Experimental setup
The basic setup of the electrodynamic balance (EDB) has been described
previously . Here, we
summarize its basic features as follows: the EDB is placed in
a double-jacketed glass chamber, with a cooling liquid flowing between
the inner walls and an insulation vacuum between the outer walls. The
temperature can be adjusted between 180 and 320 K, covering
the entire atmospheric range. A gas mixture is pumped continuously
through the chamber to adjust/control relative humidity; the total
pressure can be varied between 150 and 1000 hPa. The EDB is
loaded by a single particle generator (Hewlett-Packard 51633A ink jet
cartridge) filled with a dilute aqueous solution of the sample
material. Relative humidity (RH) is measured by a capacitive RH probe
with an integrated temperature sensor (U.P.S.I., France, model G-TUS.13R)
mounted in the upper-end cap of the EDB in close proximity
to the levitated particle (< 10 mm distance). The sensor was
calibrated with deliquescence relative humidities of common salts and
the saturation vapor pressure over ice at several
temperatures. Capacitive RH probes are known to show some hysteresis
and we conservatively estimate the accuracy to be no worse than
±3 %.
Four independent methods to characterize the aerosol particle are
used: (i) the DC voltage applied to compensate the gravitational force
is proportional to and used as a measure for the mass of the
particle. (ii) The two-dimensional angular scattering pattern is
measured over a scattering angle ranging from 78 to
101∘ and used to estimate the radius of the particle and to
detect phase changes . (iii) Mie resonance
spectroscopy with a LED-“white”-light source for illumination is
used to follow the radius change of a spherical particle
(e.g., a liquid droplet); the wavelength of the LED is centered at the
sodium D-Line (589 nm). The back-scattered light from the LED
is collected by a spectrograph with a slow scan back-illuminated CCD
(charge-coupled device) array detector as an optical multichannel analyzer, for details see
. (iv) High resolution Mie resonance
spectroscopy is used to measure size and refractive index
simultaneously with high precision as described in more detail below.
The pioneering work of showed that size and
refractive index of spherical particles may be obtained from Mie
resonance spectra with very high precision. These Mie resonances, also
called whispering gallery modes, have been observed for both elastic
(e.g., ) and inelastic scattering
(e.g., ). Conventionally, those
spectra have been measured using a fixed wavelength, while drying or
humidifying a particle and hence changing its size. In this approach,
the Mie parameter, X, varies with time (X(t)=2πr(t)/λ,
with λ being the wavelength and r being the radius). This
method becomes difficult to apply if the rate of size change is small,
because several resonances are needed to compare measured spectra with
Mie scattering computations. Hence, the technique cannot be applied
to compounds which need extended equilibration times because of low
water diffusivity.
These problems do not arise when using a wavelength tunable light
source. achieved relative errors in radius and
refractive index of 3×10-5 and determined dispersion over
the experimental spectral range. They analyzed the elastic scattering
of a levitated particle at a scattering angle of π/2 and used two
detectors in the planes parallel and perpendicular to the electric
field vector of the incident beam stemming from a scanning ring dye
laser. Conceptually, our approach is similar, but we
use a narrow bandwidth tunable diode laser (TDL, New Focus, model
Velocity 6312, tuning range 765–781 nm, linewidth
(5 s) <5 MHz) instead of a dye laser and only one
detector (Si photo diode, New Focus femtowatt photo receiver, model
2151), also at a scattering angle of π/2. At this angle,
transverse electric (TE) mode resonances can be detected in the plane
perpendicular to the plane of polarization and transverse magnetic
(TM) mode resonances can be detected in the plane parallel to the
plane of polarization . To observe both TE- and
TM-mode resonances separately, we use a λ/2-wave plate to
rotate the polarization of the incoming beam and measure both
polarizations sequentially. The detector samples the scattered light
through the same optics that are used to collect the two-dimension
angular scattering pattern. This has the advantage of measuring both
phase function and Mie resonance spectra over the same scattering
angle range and the disadvantage of a rather large collection angle
for the Mie resonance spectroscopy. To account for intensity
modulation caused by weak etaloning of the laser during scan and by
some residual interference at the windows of the chamber we use
a second detector to monitor the intensity of the reflected incoming
beam as reference.
To avoid being limited by the accuracy of the wavelength reported by
the commercial laser (approximately 0.1 nm) we use
a custom-made wavemeter, following the design of . As
a reference laser we use a HeNe-laser , which is
frequency stabilized using the design of , yielding
a relative uncertainty of the frequency stabilization of about 1 part
in 107. Overall, the precision of the wavemeter is of the order of
a few parts in 106, which was verified by measuring the hyperfine
structure of the Rubidium D2 line (centered at 780.04 nm),
see Appendix A.
(a) TE and (b) TM spectra of shikimic acid
particle under dry conditions at room temperature. Black line: experimental
data. Red line: Mie calculation for a homogeneous particle with radius
7.756 µm and refractive index of 1.540.
In the present application we need the high resolution spectroscopy
only to measure the radius and the real part of the refractive index
at a number of discrete relative humidities because we follow the
radius change with the “white”-light resonance spectroscopy (see
discussion in Sect. ). Hence, we do
analyze the spectra without any advanced fitting algorithm, but
compare measured with calculated spectra manually, as shown in
Fig. . For an initial guess of size we
use the measured phase function and apply Chylek's approximation of
the spacing between resonances . We find
the best fit in size at a fixed refractive index testing a reasonable
range of refractive indices. In this way, we can easily determine the
real part of the refractive index, mTDL, with an accuracy
of better than 0.005 and a corresponding accuracy in size of about
2×10-3 µm. This is sufficient for the type of
experiments we are discussing here, since the limiting factor in the
analysis of the data is the uncertainty in measured relative
humidity. Since at least two resonances should be fitted, there is a lower
limit in particle size of about 4–5 µm
for the tuning range of our laser. The spectra shown in Fig.
were recorded with a scanning speed of 0.04 nm s-1; i.e., a spectral scan
took a little less than 6 min. For a detailed discussion on the
accuracy of aerosol refractive index retrieval from single particle
techniques see .
As mentioned above, we continuously measure low resolution
Mie spectra using the LED centered at the wavelength of the sodium
D-Line (589 nm). These spectra are then used to track changes
in the radius. Since the radius at specific relative humidities is now
known from the concurrent high resolution measurements, the refractive
index at the sodium D-Line needed for retrieval of these data,
mD, can be determined by a Mie fit to the low resolution
spectrum using dispersion, mD>mTDL, and the
radius as a constraint.
Measurement strategy and data analysis
It has been shown previously that water diffusion constants can be
deduced by combining stepwise changes in relative humidity with an
accurate measurement of the response in size of a levitated particle
. In these previous
investigations, additional data were available (refractive indices,
densities) helping to constrain the size retrieval. Here, we want to
illustrate how we deduce the refractive index, density and water
activity of an aerosol particle if such data are either completely
lacking, or only available for a very limited concentration range.
So far, we have restricted our measurements to low-volatility compounds to
simplify the retrieval of composition from size and mass change.
Retrieval of mass growth factor
Typical experimental run on a shikimic acid particle with dry radius
of 8.385 µm at T=293.5 K. (a) Relative
humidity measured close to the droplet. (b) DC voltage compensating
gravitational force. (c) False color map of intensity of Mie
resonance spectra measured with the LED (dark color low intensity, bright
color high intensity). (d) Shift in wavelength Δλ=λ(t)-λ0 of a resonance initially (t=0) being observed at
λ0=578.99 nm. When this resonance leaves the spectral
window, we continue by following another resonance as described by
. Vertical dashed lines indicate humidity change.
Traditionally, water activity data have been obtained utilizing the DC
voltage compensating the gravitation force in the EDB . As the exact charge of the particle is not known, only
relative changes in mass can being inferred; a reference state is
needed to calculate a mass growth factor. If bulk data cannot be
obtained either because the amount of sample material is limited, or
because solubility is very low, the voltage measured under dry
conditions may serve as reference point. Figure
shows a typical experimental run performed at a constant temperature
of 293.5 K.
A closer look at the data of Fig. shows that the
accuracy of the voltage data is limited by spurious signals when
a rapid change in relative humidity is applied. The DC voltage in our
apparatus does not only compensate the gravitational force but also
counteracts the Stokes force of the gas flow. Since the relative
humidity is adjusted by changing the gas flow ratio of dry and
humidified flow, very rapid changes lead to a response in the feedback
loop adjusting the DC voltage, due to finite response of the mass flow
controllers. This limits the accuracy of the voltage data to about
±2 V. The data in panel d showing the shift in resonance
wavelength are free from this artifact.
Data of Fig. plotted vs. relative humidity.
(a) DC voltage compensating gravitational force. (b) Radius
data, see text on how to obtain those from the data of
Fig. d. (c) Mass to dry mass ratio (growth factor
g) calculated from both voltage (gray) and radius data (black).
For an aqueous aerosol particle with negligible vapor pressure of the
solute(s) (psolute≤10-7 Pa) only water is
exchanged between gas and particle phase. Under these conditions, the
particle's mass growth factor can be directly inferred from the DC
voltage compensating the gravitational force once the voltage under
dry conditions has been measured. For aqueous organic systems, the
kinetic uptake impedance due to slow water diffusion in semi-solid or
glassy aerosol may substantially lengthen the time needed to reach
thermodynamic equilibrium (whereas the transport of H2O
molecules through gas phase by ventilation and molecular diffusion is
very fast). This becomes evident when plotting the DC-voltage data of
Fig. vs. relative humidity as done in
Fig. a and the inferred mass growth as in panel c.
Below a relative humidity of about 0.3 the data show hysteresis
loops, indicating delayed water uptake upon humidification and delayed
water release upon drying . (Note that growth
factors smaller than 1 derived from DC voltage data originate from the
uncertainty of the measurement.)
However, these are not caused by deliquescence and efflorescence
(i.e., the crystallization of shikimic acid) but by kinetic limitations.
Crystalline particles in the size range of our particles show deviations
from spherical shape, which is easily detected in our setup when measuring
the 2-dimensional angular optical scattering pattern
or in fluctuations in the resonance spectra shown in Fig. 2c .
We detected no sign of crystallization in our experiments even under the driest conditions.
In this study, we determine the
equilibrium data (e.g., of growth factor) by considering the points
where both branches of the loop overlap. Such overlap occurs either at
higher RH, where equilibration within the particle phase is fast, or
after prolonged waiting time at low RH. An important measure of the
properties of the solution, which we measure here, is its water
activity aw=pH2Osol(T)/pH2Ow(T), where pH2Osol is the H2O vapor pressure of
the solution, and pH2Ow is the H2O vapor
pressure of pure water, both at the same temperature. Under
equilibrium conditions, the water activity (aw) of the
aqueous solution is equal to the measured relative humidity.
Note that the inverse of the mass growth factor
(g=m(RH)/m(RH=0)=(ms+mH2O)/ms,
with ms being the mass of the solute and
mH2O being the mass of water) is equal to the mass
fraction of solute, ws, since the change in mass is only
caused by water uptake. We will use mass fraction data to constrain
the density as explained in the following section.
Conversion of Mie resonance data to size and concentration
In Sect. we explained how we obtain size and
refractive index at a fixed RH using the high resolution Mie resonance
spectra. When the particle radius is r0 at time t0, the LED
based resonance shift, Δλ, shown in
Fig. d can be used to calculate the radius at other
times, r(t). If the refractive index did not change with size, the
radius were easily obtained by noting that the Mie parameter, X, of
a specific resonance, X0=2πr0/λ0, stays constant,
i.e., X(t)=X0 :
r(t)=(λ0+Δλ(t))r0λ0.
However, when the radius change is accompanied by a change in
composition, e.g., uptake of water by an aqueous particle, the
refractive index of the particle will change as well. A change in the
real part of the refractive index from mD,0 to
mD(t) leads to an additional shift in the wavelength of
a mode in the Mie resonance spectrum . The combined
effect can be accounted for by solving iteratively
Eq. () for the radius as a function of
time:
r(t)=1-K(mD(t),X)mD(t)-mD,0mD,0(λ0+Δλ(t))r0λ0.
An iterative calculation is needed because of the implicit radius
dependence of mD(t). In general, the proportionality
factor, K, depends on refractive index and Mie parameter, but
have shown that K(mD,X) varies between
0.94 and 0.96 for 1.30≤mD≤2.00 when the Mie
parameter, X, is of the order of 100 as is the case in our
experiments. In this study, we take K as a constant factor of 0.95.
Neither the refractive index of the solute nor its concentration
dependence in aqueous solution are known a priori. Our approach for
retrieving the concentration dependence of refractive index is
therefore as follows. The dependence of the refractive index on
concentration in aqueous solution is well described using the molar
refractivity of the solute ; i.e., the refractive index
is linear with solute molarity. Hence the refractive index,
mD(ws), as a function of mass fraction of
solute, ws, is
mD(ws)=mD,H2O+ρ(ws)ρs(mD,s-mD,H2O)ws,
with mD,s being the refractive index of the pure
solute, ρs being the density of the pure solute and
ρ(ws) being the density of the aqueous solution at the
concentration ws. To determine mD,s,
first the refractive index of an aqueous solution close to saturation
concentration was measured using an Abbe type of refractometer at the
sodium D-Line wavelength and the density at this concentration was
measured using a pycnometer, see Fig. . Since
shikimic acid is not very soluble in water (mole fraction at
saturation 0.025), these data alone lead neither to accurate estimates
of the density of the solute ρs (or the equivalent
molar volume) nor to those of mD,s (or the molar
refractivity). For other samples of interest the amount of material
available may not be sufficient to perform these type of bulk
experiments at all. Therefore, we measure a high resolution Mie
resonance spectrum and use the concurrent LED spectrum as described in
Sect. at very dry conditions to determine the
refractive indices, mTDL and mD. This yields
the refractive index, mD,s, of the solute as we
assume ws=1.
What remains to be determined is the density of the solution,
ρ(ws). We assume that the density of binary aqueous
solutions can be adequately approximated using the density of each the
pure solute and water and the conventional volume additivity rule:
ρ(ws)=1-wsρH2O+wsρs-1,
with ρH2O the density of water, and ρs
the density of the dry, amorphous solute. For a number of selected
aqueous organic mixtures (e.g., citric acid) this approximation proved
to be accurate within 1 % of the data .
(a) Density vs. mass fraction parametrization of shikimic
acid, the data point at w=0.2001, ρ=1.072 gcm-3 was
measured with a pycnometer, the density of the solute ρs=1.492 gcm-3 was determined as described in the text, the line
is a plot of Eq. (). (b) Refractive indices vs.
molarity. mTDL from high resolution Mie resonance spectra (black
symbols), mD (red symbols), lines are linear fits for the two
different wavelengths to Eq. ():
mTDL,H2O=1.3292, mTDL,s=1.541,
mD,H2O=1.3334, mD,s=1.574.
The density of the pure solute, ρs, is the only remaining
unknown. To determine it we start using an initial guess, which allows us to
calculate the refractive index mD for all concentrations using
Eqs. () and (). Then r(t) is
computed solving Eq. (). The mass growth factor can be
calculated using the corresponding density and compared to the measured data
shown in Fig. c. If mass growth from the DC-voltage data do
not agree with the mass growth calculated from the spectra, we update the
initial guess of ρs and calculate again until the agreement is
satisfactory. For aqueous shikimic acid solutions this leads to densities and
refractive indices at a temperature of 293.5 K as shown in
Fig. . In addition to measuring the refractive index at
very dry conditions, we measured the refractive index at several humidities as
shown in panel b. These measurements support the value of the refractive
index of the pure solute, mTDL,s, and through
Eq. (), also the density of the pure solute,
ρs.
Note that we implicitly assume the particle to be homogeneous in the
analysis outlined above. If there is a gradient in concentration
within a particle due to kinetic uptake limitations, its refractive
index will show a corresponding gradient. Strictly,
Eq. () is no longer valid and a numerical
modeling of the Mie resonance spectra of the inhomogeneous particle is
needed to calculate the radius. However, the difference between the
exact modeled results and those generated by applying
Eq. () to an inhomogeneous particle is small
compared to the uncertainty in our experiments (mainly related to the
accuracy of relative humidity probe) .
Parametrization of water activity
From the type of data shown in Fig. c we derive
a parametrization of water activity vs. concentration by noting that
the inverse of the mass growth factor is equal to the mass fraction of
solute (ws) provided that only water is partitioning
between gas and particle phase. The data of Fig. c
are replotted as ws vs. aw in
Fig. . From these data we select discrete data
points at humidities at which the particle is in equilibrium with the
gas phase by assuring that the same ws was measured upon
humidifying and drying. Such data were measured at 293.5 K for
three different particles injected from fresh solutions. In addition,
we used a commercial water activity meter (AquaLab, Model 3TE, Decagon
Devices, USA) to measure the aw close to a saturated
solution. As can be seen in Figs. and
, this data point does not significantly constrain
the parametrization because the water activity of the saturated
solution is very close to that of pure water.
Mass growth data retrieved from radius measurements of
Fig. c plotted as mass fraction of solute vs.
aw (gray line). The black circle marks a bulk data point of the
saturated solution. We pick some discrete data points at humidities at which
the particle is in equilibrium with the gas phase (open triangles) for
fitting.
We convert ws to mole fraction, xs, and obtain
the water activity coefficients, γw, according to
lnγw=xs2(E+3F+5G)-(4F+16G)xs+12Gxs2
, where E, F, G are fitting parameters (see
Fig. ).
(a) Natural logarithm of water activity coefficient
γw vs. mole fraction of shikimic acid, symbols are data for
three independent particles, solid circle is the bulk data point, dashed line
represents ideal behavior (Raoult's law), red line is the fit of
Eq. () to the data. (b) The same data plotted as
water activity vs. mole fraction of water, the gray line is the prediction of
the thermodynamic model AIOMFAC .
The advantage of this approach is that once the fitting parameters are
determined, it allows the direct calculation of the activity
coefficient of the solute, γs, via the
Duhem–Margules relations as :
lnγs=xw2(E+F+G)-(4F+8G)xw+12Gxw2.
For shikimic acid, we found E=-0.182, F=-0.079 and G=0.349. It
is evident from Fig. that the water activity of
aqueous shikimic acid solutions deviate only slightly from ideal
behavior (Raoult's law). The prediction by the thermodynamic model
AIOMFAC , namely lower aw than ideal for
high concentrations of shikimic acid and crossing to higher
aw than ideal at low shikimic acid concentration, is in
agreement with the data. However, the magnitude of the deviation is
smaller than predicted and the crossing is at higher concentration of
shikimic acid than predicted.
We did not study the temperature dependence of aw
systematically, but obtained some data with known concentration at low
temperatures at which the particles where equilibrated for a long
time. We take the particle as equilibrated if the growth factor at
a particular relative humidity is the same upon humidification and
drying. The time required depends on both, RH and temperature. Our
data suggest a positive slope of daw/dT of about
4×10-3 K-1, see Fig. . Since our
uncertainty in RH is almost as large as the shift in aw
over the temperature range considered in this study, we do not correct
for the temperature dependence of aw when analyzing the
kinetic data at low temperatures.
Temperature vs. aw for three different shikimic acid
particles at fixed concentrations (as indicated in the legend). The dashed
lines serve only as a guide to the eye.
Analysis of kinetic data
Having characterized the thermodynamics of aqueous shikimic acid, we
will proceed with analyzing the kinetic behavior, which is apparent in the
raw data of Fig. as hysteresis loops
(cf. discussion in ). In
Sect. we briefly summarize the numerical diffusion
model used for analysis and report water diffusivity as a function of
temperature and concentration in Sect. .
(a) Data of Fig. converted to radius vs.
time (gray crosses), equilibrium prediction of radius using the activity
parametrization of Sect. (black line), diffusion model
with a diffusivity of log(DH2O)=-8.7-7.5(1-aw)
using the same activity parametrization (red line). Relative humidity (blue
line) right axis. (b) The same data plotted vs. relative humidity.
At RH >40 % at 293.5 K we observe no kinetic limitations
to water uptake or release, while below that humidity kinetic limitations
become clearly visible by the hysteresis loops in water uptake and release.
Diffusion model
In aqueous organic solutions, water acts as a plasticizer
, and hence the water diffusion coefficient becomes
concentration dependent. We solve the diffusion equation in spherical
coordinates to retrieve concentration dependent water diffusion
coefficients. Since our approach has been already described in depth
by , we will give only a brief summary of the
underlying principles. The diffusion equation is
∂n∂t=∇DH2O(n,T)∇n=1r2∂∂rr2DH2O(n,T)∂n∂r,
where n is the number density of water molecules in the particle,
t is the time, and r is the distance from the particle center. Due to the
concentration dependence of DH2O, the diffusion equation
becomes non-linear. This leads to steep diffusion fronts instead of
the more commonly known creeping diffusion tails . It
also means that a general analytical solution for
Eq. () cannot be found, and the problem instead
needs to be solved numerically. Our numerical model separates the
particle into up to several thousands of individual shells. Growth
and shrinkage of the particle are then the result of water diffusion
between those shells. The change of the number of water molecules,
ΔNi, within the shell i is described by the following:
ΔNi=fi-12-fi+12Δt,
where fi-12 is the flux of water molecules from shell
i-1 to shell i, whereas fi+12 describes the flux of
water molecules from shell i to shell i+1. The time interval,
Δt, is chosen so that ΔNi does not vary by more
than a specified amount (usually ≤2 %) within one time
step. Shell thickness was adjusted dynamically to enable resolution of
steep gradients when necessary. However, a minimum thickness of
0.3 nm was chosen to represent the size of a water
molecule. Note that the surface layer of the particle (i.e., the
outermost shell) is kept in equilibrium with the gas phase at all
times so that mass transport is never limited by gas-phase
diffusion. While gas phase diffusion under our experimental condition
is indeed significantly faster than liquid phase diffusion
, recent experiments have shown a difference
between adsorption and desorption at low humidity
. These findings question the assumption of the
outermost shell always being in thermodynamic equilibrium, but this
does not alter the derived diffusion coefficients significantly
.
Water diffusivity parametrization of aqueous shikimic acid
To obtain water diffusivity from data as shown in
Fig. , we first calculate radius vs. time as
explained in Sect. and then run the
numerical model with different test dependencies of
logDH2O vs. aw until the fit appeared
satisfactory upon manual inspection. An example of the fit to
the data of Fig. is shown in
Fig. .
As in Fig. a typical experiment at constant
temperature covers a certain range of aw where deviations
from instantaneous equilibration are detectable. For a global fit of
diffusivity we extract data points roughly spaced 0.15 in water
activity within the humidity range covered by the specific
experiment. The diffusivities at all investigated temperatures and
concentrations are shown in Fig. . We
performed measurements between 294 and 251 K and from dry
conditions to about 80 % RH. However, above about
50 % RH it is not possible to extract diffusion coefficients
with our setup because the rate of humidity change with time has an
upper limit. This mainly due to limitations in gas flow because higher
flow rates affect the stability of the particle in the EDB.
Analogous to , we use a modified Vignes-type
equation to empirically fit these data:
DH2O=DH2O0xwαDs01-xwα,
where DH2O0 and Ds0 are the diffusion
coefficients for water in pure water and pure shikimic acid,
respectively. Their temperature dependence can be fitted to
a Vogel–Fulcher–Tammann expression:
log10DH2O0=-6.514-387.4T-118,
and
log10Ds0=-9.35-542.8T-211,
where the numbers for DH2O0 are taken from
and the units for the temperature is K and
m2s-1 for the diffusion coefficient. To be consistent with
our previous work , we introduce an empirical
correction parameter α, having the form of an activity
coefficient:
ln(α)=(1-xw)2[C+3D-4D(1-xw)],
where C and D are temperature dependent:
C=-6.55+0.025T,D=7.122-0.0261T,
with C(T>258K)=C(T=258K) and
D(T>273K)=D(T=273K).
The resulting fit to Eq. () with α calculated
according to Eq. () is shown in
Fig. . The correction parameter α
stays close to 1 in this fit for the entire temperature and
concentration range. Therefore, we plot in
Fig. also the contours for the different
temperatures without correction (i.e., α=1). This leads to
significant differences only for temperatures below 258 K.
However, as only few data are available in this temperature range and
the fits are just starting to diverge, measurements at even lower
temperatures would be helpful for a more thorough comparison of the
two fits. We conclude that the three parameter fit without correction
term describes the water diffusivity satisfactorily.
DH2O as a function of aw for the
investigated temperatures indicated by different colors. Different symbols
represent different particles. The lines represent fits to
Eq. (). Solid lines were fitted with an α calculated
according to Eq. (), dotted lines with α=1. For
comparison, the faint, short, dashed lines in corresponding colors show the
parametrization of DH2O for sucrose of Zobrist et al. (2011) for
250.5 and 293.5 K.
Figure also show water diffusivity in aqueous sucrose
for the highest and lowest temperature measured here. While the logarithm
of diffusivity of water increases with water activity almost linearly in shikimic acid,
sucrose shows less increase under dry conditions. In general the
diffusivity is smaller in sucrose, but at all temperatures the diffusivity
agrees within 1 order of magnitude for dry conditions
(up to a water activity of about 0.25) and deviates at most by 2 orders
(at water activity of about 0.5). Further investigations are needed to
determine whether water diffusivity in aqueous organic compounds behaves
similarly with temperature and water activity for different compounds and
to which degree a model compounds like shikimic acid may serve as a
proxy for secondary organic aerosol.
Conclusions
We have presented a measurement and data retrieval technique to
extract water activity, density, refractive index and water diffusion
constants from mass-to-charge data and light scattering data of single
levitated droplets in an electrodynamic balance. In particular, we
have shown that an iterative procedure combining mass-to-charge data
with Mie resonance spectroscopy yields robust data for parametrizing
activity as well as water diffusivity. If solubility and amount of
material available allow for bulk measurements of water activity,
density and refractive index, these measurements provide constrains
for simple mixing rules and hence further increase the accuracy of the
parametrizations. However, even if measurements in the bulk are not
available or possible, the technique presented here allows to
constrain parametrizations well enough to be of use for atmospheric
applications. We plan to use it to characterize secondary organic
aerosol, which was collected on filters during oxidation experiments
in which only about a milligram of material is available.
We studied aqueous shikimic acid aerosol in detail, a model system for
aged, oxygenated organic aerosol. Due to its single carbon–carbon
double bond it is especially well suited for heterogeneous chemistry
studies because the consumption of this double bond can be easily
monitored with different spectroscopic techniques. Our study shows
that its activity in aqueous solution is close to ideal; i.e., it almost
follows Raoult's law. In addition, the water diffusivity in aqueous
shikimic acid turns out to closely follow the simple empirical Vignes
equation in contrast to other binary systems, e.g., aqueous citric
acid. Comparison with secondary organic aerosol samples in the future
will show how well shikimic acid represents the physical and chemical
properties of atmospheric organic aerosol.