Controlled laboratory studies have also served as a basis for the development and evaluation of thermodynamic models (Clegg et al., 2001; Chan et al., 2005; Raatikainen and Laaksonen, 2005; Clegg and Seinfeld, 2006; Marcolli and Krieger, 2006; Svenningsson et al., 2006; Moore and Raymond, 2008; Zardini et al., 2008; Zuend et al., 2011; Lei et al., 2014), with the aim of representing water uptake by organic and mixed organic–inorganic aerosols.
Current regional and global chemical transport models include a simplified
treatment of aerosol hygroscopicity. In CMAQ (Community Multi-scale Air
Quality model), for example, only water uptake by the inorganic fraction is
considered (Binkowski and Roselle, 2003;
Recent work has demonstrated that organic and mixed organic–inorganic particles can exist in multiple phase states depending on their chemical composition and on ambient conditions such as RH and temperature (Cappa et al., 2008; Zobrist et al., 2008; Ciobanu et al., 2009; Virtanen et al., 2010; Bertram et al., 2011; Koop et al., 2011; Krieger et al., 2012). For example, non-ideal interactions between aerosol components can result in a liquid–liquid phase separation (LLPS) in which an inorganic-electrolyte-rich phase and an organic-rich phase co-exist within a single particle (Erdakos and Pankow, 2004; Ciobanu et al., 2009; Zuend et al., 2010; Bertram et al., 2011; Pöhlker et al., 2012; Song et al., 2012a; Zuend and Seinfeld, 2012; You et al., 2012, 2013, 2014). Laboratory studies have demonstrated that ambient OA can exist as a highly viscous liquid, semi-solid, or glass under atmospherically relevant conditions (Zobrist et al., 2008, 2011; Mikhailov et al., 2009; Koop et al., 2011; Tong et al., 2011). Amorphous solid (glassy) SOA has been observed both in a laboratory chamber and in the field (Virtanen et al., 2010; Saukko et al., 2012). Such complex phase behavior has major implications for the partitioning of water and semi-volatile organic species to the particle phase (Ciobanu et al., 2009; Koop et al., 2011; Krieger et al., 2012; Mikhailov et al., 2009; Bones et al., 2012; Song et al., 2012a, 2014; Zaveri et al., 2014). Diffusion coefficients in solid or semi-solid particles have been estimated to be up to 7 orders of magnitude smaller than in liquids (Vaden et al., 2011; Abbatt et al., 2012), resulting in the inhibition of mass transfer through the aerosol bulk and delayed uptake and evaporation of water (Koop et al., 2011; Bones et al., 2012; Shiraiwa et al., 2011, 2013; Lienhard et al., 2014). Assuming that multi-component particles exist as well-mixed single-phase liquids when two separate phases are actually present can result in errors as large as 200 % in predicted particle mass formed through the partitioning of organic vapors to the condensed phase (Zuend et al., 2010; Zuend and Seinfeld, 2012). The present study explores the extent to which phase separations and other complex phase behavior influence the partitioning of water vapor to the particle phase.
A variety of methods have been used to characterize the factors that
influence the prevalence of LLPS and amorphous solid OA. Coupling
single-particle techniques with microscopy has enabled the observation of
particle-phase transitions with changing ambient conditions (Krieger et al.,
2012). Song et al. (2012a), for example, evaluated the prevalence of LLPS as
a function of RH and characterized the chemical composition of phases
present within mixed organic–inorganic aerosols using a high-speed video
camera and Raman microscopy. Moisture-induced glass transitions have been
observed for sucrose solutions using single-particle techniques and
differential scanning calorimetry (Zobrist et al., 2008, 2011). Similarly,
phase states (solid/semi-solid vs. liquid) of SOA as a function of RH
have been inferred based on the fraction of particles that bounced when
impacted on a steel substrate (Sauuko et al., 2012). A combination of
bounce-fraction measurements and electron microscopy of newly formed OA in a
boreal forest provided the first evidence that SOA formed in the atmosphere
can behave as amorphous solids (Virtanen et al., 2010). These analyses have
also shown that phase separation and particle viscosity vary with chemical
composition (e.g., the organic : inorganic mass ratio), the molecular
properties of the organic fraction of the aerosols (e.g., oxygen : carbon
[O : C] ratio, molar mass, hydrophilicity), and RH (Bertram et al., 2011; Song
et al., 2012a, b; You et al., 2013).While these studies have
provided valuable information regarding the influence of RH and particle
water content on particle-phase state, investigations of the influence of
complex phase behavior on water uptake are limited. Furthermore, the
single-particle techniques commonly used to study particle-phase morphology
generally require particle sizes on the order of 1–10
Diameter hygroscopic growth factors of nine laboratory-generated aerosol
systems that serve as atmospheric aerosol surrogates were measured at RHs
ranging from 40 to 90 % with the Differential Aerosol Sizing and
Hygroscopicity Spectrometer Probe (DASH-SP). The DASH-SP has been described
in detail previously (Sorooshian et al., 2008). Briefly, in the DASH-SP,
aerosols are dried in a Nafion dryer, pass through a
With the aim of exploring the extent to which water uptake varies with
particle-phase state, hygroscopic growth curves were measured for chemical
systems for which particle-phase behavior as a function of RH has previously
been characterized. For all systems studied here, RH-dependent phase states
had previously been observed at room temperature. Most of those studies were
based on single-particle techniques, in which a single-particle (typically
supermicron-sized) is isolated in a controlled environment and probed with
various optical and microscopy techniques (Tong et al., 2011; Zobrist et
al., 2011; Song et al., 2012a; You et al., 2013). Briefly, You et al. (2013)
explored the prevalence of liquid–liquid phase separations as a function of
RH for internally mixed organic–inorganic aerosol systems comprising one
organic compound and one inorganic salt. Single particles were deposited on
a glass slide coated with a hydrophobic substrate that was then mounted in a
RH- and temperature-controlled flow cell. Phase transitions during RH
cycling were observed with an optical reflectance microscope. Song et al. (2012a) studied the phase behavior of more complex particle mixtures, each
consisting of three dicarboxylic acids with 5, 6, or 7 carbon atoms
(C
Seven aerosol systems with RH-dependent phase morphologies ranging from
well-mixed liquids to phase-separated particles to amorphous solids or
semi-solids were chosen for study in the present work from the
above-described studies. Table 1 summarizes the compositions and phase
behaviors of these chemical systems as determined in these prior studies.
Two additional chemical systems consisting of sucrose and ammonium sulfate
with varying organic : inorganic ratios were also studied here. A concurrent
study (Robinson et al., 2014) also explored the hygroscopic behavior of
submicron sucrose–ammonium sulfate particles, with the aim of characterizing
the influence of glassy aerosol components on the optical properties of
organic–inorganic particles. Sucrose was selected as a model compound in
that work and in the present study due to its high glass-transition
temperature (
In addition to differences in phase behavior, the aerosol systems represent
variations in their complexity (in terms of dry composition). Particle
compositions range from single-component organic systems, to two-component
systems consisting of one organic and ammonium sulfate, to more complex
systems consisting of dicarboxylic acid mixtures and ammonium sulfate (Table 1). To evaluate the performance of the DASH-SP and the HGF-calculation
algorithm, control runs were also performed for pure ammonium sulfate
aerosols. For all chemical systems, aerosols were generated by atomizing
aqueous solutions prepared by dissolving the organic and inorganic
components with the mass ratios given in Table 1 in Milli-Q water
(resistivity
Hygroscopic growth curves were modeled for the nine aerosol systems with the Aerosol Inorganic-Organic Mixtures Functional groups Activity Coefficients (AIOMFAC) model (Zuend et al., 2008, 2010, 2011; Appendix A). AIOMFAC is a thermodynamic model that explicitly accounts for molecular interactions between all components in an aqueous solution through the calculation of activity coefficients. A group-contribution concept based on UNIFAC (UNIversal quasi-chemical Functional group Activity Coefficients), in which the thermodynamic properties of organic compounds are determined on the basis of their molecular structures, is employed to account for interactions among organic functional groups, inorganic ions, and water (Zuend et al., 2008, 2011). In these AIOMFAC-based equilibrium calculations, the potential existence of a LLPS is determined and corresponding liquid-phase compositions are computed by the method of Zuend and Seinfeld (2013). Diameter growth factors are calculated for RH values ranging from near 0 to 99 % for both dehydration (from high RH to low RH) and hydration (low RH to high RH) cycles for all systems. For dehydration-branch calculations, growth factors at RH values lower than the particle/inorganic salt deliquescence point are representative of metastable conditions, where a supersaturated solution is present with respect to the dissolved inorganic salt. Hydration calculations include the presence of a solid inorganic phase at RH values before the full deliquescence of ammonium sulfate and the partial dissolution of ammonium sulfate into the aqueous organic solution (solid-liquid equilibrium; SLE). The hydration calculations are the most relevant to the hygroscopic growth experiments, as the atomized aerosols were dried before being exposed to elevated humidities in the DASH-SP. AIOMFAC-calculated diameter growth factors are compared to measured values to provide a detailed evaluation of the interactions likely to be occurring between aerosol chemical components.
Aerosol systems studied.
Following Zuend and Seinfeld (2012), in addition to the full AIOMFAC-based equilibrium calculations, several simplified calculations were performed to explore the influence of phase separation and the effects of other non-ideal interactions on hygroscopic growth. These comparisons also evaluate the need for accounting for such interactions in modeling the water-uptake behavior of atmospheric aerosols. Two hygroscopic growth calculations in which no LLPS was allowed to occur were performed: (1) one in which non-ideal interactions are taken into account through AIOMFAC-calculated activity coefficients and (2) one in which it is assumed that the condensed phase behaves as an ideal mixture. Water-uptake calculations were also performed in a mode in which complete separation between an aqueous inorganic electrolyte phase and an organic phase is assumed and, thus, no organic–ion interactions are accounted for. This latter case is similar to a Zdanovskii–Stokes–Robinson (ZSR) relation assumption, since the water uptake of individual components (here two separate phases) are added up to estimate the HGF. In our ZSR-like calculation case, the influence of non-ideality on water activity, and therefore water content, is accounted for within the individual phases with AIOMFAC-based activity coefficients. A calculation in which a solid organic phase is assumed at all RH values was also performed for comparison against the DASH-SP measurements in order to evaluate whether the presence of a solid organic phase was likely in any of the chemical systems studied. All growth-curve calculations were performed at 298 K.
Note that AIOMFAC predicts phase compositions, which can be used to derive
mass growth factors but not the densities of the phases necessary to
calculate diameter growth factors (assuming spherical particles). Solid and
liquid-state densities of ammonium sulfate were taken from Clegg and Wexler (2011). The density of citric acid was calculated based on the data and
parameterizations of Lienhard et al. (2012). The densities of all other
organic compounds were estimated using the structure-based method of
Girolami (1994) with the online density-calculation tools available on the
E-AIM website (
Measured and AIOMFAC-predicted HGFs for the two-component carboxylic
acid–ammonium sulfate systems (organic : inorganic dry mass ratios
Mixed diethylmalonic acid–ammonium sulfate particles demonstrated little to
no water uptake (HGF
Top panels: Measured and AIOMFAC-predicted hygroscopic diameter
growth factors for
In addition, You et al. (2013) performed dehydration experiments to explore the onset of phase separation (from high to low RH), while the present study focused on hydration experiments (from low to high RH). AIOMFAC predictions are made under the assumption that there is no hysteresis between LLPS and the merging of two liquid phases to a single phase in terms of the onset RH. This is because experiments (e.g., Song et al., 2012a) show that there is little to no hysteresis in such a phase transition, at least for systems with liquid-like viscosities. In contrast to the typical hysteresis behavior of liquid–crystal/crystal–liquid phase transitions (i.e., deliquescence vs. crystallization), liquid–liquid to single-liquid phase transitions involve only disordered phase states (rather than crystalline solids with long-range order). Exceptions to this may exist for some systems in a particular composition range involving the metastable region of a liquid–liquid equilibrium phase diagram (e.g., Zuend et al., 2010). However, the energy barrier for the nucleation and growth of a new liquid phase is small in comparison to the larger energy barrier that needs to be overcome when a new crystalline phase is formed. Because the merging of the phases is predicted to occur at an RH at which aqueous diethylmalonic acid is expected to be of low viscosity (Fig. 1a), no hysteresis behavior is expected. Thus, we do not expect that a hysteresis behavior influenced the disagreement in the RH of phase merging discussed above.
Like the diethylmalonic acid–ammonium sulfate system, the
2-methylglutaric-containing aerosols demonstrate a marked increase in water
uptake at RH
For the citric acid–ammonium sulfate particles, measured growth factors
suggest gradual, continuous water uptake at all experimental RH values (Fig. 1c). This is in agreement with measurements for this system at different dry
organic : inorganic ratios reported by Zardini et al. (2008). The
AIOMFAC-predicted growth curve indicates a small increase in slope with the
deliquescence of ammonium sulfate at RH
A comparison of hygroscopic growth curves across the three two-component systems suggests that growth curve shape reflects phase behavior in mixed organic–ammonium sulfate systems. Growth curves approach smoother, more continuous water uptake with decreasing prevalence of LLPS (i.e., looking from left to right for Fig. 1a–c). In addition to higher miscibility of the aerosol components for particles with no LLPS or those for which LLPS persists for only a small range of RH values, this can likely be attributed to the fact that both the prevalence of LLPS and aerosol hygroscopicity vary with the O : C ratios of the organic components of mixed organic–inorganic particles (Massoli et al., 2010; Bertram et al., 2011; Duplissy et al., 2011; Song et al., 2012a; You et al., 2013). Note that the O : C ratios of diethylmalonic, 2-methylglutaric, and citric acid are 0.57, 0.67, and 1.17, respectively. Thus, the smoothing of the growth curves with increasing O : C (and, incidentally, lower prevalence of LLPS) is consistent with the higher propensity of the more polar compounds to take up water and dissolve some ammonium sulfate (in an SLE) at lower RH.
In general, water-uptake behavior was similar across the more complex
dicarboxylic acid–ammonium sulfate mixtures, regardless of the carbon number
of the acids included in the system and the differences in the phase
morphologies of the particles observed previously in experiments by Song et
al. (2012a). All systems demonstrated gradual water uptake with growth
factors increasing from 1.0 to
As determined both through previous experimental work and with the AIOMFAC
modeling, there is variability in phase behavior across the mixed
dicarboxylic acid–ammonium sulfate aerosol systems. For the C
Top panels: measured and AIOMFAC-predicted hygroscopic diameter
growth factors for
The pure sucrose aerosols demonstrate continuous, but limited, water uptake
with growth factors reaching only 1.25 at RH
Like pure sucrose, the sucrose–ammonium sulfate systems demonstrate
continuous water-uptake behavior, with smaller HGFs compared to pure
ammonium sulfate at RH
Top panels: Measured and AIOMFAC-predicted hygroscopic growth
factors for
Evidence for the influence of a highly viscous phase state on hygroscopic
behavior is stronger for the mixed sucrose–ammonium sulfate aerosols. While
for stable thermodynamic equilibrium AIOMFAC predicts distinct deliquescence
behavior at RH
The formation of a highly viscous liquid or semi-solid phase may also lead
to kinetic limitations, affecting the loss of water by evaporation during
the drying process prior to humidification in the DASH-SP. There is
increasing evidence from laboratory and field studies that viscous liquid or
semi-solid SOA components may be present in atmospheric aerosol (e.g.,
Virtanen et al., 2010; Vaden et al., 2011; Saukko et al., 2012; Renbaum-Wolff
et al., 2013). Thus, accounting for kinetic limitations to water uptake and
release is crucial to accurately modeling the dynamic hygroscopic behavior
of SOA. However, the good agreement between measured HGFs and the
AIOMFAC-based dehydration-branch equilibrium calculations indicates that
water loss was not substantially inhibited during particle drying. If a
glassy sucrose shell had formed in these particles and this shell was of
sufficient thickness to inhibit water evaporation during the
As noted above, data availability limitations and variability in experimental conditions for the data sets used in developing parameterizations of functional-group–ion interactions in AIOMFAC contribute to uncertainties in ether–ion interactions and other functional-group–ion interactions. In addition, other measurement and modeling limitations can contribute to uncertainty in measured and predicted HGFs. Because experimental data regarding the densities of organic compounds are limited, the densities of many of the organic compounds studied in this work were estimated with a group-contribution method (Girolami, 1994). Furthermore, for all aerosol systems and all phases present within the particles it was assumed that the molar volumes of the aerosol components are additive (i.e., ideal mixing in terms of volume and density contributions), regardless of the thermodynamic properties of the mixture under consideration.
Complex particle-phase morphologies can also present unique sources of error
and uncertainty in HGF measurement methods that use optical methods, such as
the DASH-SP. For example, the algorithm that calculates diameter growth
factor assumes that the refractive index of the non-water aerosol components
is constant at the value measured in the dry DASH-SP channel. For systems
with non-uniform surfaces (e.g., the C
In addition, as noted above, the DASH-SP HGF experiments were performed with
particles much smaller than those used in the microscopy or electrodynamic
balance experiments that had previously been used to directly characterize
LLPS and glass transitions in the particle systems studied. Thus, the phase
behavior of the particles studied here was not characterized directly. There
is some limited evidence that the prevalence of LLPS can vary with particle
size. Veghte et al. (2013) observed that LLPS did occur in larger particles
comprised of ammonium sulfate and succinic acid or pimelic acid (diameters
Comparison of simplified thermodynamic assumptions to the full
AIOMFAC hygroscopic growth calculations for the multi-component systems for
which we expect observed water-uptake behavior to be governed by
thermodynamic equilibrium conditions. Organic : inorganic dry mass ratios,
which can substantially influence the extent to which non-ideal interactions
affect water uptake, are given in parentheses. The performance of the
simplified modeling approaches varies across the systems with variations in
phase behavior. Disagreement between the full AIOMFAC-based equilibrium
calculations and the simplified models is greatest at low to moderate RH (RH
For the multicomponent systems for which we expect that observed
water-uptake behavior is governed by thermodynamic equilibrium conditions
(i.e., excluding the sucrose-containing systems, which display evidence of
kinetic limitations to the crystallization of ammonium sulfate), we compared
the rigorous thermodynamic modeling of the AIOMFAC-based equilibrium HGF
predictions (“AIOMFAC, equilibrium” in Fig. 4) to that based on several
simplified thermodynamic assumptions: (1) representing particles as ideal,
well-mixed liquids (“ideal – well-mixed liquid”), (2) forcing a single
liquid phase following the deliquescence of ammonium sulfate but accounting
for non-ideal interactions through activity coefficient calculations and
allowing for a SLE of ammonium sulfate (“no LLPS – non-ideal”), and (3) a
ZSR-like calculation in which complete separation of the inorganic and
organic components is assumed at all RH levels (“complete phase separation
(ZSR)”). Water is the only component allowed to partition to both phases in
this ZSR-like calculation case. In all of these simplified calculation
cases, the formation of a solid ammonium sulfate phase is allowed to occur
(below its deliquescence point at the given temperature), except for the
single-phase, ideal mixture case. We evaluate the extent to which these
simple, relatively computationally inexpensive modeling approaches capture
the hygroscopic behavior of particles with varied and complex phase states.
Note that for the diethylmalonic acid–ammonium sulfate system, we first
focus on the calculation for which the presence of a solid organic is
predicted prior to particle deliquescence (“solid organic” in Fig. 4).
At RH
Figure 4 shows a comparison of the AIOMFAC-predicted HGFs for the
hydration branch of a humidity cycle and those calculated with the
simplified modeling approaches. The performance of each of the simplified
modeling approaches differs for particles depending on phase state. This
suggests that a single simplified modeling approach cannot be used to
capture the water-uptake behavior for the diversity of particle-phase
behaviors expected in the atmosphere. For all systems except the citric
acid–ammonium sulfate particles, the assumption that the particles could be
represented as thermodynamically ideal liquid mixtures leads to the greatest
deviation from AIOMFAC-predicted growth curves. We also note that such
discrepancies depend on the organic : inorganic dry-state mass ratios.
Generally, the smaller the ammonium sulfate mass fraction, the lower the
degree of hysteresis behavior of hydration/dehydration processes.
Overpredictions of diameter growth factors increase from those at low RH to
a maximum just prior to the rapid increase in water uptake associated with
deliquescence of ammonium sulfate, then drop to within
Not surprisingly, the forced single-phase calculations, in which non-ideal
interactions are taken into account but LLPS is not, perform well for the
C
For systems that do undergo LLPS, the ZSR-like calculation also performs relatively well across the range of RH values studied but displays discrepancies to the AIOMFAC-based equilibrium prediction of 12–18 % at moderate RH values due to deviations in the predicted SLE and deliquescence transition of ammonium sulfate. For these systems, the ZSR-like calculation also underpredicts water uptake at RH values above the point at which separated liquid phases merged to a single phase, with relative deviations approaching 10 %. As expected, growth curves begin to converge towards the AIOMFAC equilibrium predictions as RH approaches 100 % for all systems, as the solutions become very dilute (Fig. 4). Our results suggest that a lack of accounting for non-ideal interactions and phase separations leads to errors in predicted sub-saturated hygroscopic growth. Note that while maximum deviations in HGFs for the simplified approaches (compared to the AIOMFAC-based equilibrium calculation) are generally on the order of 10–25 %, the corresponding errors in particle size and refractive index can substantially impact estimates of aerosol scattering and radiative forcing (Finlayson-Pitts and Pitts, 2000).
Measurements and detailed thermodynamic modeling of the water uptake of
model organic–inorganic atmospheric aerosol systems demonstrate variability
in hygroscopic behavior across aerosol systems with differing RH-dependent
phase behavior. Measured and modeled growth curves approach smoother, more
continuous water uptake with decreasing prevalence of LLPS and
increasing O : C ratios of the OA components. AIOMFAC-predicted growth curves
reproduce the measured hygroscopic behavior reasonably well for all systems.
A comparison of measured and modeled HGFs for the sucrose–ammonium
sulfate particles indicates the presence of a viscous semi-solid phase that
inhibits the crystallization of ammonium sulfate. We conclude that particle
drying within HGF instrumentation may induce the formation of a highly
viscous, amorphous phase (potentially accompanied by a moisture-loss-related
glass transition). As a result, such measurements may not accurately reflect
equilibrium water-uptake behavior. This is an important consideration when
applying similar instruments to measure the hygroscopic behavior of ambient
aerosols, particularly for the highly oxygenated SOA for which sucrose
serves as a surrogate in our experiments. Our results add support to the
growing body of literature suggesting that accounting for the influence of
viscous liquid or semi-solid phases to water uptake and release can be
important for accurately modeling the hygroscopic behavior of atmospheric
aerosols. The performance of simplified approaches for modeling water uptake
differs for particles with differing phase states/equilibria, suggesting
that a single simplified modeling approach cannot be used to capture the
water-uptake behavior for the diversity of particle-phase behavior expected
in the atmosphere. Errors in HGFs calculated using the simplified models are
of sufficient magnitude to contribute substantially to uncertainties in
estimates of particle optical and radiative properties. Parameterizations of
LLPS and other complex phase behavior based on commonly measured variables
such as O : C (e.g., Bertram et al., 2011; Koop et al., 2011; Song et al.,
2012a) may prove valuable in applying the simplified HGF calculation
approaches explored here in large-scale models. Average carbon oxidation
state (
AIOMFAC is a group-contribution, thermodynamic model for the calculation of
component activity coefficients in binary and multicomponent mixtures. It
was developed to explicitly account for molecular interactions among
organic functional groups and inorganic ions in aqueous solutions relevant
to atmospheric aerosol chemistry. Descriptions of model details and
parameterizations are available elsewhere (Zuend et al., 2008, 2010, 2011;
Zuend and Seinfeld, 2012;
Within the model, organic molecules are represented as assemblies of
functional groups. This treatment of organic molecules is based on the
concept that the physiochemical properties of organic compounds can be
related to their chemical structure and characteristic structural groups,
which allows for treatment of the hundreds to thousands of organic compounds
that characterize atmosphere organic aerosol. The organic functional groups
included in AIOMFAC (alkyl (standard), alkyl (in alcohols), alkyl (in
hydrophobic tails of alcohols), alkyl (bonded to hydroxyl group), alkenyl,
aromatic hydrocarbons, hydroxyl, aromatic carbon-alcohol, ketone, aldehyde,
ester, ether, carboxyl, hydroperoxide, peroxy acid, peroxide (organic),
peroxyacyl nitrate, organonitrate) allow for the representation of a large
variety of compounds observed in atmospheric aerosols. In addition, AIOMFAC
includes seven atmospherically relevant cations (H
Non-ideality (i.e., deviations from Raoult's law) in organic–inorganic
aqueous solutions is accounted for through the calculation of activity
coefficients for all components in a given mixture. When considering the
partitioning of water vapor to a multicomponent liquid mixture, the vapor
pressure of water (
In AIOMFAC, activity coefficients are derived from expressions for the long-range, middle-range, and short-range molecular interactions that contribute to total Gibbs excess energy, which is a descriptor of the overall non-ideality of a thermodynamic system. In addition to their application in calculations of the gas-particle partitioning of water and other semi-volatile species (i.e., vapor-liquid equilibria), activity coefficients of all components in a multi-component mixture are required for the calculation of solid-liquid (SLE) and liquid–liquid equilibria. The prevalence of liquid–liquid phase separation and the composition of each phase is calculated in this work by application of AIOMFAC to compute activity coefficients in distinct liquid phases based on a reliable and efficient algorithm for finding the phase compositions that correspond to an equilibrium state. A liquid–liquid equilibrium state of a closed thermodynamic system is a state of minimum Gibbs energy of that system. The same applies to SLE and, likewise, to coupled vapor–liquid–liquid–solid equilibrium calculations, such as those performed in this work at given temperature and relative humidity to determine the number and composition of the particle phases at equilibrium. Hence, while the AIOMFAC model is at the heart of such equilibrium calculations, the distinct phases and their compositions are determined using a more general thermodynamic equilibrium model, as described by Zuend et al. (2010) and Zuend and Seinfeld (2012). For the calculation of a potential liquid–liquid phase separation, the equilibrium model essentially solves a system of nonlinear equations numerically to determine the phase state (i.e., one liquid phase vs. two liquid phases) that achieves a minimum in Gibbs energy for a given overall particle-phase composition at constant temperature and pressure. Full details regarding the algorithm used to diagnose the prevalence of LLPS and to calculate the corresponding phase composition are available in Zuend and Seinfeld (2013).
Following the same methods as described in the main text of the paper,
control hygroscopic growth experiments were conducted for pure ammonium
sulfate aerosols with dry mobility diameters of 250 nm. HGF experiments were
conducted at room temperature (
Measured and modeled hygroscopic growth factors for ammonium sulfate particles with dry mobility diameters of 250 nm. The black circles indicate the average growth factor measured across 10 experiments and error bars indicate the standard deviation of the measured growth factors.
N. Hodas, J. H. Seinfeld, and R. C. Flagan designed the experiments. N. Hodas carried out the experiments with assistance from W. Mui. A. Zuend developed the modeling tools and performed all simulations. N. Hodas prepared the manuscript with contributions from all co-authors.
This work was supported by the National Science Foundation under award no. 1433246 and the Office for Naval Research under award no. N00014-14-1-0097. W. Mui was supported by an NSF graduate research fellowship (grant no. DGE-1144469) and NSF grant no. CBET-1236909. A. Zuend was supported by a McGill University start-up grant. Edited by: T. Koop