The role of surface tension (σ) in cloud droplet activation has long
been ambiguous. Recent studies have reported observations attributed to the
effects of an evolving surface tension in the activation process. However,
the adoption of a surface-mediated activation mechanism has been slow and
many studies continue to neglect the composition dependence of
aerosol–droplet surface tension, using instead a value equal to the surface
tension of pure water (σw). In this technical note, we
clearly describe the fundamental role of surface tension in the activation of
multicomponent aerosol particles into cloud droplets. It is demonstrated that
the effects of surface tension in the activation process depend primarily on
the evolution of surface tension with droplet size, typically varying in the
range 0.5σw≲σ≤σw due to
the partitioning of organic species with a high surface affinity. We go on to
report some recent laboratory observations that exhibit behavior that may be
associated with surface tension effects and propose a measurement coordinate
that will allow surface tension effects to be better identified using
standard atmospheric measurement techniques. Unfortunately, interpreting
observations using theory based on surface film and liquid–liquid phase
separation models remains a challenge. Our findings highlight the need for
experimental measurements that better reveal the role of
composition-dependent surface tensions, critical for advancing predictive
theories and parameterizations of cloud droplet activation.
Introduction
The formation of a cloud involves a complex series of steps as nanometer-sized aerosol particles, termed cloud condensation nuclei (CCN), grow by
condensation of water vapor to become supermicron-sized cloud droplets in a
process known as CCN activation. Activation depends on the physicochemical
properties of the aerosol, such as hygroscopicity and surface tension, as
well as atmospheric conditions, such as temperature and humidity. To
accurately predict cloud formation and properties, these factors must be
included in modeling schemes. However, due to computational limitations,
approximations and simplifications are needed, which often obscures the
underlying physics and may limit the accuracy of predictions. A key
challenge is in the development of a simple model that captures the basic
processes involved in CCN activation, while allowing complicating factors
such as surface tension variability, solubility, and phase separation to be
included in a physically representative manner. In this note, we focus on
the role of surface tension and discuss the limitations of current
approximations in light of recently published works that reveal how it is
primarily the evolution of surface tension that impacts the activation
process.
In recent publications, the role of surface tension in the activation of
aerosol particles to cloud droplets has been reexamined (Forestieri et al.,
2018; Ovadnevaite et al., 2017; Ruehl et al., 2016). These studies show that the evolution of
surface tension can have a large effect during the activation process
compared to when surface tension is assumed to be a static parameter. It is
well established that surface tension is a factor in activation and that
dissolved species can suppress surface tension (Li et al., 1998).
Traditionally, however, surface tension has been reduced to a fixed term in
the Köhler equation (Abdul-Razzak and Ghan, 2000; Facchini et al., 2000;
Petters and Kreidenweis, 2007) and is usually given a
temperature-independent value equal to that of pure water at 25 ∘C.
This is because for any decrease in surface tension due to bulk–surface
partitioning and surface adsorption, it is assumed that there is an increase
in the solution water activity because adsorbed material, previously acting
as a hygroscopic solute, is removed from the droplet (bulk) solution
(Fuentes et al., 2011; Prisle et al., 2008; Sorjamaa et al., 2004). Thus,
the effects approximately cancel out in the calculation of a droplet's
equilibrium saturation ratio via the Köhler equation and so are often
neglected. Furthermore, it has been shown in some cases that there is
insufficient material in a droplet at the sizes approaching activation to
sustain a surface tension depression (Asa-Awuku et al., 2009; Prisle et al.,
2010). The lack of experimental evidence to the contrary has led to the
adoption of these assumptions in popular single-parameter models, such as
κ-Köhler theory, that reduce the complexity of the activation
process (Petters and Kreidenweis, 2007). These parameterizations provide a
compact and useful means of relating key observables, such as the critical
supersaturation and activation diameter, to hygroscopicity and allow for a
general comparison between systems with arbitrary compositions. The
κ-Köhler framework has also been adapted to account for surface
tension effects (Petters and Kreidenweis, 2013). However, a single-parameter
implementation cannot account for the full effects of an evolving surface
tension and, by omitting the microphysical processes associated with
bulk–surface partitioning, the presence and magnitudes of any surface
effects are often difficult to ascertain.
In the works of Ruehl and coworkers (Ruehl et al., 2016; Ruehl and Wilson,
2014), Forestieri and coworkers (Forestieri et al., 2018), and Ovadnevaite
and coworkers (Ovadnevaite et al., 2017), laboratory and observation-based
measurements, respectively, combined with a partitioning model have revealed
key signatures of surface tension lowering in the activation process due to
non-surfactant organic compounds. Notably, a modification of the
Köhler curve can result in lower critical supersaturations and vastly
different droplet sizes at activation compared to the expectation when
assuming a constant surface tension. Dynamic factors may also play a role,
as discussed by Nozière and coworkers (Nozière et al., 2014), who
have shown that surface tension can vary over time due to slow changes in
the bulk–surface partitioning of material, leading to a time dependence in
the role of surface tension. This may be especially important for droplets
that initially contain micelles or oligomers that exhibit slow breakdown
kinetics and diffusion. Furthermore, surface partitioning may be influenced
by non-surface active components in the system, such as the presence of
inorganic material and co-solutes (Asa-Awuku et al., 2008; Boyer et al.,
2016; Boyer and Dutcher, 2017; Frosch et al., 2011; Petters and Petters,
2016; Prisle et al., 2011; Svenningsson et al., 2006; Wang et al.,
2014).
Other factors that have been shown to influence the shape of Köhler
curves are (1) solute dissolution, encompassing both water solubility and
solubility kinetics (Asa-Awuku and Nenes, 2007; Bilde and Svenningsson,
2017; McFiggans et al., 2006; Petters and Kreidenweis, 2008; Shulman et al.,
1996), (2)
liquid–liquid phase separation (i.e., limited liquid–liquid solubility)
(Rastak et al., 2017; Renbaum-Wolff et al., 2016), and (3) the dynamic
condensation (or gas–particle partitioning) of organic vapors (Topping et
al., 2013; Topping and McFiggans, 2012). While measured cloud droplet number
concentrations in the atmosphere have been explained in several cases with
simple parameterizations that neglect dynamic surface effects (Nguyen et
al., 2017; Petters et al., 2016), there are many observations that are not
fully explained in such simple terms and in those cases a substantial
population of CCN may exhibit behavior characteristic of surface effects
(Collins et al., 2016; Good et al., 2010; Ovadnevaite et al., 2011;
Yakobi-Hancock et al., 2014). In order to gain a robust and predictive
understanding of CCN activation, a molecular-level theory must be developed
and adopted by the atmospheric chemistry community.
In this technical note, we offer a perspective on the role of surface
tension in the activation process, drawing on recent studies and
interpretations of cloud droplet activation measurements (e.g., Forestieri
et al., 2018; Ovadnevaite et al., 2017; Ruehl et al., 2016; Ruehl and
Wilson, 2014). We go on to discuss how surface tension may be considered in
the activation process and finally present some new data highlighting
potential indicators of surface tension effects in measurements of critical
supersaturation. Our aim is to provide a platform for discussion and help
foster a molecular-based interpretation of the role of organic material in
the activation of aerosol to cloud droplets.
Clarifying how surface tension alters cloud droplet activation
On a fundamental level, the influence of surface tension on droplet
activation is straightforward and was discussed in the late 1990s for
aerosol particles containing surfactants (Li et al., 1998).
Unfortunately, the simplicity of the role of surface tension in CCN
activation has been lost in the complex descriptions of surface and
phase partitioning models, limiting the broader application of the insights
gained from recent experimental results. For context, we begin our
discussion with Köhler theory (Köhler, 1936), which describes the
thermodynamic conditions required for CCN activation based on two
contributions that control the equilibrium (saturation) vapor pressure of
water above a liquid surface. The classic Köhler equation is often
written as (Petters and Kreidenweis, 2007)
Sd=pw,dDpw0=awexp4MwσRTρwD
where Sd is the equilibrium saturation ratio of water in the vapor phase
surrounding a droplet surface, pw,dD is
the equilibrium partial pressure of water vapor above a droplet (subscript
d) of diameter D and a certain chemical composition, pw0 is the
pressure of water above a flat, macroscopic surface of pure liquid water at
temperature T, aw is the mole-fraction-based water activity of the
droplet solution, Mw is the molecular mass of water, σ is the
surface tension of the particle (at the air–liquid interface), R is the ideal gas
constant, and ρw is the density of liquid water at T. The water
activity contribution, known as the solute or Raoult effect, describes a
lowering of the equilibrium water vapor pressure above a liquid surface due
to the presence of dissolved (hygroscopic) species that reduce the water
activity to a value below 1. The second contribution, known as the Kelvin
effect, describes an increase in the equilibrium water vapor pressure above
a microscopic curved surface and is dependent upon the surface-area-to-volume ratio of the droplet (a size effect) and the surface tension,
i.e., the gas–liquid interfacial energy per unit area of surface. The latter
term arises from the energy associated with creating and maintaining a
certain surface area and is thus reduced when the surface tension is
lowered or when the droplet size increases, leading to a smaller
surface-to-volume ratio. The magnitude of the Kelvin effect scales with the
inverse of the droplet radius and is sometimes referred to as the
“curvature effect”. The combined contributions from the Raoult and Kelvin
effects in Köhler theory define a thermodynamic barrier to droplet
growth. It is important to note that the Köhler equation describes the
specific saturation ratio Sd in thermodynamic equilibrium with a certain
solution droplet of interest; however, the value of Sd may differ from
that of the environmental saturation ratio, Senv, present in
the air parcel containing the droplet, since Senv is
established by an interplay of moist thermodynamic processes. The
environmental saturation ratio is defined by
Senv=pwpw0, where
pw is the partial pressure of water in air at a specific location and
time, irrespective of the presence or absence of aerosols and cloud
droplets. The global maximum in a Köhler curve marks the point of
activation for a certain CCN, as shown in Fig. 1a. For conditions of
Sd≤Senv, e.g., in a rising, adiabatically expanding air
parcel, aqueous CCN equilibrate relatively quickly to their environmental
conditions such that Sd=Senv is maintained (stable
growth and evaporation). However, when Senv exceeds the global
maximum in Sd for a certain CCN, such an equilibration becomes
unattainable and net condensation of water prevails, leading to so-called
unstable condensational growth for as long as Senv>Sd
holds (while Sd varies according to the pertaining Köhler curve).
(a) Köhler curve construction from the combination of the
water activity term and the Kelvin effect, shown here for 50 nm particles of
ammonium sulfate. The arrows indicate the critical supersaturation
(SScrit) and the critical wet activation diameter (Dcrit). (b)
Köhler curves (NB. SS=(S-1)×100 %) of varying fixed
surface tension values for 50 nm (dry diameter) particles with water
activity treated as an ammonium sulfate solution. A schematic linear
dependence of surface tension on droplet diameter is shown in black, and the
Köhler curve construction that takes into account the change in surface
tension is shown in bold and with diamond symbols. Additional surface
tension dependencies are shown in red, which exhibits activation at σ<σw, and in blue, which shows a dramatic increase in
the critical wet diameter.
A Köhler curve shows the relationship between the droplet's equilibrium
water vapor saturation ratio and the wet droplet size. The wet droplet size,
or more specifically the chemical composition (solute concentration),
solubility, and nonideal mixing determines the water activity, while the
size and surface tension determine the Kelvin effect. Since the solute
concentration changes with the droplet size, e.g., during net growth
conditions when the environmental saturation ratio in an air parcel
increases and water vapor condenses, the water activity term varies
accordingly, typically in a nonlinear manner. The Kelvin term should also
change with droplet size due to both the changing surface-to-volume ratio
of the droplet and changes in surface tension as a result of changes in
solute concentration and related surface composition. In most scenarios,
only the diameter change is accounted for, while the surface tension is
assumed to remain constant, usually with the value for pure water (σ=σw≈72 mN m-1 at 298 K). This oversimplifies the
problem, especially when organic solutes are present that adsorb at the
surface of the growing droplet. In experimental studies in which only the
critical supersaturation or critical dry diameter are measured, this
assumption can lead to errors, as the complexity of the system may not allow
for such simplified treatments to yield sufficiently accurate
representations of a real-world problem. In such cases, one must consider
how the changing size of the droplet (or, again, more specifically the
solution composition) results in changes in bulk–surface partitioning and
ultimately surface tension.
Recent work has shown that a rigorous account of bulk–surface partitioning
leads to complex Köhler curves whose shapes are often difficult to
interpret (Ruehl et al., 2016). These shapes can be more easily understood by
considering a very simple example, shown in Fig. 1b. Here, a series of fixed
surface tension (iso-σ) Köhler curves with values ranging from 72 to
30 mN m-1 are shown, using the same 50 nm particle (of ammonium
sulfate) from Fig. 1a. Distinct schematic dependences of the surface tension
on the droplet size, representative of the types of dependence that might be
encountered in real aerosol, are
imposed for the purpose of illustration, shown in the lower panel of Fig. 1b.
At each point along these dependences, the saturation ratio will be
determined by the position on the Köhler curve corresponding to that
specific surface tension. This means that instead of following a single
trajectory along an iso-σ curve, the system is better
envisioned as traversing across these curves, producing a very different
final shape to the Köhler curve than would normally be expected. In the
case of a linear dependence of σ on D (black curve), the Köhler
curve cuts across the iso-σ lines until σ reaches
the value of pure water. In this case, this coincides with reaching the
maximum in the droplet's saturation ratio and thus reflects the activation
point. In the case shown in red, activation occurs prior to the surface
tension returning to the value of pure water. In the case shown in green,
activation follows a pseudo two-step process, whereby initially a large
increase in size occurs for a small increase in supersaturation, and thus the
droplet may appear to be activated, while in this case true activation occurs
at the point corresponding to the intersection with the Köhler curve of
σ=σw. It is important to note that it is not
necessarily the magnitude of the suppression of surface tension that drives
unusual activation behavior, but the dependence of the surface tension on
concentration, which is dictated by the droplet size and the thermodynamics
of the system.
It is apparent from these examples that an evolving surface tension may
introduce abrupt changes in the activation curve that arise due to the phase
behavior of monolayer systems. The most obvious change is where the surface
tension returns to the value of pure water. Following this point, the system
will follow the iso-σ curve corresponding to pure-water surface tension
(under continued and sufficient supersaturation conditions). Depending on
the exact relationship of surface tension and droplet size, this point can
mark the activation barrier of the system, as is the case in Fig. 1b for
the black and green curves. This also seemingly supports previous
assertions, as discussed in Sect. 1, that surface tension does not impact
activation, since it is generally argued that at the point of activation the
droplet is sufficiently dilute and essentially exhibits a surface tension
like pure water (Fuentes et al., 2011; Prisle et al., 2008; Sorjamaa et al.,
2004). While that is the case in this example, the trajectory of the
activation process is significantly altered by the surface tension history
of the droplet. In other words, for the systems described by the black or
green curves in Fig. 1b, the surface tension at the point of CCN activation
is that of pure water, yet if one assumed the surface tension of the
droplet to be constantly that of pure water at any size prior to activation,
the critical supersaturation, SScrit, would be significantly higher and
the critical (wet) activation diameter, Dcrit, substantially smaller
(see the Köhler curve for σ=σw). Clearly, an
evolving surface tension prior to activation can matter in such systems and,
consequently, knowing the surface tension only at the point of activation is
in a general case insufficient for determining the critical properties at
activation (absent any droplet size measurement) because the position of
the maximum in the Köhler curve, and thus the droplet size at
activation, will depend on the trajectory of surface tension evolution.
Moreover, knowing the surface tension at the activation point only may not
allow for an accurate prediction of whether a droplet of given dry diameter
will activate at a given environmental supersaturation (compare the green
curve with the iso-σ curve of 72 mN m-1 in Fig. 1b, both having the
same surface tension at their points of CCN activation, yet different
critical supersaturations and wet diameters). Similar conclusions have been
drawn previously (e.g., Prisle et al., 2008), although the results of Ruehl
et al. (2016) were the first to verify this experimentally.
Surface tension evolution during activation
A major consequence of an evolving surface tension is that the droplet size
at activation is larger, and the actual critical supersaturation depends on
how surface tension varies in the droplet as it grows. These effects were
directly measured using a thermal gradient chamber (TGC) (Roberts and Nenes,
2010; Ruehl et al., 2016). In the 2016 work, mixed ammonium sulfate and
organic aerosols were introduced into the TGC at various supersaturations
(up to and including the activation supersaturation). The size of the
aerosol particles was measured under these conditions, allowing for a direct
measurement of the stable equilibrium branch of the Köhler curve (i.e.,
the size up to the point of activation). It was shown that for highly
soluble and surface inactive solutes such as ammonium sulfate and sucrose,
the data exhibit the behavior expected when assuming an iso-σ
Köhler curve. However, for the case when organic acids, spanning a range
of water solubilities, were coated on ammonium sulfate particles of specific
dry sizes, the measurements clearly show modifications to the Köhler
curve in comparison to an iso-σ Köhler curve, which were explained
by changes in surface tension corresponding to bulk–surface partitioning as
predicted by a compressed film model. Without these observations, assuming
σ=σw, one could attribute the critical
supersaturation to a single, apparent κ value that describes the
hygroscopic effect of the mixture of solutes in the absence of any surface
tension constraints (Petters and Kreidenweis, 2007). Low-solubility and low-hygroscopicity species should exhibit very small κ values. However,
in the case of suberic acid, for example, the CCN activation data of Ruehl
et al. would require a κ value of approximately 0.5 for the organic
component, assuming a fixed surface tension equal to that of water. This
κ value is unphysically large considering that the molar volume
ratio suggests a value of ∼0.13 for suberic acid when
assuming full solubility, the surface tension of pure water, and ideal mixing
with water. A different prediction, accounting for limited solubility and
assuming a constant surface tension using the value of the saturated aqueous
solution, estimates its value as κ≈0.003 (Kuwata et al.,
2013). Moreover, the apparent κ value derived from CCN activation
data of pure suberic acid particles indicates a value of ∼0.001 (Kuwata et al., 2013). Invoking a surface tension model here is the
only way to make physical sense of these observations, allowing even low-solubility and nonhygroscopic solutes to contribute significantly to the
activation efficiency in mixed droplets. The modeling approaches of Ruehl
and coworkers (Ruehl et al., 2016) and Ovadnevaite and coworkers
(Ovadnevaite et al., 2017) use Köhler theory with
either a bulk–surface partitioning model (compressed film model) or an
equilibrium gas–particle partitioning and liquid–liquid phase separation
(LLPS) model with variable surface tension. Both studies also employed
simplified organic film models, in which the assumption is made that all
organic material resides in a water-free surface film, as options for
comparison with the more sophisticated approaches.
A bulk–surface partitioning model is comprised of two components: a
two-dimensional equation of state that relates the surface tension to the
surface concentration and a corresponding isotherm that relates the surface
and bulk solution concentrations. In the work of Ruehl et al., the
compressed film (Jura and Harkins, 1946) and Szyszkowski–Langmuir equations
of state were compared. The latter has been used in several studies
exploring bulk–surface partitioning in organic aerosol (Prisle et al., 2010;
Sorjamaa et al., 2004; Topping et al., 2007). The compressed film model
reproduced the experimental observations, capturing the complex shapes of
the measured Köhler curves. The Szyszkowski–Langmuir method was unable
to explain several of the observations, attributed partly to the lack of a
two-dimensional phase transition between a film state and a non-film state,
which is a unique feature of the compressed film model. Earlier work by
Ruehl and coworkers successfully used a van der Waals equation of state to
model the behavior of organic and inorganic mixed droplets at high relative
humidity (Ruehl and Wilson,
2014), demonstrating the effect
of surface tension following the onset of film formation once sufficient
organic material was present. While we know the factors that contribute to
the equation of state and isotherm for well-controlled systems, the enormous
complexity of atmospheric aerosol presents a significant challenge in
developing and utilizing a predictive general model or theoretical
framework.
The equilibrium gas–particle partitioning and liquid–liquid phase
separation model is based on the Aerosol Inorganic–Organic Mixtures
Functional groups Activity Coefficients (AIOMFAC) model (Zuend et al., 2008,
2011), coupled to a relatively simple phase-composition- and
morphology-specific surface tension model. A detailed description of this
AIOMFAC-based model, its variants, and sensitivities to model parameters and
assumptions is given in the Supplement of Ovadnevaite et al. (2017). Briefly,
the equilibrium gas–particle and liquid–liquid
partitioning model is used to predict the phases and their compositions for
a bulk mixture “particle”, here of known dry composition, at given RH and
temperature. For other applications with given total gas + particle input
concentrations, the equilibrium condensed-phase concentrations can be
computed as a function of RH (accounting for the partitioning of semivolatiles).
Assuming spherical particles of a certain dry diameter with a core–shell
morphology of liquid phases in the case of LLPS, density information from
all constituents is used to compute volume contributions and the size of the
particle at elevated RH. In addition, the surface tension of each individual
liquid phase is computed as a volume-fraction-weighted mean of the
pure-component surface tension values. In the case of LLPS, the surface
coverage of the (organic-rich) shell phase is evaluated by considering that
it must be greater than or equal to a minimum film thickness (monolayer as a
lower limit); this determines whether complete or partial surface coverage
applies for a certain wet diameter. The effective surface tension of the
whole particle is then computed as the surface-area-weighted mean of the
surface tensions of contributing phases. This way the surface tension
evolves in a physically reasonable manner as a droplet grows, including the
possibility for abrupt transitions from a low surface tension, established
due to full organic droplet coverage under LLPS, to partial organic film
coverage after monolayer film breakup, and further to the complete dissolution
of organics in the aqueous inorganic-rich phase (single aqueous phase). This
equilibrium model is referred to here as AIOMFAC-EQUIL. We also employed two
AIOMFAC-CLLPS model variants, in which the organic constituents are assumed
to reside constantly in a separate phase from ammonium sulfate (complete
LLPS, an organic film) either with or without water present in that phase,
as discussed in Sect. 4. This approach, introduced by Ovadnevaite and
coworkers (Ovadnevaite et al., 2017), shows promise due to its ability to
predict the existence of a surface tension activation effect consistent with
CCN observations taken in marine air containing a nascent ultrafine aerosol
size mode. In that study, enhanced CCN activity of ultrafine particles was
observed for aerosols consisting of organic material mixed with inorganic
salts and acids in North Atlantic marine air masses, which could not be
explained when accounting for hygroscopicity or solubility alone (when
assuming the surface tension of water). While the LLPS-based model and the
compressed film model of Ruehl et al. (2016) employ different principles and
descriptions to account for the surface composition, both agree that gradual
surface tension changes dominate the CCN activation process for these
systems. Interestingly, while the observations of Ruehl et al.. (2016) showed
activation occurring when the surface tension returns to its maximum value
(i.e., that of pure water), the phase separation model predicted activation
prior to the surface tension returning to its maximum (for ultrafine
particles). As discussed by Ovadnevaite et al. (2017), this difference in
the surface tension value reached at the point of CCN activation depends in
some cases on the size range of the (dry) particles considered (for the same
dry composition). Ovadnevaite et al.. (2017) show that for particles of larger dry
diameters (e.g., 175 nm for the case of their aerosol model system), CCN
activation is predicted to occur at a point at which the particle's surface
tension has reached the value of pure water (see the Supplement
to that study). Hence, both observations are consistent with the
picture developed in Fig. 1b and the details depend on the particle size
range and functional form describing the change in surface tension of the
system considered. Moreover, it is important to recognize that – regardless
of whether the surface tension is equivalent to or lower than that of pure
water at the CCN activation point – a CCN exhibiting an evolving, lowered
surface tension while approaching the activation point during hygroscopic
growth will activate at a lower supersaturation than a CCN of constant
surface tension equivalent to the pure-water value, since the former
activates at a larger diameter, as is evident from the examples of the red
and green Köhler curves shown in Fig. 1b. This predicted size effect
indicates that it is not generally valid to assume that all activating CCN
will have a surface tension equivalent to or close to that of pure water,
nor is it appropriate to use a single measurement of the surface tension of
a multicomponent CCN of known dry composition at its activation size (only)
to determine its Köhler curve, as also noted in previous studies (Prisle
et al., 2010, 2008; Sorjamaa et al., 2004). Furthermore, these model
predictions also suggest that measurements of the surface tension of larger
CCN particles (e.g., >150 nm dry diameter) may not allow for
conclusions about the surface tension of much smaller CCN, e.g., of 50 nm dry
diameter.
Identifying surface tension effects from critical supersaturation
Although the LLPS-based and compressed film models of CCN activation have had
some success in capturing surface tension effects, there remain substantial
challenges in developing a generalized theory. One challenge is that CCN
techniques do not measure surface tension directly but instead observe the
effects of changes in surface tension, which may often be attributed to
other factors. In order to identify surface tension effects using these
techniques, experiments must be performed to maximize the scope of surface
tension effects while minimizing changes in other variables that might
influence observations. Here, we propose new experiments, using a model
system as an example, which allows surface tension effects to be identified
in the absence of other complicating factors.
Using a cloud condensation nucleus counter (CCNC; Droplet Measurement
Technologies), we measured the supersaturation required to activate mixed
suberic acid and ammonium sulfate particles. Suberic acid was chosen to
represent the low-solubility oxygenated organic material typical of atmospheric
secondary organic aerosol. It is not a traditional surfactant, but its role
in suppressing surface tension and modifying the shape of the Köhler curve
has been previously identified (Ruehl et al., 2016). Ammonium sulfate
particles were generated using an atomizer and dried using silica gel and a
Nafion drier with dry N2 counter flow. The size distribution was
measured and a size-selected seed was introduced into a flow tube containing
suberic acid and housed within a furnace oven. The temperature was set to
volatilize the organic material and allow it to condense onto the seed
particles up to a desired thickness. The coated particles were size-selected
again and introduced into a particle counter and a CCNC at a concentration
of around 2000 cm-3. The activated fraction was measured as a function
of saturation ratio, and the critical supersaturation was determined from the
half-rise times of a sigmoid fit to the data. A range of dry particle sizes
and organic volume fractions (forg) were selected for measurements under
humidified conditions at room temperature (∼20∘C). Notably, the coated particle (i.e., total size) of the
aerosol in its dry state was kept constant across a dataset spanning a range
of organic volume fractions. The CCNC was calibrated with ammonium sulfate
particles at room temperature at regular intervals, although typically the
calibration remained stable during continued usage.
(a) Measured critical supersaturation (SScrit) of
size-selected ammonium sulfate particles coated with suberic acid (points)
to a set dry diameter of 100 nm at T≈293 K. The curves show
predictions from the compressed film model of Ruehl et al.. (2016), a simple κ-Köhler model with constant surface tension, and model variants from
the AIOMFAC-based framework (see text). (b) Analogous to (a) but for
particles of ammonium sulfate coated to 40 nm dry diameter by suberic acid.
(c) Using the data from (a) and (b), SScrit is shown as a function
of coated diameter with a fixed inorganic seed of 33 nm (points). The lines
indicate the κ-Köhler model with constant surface tension using
different but constant values of κorg.
The organic volume fraction (forg) was varied while maintaining
fixed dry particle sizes (Prisle et al., 2010; Wittbom et al., 2018),
ensuring that any surface tension effect would not be masked by changes in
the overall size, in contrast to other studies that allow both coated
particle size and organic volume fraction to vary simultaneously (e.g., Hings
et al., 2008; Nguyen et al., 2017). Figure 2a shows the critical
supersaturation as a function of forg for 100 nm (dry diameter)
mixed ammonium sulfate and suberic acid particles. Remarkably, despite the
much lower hygroscopicity of suberic acid relative to ammonium sulfate, there
is very little increase in the required supersaturation as the organic volume
fraction increases (while the ammonium sulfate volume fraction is reduced
accordingly). In fact, considering a fixed surface tension of pure water, a
κorg value of 0.35 for the organic fraction is required to
explain these data (using κ=0.62 for ammonium sulfate). This
κorg value is lower than that reported by Ruehl et
al. (2016) (where κorg=0.5), although those measurements
were performed on 150 nm particles at forg=0.963. If we apply
the compressed film model (using the parameters established in Ruehl et
al. (2016) for 150 nm particles at forg=0.963) to predict the
critical supersaturation as a function of forg, we obtain a
dependence that shows a peak SScrit at forg=0.4
(Fig. 2), followed by a decrease towards higher forg. This shape
is consistent with the lower value of SScrit reported by Ruehl
et al. (2016) at forg=0.963. If we use the
ideal molar-volume-derived κorg value of 0.131 and a
constant surface tension of σ=σw, the bulk solubility
prediction significantly overestimates SScrit for
forg>0.5. It must be noted here that without prior
knowledge that suberic acid is inherently of very low hygroscopicity and
exhibits low water solubility, the prediction using κorg=0.35 could be mistaken as the correct answer. However, a
κorg value of this magnitude is unphysical when considering
the original definition of κ. One could ignore the physical meaning
of κ and simply use it as an all-encompassing parameter to describe
activation efficiency. In this case, the generality of the parameter to
interpret observations in different conditions is lost. The compressed film
model decouples the water activity component from the surface tension
component and thus should better represent the physical processes at work.
However, the agreement for all these models breaks down further when looking
at differently sized particles. For example, Fig. 2b shows the same system of
ammonium sulfate and suberic acid, this time using 40 nm dry diameter
particles. In this case, the required supersaturation decreases with
increasing organic fraction, suggesting that suberic acid is more hygroscopic
than ammonium sulfate (requiring κorg=0.72). For the
ultrafine aerosol size reported here, the compressed film model does a worse
job at predicting the behavior, suggesting that it too suffers from a lack of
generality in its applicability. What is clear, however, is that a specific
suberic acid hygroscopicity alone cannot explain the observations across a
range of particle sizes and compositions.
These observations are obscured when the data are reported with a fixed
inorganic seed size with an increasing organic fraction achieved through an
increase in the coated diameter. The data as a function of forg
with a fixed total diameter were used to plot SScrit as a
function of forg with a fixed inorganic seed size, shown in
Fig. 2c with an arbitrarily chosen inorganic seed size of 33 nm dry
diameter. The value of SScrit for coated diameters 40, 50, and
100 nm was found by linear interpolation of the data in Fig. 2a and b (and
the 50 nm case in Fig. 3). The data are compared against a bulk κ-Köhler prediction, which exhibits a similar trend, although with a
slightly smaller slope when κorg=0.15. These data are
brought to agreement using κorg=0.4. However, we have
already shown that for the 40 nm case, a value of κorg
greater than that of AS is required to explain the data as a function of
forg with a fixed dry diameter. Specifically, in Fig. 2c, the
organic volume fractions are distinctly different for the three points shown:
forg=0.40, 0.70, and 0.96 for the 40, 50, and 100 nm coated
diameter cases, respectively. Thus, the choice of experimental procedure or
data presentation can impact the interpretation of experimental observations,
and we suggest caution when presenting such data. When composition and particle
size are coupled in Dcoated, the sensitivity to surface tension
effects is diminished, as smaller particles will contain a lower volume
fraction of organic material.
The measured critical supersaturation for 50 nm dry diameter
particles comprised of different salts (ammonium sulfate, sodium iodide, and
sodium carbonate) and variable volume fractions of suberic acid (forg) at T≈293 K.
For both sets of measurements, we also applied three model predictions based
on the AIOMFAC (Zuend et al., 2008, 2011) model with LLPS and a
phase-specific surface tension mixing rule considered. The full equilibrium
calculation, labeled as AIOMFAC-EQUIL in Fig. 2, considers the potential
existence of a bulk liquid–liquid equilibrium, resulting in two liquid
phases of distinct compositions yet each containing some amounts of all
three components. The chemical compositions affect the surface tensions of
the individual phases and, using a core–shell morphology assumption and
minimum phase (film) thickness, that of the overall droplet. For the
calculations performed, suberic acid is assumed to be in a liquid state at
high water activity. This model predicts an LLPS for the aqueous suberic
acid + ammonium sulfate system, but only up to a certain water activity
level <0.99, beyond which a single liquid phase is the stable
state. The upper limit of LLPS predicted increases with the fraction of
suberic acid in the system: LLPS onset aw≈0.942 for
forg=0.27 to aw≈0.983 for forg=0.88. This
results in the absence of LLPS at supersaturated conditions prior to CCN
activation for both dry particle diameters considered. Therefore, the
AIOMFAC-EQUIL prediction does not lead to a significant surface tension
reduction here, which explains why the predicted SScrit in Fig. 2 is
similar to that of an iso-σκ-Köhler model with
κorg≈0.13. The two AIOMFAC-CLLPS variants represent
simplified model calculations in which the assumption is made that dissolved
aqueous electrolytes and organics always reside in separate phases
regardless of water content. In the variant labeled AIOMFAC-CLLPS (with
org.
film), all organic material is assumed to reside in a water-free organic
shell phase (an organic film) at the surface of the aqueous droplet. This
assumption leads to a maximum possible surface tension lowering up to
relatively large droplet sizes (for intermediate to high forg), yet a
reduced solute effect, especially for high forg. The variant labeled
AIOMFAC-CLLPS (without org. film) in Fig. 2 differs by allowing water to
partition to the organic-rich shell phase (in equilibrium with the target
water activity), which may affect the surface tension of that phase. Due to
a significant water uptake by suberic acid, predicted to occur for aw>0.99, the resulting surface tension prior to and near
activation is that of pure water and the SScrit prediction resembles
that of the AIOMFAC-EQUIL case. Physical parameters used in these
simulations are presented in Table 1 and a schematic representation of these
cases is shown in Fig. A1. A comparison of predicted Köhler curves
from these model variants is shown in Fig. A2 for the case of forg=0.58. The AIOMFAC-based predictions of critical dry diameters and
SScrit are listed in Table 2 for a range of dry diameters. A comparison
of the different models with experimental data in Fig. 2 indicates that for
forg>0.3, the simplified organic film model variant
AIOMFAC-CLLPS (with org. film) offers the best agreement with the measurements.
This observation is consistent with the results of Prisle et al. (2011), who
applied a similar simple model to droplets containing ionic surfactants and
hint at a significant suppression of surface tension by suberic acid, which
is likely highly enriched at the droplet surface.
Values of physical parameters used in AIOMFAC calculations. Density
of mixtures were calculated as a linear (additive) combination of the
apparent molar volumes of the contributions of water, ammonium sulfate (AS),
and suberic acid.
Calculation parameterValueUnitTemperature, T293.15KPure-comp. surface tension of water (at T) (Vargaftik et al., 1983)72.75mJ m-2Pure-comp. surface tension of suberic acid (at T)a35.00mJ m-2Surface tension of aqueous AS (at T)b72.75mJ m-2Density of pure water (liq.) at T997kg m-3Density of pure suberic acid (liq.) at T1220kg m-3Density of pure AS (liq.) at T (Clegg and Wexler, 2011)1550kg m-3Density of pure AS (solid) at T (Clegg and Wexler, 2011)1770kg m-3Minimum shell-phase thickness, δβ,min0.3nm
a Value taken from measurements for adipic acid (Riipinen et al., 2007) on
the basis of structural similarity to suberic acid. b Assumption of no
influence on droplet surface tension compared to water here (since highly
dilute).
Critical supersaturation SScrit (%) for given dry diameters
(Ddry,crit) and organic volume fractions (forg) in dry particles at T=293.15 K; predicted by the different AIOMFAC-based models.
Mixture Dry diameter (nm) (of overall particle) Solutesforg30354045506080100120140160200AIOMFAC-EQUIL; with liquid–liquid phase separation considered when predicted AS0.001.0050.7880.6390.5320.4510.3390.2170.1540.1160.0910.0740.053Suberic + AS0.271.1350.8930.7260.6050.5130.3870.2480.1760.1330.1050.0850.061Suberic + AS0.401.2140.9570.7790.6490.5520.4160.2670.1900.1430.1130.0920.066Suberic + AS0.581.3501.0680.8710.7270.6190.4680.3010.2140.1620.1280.1050.074Suberic + AS0.751.5321.2140.9930.8310.7080.5370.3470.2470.1870.1480.1210.086Suberic + AS0.881.7511.3891.1360.9510.8110.6160.3990.2850.2160.1720.1400.100AIOMFAC-CLLPS (with org. film); organic phase assumed water free Suberic + AS0.270.9720.7660.6240.5200.4420.3340.2150.1530.1160.0910.0750.053Suberic + AS0.400.9610.7590.6180.5160.4390.3330.2140.1530.1160.0920.0750.053Suberic + AS0.580.9500.7510.6130.5130.4370.3310.2140.1530.1160.0920.0750.054Suberic + AS0.750.9440.7470.6110.5110.4360.3310.2140.1530.1160.0920.0760.054Suberic + AS0.880.9870.7810.6370.5320.4530.3420.2200.1560.1180.0930.0760.054AIOMFAC-CLLPS (without org. film); water uptake by organic-rich phase considered Suberic + AS0.271.1080.8780.7160.5980.5090.3850.2470.1760.1330.1050.0850.061Suberic + AS0.401.1970.9480.7740.6460.5500.4160.2670.1900.1440.1130.0920.066Suberic + AS0.581.3571.0750.8770.7330.6240.4720.3030.2160.1630.1290.1050.075Suberic + AS0.751.5791.2461.0170.8490.7230.5470.3520.2500.1890.1500.1220.087Suberic + AS0.881.9991.5921.3031.0890.9260.6970.4430.3010.2200.1740.1420.101
Unfortunately, neither of the models fully captures the observed behavior at
all forg and size regimes, and is suggestive that additional factors
that have yet to be fully identified may influence the activation process.
As discussed by Ovadnevaite and coworkers (Ovadnevaite et al.,
2017), the AIOMFAC-EQUIL and AIOMFAC-CLLPS (with org. film)
calculations may provide upper and lower bounds on the prediction of
SScrit for a given system, which is roughly in agreement with the data in
Fig. 2. In reality, it is likely that some portion of suberic acid dissolves
into the aqueous droplet bulk at high relative humidity, itself contributing
to the water uptake of the droplet, as predicted by AIOMFAC-EQUIL, while a
significant organic enrichment prevails at the surface, lowering the surface
tension and consequently SScrit. Such behavior could explain the data and
the increasing model–measurement deviations towards higher forg.
Improvements of the AIOMFAC-based models with more sophisticated
bulk–surface partitioning treatments in individual liquid phases seem to
offer a way forward to address some of the observed shortcomings in future
work. At this point, it remains intriguing that the simplified organic film
model provides the best description of these experimental data, even though
its restrictive assumptions about phase separation and organic water content
seem to make it a less physically realistic model variant.
Experimentally measured critical supersaturation for given dry
diameter, inorganic particle core, and organic volume fraction.
These types of experiment also expose further factors that influence CCN
activation, possibly through modification to surface partitioning, such as
the role of inorganic ions. We performed additional measurements using
different inorganic seed particles coated with suberic acid and observed
vastly different behavior across three different salts (ammonium sulfate,
sodium iodide, and sodium carbonate), shown in Fig. 3 for 50 nm dry
diameter particles. We see for ammonium sulfate the same qualitative
behavior as for the other two sizes already discussed; in contrast, the
responses of the systems containing the other salts (all with suberic acid
as the organic component) are very different. Sodium carbonate exhibits an
increase in the required critical supersaturation across the range of
compositions, a trend that could reasonably be predicted without invoking
surface tension effects. The trend with sodium iodide is more complex and
appears to show a sharp discontinuity near forg=0.5, which was
highly reproducible across multiple repeat experiments over multiple days.
These salts were chosen to span the range of the Hofmeister series, which
describes the propensity of inorganic ions to salt in or salt out organic
molecules (proteins in particular). Sulfate and carbonate are the best
salting-out ions, while iodide has a relatively weak salting-out effect due
to its own surface propensity (Santos et al., 2010). It is interesting to
note the differences between carbonate and sulfate, despite their similar
position on the Hofmeister scale. The role of the cation is generally
considered to be much smaller than that of the anion, and thus these differences
are nontrivial. These results serve to further highlight a key conclusion
of this work – that we currently lack a robust molecular model that is
capable of describing and therefore accurately predicting CCN hygroscopicity
and activation even in a relatively simple model system. We hope to prompt
further discussions and experimental studies to explore these observations
and bulk–surface composition effects on surface tension and CCN activation
in more detail.
Summary and conclusions
Surface tension effects can lead to significant differences from classic,
hygroscopicity mixing rule mechanisms for CCN activation (Hansen et al.,
2015; Kristensen et al., 2014). While it has already been made clear that the
activation diameter can be significantly different from that determined by an
iso-σ Köhler curve, in this work we reveal the potential
for more subtle changes in CCN activity (both increases and decreases
relative to pure ammonium sulfate particles) as a result of the
organics-influenced surface tension evolution during droplet growth. These
changes were captured by measuring particles at a fixed diameter with a range
of organic volume fractions. Ultimately, to derive an accurate picture of CCN
activity across the relevant ranges of chemical compositions and size
distributions, the effects of surface tension variability must be taken into
account. It should be noted, however, that there are many situations in which
using simple mixing rules with inferred values for κorg can
lead to sufficiently accurate predictions without the need for more complex
analyses or simulations. It is therefore of key importance to constrain the
conditions under which simple approaches are justified – and to know when
they may be inappropriate. Taking the activation model based on Köhler
theory forward will require a more rigorous interrogation of the role of
co-solutes in partitioning and ultimately an assessment of its effect in
real-world simulations of cloud formation.
In the meantime, it is important for environmental scientists to recognize
the conditions under which surface effects may be influencing cloud droplet
formation, e.g., low solubility or insoluble organics mixed with inorganic
salts, high-RH phase separation, small particle sizes with critical
supersaturations close to the peak supersaturations experienced in clouds,
etc. We suggest, if possible, that experimental data be explored as a
function of organic volume fraction while keeping the overall dry particle
size the same, as from our laboratory experiments this dependence shows the
most clear indicator of an unexplained size effect that may be attributed to
bulk–surface partitioning. In experiments in which both size and composition
vary, the contribution from each is less clear and the effect of the organic
component due to bulk–surface partitioning could be hidden. Further
fundamental laboratory and modeling studies being performed will allow for
in-depth testing and refinements of the proposed models and mechanisms that
describe bulk–surface partitioning and surface tension, ultimately achieving
a robust and universal mechanism that allows both hygroscopicity and
surface tension effects to be coupled into a practical framework.
Data availability
Model input data may be found in Table 1, simulation
results may be found in Table 2, and experimental results may be found in
Table 3.
Schematic representation of the three model variants.
AIOMFAC-EQUIL treats the droplets as a fully mixed single phase, with the
surface tension of the wet droplet sharply approaching σw. The
phase-separated variants considered a surface phase that is water rich, with
surface tension close to σw, and a surface phase that excludes
water, behaving as an organic surface film, with σ<σw. The output from these scenarios is shown in Fig. A2.
Predicted Köhler curves and associated droplet surface
tensions for 100 nm (a, b, c) and 40 nm (d, e, f) dry diameter particles of
ammonium sulfate with suberic acid at forg=0.58 using the AIOMFAC models
described in the main text. The AIOMFAC-CLLPS with org. film gives the
closest predictions to the experimental observations and predicts similar-shaped curves to those measured experimentally by Ruehl et
al. (2016).
Author contributions
JFD and KRW conceived and performed the experiments. AZ carried out
model simulations. JFD, KRW, and AZ analyzed the data and wrote the
paper.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
Andreas Zuend acknowledges the support of the Natural Sciences and Engineering Research
Council of Canada (NSERC) through grant RGPIN/04315-2014. Work on this
topic by Kevin R. Wilson is supported by the Condensed Phase and Interfacial Molecular
Science Program, in the Chemical Sciences Geosciences and Biosciences
Division of the Office of Basic Energy Sciences of the U.S. Department of
Energy under contract no. DE-AC02-05CH11231.
Edited by: Markus Ammann
Reviewed by: two anonymous referees
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