ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus GmbHGöttingen, Germany10.5194/acp-15-13599-2015 Viscous organic aerosol particles in the upper troposphere: diffusivity-controlled water uptake and ice nucleation?LienhardD. M.HuismanA. J.KriegerU. K.https://orcid.org/0000-0003-4958-2657RudichY.https://orcid.org/0000-0003-3149-0201MarcolliC.https://orcid.org/0000-0002-9125-8722LuoB. P.BonesD. L.ReidJ. P.https://orcid.org/0000-0001-6022-1778LambeA. T.CanagaratnaM. R.DavidovitsP.OnaschT. B.https://orcid.org/0000-0001-7796-7840WorsnopD. R.SteimerS. S.https://orcid.org/0000-0002-1955-9467KoopT.https://orcid.org/0000-0002-7571-3684PeterT.Institute for Atmospheric and Climate Science, ETH Zürich, 8092 Zürich, SwitzerlandDepartment of Environmental Sciences, Weizmann Institute, Rehovot 76100, IsraelMarcolli Chemistry and Physics Consulting GmbH, 8092 Zürich, SwitzerlandPhysikalisch-Meteorologisches Observatorium Davos and World Radiation Center PMOD/WRC, 7260 Davos, SwitzerlandSchool of Chemistry, University of Bristol, BS8 1TS Bristol, UKChemistry Department, Boston College, Chestnut Hill, MA 02467, USAAerodyne Research Inc., Billerica, MA 01821, USALaboratory of Radiochemistry and Environmental Chemistry, Paul Scherrer Institute, 5232 Villigen, SwitzerlandFaculty of Chemistry, Bielefeld University, 33615 Bielefeld, Germanypresent address: Department of Chemistry, University of Cambridge, Cambridge, UKpresent address: Chemistry Department, Union College, Schenectady, NY, USApresent address: School of Chemistry, University of Leeds, Leeds, UKU. Krieger (ulrich.krieger@env.ethz.ch)9December20151523135991361320August20159September201519November201525November2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/15/13599/2015/acp-15-13599-2015.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/15/13599/2015/acp-15-13599-2015.pdf
New measurements of water diffusion in
secondary organic aerosol (SOA) material produced by oxidation
of α-pinene and in
a number of organic/inorganic model mixtures (3-methylbutane-1,2,3-tricarboxylic acid (3-MBTCA), levoglucosan,
levoglucosan/NH4HSO4, raffinose) are presented. These indicate that water diffusion coefficients are determined by several properties of the
aerosol substance and cannot be inferred from the glass transition temperature or bouncing properties. Our results suggest that
water diffusion in SOA particles is faster than often assumed and imposes no significant kinetic limitation on water uptake and
release at temperatures above 220 K. The fast diffusion of water suggests that heterogeneous ice nucleation on a glassy
core is very unlikely in these systems. At temperatures below 220 K, model simulations of SOA particles suggest that
heterogeneous ice nucleation may occur in the immersion mode on glassy cores which remain embedded in a liquid shell when
experiencing fast updraft velocities. The particles absorb significant quantities of water during these updrafts which
plasticize their outer layers such that these layers equilibrate readily with the gas phase humidity before the homogeneous ice
nucleation threshold is reached. Glass formation is thus unlikely to restrict homogeneous ice nucleation. Only under most
extreme conditions near the very high tropical tropopause may the homogeneous ice nucleation rate coefficient be reduced as
a consequence of slow condensed-phase water diffusion. Since the differences between the behavior limited or non limited by
diffusion are small even at the very high tropical tropopause, condensed-phase water diffusivity is unlikely to have significant
consequences on the direct climatic effects of SOA particles under tropospheric conditions.
Introduction
Recent field measurements showed that secondary organic aerosol (SOA)
particles are often amorphous glasses under dry and/or cold conditions
. This observation is consistent with the
glass-forming properties of many organic components of atmospheric particles
. Further, it has been shown that
chemical and physical processes occurring in the interior of the particle and
at the gas/condensate interface are influenced by the viscous state in which
condensed-phase diffusion is expected to slow down considerably
. A much
reduced water diffusivity slows down the growth of droplets compared with
that predicted by equilibrium thermodynamics, but its significance for the
ability of the droplets to act as ice nuclei or provide a medium for
multi-phase chemistry is still poorly quantified
.
This is mainly because viscosity, bounce factors and glass transition
temperatures only provide indirect evidence for kinetic limitations of water
diffusivity, whereas diffusion coefficients in the amorphous state span many
orders of magnitude. Previous studies investigated the viscosity of
atmospherically relevant model systems at around room temperature and used the
Stokes–Einstein relation to derive diffusion coefficients
.
However, diffusivity and viscosity decouple below approximately
1.2 Tg or higher, where Tg refers to the thermal
glass transition temperature as measured by differential scanning calorimetry
. As a result of this decoupling,
diffusion coefficients predicted with the Stokes–Einstein relation may be
orders of magnitude smaller than observed
. In addition, the
relationship between the viscosity of mixtures such as aqueous solutions of
SOA materials and the diffusion coefficients of the different components
present in the solution is not well characterized.
Only a few studies have measured the diffusion of water in glassy model
systems for atmospherically relevant relative humidities at room temperature
and even fewer studies at lower temperatures
.
Estimations of the influence of slow water diffusivity on homogeneous and
heterogeneous ice nucleation as well as on multi-phase chemistry have been
extrapolated from sucrose properties as a model system towards different
types of SOA . Only very
recently reported water diffusivities in
α-pinene secondary organic material (SOM) using a Raman isotope tracer
method.
In this study we present measurements of water diffusion in levitated aerosol
particles for a few binary model compounds representing SOA as well as in
chamber-generated α-pinene SOA material that cover a large range of
atmospherically relevant conditions. We then use these new data to
investigate how water diffusion affects the ability of such particles to act
as cloud condensation and ice nuclei.
Methods
The response time of organic particles to changes in relative humidity (RH)
is studied by observing the change in the mass and size of single levitated
organic particles of different compositions between 206.5 and 291 K
and relative humidities up to 0.7. The method to determine water diffusion
coefficients, Dw(T,aw), from such experiments as
a function of temperature and water activity, aw, has been
described in detail previously
. In
short, we use a double ring electrodynamic balance (EDB) in a three-wall
glass chamber with a circulating cooling liquid between the innermost two
walls which controls the temperature with a stability better than
0.1 K and accuracy of ±0.5K and an insulation vacuum
between the outer walls. Single particles are injected using a Hewlett
Packard 51633A ink jet cartridge and are inductively charged, thus allowing
levitation by the electric fields generated by two ring electrodes (AC field)
and two end-cap electrodes (DC field, which tracks the mass change of the
particle when the RH is changed). The RH in the EDB is controlled by
adjusting the flows of dry and humidified nitrogen gas via mass flow
controllers. The levitated particle is illuminated by a HeNe laser
(633 nm), an LED (560 to 610 nm) and a narrow bandwidth
tunable diode laser (765 to 781 nm) which allow tracking of changes
in composition and size by analyzing resonances in the Mie scattering spectra
. Mass and radius growth
factors as well as density and refractive index of the particles can be
derived from these measurements over the entire concentration range after
allowing sufficient time for equilibration
(examples are given in
Appendix ). Note that the mass fraction of solute
can be directly inferred from the mass growth factor, without knowledge of
the molar mass of the solute. In addition, the volatility of solutes can be
determined by measuring evaporation rates .
The changes in composition and size of the droplets upon varying the
conditions in the chamber are compared to predictions from a diffusion model
. The numerical model
subdivides the particle into up to several thousand individual shells and
solves the non-linear diffusion equation in spherical coordinates while
accounting for the concentration dependence of the water diffusion
coefficient, i.e. accounting for the plasticizing effect of water
. The
number of shells and the timesteps are adjusted dynamically to provide
numerical stability. The minimum width of the shells are kept larger than the
molecular dimension of water of about 0.3 nm. The diffusion coefficients of
the solutes investigated in this study are expected to be much slower than
that of water and are thus not accounted for in the calculations.
We measured water diffusion coefficients in a few model systems representing
organic aerosol: raffinose (Sigma, 98 %), levoglucosan (ABCR, 99 %)
and a levoglucosan/NH4HSO4 mixture were used without further
purification. 3-MBTCA, a second generation oxidation product of
α-pinene, was synthesized as described by .
The α-pinene SOA samples investigated in this study were generated
with a Potential Aerosol Mass (PAM) flow tube reactor as described in detail
by from the gas phase oxidation of α-pinene
with OH radicals and collected onto 47 mm teflon filters. To collect
sufficient sample mass (4–5 mg) for the offline analysis, steady-state SOA
mass concentrations of approximately 300–400 µgm-3 were produced
in the reactor and collected at 8.5 Lmin-1 for 24 h. In order to prepare
injection into the EDB, the material was extracted from the filter with
methanol which was subsequently evaporated in N2 gas. It was shown
previously that the extraction in methanol does not significantly change the
optical properties or the composition of the extract
. Accurate weighing before and
after the extraction confirmed that all the material was extracted from the
filter. An aerodyne time-of-flight aerosol mass spectrometer was used to
calculate the O : C and H : C ratios of α-pinene SOA of 0.53 and
1.50, respectively.
Experimental data of the hygroscopic response of an SOA particle levitated in the EDB at 263 K that was initially
equilibrated at 60 % RH. (a) and (c): change in RH upon drying and humidifying. (b) and (d): corresponding size change measured
by Mie-resonance spectroscopy (black crosses) together with the response expected based on the thermodynamic properties (gray
lines) and the predictions from the diffusion model (red lines). The orange and blue lines represent the upper and lower limits
of the uncertainty range associated with the concentration dependence of the water diffusion coefficients, Dw, shown
in panel (e). The values of Dw at water activity intervals of about 0.1 were used to produce the temperature and
concentration dependent fit shown in Fig. a.
Water diffusion coefficients, Dw(T,aw), derived from kinetic response experiments shown together
with the available data from the literature . The color
and shape of the data points indicate the temperature at which the data were obtained. The dashed lines are the temperature and
composition dependent fits through all data points using the modified Vignes equation (see Appendix A). The fits were also used to
calculate water diffusivity along the ice melting temperature, Dw(Tm,aw), green lines, where
Tm is calculated according to and along the homogeneous ice freezing temperature,
Dw(Thom,aw), brown lines, where Thom is calculated according to
for a droplet of 100 nm radius and a homogeneous nucleation rate of ω=1min-1. The orange
line in panel (a) represents water diffusivity at conditions required for heterogeneous ice nucleation in SOA particles,
Dw(Thet,aw), where Thet is calculated according to
. The yellow areas mark the regions where the mixtures are in the glassy state according to glass
transition temperatures given in Appendix A. (a)α-pinene SOA O : C= 0.53, H : C= 1.50, (b) 3-methylbutane-1,2,3-tricarboxylic
acid (3-MBTCA), O : C= 0.75, H : C= 1.5 (c) levoglucosan, O : C= 0.83, H : C= 1.67,
(d) levoglucosan/NH4HSO4 mixture with
a dry molar ratio of 1:1, (e) raffinose, O : C= 0.89, H : C= 1.78, (f) sucrose, O : C= 0.92, H : C= 1.83.
Note that the range of
temperatures for which measurements have been performed and the scales for the water diffusion coefficients vary between the
different compounds.
Results and discussion
Figure shows an example of the experimental data together
with results from the diffusion model for an α-pinene SOA particle
levitated at 263 K. The relative humidity is shown in panels (a) and
(c) with the corresponding size changes shown in panels (b) and (d),
respectively. These size changes do not follow the thermodynamic growth curve
(gray lines, calculated according to the parametrizations in
Appendix ) but show an impeded response upon
drying and humidifying. This response is compared to three predictions from
the diffusion model which assume different concentration dependences of
Dw covering about one order of magnitude, shown in panel (e).
Although the agreement between measurement and simulation is not perfect for
all calculations, the upper curve in panel (e) (orange line) results in
a significantly faster response while the lower curve (blue line) results in
a significantly slower response than observed. The uncertainty associated
with the concentration dependence of Dw as derived from one
individual experiment as shown in Fig. is thus smaller than
the range between the orange and the blue line in panel (e), but we estimate
the uncertainty to be one order of magnitude to account for differences
between the individual experiments.
It was recently suggested by that the water
uptake by slightly oxygenated SOA particles under subsaturated conditions is
dominated by adsorption processes and that the low solubility inhibits water
uptake rather than slow diffusion. These findings are in contrast to the
water uptake of a SOA particle shown in Fig. c which shows
a growth of more than 50 nm upon a change in relative humidity from
close to 0.0 to about 0.3. This growth is much larger than can be expected
based on surface adsorption alone. Hence we believe that the water uptake of
the α-pinene SOA particles investigated in this study was limited by
water diffusion rather than solubility or other surface-related processes as
previously observed for the citric acid model system
, in agreement with the interpretation of
. In addition, we suggest that the observations by
reflect the non-ideality of the solution mixture
which is not accounted for by a single parameter representation for
hygroscopic growth see, e.g..
Figure shows results for five compounds not published
previously together with the measurements for sucrose reported by
which are based on experiments and diffusion
model calculations as described above. The values of Dw at
certain water activity intervals from one individual experiment were chosen
to produce the temperature and concentration dependent fits shown in
Fig. . For completeness, previously published results for other
compounds are shown in Fig. in Appendix A.
The experimentally determined water diffusion coefficients in these organic
materials span about 12 orders of magnitude, from about
10-20cm2s-1 (sucrose: aw=0.4,
T=223K) to about 10-8cm2s-1 (levoglucosan:
aw=0.55, T=243K). Higher values of water
diffusivity can not be measured because equilibration times become too short
to be resolved within our experiments. At lower temperatures, ice formation in the chamber of
the EDB limits the range of RH that can be investigated to conditions below
ice saturation. However, it is possible to parametrize
Dw(T,aw) over the entire two-dimensional
concentration and temperature range in a self-consistent manner by
constraining the fits at the two limiting cases of aw=1 and
at aw=0. The diffusion coefficient of water in pure water,
Dw(T,1), is taken from and the
diffusion coefficient of water in the matrix of the pure organic compounds,
Dw(T,0), is considered an activated process and can thus be
expressed by an Arrhenius equation. In between these constraints, we
parametrize the modeled Dw(T,aw) over the entire
range of aw using a modified Vignes equation more
details about the equations used and the fit parameters for the compounds are
given in Appendix A.
The measured water diffusion coefficients for the different compounds are not
trivially linked to their physicochemical properties. However, some general
observations may be drawn from Fig. . First, the model shows
that the dependence of water diffusion on water activity at different
temperatures generally shows an “S-shape”, which is reproduced by the
empirical Vignes equation. Second, we find that water diffusivity is not
easily correlated with the glass transition temperature. This is evident from
the comparison between Dw(T,0) of the mixture of ammonium
bisulfate with levoglucosan and raffinose at about 253 K. Although
Tg of raffinose is about 170 K higher, water diffusion
in pure raffinose is more than 1 order of magnitude faster than in the
ammonium bisulfate and levoglucosan mixture.
(a) Logarithm of the water diffusion coefficient in the pure component model mixtures, Dw(T,0), from this and
previous work , displayed as a function of temperature
(bottom scale) and inverse temperature (top scale). The green solid line and the brown dashed line are the parameterizations of
α-pinene SOA and sucrose, respectively. The light-gray shaded area marks a range of water diffusivity in the SOA extract
± 1 order of magnitude. The solid black line represents the self-diffusion coefficient of water, Dw(T,1),
according to with measurements indicated by black crosses
. Circles with a centered dot indicate that the data point is below
the glass transition temperature. Water diffusivities in an α-pinene SOM of unknown O : C ratio reported recently by
are shown for comparison. (b) Upper limits of equilibration times for particles of different sizes
calculated by assuming that the diffusivity follows Fick's law according to Eq. ().
In Fig. a we show water diffusivity extrapolated to dry
conditions (Dw(T,0)) for all measured compounds together with
the diffusion coefficient of water in pure water (Dw(T,1)).
When extrapolated to 310 K, the values for Dw(T,0) seem
to be of similar magnitude for all compounds. At lower temperatures we find
that the water diffusivity of 3-MBTCA, levoglucosan and raffinose behaves
similarly to that of the SOA extract (within ± 1 order of magnitude as
indicated by the gray shaded area). Sucrose and shikimic acid, however, have
a significantly stronger temperature dependence leading to differences in
Dw(T,0) of about ten orders of magnitude at temperatures
typical for the upper troposphere. Citric acid and the mixture of
levoglucosan and ammonium bisulfate fall in between the two groups mentioned
above. At present we are not able to correlate these significant differences
to any individual macroscopic physical property of the compounds. Based on
these results we take the water diffusivity of the α-pinene SOA
extract (within ± 1 order of magnitude) as being representative for water
diffusivity in SOA. Clearly, further work is needed to prove that this choice
is justified.
For comparison we also show in Fig. a the recent data of
who parametrized the water diffusion coefficient in
α-pinene SOM (of unspecified O : C ratio) based on Raman isotope
tracer experiments. Their water diffusion coefficients in the matrix of the
α-pinene SOM are about 2 orders of magnitude larger than those we
measured but show qualitatively the same temperature dependence. The
difference could be due to the different material under investigation, but
also due to systematic differences between the two experimental techniques.
We believe our experimental method to infer water diffusivity is closely
related to the atmospheric application as it is based on the response time to
changes in RH but at present we cannot account for the differences between
the two methods. However, those differences do not influence our conclusions
on the atmospheric implications described and discussed below.
If we neglect the plasticizing effect of water, we can use the
Dw(T,0)-values as lower limits for water diffusion in natural
particles. This allows to estimate the absolute upper limit for the
atmospheric equilibration times (τaq) for organic aerosols
using the characteristic time for aqueous phase diffusion of a tracer
:
τaq=dp24π2Dw(T,aw)≤dp24π2Dw(T,0).
Figure b shows upper limits of these equilibration times vs. particle diameter, dp. For water diffusion constants in the gray
shaded area (panel a) this implies equilibration times for large accumulation
size particles of about 1 s at room temperature and up to several
hours at 200 K. However, equilibration times for realistic
atmospheric water uptake scenarios may be significantly shorter when the
plasticizing effect of water is taken into account, as will be discussed in
Sect. .
Simulation of secondary organic aerosol particles with an initial radius of 100 nm in an air parcel experiencing
adiabatic updraft conditions typical of the upper troposphere in mid-latitudes below 220 K. (a) Air parcel temperature (blue
line, top scale) and relative humidity (black line, bottom scale). (b) Ratio of modeled radius over thermodynamic equilibrium
radius when experiencing 0.1 (green line), 1 (orange line) and 3 ms-1 (red line) linear updraft velocities. The gray
shaded area indicates the effect of ± 1 order of magnitude difference in the water diffusivity in the pure α-pinene
SOA for an updraft velocity of 3 ms-1 (see also gray shaded area in Fig. ). (c) Homogeneous ice nucleation
rates, ω, in the current case overlapping with each other and with equilibrium conditions (black dashed line). Also shown
are the water concentration profiles upon reaching (d) ice saturation at the frost point, Tfrost, (e) heterogeneous
ice nucleation conditions typical for SOA particles , and (f) homogeneous ice nucleation
conditions, i.e. the altitude where the black dotted line in panel (c) is equal to 1 min-1, marked by the blue
circle. Since the particles are well equilibrated under these conditions for all updraft velocities, the concentration profiles
in panel (f) overlap with each other. The yellow areas indicate the concentrations at which the mixtures are in the glassy
state.
Same as Fig. but for organic aerosol particles experiencing adiabatic updrafts under conditions typical of
the very high upper troposphere in the tropics, starting at 40 % RH and 195 K with linear updraft velocities of 0.1, 1 and
3 ms-1. In (c) the homogeneous freezing temperatures are lowered by 0.10 K for 0.1 ms-1 updraft velocity
and 0.28 K for 3 ms-1 updraft velocity.
Atmospheric implications
Our previous measurements showed that sucrose particles may become glassy
under cold, dry conditions, resulting in drastic limitations of water uptake
and particle growth, with potential repercussions for ice nucleation and
heterogeneous chemistry . To the degree that
sucrose particles could be considered suitable proxies for organic particles
in the natural atmosphere, the same internal transport limitations would
apply to atmospheric aerosols. However, here we show that water diffusion in
particles with compositions that are more representative of natural particles
is much higher than in previously investigated proxies such as sucrose
particles. Our new measurements suggest that water diffusivity does not
hinder water uptake by atmospheric organic aerosols under most tropospheric
conditions, and that water diffusivity in organic particles is faster than
recently assumed by and
, but lower than measured by
. Our results also suggest that SOA particles are
most likely equilibrated with the surrounding relative humidity even when
measurements of bounce factors or viscosities imply that the particles are in
the amorphous solid state
.
We simulated two scenarios representative of prevailing cloud types in order
to explore the effect of water diffusion on cloud activation by accumulation
size particles with typical radii of 100 nm: upper tropospheric
clouds in the mid-latitudes (Fig. ) and very high clouds near
the tropical tropopause (Fig. ). The trajectory of the first
scenario, shown in Fig. a, starts at 40 % RH and
220 K and reaches conditions close to water saturation through
typical adiabatic updrafts of 0.1 ms-1, characteristic for
ubiquitous small-scale temperature fluctuations and 1 and 3 ms-1
for convectively more perturbed conditions. Panel (b) of Fig.
indicates that the particle radius in these simulations never deviates by
more than 8 % from the equilibrium radius upon the formation of upper
tropospheric clouds in the mid-latitudes, even when fast updrafts are
assumed. These deviations from equilibrium stem from the liquid-phase
impedance, while gas-phase diffusion is rapid for particles with radii of
about 100 nm. The deviation for the simulation with the fastest
updraft increases to about 10 % when the diffusion of water in pure SOA
is assumed to be 1 order or magnitude smaller (corresponding to the lower
limit of the gray shaded area in Fig. ) and decreases to about
5 % for 1 order of magnitude faster diffusion (corresponding to the
upper limit of the gray shaded area of Fig. ), which provides an
estimation for the uncertainties in our simulations.
Figure also shows the water concentration profile of the
droplets upon reaching (d) ice saturation, (e) conditions required for
heterogeneous ice nucleation according to the estimates of
and (f) conditions required for homogeneous
ice nucleation according to (i.e. the homogeneous
nucleation rate ω=1min-1 for an equilibrated droplet of
100 nm radius). The model results for cirrus cloud conditions
demonstrate that SOA particles might still be glassy when reaching ice
saturation, but they establish a liquid shell when reaching conditions
required for heterogeneous ice nucleation or will even be entirely
equilibrated under slow updraft velocities. Hence heterogeneous ice
nucleation may only be possible for medium to fast updraft velocities where
the droplets still contain a highly viscous core. When homogeneous ice
nucleation conditions are reached, only the droplets undergoing fast updrafts
still contain a small viscous core, but the liquid shell is well
equilibrated. Thus, the homogeneous ice nucleation rates shown in panel (c)
for all updraft velocities coincide with the rate coefficient of a droplet
with no condensed-phase limitations for all updraft velocities (red, orange
and green lines coincide with the black dotted line). In this study, we
calculate ω according to and assume that ice
nucleation occurs only when the thickness of the diluted layer is equal to or
larger than the diameter of the critical ice nuclei. A simulation starting at
228 K provided as Fig. in the Appendix shows that for
these slightly warmer conditions, condensed-phase diffusion in SOA particles
is fast enough to have no influence on ice nucleation. This means in effect
that 220 K is the highest temperature at which condensed-phase
diffusion influences ice nucleation for SOA particles with water diffusion
coefficients as the ones shown in Fig. a.
In the second scenario, simulating very high convective clouds near the
tropical tropopause in Fig. , the droplets show delayed
homogeneous ice nucleation for all updraft velocities. Condensed-phase
diffusion is slow enough such that homogeneous ice nucleation occurs only
about 50 m (or about 5 % RH) higher than expected, because of the slow
formation of liquid layers. Heterogeneous ice nucleation prior to homogeneous
nucleation may only occur via the deposition mode as the droplets only
consist of glassy layers, in agreement with the observations of Wang
et al. who used naphthalene as precursor for SOA .
The results in Fig. show that even for these extreme
conditions, the radii of the droplets never deviate by more than about
18 % from the equilibrium radius. Hence we believe that water diffusivity
in SOA particles is sufficiently fast under realistic atmospheric water
uptake scenarios such that global models can treat these particles as if they
are in equilibrium with the surrounding relative humidity. The direct
climatic effects of SOA particles, i.e. their scattering and absorptive properties, are thus unlikely to be significantly
affected by condensed-phase water diffusivity.
Conclusions
Water diffusivity in organic aerosol particles does not strictly correlate
with the glass transition temperature and is not trivially linked to
physicochemical properties but may vary by several orders of magnitude
between the different model systems investigated in this study. Our
measurements suggest that water diffusion coefficients in secondary organic
material are sufficiently high such that SOA particles can be considered as
equilibrated with the surrounding water vapor at temperatures above
220 K, even when the particles are in the amorphous solid state.
The model simulations of realistic atmospheric water uptake scenarios in the
upper troposphere show that homogeneous ice nucleation is only suppressed for
a short period of time for the model runs starting at 195 K, i.e. under conditions found only near the tropical tropopause. For all other
conditions in the troposphere, homogeneous ice nucleation rates are
unaffected by condensed-phase water diffusion. SOA particles undergoing fast
convective updrafts at temperatures below 220 K may still contain
a glassy core when conditions required for homogeneous ice nucleation are
reached. Hence ice may freeze heterogeneously on this glassy core before
reaching the homogeneous nucleation threshold. Under the very cold conditions
near the tropical tropopause, heterogeneous ice nucleation can only occur via
deposition freezing because the hydrated outer layers of the particles are
still in the glassy state at the homogeneous nucleation threshold.
The measurements and simulations presented in this study show that water
diffusion in SOA particles affects ice nucleation rates and results in
deviations from equilibrium growth only under conditions found in the upper
troposphere. Condensed-phase water diffusivity is thus unlikely to
significantly influence the direct climatic effects of SOA particles under
tropospheric conditions.
Model calculation at 228 K
Figure shows a simulation of SOA droplets experiencing updraft
velocities of 0.1, 1 and 3 ms-1 starting at 40 % RH and
228 K, slightly warmer than the conditions outlined in
Fig. in the main text. The calculations indicate that water
diffusion at these temperatures is fast enough for complete equilibration
with the gas phase before the conditions required for heterogeneous
nucleation are reached. The simulated radius deviates by no more than 5 %
from the equilibrium radius.
Same as Fig. in the main text but for organic aerosol particles experiencing adiabatic updrafts starting
at 40 % RH and 228 K with linear updraft velocities of 0.1, 1 and 3 ms-1.
a with A(T)=a1+a2T for T≤Ta and A(T)=A(Ta) for T>Ta, and B(T)=b1+b2T for T≤Tb
and B(T)=B(Tb) for T>Tb. The temperature range for the parameterization is indicated.b The molar mass of SOM is assumed to be 150 g for this parameterization. This value is only needed for the fit
equation but does not influence the measurements of the concentration dependent diffusion coefficients as it is not needed to
describe the thermodynamic and optical properties in Eqs. () to ().c The parameterization of Dw(T,aw) is based on literature data and measurements in our previous work
.d From .e Based on a Gordon-Taylor fit between Tg of
levoglucosan and Tg of NH4HSO4 taken from .f From .g From .h As estimated by . In this study, we assume a Gordon-Taylor constant of 3.5.i From .j We estimated the Gorden-Taylor constant to be 2.32 based on the change in heat capacity at Tg.
Same as Fig. in the main text but for the previously measured model mixtures of (a) shikimic acid,
O : C= 0.71, H : C= 1.43 and (b) citric acid, O : C= 1.17, H : C= 1.33.
Water diffusivity at the glass transition temperatures of the pure component model mixtures,
Dw(Tg,0), and at the glass transition of water, Dw(Tg,1), according to
. Also shown are data from the literature for glucose, maltose and polyvinyl chloride
. The values for shikimic acid, sucrose and raffinose are extrapolations
of the parameterizations given in Table .
(a) Radius growth factor of a α-pinene SOA particle (O : C= 0.53) at 273 K as derived from Mie resonance spectroscopy
(light-gray crosses) and from mass balance (dark gray crosses) yielding 1.40±0.05gcm-3 for the density of the pure
solute. (b) Mass fraction of solute vs. water activity calculated from the data of panel (a). The red line represents the
fit according to Eq. (). (A fit to a single parameter, κ, for describing hygroscopic growth as in
yields a value of 0.081±0.005, ).
(a) Radius growth factor of a 3-MBTCA particle at 290 K as derived from Mie resonance spectroscopy (light-gray crosses)
and from mass balance (dark gray crosses) using 1.428±0.05gcm-3 for the density of the pure solute to convert from mass
to size. (b) Mass fraction of solute vs. water activity calculated from the data of panel (a). The black cross represents
a dew point measurement of a bulk solution. The red line represents the fit according to Eq. ().
Vapor pressure of 3-MBTCA as function of inverse temperature (bottom scale) and temperature (top scale). An Arrhenius fit
(red line) yields a vapor pressure at 298.15 K of (1.4±0.5)×10-6Pa.
Parameterization of Dw(T,aw)
Figures and show all measurements of water diffusivity from this study and our previous
work in levitated particles at temperatures between 206.5 and 291.0 K, covering a large range of atmospherically relevant
temperatures, together with the available data from the literature
. These
data show that water diffusivity strongly depends on temperature and concentration. The diffusion coefficient of water in pure
water, Dw(T,1), and the diffusion coefficient of water in a pure matrix of larger molecules, Dw(T,0), have
been subject to a number of investigations . Their temperature dependence is typically expressed by the
Arrhenius equation if diffusion is treated as an activated process or by the Vogel–Fulcher–Tammann (VFT) equation as implied by
the free-volume theory . These equations have the form
Dw(T,aw)/(cm2s-1)=expζ,
where for the Arrhenius equation (ζ=ζA)
ζA=ζAo-EactRT,
and for the VFT equation (ζ=ζV)
ζV=ζVo-ST-To.R denotes the gas constant, Eact is the activation energy and
ζAo, ζVo, S and
To are fit parameters. In this work, we apply the VFT equation
for Dw(T,1) using the values found by
which covers the atmospherically relevant
temperature range while the Arrhenius equation represents
Dw(T,0) reasonably well for all model systems. For SOA
particles, we found an activation energy of about 65 kJmol-1.
This value is in the same range as other Eact reported in the
literature, e.g. 16 kJmol-1 in hydrocarbons (298 to
317 K), 60 kJmol-1 in carbohydrates (285 to
345 K) and between 10 and 80 kJmol-1 in polymers (293 to
359 K)
.
Table lists the activation energies of our other
model systems, which in general are slightly higher than those reported in
the literature.
For the limited temperature range investigated in this work Eact is assumed to be independent of temperature. Strictly
speaking, Eact might change at Tg of the matrix and is also a function of temperature above
Tg, thus complicating the interpretation of this value as an Arrhenius activation energy
. Since our measurements are either mostly below or mostly
above the Tg of the respective matrix, we relate ζAo to Tg according to
ζAo=lnDw(Tg,0)/(cm2s-1)+EactRTg,
where Dw(Tg,0) is the water diffusion coefficient at the glass transition of the matrix. The values for
lnDw(Tg,0)/(cm2s-1) and Tg are listed in
Table and shown in Fig. to illustrate the wide range of water diffusivities at the glass
transition temperatures of the model mixtures.
A number of models exist to describe the concentration dependence of water
diffusivities in mixtures. Of these, only molecular dynamics simulations and
the free-volume theory explicitly address the transition from a liquid or
rubbery system to a glass as the concentration is varied
.
A validation of these two models with the data presented here is beyond the
scope of this work since many material properties needed to simulate
Dw(T,aw) are unknown. However the free-volume
theory qualitatively predicts an “S-shaped” curve when the system turns
into a glass, in agreement with our observations in Figs. and
.
This concentration dependence is interpreted as a change in the
redistribution of free volume from the large coordinated motion of the matrix
molecule (α-relaxation) above Tg to the opening and
closing of voids by faster processes β-relaxation,
see.
The glassy regions in Figs. and refer
to a condition where the heat capacity of the system is markedly lower than
in the liquid state owing to the loss of configurational degrees of freedom,
typically measured with differential scanning calorimetry (DSC). The
composition at which the system turns into a glass according to this
interpretation differs from the composition where the water diffusivity shows
a rapid change. This behavior, also observed in non-aqueous polymer systems,
can be explained in terms of the different properties being investigated
.
Dw(T,aw) represents a property that describes
a rate of transport and ultimately depends on the history of the formation of
the material while Tg obtained from DSC measurements is
governed by near-equilibrium micro-structures
.
In order to find a simple parameterization for Dw(T,aw) between the Arrhenius equation for
Dw(T,0) and the VFT equation for Dw(T,1) we apply the linear relationship
ζ=ζA+xwαζVFT-ζA,
where xw is the water mole fraction and α satisfies the Duhem–Margules relation
:
ln(α)=(1-xw)2[A(T)+3B(T)-4B(T)⋅(1-xw)],
corresponding to a modified Vignes equation ,
Dw(T,aw)=Dw(T,0)1-xwαDw(T,1)xwα,
which represents all our model systems reasonably well. The parameters A and B are temperature dependent and described in
Table for all investigated systems.
The “S-shaped” percolation equation as suggested by was not considered because the underlying
physical process does not allow for droplet growth or shrinkage over the entire range of relative humidities.
Thermodynamic and optical properties
The thermodynamic and optical properties needed for the model calculations are taken from for
raffinose, levoglucosan and the levoglucosan mixture with NH4HSO4. For the water activity parameterization of raffinose,
which is not given by , we use
aw=xwexp((1-xw)2(-7.359+1.805(1-xw))).
We used the procedure described in detail by to
determine density, refractive index and water activity of 3-MBTCA and the SOA
extract. Growth curves of the SOA particles were measured at 273 K
while illuminating the particle only with the tunable diode laser between 765
and 781 nm to prevent photochemical reactions. The changes in mass
and size were measured simultaneously. The results for 3-MBTCA and SOA
particles are shown in Figs. and .
The independent measurements of mass and size change agree over the entire
range of relative humidity. The small hysteresis loop seen at relative
humidities below 35 % in Fig. is related to kinetic
limitations to water uptake and release which is used to derive water
diffusivity. For the water activity, density (ρ) and refractive index
(n) of the α-pinene SOA mixtures with water used in this study we
found as a function of mass fraction of solute (mfs):
aw=1-mfs1-0.85848mfs-0.09026mfs2,ρ=0.9989+0.27352mfs+0.12477mfs2+0.00381298-T298,n(589nm)=1.33266+0.19104ρmfs.
For 3-MBTCA mixtures with water we found
aw=xwexp((1-xw)2(1.09979-1.7392(1-xw)),ρ=18xw+204(1-xw)18xw+142.9(1-xw),n(589nm)=1.33243+0.02593M,
where M is the molarity.
We also performed vapor pressure measurements for 3-MBTCA as shown in
Fig. as described by . These
show that typical vapor pressures at temperatures below 290 K are at
most 10-7Pa, corresponding to a typical evaporation rate of
10-7µm2s-1 which yields an evaporative change in
size of a particle with 8 µm radius of less than 40 nm
in 5 days. The evaporational loss of the α-pinene SOA particles was
similar in magnitude. We therefore conclude that the compositional change of
our particles once injected in the EDB may safely be neglected.
Acknowledgements
The ETH group acknowledges the ETH Research Grant ETH-0210-1. Y. Rudich acknowledges support from the Minerva Foundation with funding from the
Federal German Ministry for Education and Research and from the Dollond Charitable Trust. A. J. Huisman was supported by US National Science Foundation under award
no. IRFP 1006117. J. P. Reid acknowledges the NERC award NE/M004600/1. The BC/ARI group acknowledges support by the Atmospheric
Chemistry Program of the US National Science Foundation under grants AGS-1244918, ATM-0854916, AGS-1244999 and AGS-0904292 and
by the US Office of Science (BER), Department of Energy (Atmospheric Systems Research) under grants DE-SC0006980 and
DE-SC0011935. We thank Hans Peter Dette, Mian Qi, David Schröder and Adelheid Godt for providing the 3-MBTCA sample and Thomas Berkemeier for helpful discussions.
Edited by: H. Grothe
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