Secondary organic aerosols (SOA) account for a substantial fraction of air
particulate matter, and SOA formation is often modeled assuming rapid
establishment of gas–particle equilibrium. Here, we estimate the
characteristic timescale for SOA to achieve gas–particle equilibrium under
a wide range of temperatures and relative humidities using a
state-of-the-art kinetic flux model. Equilibration timescales were
calculated by varying particle phase state, size, mass loadings, and
volatility of organic compounds in open and closed systems. Model
simulations suggest that the equilibration timescale for semi-volatile
compounds is on the order of seconds or minutes for most conditions in the
planetary boundary layer, but it can be longer than 1 h if particles
adopt glassy or amorphous solid states with high glass transition
temperatures at low relative humidity. In the free troposphere with lower
temperatures, it can be longer than hours or days, even at moderate or
relatively high relative humidities due to kinetic limitations of bulk
diffusion in highly viscous particles. The timescale of partitioning of
low-volatile compounds into highly viscous particles is shorter compared to
semi-volatile compounds in the closed system, as it is largely determined by
condensation sink due to very slow re-evaporation with relatively quick
establishment of local equilibrium between the gas phase and the
near-surface bulk. The dependence of equilibration timescales on both
volatility and bulk diffusivity provides critical insights into
thermodynamic or kinetic treatments of SOA partitioning for accurate
predictions of gas- and particle-phase concentrations of semi-volatile
compounds in regional and global chemical transport models.
Introduction
Secondary organic aerosols (SOA) play a central role in climate, air quality,
and public health. Accurate descriptions of formation and evolution of SOA
remain a grand challenge in climate and air quality models (Kanakidou et
al., 2005; Shrivastava et al., 2017a). Current chemical transport models
usually employ instantaneous equilibrium partitioning of semi-volatile
oxidation products into the particle phase (Pankow, 1994), assuming that SOA
partitioning is rapid compared to the timescales of other major atmospheric
processes associated with SOA formation. The timescale of SOA to reach
equilibrium with their surrounding condensable vapors needs to be evaluated
under different ambient conditions to validate this assumption.
SOA particles can adopt liquid (dynamic viscosity η<102 Pa s),
semi-solid (102≤η≤1012 Pa s), or glassy
or amorphous solid states (η>1012 Pa s), depending
on chemical composition, temperature (T), and relative humidity (RH; Virtanen
et al., 2010; Koop et al., 2011; Zhang et al., 2015; Reid et al., 2018). The
occurrence of glassy or amorphous solid states may lead to kinetic
limitations and a prolonged equilibration timescale in SOA partitioning
(Shiraiwa and Seinfeld, 2012; Booth et al., 2014; Zaveri et al., 2014; Mai
et al., 2015), affecting evolution of particle size distribution upon SOA
growth (Maria et al., 2004; Shiraiwa et al., 2013a; Zaveri et al., 2018). A
number of experimental studies have indeed observed kinetic limitations of
the bulk diffusion of organic molecules (Vaden et al., 2011; Perraud et al.,
2012; J. Ye et al., 2016; Zhang et al., 2018), while chamber experiments
probing the intraparticle mixing did not find kinetic limitations at
moderate and high RH and room temperature (Q. Ye et al., 2016; Gorkowski et
al., 2017; Ye et al., 2018).
Recently, global simulations predicted that SOA particles are expected to be
mostly in a glassy solid phase state in the middle and upper troposphere and
also in dry lands in the boundary layer (Shiraiwa et al., 2017), which can
lead to prolonged characteristic bulk diffusion timescales of organic
molecules within SOA particles (Shiraiwa et al., 2011; Maclean et al.,
2017). Slow bulk diffusion associated with a glassy phase state can prevent
atmospheric oxidants from reacting with organic compounds such as polycyclic
aromatic hydrocarbons (Shrivastava et al., 2017b; Mu et al., 2018),
contributing to long-range transport of organic compounds. Recent ambient
observations have shown that the condensation of highly oxygenated molecules (HOMs),
which play an important role in new particle formation, can be
governed by kinetic partitioning in the free troposphere (Bianchi et al.,
2016). Diffusivity measurements of volatile organics in levitated viscous
particles have shown strong temperature dependence of bulk diffusivity and
the evaporation timescale (Bastelberger et al., 2017). Slow bulk diffusion may
impact multiphase processes such as browning of organic particles (Liu et
al., 2018), cloud droplet activation (Slade et al., 2017), and ice
nucleation pathways (Knopf et al., 2018).
Given these observations and strong implications of SOA phase states, it is
important to evaluate the common assumption of gas–particle partitioning
equilibrium at different ambient conditions. In this study we provide
theoretical analysis of partitioning kinetics of organic compounds using the
kinetic multi-layer model of gas–particle interactions in aerosols and
clouds (KM-GAP; Shiraiwa et al., 2012), which accounts for mass transport
in both gas and particle phases. The equilibration timescale (τeq)
of organic compounds partitioning into mono-dispersed particles is
evaluated systematically under a wide range of temperatures and RH values,
considering the effects of the particle phase state, particle size, mass
loadings, and volatility of organic compounds in a closed system with finite
amount of vapor. For comparison we also present simulations in an open
system with vapor concentration maintained as a constant. This is the first
study to directly relate the equilibration timescale of SOA partitioning to
ambient temperature and relative humidity, which has important implications
on the treatment of SOA evolution in chemical transport models.
Methods
We evaluate the timescale to achieve gas–particle equilibrium by simulating
condensation of a compound Z into preexisting non-volatile mono-dispersed
particles using the KM-GAP model. KM-GAP consists of multiple model
compartments and layers: the gas phase, near-surface gas phase,
sorption layer, surface layer, and a number of bulk layers (Shiraiwa et al.,
2012). The following processes are treated as temperature-dependent in
KM-GAP: gas phase diffusion, adsorption, desorption, surface–bulk exchange,
and bulk diffusion (Fig. S1 in the Supplement). The physical and kinetic parameters are
summarized in Table S1 in the Supplement. The gas-phase diffusion coefficient depends on
temperature (T) and ambient pressure (P). P is calculated as a function of T
based on the International Standard Atmosphere
(International Organization for Standardization, 1975,
https://www.iso.org/standard/7472.html, last access: 3 May 2019). The adsorption rate coefficient is
related to the mean thermal velocity as a function of T and the surface
accommodation coefficient, which is assumed to be 1 (Julin et al., 2014).
The T dependence of desorption rate coefficient is described by an Arrhenius
equation with an assumed typical adsorption enthalpy of 40 kJ mol-1.
Phase state and viscosity can be characterized by the glass transition
temperature (Tg), at which phase transition between amorphous solid and
semi-solid states occurs (Koop et al., 2011). When the Tg of organic
particles under dry conditions (Tg,org) is known, the Tg of
organic-water mixtures at given RH can be estimated considering hygroscopic
growth combined with the Gordon–Taylor equation. In this work, we assumed
the effective hygroscopicity parameter to be 0.1 (Petters and Kreidenweis,
2007; Gunthe et al., 2009) and the Gordon–Taylor constant to be 2.5 (Koop et
al., 2011). Then, the T dependence of viscosity is calculated using the
Vogel–Tammann–Fulcher equation (Angell, 1991; Rothfuss and Petters, 2017;
DeRieux et al., 2018; Li and Shiraiwa, 2018).
Figure 1 shows the T- and RH-dependent viscosity of SOA particles
with Tg,org of 240 K (Fig. 1a), 270 K (Fig. 1b), and 300 K (Fig. 1c). We chose these three
Tg,org values to represent different phase states of liquid, semi-solid,
and glassy states, respectively, at T of 298 K under dry conditions, and these
values are within the range recently reported for monoterpene-derived SOA
(Petters et al., 2019). The decrease in T leads to an increase in viscosity,
while the increase in RH leads to a decrease in viscosity due to the
plasticizing effect of water (Koop et al., 2011). For simplicity we assume
that particles are ideally mixed, even though phase-separated particles are
observed for ambient and laboratory-generated SOA particles under certain
conditions (You et al., 2012; Renbaum-Wolff et al., 2016). The bulk
diffusion coefficient Db (Fig. S2) is calculated by the Stokes–Einstein
equation, which has been shown to work very well for organic molecules
diffusing through materials with viscosity below ∼103 Pa s
(Chenyakin et al., 2017). Note that the Stokes–Einstein equation may
underpredict Db in highly viscous SOA; thus, it gives lower limits
of Db (Price et al., 2015; Marshall et al., 2016; Bastelberger et al.,
2017; Reid et al., 2018). Db is fixed at any given depth in the particle
bulk in each simulation, assuming that condensation of Z would not alter
particle viscosity and diffusivity, as only trace amounts of Z condense to
preexisting particles in our simulations. Particle-phase reactions and
their potential impacts on particle viscosity are also not considered in this study.
Viscosity of preexisting particles as a function of temperature and
relative humidity. The glass transition temperatures under dry conditions (Tg,org)
are (a) 240 K, (b) 270 K, and (c) 300 K.
We mainly consider a closed system in which condensation of Z would lead to
a decrease in its gas-phase mass concentration (Cg) and an increase
in its particle-phase mass concentration (Cp). The particle diameter stays
practically constant throughout each simulation, as the amount of condensing Z
is set to be much smaller than the non-volatile preexisting particle mass (COA).
The gas-phase mass concentration of Z right above the
surface (Cs) is also calculated based on Raoult's law and partitioning
theory (Pankow, 1994) in equilibrium with the near-surface bulk, which is
resolved by KM-GAP (Shiraiwa and Seinfeld, 2012). We also calculate the mass
fraction of Z in the near-surface bulk (fs) and the average mass
fraction of Z in the entire bulk (fb) to infer the radial concentration
profile (Fig. S3). The equilibration timescale (τeq) is
calculated as the e-folding time t when the following criterion is met:
|Cp(t)-Cp,eq||Cp,0-Cp,eq|<1e,
where Cp,0 and Cp,eq are the initial and equilibrium mass
concentration of Z in the particle phase, respectively. Note that
practically the same values can also be obtained by using initial and
equilibrium gas-phase concentrations in Eq. (1), as the mass change of Z in
the gas and particle phases is the same in these simulations.
ResultsImpacts of volatility and diffusivity on equilibration timescales
Figure 2 shows exemplary simulations of temporal evolution of Cg (blue
line) and Cp (red line) of the compound Z in the closed system along
with τeq, which is marked with red circles. The initial mass concentration
of preexisting non-volatile mono-dispersed particles (COA) is assumed
to be 20 µg m-3 with the number concentrations
of 3×104 cm-3 and the initial particle diameter of 100 nm. Initial mass
concentrations of Z in the gas (Cg,0) and particle (Cp,0) phases are
set to 0.3 and 0 µg m-3, respectively.
Tg,org is assumed to be 270 K. Figure 2a presents simulations for a
semi-volatile organic compound (SVOC) with the pure compound saturation mass
concentration (C0) of 10 µg m-3 condensing on particles
with Db of 10-11 cm2 s-1 at RH = 60 % and T=298 K
(Fig. S2). Upon condensation, Cg decreases while Cs and Cp increase,
and the gas–particle equilibrium is reached within about 20 s, as indicated
by τeq. For a low-volatile organic
compound (LVOC) with C0=0.1µg m-3, it takes a longer time to reach the equilibrium
with a τeq of ∼30 s (Fig. 2b), as the partial pressure
gradient between the gas phase and the particle surface (represented by the
difference between Cg and Cs) is larger for lower C0. For both
cases SOA growth is governed by gas-phase diffusion
as indicated by Cs<Cg. The mass fraction of Z in the near-surface bulk is
identical to the average mass fraction in the entire bulk (Fig. S3a and b),
indicating that Z is homogeneously well-mixed in the particle without
kinetic limitations of bulk diffusion in low viscous particles (Fig. 3a).
Temporal evolution of mass concentrations of the condensing compound Z
in the gas phase (Cg), just above the particle surface (Cs),
and in the particle phase (Cp) in the closed system. τeq is
marked with the red circle. RH is 60 % and T is (a, b) 298 K
and (c, d) 250 K. The C0 of Z is (a, c) 10 µg m-3
and (b, d) 0.1 µg m-3. The glass transition temperature
of preexisting particles under dry conditions (Tg,org) is set to
270 K, which leads to Db of (a, b) 10-11 cm2 s-1
and (c, d) 10-18 cm2 s-1. The initial mass concentration
of preexisting particles is set to 20 µg m-3 with the number
concentrations of 3×104 cm-3 and the initial particle diameter of 100 nm.
Dimensionless radial concentration profiles in the particle for the
condensation of the LVOC species (C0=0.1µg m-3) at
RH = 60 % and (a)T=298 K with Db=10-11 cm2 s-1
and (b)T=250 K with Db=10-18 cm2 s-1.
The x axis indicates the radial distance from the particle center (r)
normalized by the particle radius (rp), ranging from the particle
core (r/rp≈0) to the surface (r/rp=1). The
y axis indicates the bulk concentration of the condensing compound at a given
position in the bulk (r) normalized by the bulk concentration at particle
surface (rp).
At a lower T of 250 K, the phase state of preexisting particles that occurs
is highly viscous with Db of ∼10-18 cm2 s-1
(Fig. S2), resulting in much longer equilibration timescales
(∼105 s) for SVOC with C0=10µg m-3
(Fig. 2c). After Cg and Cs converge, they continue to decrease
simultaneously while Cp increases slowly, showing that the particle
undergoes quasi-equilibrium growth (Shiraiwa and Seinfeld, 2012; Zhang et
al., 2012). For LVOC (C0=0.1µg m-3) condensation,
τeq is short (∼140 s) because a local thermodynamic
equilibrium between the gas phase and the near-surface bulk is established
relatively quickly (as mostly controlled by the condensation sink; Riipinen
et al., 2011; Tröstl et al., 2016) due to very slow re-evaporation of the LVOC.
Contour plot of equilibration timescale (τeq) as a
function of bulk diffusivity (Db) and saturation mass concentration (C0)
for (a) condensation in the closed system and (b) evaporation
in the open system. The initial mass concentration of preexisting particles is
set to 20 µg m-3 with the number concentrations of
3×104 cm-3 and the initial particle diameter of 100 nm.
Viscosity is calculated from the Stokes–Einstein equation, assuming the effective
molecular radius of 10-8 cm at T of 298 K.
The characteristic timescale of mass transport and mixing by molecular
diffusion τmix can be calculated by τmix=rp2/(π2Db),
where rp is the particle radius
(Seinfeld and Pandis, 2006). Figure 3 shows dimensionless radial
concentration profiles of Z (C0=0.1µg m-3) in the
particle at (Fig. 3a) Db=10-11 cm2 s-1 and
(Fig. 3b) 10-18 cm2 s-1. For low viscous particles,
τmix is very short and particles are homogeneously well-mixed at τeq,
which is consistent with previous analytical calculations (Liu et al., 2013;
Mai et al., 2015). In contrast, a large concentration gradient
exists between the particle surface and the inner bulk (Figs. 3b and S3d) at τeq
in highly viscous particles due to strong kinetic limitations of
bulk diffusion (as indicated by a very long τmix), which prevents
the entire particle bulk from reaching complete equilibrium. Thus, for LVOC
condensation on highly viscous particles (Fig. 2d), τmix
represents the timescale that establishes full equilibrium with homogeneous
mixing in the entire particle bulk. These results are consistent with Mai et
al. (2015) and Liu et al. (2016), who showed that an establishment of full
equilibrium is limited by bulk diffusion in highly viscous particles, even
though the local equilibrium of the LVOC may be achieved faster. Note that
τmix is solely a function of particle size and bulk diffusivity,
while τeq is also affected by volatility and mass loadings. At
lower particle concentrations, the total accommodation of molecules to the
particle surface decreases, resulting in longer equilibration timescales (Fig. S4).
We further computed τeq as a function of Db and C0 in the
closed system. As shown in Fig. 4a, when Db is higher than
∼10-13 cm2 s-1, τeq is insensitive
to bulk diffusivity but sensitive to volatility: decreasing volatility
increases τeq in this regime. In the regime with Db lower
than ∼10-13 cm2 s-1 and C0 higher than
∼10µg m-3, τeq is controlled by bulk
diffusivity: τeq increases from 30 s to longer than 1 year as
Db decreases from 10-13 to 10-20 cm2 s-1.
In the regime with Db<∼10-13 cm2 s-1 and
C0<∼10µg m-3,
τeq depends on both diffusivity and volatility. Decreasing
volatility would lead to shorter τeq due to an establishment of
local equilibrium of the LVOC.
In an open system with fixed vapor concentration (Fig. S5), the τeq of
SVOC is slightly longer but on the same order of magnitude as the τeq
in the closed system, as relatively small amounts of SVOC need to
condense to reach equilibrium. In contrast, the τeq of the LVOC in the
open system become dramatically longer as the LVOC continues to condense into the
particle phase because of low volatility (Pankow, 1994). For further
simulations we focus mainly on the closed system, and the corresponding
simulations for the open system are provided in the Supplement.
We also simulated evaporation in the closed system with the same parameters as
in the condensation simulations (Table S2). Initially Cg=0µg m-3
and trace amounts of semi-volatile or low-volatile species were
assumed to be homogeneously well-mixed in preexisting particles. Figure S6
shows that for the evaporation of SVOC species with C0=10µg m-3,
decreasing Db from 10-11 to 10-18 cm2 s-1
would increase τeq from ∼20 to
∼105 s. These evaporation timescales are close to those
derived from condensation (Fig. 2a and c) and consistent with previous kinetic
simulations (Liu et al., 2016). In the closed system, the evaporation of a
very small amount of LVOC species from the particle surface is already
sufficient for reaching the particle-phase equilibrium concentration, resulting
in a short τeq (Fig. S6b and d). For an open system with continuous
removal of gas-phase compounds, which is often employed in evaporation
experiments, the equilibrium timescale in the evaporation of the LVOC
species from highly viscous particles can be longer than hours or days
(Vaden et al., 2011; Liu et al., 2016). Figure 4b shows simulated
evaporation timescales as a function of Db and C0 in an open system,
which agrees very well with Fig. 3 in Liu et al. (2016). It shows that for
less-viscous particles, τeq is limited by volatility, while for
highly viscous particles, τeq is insensitive to volatility and
controlled by bulk diffusivity.
Equilibration timescale (τeq) as a function of
temperature and relative humidity in the closed system. The glass transition
temperatures of preexisting particles at dry conditions (Tg,org)
are (a) 240 K, (b) 270 K, and (c) 300 K. The saturation mass concentration (C0) of the condensing
compound is 10 µg m-3 (SVOC). The mass concentration of
preexisting particles is set to 20 µg m-3 with the number
concentrations of 3×104 cm-3 and the initial particle diameter of 100 nm.
Equilibration timescales at different RH and T
We conducted further simulations to estimate τeq with a wide
range of atmospherically relevant temperatures (220–310 K) and relative humidities (0 %–100 %). Figure 5 shows the temperature and
humidity-dependent diagrams of τeq for SVOC (C0=10µg m-3)
condensation on particles with Tg,org of 240, 270, and
300 K, in the closed system. For particles with Tg,org of
240 K (Fig. 5a), τeq is on the order of seconds under boundary
layer conditions (T>270 K). In these conditions particles are
liquid with high bulk diffusivity (Figs. 1a and S2a); thus gas–particle
partitioning is controlled by gas-phase diffusion and interfacial transport
(Shiraiwa and Seinfeld, 2012; Mai et al., 2015). At low T (<260 K)
with low or moderate RH (<70 %), τeq can increase from
minutes to 1 year with decreasing T and RH mainly due to strong kinetic
limitations of bulk diffusion with low Db (Fig. S2a).
With Tg,org of 270 K (Fig. 5b) or 300 K (Fig. 5c), τeq is still on
the order of minutes in most of boundary layer conditions. At low RH
τeq can be extended to hours when particles may occur as semi-solid or amorphous
solid. When T<270 K, τeq can be longer than
months even at moderate RH, while τeq may stay very short at very
high RH. The corresponding simulations of SVOC partitioning in the open
system (Fig. S7) show a similar pattern to τeq in the closed system.
τeq for C0=103 and 0.1 µg m-3 in the
closed system is presented in Fig. A1. In general, τeq would be
shorter at higher C0 when particles are liquid, as the partial pressure
gradient between the gas phase and the particle surface is smaller for
higher C0 (Shiraiwa and Seinfeld, 2012; Liu et al., 2016). For example,
the increase in C0 from 10 to 103µg m-3
leads to τeq decrease from 30 to 1 s with Tg,org of 240 K
at boundary layer conditions (Figs. 5a and A1a). At low T and RH (e.g.,
T<250 K and RH < 50 %), where particles are highly
viscous, τeq is on the same order of magnitude for the
condensation of the intermediate-volatility organic compound (IVOC)
and the SVOC, as gas–particle partitioning is limited by
bulk diffusion. Figure A2 shows bulk diffusion and mixing timescales (τmix)
as a function of RH and T. It is interesting to note that
τmix is very similar to the τeq of the IVOC (Fig. A1a–c), as
gas diffusion and interfacial transport of the IVOC are fast. For the LVOC
τeq is generally shorter than τmix, as its mass transfer to
the particle surface is governed by condensation sink with negligible
re-evaporation, while τmix still takes a long time
to achieve homogeneous mixing in the particle phase if particles are viscous.
Previous studies have shown that τeq depends on particle size
(Liu et al., 2013; Zaveri et al., 2014; Mai et al., 2015) and particle mass
loadings (Shiraiwa and Seinfeld, 2012; Saleh et al., 2013). For further
examination of these effects at the different T, Fig. 6 shows the dependence
of τeq of the SVOC (C0=10µg m-3) and LVOC
(C0=0.1µg m-3) on the mass concentration and the diameter of
preexisting particles, over the range of 0.1–100 µg m-3 and
30–1000 nm, respectively, with the particle phase state being less viscous with
Db=10-11 cm2 s-1 at 298 K and highly viscous with
Db=10-18 cm2 s-1 at 250 K. In this comparison, when
ambient particle mass concentration is held constant, increasing particle
size will translate to a decrease in the number and surface area
concentration of particles, and a decrease in total accommodation of
molecules to the particle surface, thereby leading to an increase in τeq.
When particle diameter is held constant, an increase in particle
concentration leads to an increase in surface area concentration, resulting
in a shorter τeq. When particles are less viscous at 298 K
(Db=10-11 cm2 s-1) τeq of the SVOC is shorter
than that of the LVOC for the same particle size and mass loadings. For
partitioning into highly viscous particles at 250 K (Db=10-18 cm2 s-1),
the SVOC takes a longer time than the LVOC to reach equilibrium.
Equilibration timescale (τeq) for (a, c) SVOC
(C0=10µg m-3) and (b, d) LVOC (C0=0.1µg m-3)
as a function of particle diameter (nm) and mass concentration (µg m-3)
of preexisting particles at 60 % RH and T of (a, b) 298 K and
(c, d) 250 K in the closed system. The glass transition temperature
of preexisting particles under dry conditions (Tg,org) is set to
270 K, which leads to Db of (a, b) 10-11 cm2 s-1
and (c, d) 10-18 cm2 s-1. Ambient organic mass
concentrations are indicated with arrows.
Typical ambient organic mass concentrations in Beijing, Centreville in the
southeastern US, the Amazon Basin, and Hyytiälä, Finland, are indicated
in Fig. 6. The particle phase state was observed to be mostly liquid in
highly polluted episodes in Beijing (Liu et al., 2017), under typical
atmospheric conditions in the southeastern US (Pajunoja et al., 2016), and
under background conditions in Amazonia (Bateman et al., 2017). At these
conditions τeq should be mostly less than 30 min (Fig. 6a
and b). Particles were semi-solid or amorphous solid on clear
days in Beijing (Liu et al., 2017), when influenced by
anthropogenic emissions in Amazonia (Bateman et al., 2017), and in the boreal forest in
Finland (Virtanen et a., 2010). Under these conditions and also when
particles are transported to the free troposphere, τeq can be
longer than 1 h, especially in remote areas with low mass loadings (Fig. 6c
and d). Particles in the nucleation mode (diameter < 30 nm) are not
considered in this study, as the particle size may affect the phase
transition of these nanoparticles (Cheng et al., 2015). The role and impact
of phase transition on nucleation and growth of ultrafine particles are
beyond the scope of current simulations and need further investigation in future studies.
Discussion
The timescale to reach equilibrium for SOA partitioning has been
investigated in several laboratory experiments at room temperatures (Vaden
et al., 2011; Saleh et al., 2013; Liu et al., 2016; J. Ye et al., 2016; Gong
et al., 2018; Ye et al., 2018). These experiments monitored particle mass or
composition, finding that equilibration timescales are longer at low RH,
consistent with our model simulations. Note that, for condensation on highly
viscous particles, even though particle mass or particle-phase
concentrations appear to reach equilibrium, complete equilibrium with
homogeneous mixing in the particle may not have been reached,
driven by strong kinetic limitations and concentration gradients in the particle bulk
(Figs. 2d and 3b). This is also supported by evaporation experiments showing
that the local thermodynamic equilibrium established between the vapor and
the near-surface bulk should be differentiated from the global equilibrium
between the vapor and the entire bulk (Liu et al., 2016). Note that SOA
evaporation is also influenced by volatility and oligomer decomposition
(Roldin et al., 2014; Yli-Juuti et al., 2017). The timescale of gas–particle
partitioning can be different in closed or open systems, especially for the LVOC
(Figs. 4 and S5). The closed system simulations represent SOA partitioning in
chamber experiments and in closed atmospheric air mass, which could be
justified well within timescales of seconds to minutes and possibly up to
hours, depending on meteorological conditions. The real atmosphere may be
better approximated as an open system due to dilution and chemical
production and loss, especially at longer timescales. Thus, particular care
needs to be taken in comparing modeling results with different field
observations or with experiments probing
equilibration timescales (i.e.,
evaporation vs. condensation, open vs. closed system, and local vs. full equilibrium).
The simulated equilibration timescales of atmospheric SOA are mostly on the
order of minutes to hours under conditions of the atmospheric boundary layer
(Figs. 5 and A1). This agrees with previous experimental results that the
gas–particle interactions can be regulated by both thermodynamic and kinetic
partitioning (Booth et al., 2014; Liu et al., 2016; Saha and Grieshop, 2016;
J. Ye et al., 2016; Gong et al., 2018), depending on several factors including
particle phase state, size, mass loadings, and volatility. Organic particles
containing high-molar-mass compounds tend to have high glass transition
temperatures (Koop et al., 2011), and the occurrence of kinetic limitation
will increase with higher Tg,org (Fig. 5). This is consistent with the
results of intraparticle mixing experiments showing that as the carbon
number of precursor (e.g. terpene) increased (that would lead to higher Tg,org),
it took a longer time for the SVOC (evaporated from another type of
SOA, e.g. toluene SOA) to partition into the terpene SOA, leading to slower
molecular exchange among different types of SOA (Ye et al., 2018).
At low temperatures, the particles can occur as highly viscous at relatively
high RH (Fig. 1), and τeq of SVOC partitioning can be longer than
hours or days (Figs. 5 and S7). Equilibration timescales of LVOC condensation at
low particle mass loadings (Fig. 6) may represent the clean conditions where
new particle formation and growth often occur (Wang et al., 2016). It has
been reported that highly oxygenated molecules play an important role in the
initial growth of atmospheric particles in the free troposphere (Bianchi et
al., 2016). Bulk diffusion would likely be a limiting step in the
condensation of semi-volatile and low-volatility compounds at low
temperatures, where particles may occur as highly viscous (Shiraiwa et al.,
2017). In this case, particle growth would need to be treated kinetically,
rather than thermodynamic equilibrium partitioning, as it would affect SOA
growth kinetics and size distribution dynamics, with significant
implications for the growth of ultrafine particles to climatically relevant
sizes (Riipinen et al., 2011, 2012; Shiraiwa et al., 2013a;
Zaveri et al., 2018). Chemical transport models usually have time steps on
the order of minutes, in which the partitioning equilibrium may not be
reached, for most SVOC species (C0>1µg m-3) when
Db is less than 10-15 cm2 s-1 (Fig. 4). Note that
condensation of extremely low-volatility organic compounds (ELVOCs;
Tröstl et al., 2016) into highly viscous particles may be governed by
gas-phase diffusion, and timescales to reach local equilibrium could be
shorter, as determined by the condensation sink (Riipinen et al., 2011; see
also Fig. S4b), which may be more relevant for the practical application in
chemical transport models.
In this study we assume that the bulk diffusivity within organic particles
is independent of particle mixing state and morphology. Chamber experiments
have demonstrated that evaporation of organic aerosol may be hindered if it
is coated with organic aerosol from a different precursor (Loza et al.,
2013; Boyd et al., 2017). Moreover, the phase separation has been observed
in organic particles mixed with inorganic salts (You et al., 2014) and even
without inorganic salts (Pöhlker et al., 2012; Riedel et al., 2016).
Future simulations on equilibration
timescales should consider the effects of
the immiscibility (Barsanti et al., 2017; Liu et al., 2013) and the phase
separation (Shiraiwa et al., 2013b; Pye et al., 2017; Fowler et al., 2018)
as well as composition-dependent bulk diffusivity (O'Meara et al., 2016) and
the evolution of the particle phase due to reactive uptake and
condensed-phase chemistry (Hosny et al., 2016). Incorporation of the
particle-phase formation of oligomers and other multifunctional high molar
mass compounds can lead to a reduced bulk diffusivity (Pfrang et al., 2011;
Hosny et al., 2016), which may prolong the equilibration timescales.
Decomposition of highly oxidized molecules (e.g., organic hydroperoxides) in
water may also affect gas–particle partitioning (Tong et al., 2016). Current
simulations are focused on trace amount of the SVOC or LVOC condensing on
mono-dispersed particles with negligible particle growth. Potential phase
transition in the course of particle growth or evaporation should also be
incorporated in future simulations. The shift in the particle phase state and
gas–particle partitioning in response to temperature and RH may need to be
considered in chemical transport models and laboratory experiments to better
understand the fate of organic compounds.
Data availability
The simulation data may be obtained from the corresponding
author upon request.
Equilibration timescale (τeq) as a function of
temperature and relative humidity in the closed system. The glass transition
temperatures of preexisting particles at dry conditions (Tg,org)
are set to (a, d) 240 K, (b, e) 270 K, and
(c, f) 300 K. The mass concentration of preexisting particles is
20 µg m-3. The saturation mass concentration (C0) of the
condensing compound is (a–c) 103µg m-3 and
(d–f) 0.1 µg m-3.
Characteristic timescale of bulk diffusion or mixing timescale (τmix)
as a function of temperature and relative humidity. The particle diameter is
assumed to be 100 nm with the glass transition temperatures of preexisting
particles at dry conditions (Tg,org) of (a) 240 K,
(b) 270 K, and (c) 300 K.
The supplement related to this article is available online at: https://doi.org/10.5194/acp-19-5959-2019-supplement.
Author contributions
YL and MS designed and conducted modeling and wrote the paper.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This work was funded by the National Science Foundation (AGS-1654104) and the
Department of Energy (DE-SC0018349).
Review statement
This paper was edited by David Topping and reviewed by two anonymous referees.
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